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Applications of Stress from Boron Doping and Other Challenges in Silicon Technology

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APPLICATIONS OF STRESS FR OM BORON DOPING AND OTHER CHALLENGES IN SILICON TECHNOLOGY By HEATHER EVE RANDELL A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2005

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Copyright 2005 by Heather Eve Randell

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This document is dedicated to my mom, dad, and brother Aaron.

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ACKNOWLEDGMENTS First and foremost, I would like to thank my advisor, Dr. Mark E. Law, for all the support, encouragement, and assistance he has given me throughout my graduate studies, and for the opportunity to do research in the SWAMP group. No matter how busy Dr. Law is, even as the department chairman, he always has the time to discuss research and sports with his students. During our research conferences to San Francisco, California, he was a great tour guide, brought his students to excellent restaurants, and had great recommendations for wineries in Napa Valley. I am also very grateful to Dr. Kevin S. Jones and Dr. Scott E. Thompson for supporting my research activities and for their guidance and support as my supervisory committee. This research could not have been completed without the financial support of the Semiconductor Research Corporation. Ginny Wiggins always made sure that all of the SRC Scholars and Fellows were properly accommodated. From IBM, I would like to thank Rick Wachnik for being a great industry mentor and for all of our stimulating conversations. I would like to thank Ana Cargile for her making sure that IBM had a close correspondence with their scholars. I would like to thank the University of Floridas Department of Electrical and Computer Engineering for funding me in the beginning of my masters studies. During the research process, it was beneficial to have previous SWAMPies in industry to consult as resources. I would like to thank Steve Cea and Hernan Rueda for the time and support in my research activities. There are also some current SWAMPies iv

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who I would like to specifically thank. Sharon Carter and Teresa Stevens have been fantastic program assistants at the SWAMP Center. I thank them for all of their assistance. I am very grateful to Ljubo Radic for providing patience and assistance since my first day in the group. Whenever I had FLOOPS or coding questions, I could always turn to Ljubo for help. I will miss being enlightened with all of his online Ph.D. comics and jokes. I would like to thank Renata Camillo-Castillo and Jeanette Jacques for being helpful people over the years. They were both a part of the research group before I joined, and have been valuable resources over the years. I wish Renata the best of luck with little Naysan Victor, he is such a precious baby boy! I would like to thank Michelle Phen, Nina Burbure, and Nirav Shah for being available for research related discussions. I will really miss having Nicole Staszkiewicz around as a great friend and inspiration over the last two years. I owe a lot of my good health habits to her. I would also like to thank all the old and new SWAMPies who have been around for Friday lunches, good conversations, and for creating an enjoyable work environment over the years. My time at the University would not be complete without the late nights at NEB crew: Xavier Bellarmine (and research colleague), Sid Pandey, DaeVi Hwang, and Seth Lakritz. I will try to, but will never forget the many long nights we spent in that building doing homework and studying for exams. Occasionally we were treated with a beautiful sunrise. I thank them all for being great colleagues and even better friends. I thank my roommate, Jennifer Lavery, for all her support during this process, for being a great friend, and for watching after my kitties whenever I left town. v

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To my mom, dad, brother Aaron, and the rest of my family, I love them so much. None of this would be possible without them. I thank them so much for their unconditional love and support my entire life. Last, but definitely not least, I am ever grateful to Ryan Smith. He has been an everlasting source of love, encouragement, and support. I thank him for always believing in me like I believe in him. vi

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TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................iv LIST OF TABLES ...............................................................................................................x LIST OF FIGURES ...........................................................................................................xi ABSTRACT .....................................................................................................................xiv CHAPTER 1 INTRODUCTION........................................................................................................1 1.1 Motivation...............................................................................................................2 1.2 Stress Induced Defects in Patterned Structures......................................................4 1.3 Mechanically Induced Channel Stress from Shallow Trench Isolation..................7 1.4 Strained Silicon.....................................................................................................12 1.4.1 Strained Silicon Physics.............................................................................13 1.4.1.1 Biaxially Strained MOSFETS..........................................................15 1.4.1.2 Uniaxially Strained MOSFETS........................................................18 1.4.2 Stress effects on electrical characteristics..................................................19 1.5 Organization.........................................................................................................21 2 LINEAR ELASTICITY, STRESS, AND STRAIN...................................................23 2.1 Linear Elastic Materials........................................................................................23 2.2 The Stress Tensor.................................................................................................24 2.3 The Strain Tensor.................................................................................................26 2.4 Plane Stress...........................................................................................................29 2.5 Plane Strain...........................................................................................................30 2.6 The Stress-Strain Relationship.............................................................................31 2.7 Summary...............................................................................................................33 3 STRAIN SOURCES...................................................................................................34 3.1 Oxidation Induced Stress......................................................................................34 3.2 Thin Film Stress....................................................................................................37 3.2.1 Thermal Mismatch Stress...........................................................................37 3.2.2 Intrinsic Stress............................................................................................38 vii

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3.3 Stress from STI.....................................................................................................39 3.4 Dopant Induced Stress..........................................................................................42 3.5 Dopant Diffusion in Silicon and Silicon Germanium (SiGe)...............................45 3.6 Summary...............................................................................................................48 4 SOFTWARE ENHANCEMENTS TO FLOOPS.......................................................50 4.1 FLOOPS Background...........................................................................................51 4.2 The Finite Element Method..................................................................................52 4.2.1 Constructing FEM Elements for the Elastic, Bodyforce, Stress, and Strain Operators...............................................................................................54 4.2.1.1 Plane Strain Assumption..................................................................56 4.2.1.2 Boundary Conditions........................................................................57 4.2.2 Forces from Boron Doping.........................................................................58 4.2.3 Strain and Stress Computation...................................................................60 4.3 Summary...............................................................................................................61 5 APPLICATIONS AND COMPARISONS OF TWO-DIMENSIONAL SIMULATIONS.........................................................................................................63 5.1 Boron-Doped Beam Bending...............................................................................64 5.1.1 Beam Bending Simulation Results.............................................................66 5.1.2 Effect of Varying Beam Length..........................................................66 5.1.3 Effect of Varying Beam Width...........................................................67 5.1.4 Effect of Varying Dopant Profile........................................................68 5.2 Multiple Material Layer Bending Simulations.....................................................68 5.3 Channel Stress from Boron Source/Drain Doping...............................................76 5.3.1 Effects of Channel Length Scaling.............................................................77 5.3.2 Effect of Source/Drain Length Scaling......................................................78 5.3.3 Effect of Boron Concentration Scaling......................................................79 5.4 Summary...............................................................................................................80 6 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE WORK........................................................................................................................83 6.1 Summary and Conclusions...................................................................................83 6.2 Recommendations of Future Work.......................................................................86 6.2.1 Additions to Software.................................................................................86 6.2.2 Stress-Dependent Diffusivity Model..........................................................91 6.2.3 STI Induced Stress Modeling.....................................................................92 6.2.4 Modeling Silicon at the Elastic/Plastic Limit.............................................94 APPENDIX A CODE.........................................................................................................................97 B SIMULATION FILES..............................................................................................112 viii

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LIST OF REFERENCES.................................................................................................117 BIOGRAPHICAL SKETCH...........................................................................................124 ix

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LIST OF TABLES Table page 1 Material parameters used for nitride on silicon simulations....................................70 2 Results summarizing the effect of boron doping on channel stress.........................81 x

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LIST OF FIGURES Figure page 1-1 Evolution of transistor minimum feature size and transistor cost vs. year.................3 1-2 Evolution of the MOSFET from 1947 to 2002 .........................................................3 1-3 Dislocation formation at the edge of a nitride strip after solid-phase epitaxial regrowth (left) before annealing and (right) after annealing......................................5 1-4 Application of stress to patterned wafers prevented line defects from forming........6 1-5 Linear variation of mobility enhancement for a bulk NMOS transistors...................8 1-6 Dopant profiles, vertical profiles are taken at the gate edge and lateral profiles are taken 15 nm below the device surface.....................................................................12 1-7 Strained silicon hole mobility enhancement vs. vertical electric field ....................15 1-8: Formation of biaxially strained NMOS transistors....................................................15 1-9 Critical thickness as a function of Ge composition for SiGe on Si..........................16 1-10 Drain current leakage mechanism in strained silicon films ....................................17 1-11 Subthreshold characteristics of strained silicon MOSFETS with strained silicon thicknesses above the critical thickness...................................................................17 1-12 Stress along the channel in a strained silicon NMOS transistor..............................18 1-13 Stress along the channel in a strained silicon PMOS transistor...............................19 1-14 Calculated and measured threshold voltage shift for NMOS under biaxial and uniaxial stress...........................................................................................................21 2-1 Linear elastic deformation........................................................................................23 2-2 Deformation of a spring with an applied force........................................................23 2-3 Stress components of an infinitesimal cubic element..............................................25 2-4 Normal Strain in the x, y, and z directions...............................................................27 xi

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2-5 Example of shear strain in the x-y direction............................................................28 2-6 Plane stress in a thin film.........................................................................................29 2-7 Example of plane strain in the x-y direction............................................................30 3-1 Forces present in LOCOS formation........................................................................36 3-2 Top corner of an STI structure.................................................................................41 3-3 Lattice contraction due to boron atom, and lattice expansion due to germanium atom..........................................................................................................................43 4-1 Triangular element in coordinate system.................................................................54 4-2 Flowchart to create element stiffness matrix............................................................56 4-3 Verification of boundary conditions........................................................................57 4-4 Flowchart to solve for forces from boron doping....................................................60 4-5 Flowchart to calculate strain and stress....................................................................61 5-1 A uniform or symmetric doping profile about the center of the cantilever beam thickness results in no bending.................................................................................65 5-2 The strain from boron causes bending towards the more heavily doped boron side of the beam (a) downwards bending (b) upwards bending......................................65 5-3 Beam deflection vs. beam length.............................................................................67 5-4 Beam deflection vs. beam length for varying beam widths.....................................67 5-5 Beam deflection vs. beam length for varying doping profiles.................................68 5-6 Nitride curling up at edges due to tensile residual stress.........................................69 5-7 Deflection vs. distance for varying nitride thicknesses............................................71 5-8 Deflection vs. distance for varying silicon thicknesses............................................71 5-9 Stress.yy from silicon nitride on silicon...................................................................72 5-10 Stress.xx from silicon nitride on silicon...................................................................73 5-11 Stress.xy from silicon nitride on silicon...................................................................73 5-12 Stress.xx for reflecting bottom and reflecting left and right boundary...................74 xii

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5-13 Stress.yy for reflecting bottom and reflecting left and right boundary ...................75 5-14 Stress.xy for reflecting bottom and reflecting left and right boundary ...................75 5-15 Silicon doped with boron source drain regions general structure.........................77 5-16 The effect of scaling channel length on stress from boron doping..........................78 5-17 The effect of scaling the source/drain length on channel stress for 100 nm and 45 nm channel lengths...................................................................................................79 5-18 The effect of scaling the source/drain length on channel stress for 100 nm and 45 nm channel lengths...................................................................................................80 6-1 Intrinsic stresses are oriented parallel to the interface on which the film is grown or deposited (left) planar film, (middle) non-planar film.............................................89 6-2 Reflecting boundary condition displacement and velocity perpendicular to the interface is set to zero, but can have vertical movement..........................................90 6-3 Diffusion of B in (left) relaxed Si, tensile Si, and Si 0.99 Ge 0.01 and (right) diffusion of B in strained and relaxed Si 0.76 Ge 0.24 ........................................................................92 xiii

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science APPLICATIONS OF STRESS FROM BORON DOPING AND OTHER CHALLENGES IN SILICON TECHNOLOGY By Heather Eve Randell May 2005 Chair: Mark E. Law Major Department: Electrical and Computer Engineering Semiconductor device performance has been improving at a dramatic rate due to scaling to nanometer dimensions. Strain engineering of the substrate has also proven to increase drive currents in MOSFETS and other advanced devices. An active area of research and development is focused on intentionally straining the channel of MOSFETS to enhance mobility. However, increased scaling can also magnify the mechanical forces that arise during IC fabrication. Multiple material layers with differing thermal expansion coefficients and deposited stress levels become closer in proximity to one another and to the device channel. Shallow trench isolation (STI) can create large stresses due to thermal mismatch, oxide growth, and trench fill, and the sharp corners at the top and bottom of the trenches are major contributors to the stress behavior. Stress will influence dopant and defect behavior in unexpected ways. It has been predicted that the proper stress can double the solubility of dopants such as boron in silicon. Thus, accurate process models xiv

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need to be developed to incorporate both the intentional and unintentional stress sources in order to maximize device performance. This work focuses on the unintentional stress source from dopant incorporation. The model that FLorida Object Oriented Device and Process Simulator (FLOOPS) currently utilizes to compute stress and strain was developed for LOCOS processes, which are largely no longer employed. In addition, these computations are decoupled from the solution of the diffusion equations. Most of the materials used in silicon processing can be modeled as simple elastic materials, which makes process modeling easier. New models must be developed to more accurately calculate the stresses in the silicon substrate. To achieve this goal, new software operators were developed in FLOOPS to calculate the displacements and stresses in the silicon substrate due to boron doping. This elastic stress solver was integrated into the Alagator scripting language, and the simulation results provide a more accurate description of the stress evolution. Part of the future work is to enable the elastic stress solver to be coupled to defect and dopant evolution. xv

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CHAPTER 1 INTRODUCTION Strain engineering has become a key component of emerging technologies, however due to the great complexity and cost in IC fabrication, it is difficult to physically develop new processes. Technology Computer Aided Design (TCAD) tools are invaluable for shortening new technology development and for optimizing existing processes [Cea96]. Front-end process modeling of stress effects from oxidation, thermal mismatch, and intrinsic stress have been demonstrated over the last 15 years, beginning with 2D and 3D modeling of oxide growth for viscous and viscoelastic materials [Cea96]. Recently stress simulations for strained silicon have been performed to understand the effects of strain on device mobility and drive current enhancements, and threshold voltage shifts [Lim04, Tho04a, Tho04c, Uch04]. While applying the proper strain has clearly demonstrated enhancements in transistor performance, the effects of mechanical stress can also degrade device characteristics. In the front-end process, shallow trench isolation (STI) is a major source of stress in the MOSFET channel. The proximity and amount of the stress in the silicon substrate limits the density of ICs, and when the too much stress is exerted in the silicon, it will yield by releasing dislocations that lead to leakage currents and degraded device performance. Thus, having an in depth understanding of how stress affects the semiconductor fabrication processes is critical. As we enter the nanometer regime, stress from standard process steps such as source/drain doping introduce significant stress in the channel of MOSFETs. In PMOS 1

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2 devices, the tensile stress generated in the channel from source/drain boron doping is nearing values large enough to compensate the engineered strain engineered intended for performance enhancement. This focus of this chapter is to provide a survey of the existing literature on stress applications in silicon technology. Section 1.1 provides a brief history of the transistor and discusses scaling trends over the past 50 years. Section 1.2 presents work that explored the effects of stress on defect evolution and regrowth velocities in patterned structures. Section 1.3 discusses mechanically induced channel stress from shallow trench isolation structures (STI). Section 1.4 introduces strained silicon and demonstrates various methods of applying stress to enhance device performance. Section 1.5 will provide a brief summary of each chapter of the thesis. 1.1 Motivation The semiconductor industry is on an eternal hunt for methods to continue Moores Law. Since the invention of the transistor in 1947 by William Shockley, John Bardeen, and Walter Brattain, and the fabrication of the first Metal Oxide Semiconductor Field Effect Transistor (MOSFET) at Bell Labs in 1960, much innovation in the forms of transistor scaling and new materials has led to the recent MOSFET [Tho04a,Tho05]. In 1965, Gordon Moore proposed that the number of transistors on an integrated circuit (IC) will approximately double every 2 years [Moo65]. Since then, much work in the area of transistor scaling has been accomplished. The goal of technology scaling is to create faster, denser, low power circuits per chip for the same amount of money. For long channel devices, dimensions and supply voltages scaled by the same factor in order to maintain a constant electric field. The next trend in scaling was to maintain a fixed supply voltage and scale only device dimensions. Modern short channel devices scale both the

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3 supply voltage and device dimensions by different factors. Moores prediction has held over the last 4 decades and will continue as long as the price of a transistor continues to drop in price [Tho04a]. The scaling of minimum feature size over the years and the evolution of the transistor is illustrated in Figures 1-1 and 1-2. Figure 1-1: Evolution of transistor minimum feature size and transistor cost vs. year [Tho04a] Figure 1-2: Evolution of the MOSFET from 1947 to 2002 [Pbs47].

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4 1.2 Stress Induced Defects in Patterned Structures Thin films such as silicon nitride, silicon dioxide, and polysilicon are frequently encountered in device fabrication; these films contain intrinsic stresses as a result of the deposition process. Continuous films deposited over the entire silicon substrate produce low levels of stress in the silicon because the substrate is generally a few orders of magnitude thicker than the film. Large stresses occur when films are not planar or have discontinuities, and silicon substrate yields by forming dislocations. In MOSFET fabrication, high dose ion-implantation is used to accurately dope the source/drain regions to desired junction depths. The implanted region becomes amorphized and upon subsequent annealing dislocations form at the original amorphous-crystalline interface. Dislocations have been known to affect dopant redistribution during thermal cycling by capturing and emitting point defects, leading to variations in junction depths. Calculations of the stress around a dislocation loop with observed density and size shows that the pressure around the loop layer can locally be on the order of 10 9 dyne/cm 2 This value is comparable to stresses induced from patterned nitride films and isolation structures [Par95]. Thus, the control and understanding of dislocation loops formation is critical. The effect of multiple nitride stripes on stress and dislocation loop formation was investigated by Chaudhry. His work demonstrated that the stress in the silicon substrate is a strong function of the nitride stripe thickness and width. Narrow stripes resulted in higher levels of stress than significantly wider stripes. Large shear stresses developed at the nitride/silicon interface which can lead to slip in silicon. Hu reported the critical shear stress slip in silicon to be 3x10 7 dyne/cm 2 These dislocations lie on the {111} plane and glide in the [110] direction [Fah92]. Dislocations in regions of shear stress

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5 higher than this value will glide. Placing the nitride stripes in closer proximity offset the shear stress components. The tensile component of one strip offset the compressive component of the adjacent strip [Cha96]. Ross demonstrated the effect of stress on defect formation at the mask edge of patterned structures and on the regrowth velocity [Ros03, Ros04]. Line and square structures were formed by depositing 80 of SiO 2 and 1540 of nitride on silicon. An amorphizing silicon implant with a dose of 1x10 15 atoms/cm 2 at 40keV was performed after patterning the wafer, and samples were anneals between 550C and 750C. Cross-sectional Transmission Electron Microscopy (XTEM) samples were prepared at different stages of the solid-phase epitaxial regrowth process to observe the formation of half-loop dislocations at the mask edge. The defects only occurred around the line edges and not the square edges. When the square structures were etched and re-annealed, defects formed around the mask edge. Dislocation loops migrate to regions of tension to relieve stress, and FLOOPS simulations confirmed a tensile pocket at the nitride/silicon interface where the defects formed. It was concluded that the stress from the nitride square structure suppressed the defect formation. Figure 1-3: Dislocation formation at the edge of a nitride strip after solid-phase epitaxial regrowth (left) before annealing and (right) after annealing.

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6 Low defects densities are required in the areas where devices are fabricated on wafers because they lead to leakage current and performance degradation. In a study performed by Phen [Phe04], a wafer bending study was performed in which the patterned wafers aforementioned were bent to a stress of 86 MPa of tension and annealed at 750C for five minutes. Transmission electron microscopy micrographs confirmed that the tensile mechanically-induced stress removed defects from the samples. This is further proof that suggests stress affects defect formation and is worthwhile investigating. Figure 1-4: Application of stress to patterned wafers prevented line defects from forming [Phe04]. Isolation structures such as deep and shallow trench isolation are also known to generate dislocations. After the formation of isolation structures, residual stresses are present in the silicon and trench area; however they are not significant enough to generate dislocations. These stresses will be addressed in Chapter III. After processing steps such as ion implantation, point defects are introduced into the silicon and can serve as nuclei for dislocation formation. Once the dislocations form, the stress in the silicon from the trench formation can cause the dislocations to glide. The energy for dislocation glide is much less than the energy for dislocation formation, thus the glide process can even occur in materials with moderate stress [Fah92]. Fahey et al. observed the formation of dislocations in a deep trench isolation structure filled with poly for a bipolar process. A phosphorus implant was performed to

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7 make contact with the deep subcollector. After annealing to activate the dopant, defects formed near the corners of the structure. The defects did not form in similar patterned structures that did not receive the implant. In addition, no defects formed in unpatterned wafers that received identical implantation implants and anneals. This phenomenon was further investigated for a DRAM trench capacitor process, in which a deep trench filled with poly, is fabricated next to a PMOS device. The source and drain are doped with boron, and after the annealing step, gliding dislocations formed next to the trench on the {111} plane and glided in the [110] direction towards the PMOS transistor. Again, the defects did not form in identical structures with no implantation. This study concluded that the ion implantation can reduce the stress in silicon because it provides nuclei for dislocations, and the dislocations glide due to the stress from forming the isolation structures. However, if the dislocations glide out of the implanted area, they could become deleterious to device performance [Fah92]. 1.3 Mechanically Induced Channel Stress from Shallow Trench Isolation (STI) Experimental data and simulations show that while the stress introduced by the STI formation enhances PMOS drive current, it also demonstrates sensitivity to layout for NMOS transistors [Jeo03, Gal04, Sco99, She05]. The STI process introduces a compressive stress in the channel direction, which enhances hole mobility. The physics behind this improvement in carrier mobility are discussed in Section 1.4. Scott et al. observed a mobility reduction in NMOS devices due to stress from isolation trenches. The proximity of the gate to the trench edge and the active area were critical factors that made NMOS devices sensitive to layout. Linear current was reduced by as much as 13% for diffusion lengths less than 2 um, and the extracted mobilities agreed with piezoresistance calculations [Sco99]. Current reduction was also observed as the width

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8 of the NMOS devices were decreased from 20 um to 0.5 um, where PMOS devices were relatively insensitive to the width variation. Jeon et al. investigated the effects of mechanical stress from STI formation on silicon-on-insulator wafers for a silicon thickness of 50 nm and 90 nm. For the 50 nm wafers, he observed a 13.5% current degradation in NMOS and a 23% current increase in PMOS current as the gate-edge-to-STI distances were decreased from 2.69 um to 0.26 um [Jeo03]. Thus, it is critical to compute the stresses throughout the IC fabrication process, and use those values as parameters to for future technology development. Gallon et al. performed wafer bending experiments to investigate the effect of STI mechanical stress on 0.13 um bulk and SOI transistors. For both bulk and SOI devices, an increase in PMOS and reduction in NMOS current was observed as the gate-to-STI distance was decreased from 10 um to 0.34 um, which was in accordance with the findings of both Scott and Jeon. For small stresses ranging from |0-130| MPa, a linear change in mobility enhancement/reduction was observed for NMOS and PMOS bulk devices. Figure 1-5: Linear variation of mobility enhancement for a bulk NMOS transistors [Gal04].

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9 Lower values of stress were applied because silicon yields for a mechanical stress between 175-220 MPa. The modeling of silicon in the plastic regime will be addressed in the future work Chapter IV. For both NMOS and PMOS devices, higher stresses were observed in SOI vs. bulk transistors. This is because the silicon can reoxidize at the buried-oxide/silicon interface at the STI edge, and the bending of the silicon adds to the compressive stress in the channel from the STI formation [Gal04]. Gallon et al proposed that the enhanced performance for SOI PMOS and decreased performance for NMOS devices is a result of the implantation, amorphization, recrystallization process rather than from bandgap effects and reduction in conductivity effective masses. Amorphous silicon relaxes by viscous flow under compressive stress with a temperature dependence, which is driven by a decrease in concentration of defects [Wit93]. When fabricating NMOS transistors, an arsenic implant of 2x10 15 /cm 2 created an amorphous layer approximately 50 nm below the surface. Simulations demonstrated that due to the compressive stress from the STI, the amorphous layer was able to relax, causing a reduction of internal stress from -1650 GPa to -750 MPa [Gal04]. The boron implant for PMOS transistors however was non-amorphizing, and no initial stress relaxation occurred. Bulk devices on the contrary did not show significant relaxation after recrystallization because the stress from the STI formation is not large enough to relax the amorphous layer (~400 MPa). As a result, bulk NMOS and PMOS transistors retain their initial stress levels. Strain relaxation of a SiGe layer upon regrowth was also observed by Crosby [Cro04]. Fifty nm of strained silicon was grown on top of a graded SiGe buffer layer up to 30% germanium incorporation. High Resolution X-ray Rocking Curves confirmed

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10 that the strain varied from 0-2.4% throughout the structure. Low energy implants of 12 keV, creating at 30 nm amorphous layer, and high energy implants of 60 keV, creating a 100 nm amorphous layer were implanted with 1x10 15 /cm 2 Si + into the SiGe structure. Both structures were annealed at 600C and 675C for up to 30 minutes. Similar to and STI structure, SiGe creates a compressive stress due to the increased lattice constant of germanium compared to silicon. For germanium contents exceeding a critical thickness, the strained silicon layer will relax by emitting misfit dislocations at the Si/SiGe interface. This will be described in more detail in Section 1.4. The strain relaxation occurred in the structures for both implant conditions, but did not occur in unimplanted samples. These finding further support the work of Gallon et al. suggesting that compressive stress causes stress relaxation after amorphous regrowth. Cowern et al. developed an Arrhenius relationship for dopant diffusion in a biaxially strained SiGe layer to be [Cow94]: ]'exp[kTsQDDIS (1-1) where D S is the dopant diffusivity under strain, D I is the dopant diffusivity without strain, s is the biaxial strain in the plane of the SiGe layer, and Q is the activation energy per strain. Similar to this relationship, Sheu et al. developed a sophisticated stress-dependent dopant diffusivity model to calculate the mechanical stress from STI formation. The model was calibrated to account for implant damage, dopant-point defect pairing diffusion, silicon-oxide dopant segregation, oxidation-enhanced diffusion models, dopant clustering models, dopant-defect clustering models, and intrinsic diffusion models. The relationship for dopant diffusivity due to STI mechanical stress is [She05]:

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11 ]),,(exp[)(),,(kTyxTETDyxTDtSIS (1-2) where D S is the dopant diffusivity under strain, D I is the dopant diffusivity without strain, and E S is the activation energy per volume change ratio (V CR ) depending on dopant species and temperature (T). The V CR is the volume change ratio due to stress, and for small applied stresses, the V CR can be approximated as [She05]: zzyyxxtCRyxTyxTyxTyxTV ,,),,(),,(),,( (1-3) where xx is the strain in the direction of the channel, yy is the strain perpendicular to the channel, and zz is the strain in the channel width direction. For simulations, a wide width was chosen, so zz is zero. Stress simulations involved the STI and other main process steps, and the model was tested for MOSFETS with varying gate and active lengths. Unsurprisingly, the compressive stress in the channel direction increased as the active area decreased. Tensile stress was also observed in the bulk direction with magnitudes significantly less than in the channel direction. For active areas = 0.6 um, the stress and strain magnitudes were simulated to be -5x10 9 dyne/cm 2 and -0.4% respectively, which is equated to the strain from incorporating 10% germanium in silicon [Cow94, Gal04]. It was concluded that the dopant distributions were properly computed in the operating region of the device because device simulations matched subthreshold NMOS I-V experimental data curves. Boron, a known interstitial diffuser, exhibited retarded diffusion as a result of the compressive STI stress.

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12 Figure 1-6: Dopant profiles, vertical profiles are taken at the gate edge and lateral profiles are taken 15 nm below the device surface [She05]. Threshold voltage increased with decreasing NMOS active areas, while PMOS exhibited negligible voltage shift to the decreasing active area, which was also verified by experimental data. This will be further explored in Section 1.4. 1.4 Strained Silicon Two main factors that control the switching speed of an ideal transistor are the channel length and the speed at which carriers move through the semiconductor material. In this section, the speed of the carrier through the semiconductor material is discussed, and is described by the strained silicon concept. Strained silicon can be applied biaxially or uniaxially to improve the drive currents in MOSFETs and other advanced devices through mobility enhancements. An important and promising feature of strained silicon for future technology nodes is that it increases device performance without decreasing the channel length or increasing the off-state leakage current. This is done by increasing the

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13 carrier mobility through the channel by reducing the conductivity effective mass, and/or scattering rate [Moh04]. 1.4.1 Strained Silicon Physics Carrier mobility () in semiconductors can be expressed as a linear relationship between the velocity (v) and the external electric field (E) [Cro04]: Ev (1-1) The mobility is also function of transport scattering time () and effective mass (m ): *me (1-2) where e is the electron charge. Both effective mass and scattering reductions have demonstrated mobility enhancements for electrons, while only effective mass reduction is necessary for hole mobility enhancement. This is because the valence band splits less than the conduction band under strain [Moh04]. For electron transport, the conduction band of silicon is sixfold degenerate. When strain is applied, the degeneracy is lifted and lowest energy level of the band is split. Two states drop to a lower energy level and the remaining four states occupy a higher energy level. As a result of the band splitting, electron scattering is reduced, and the average velocity in the conduction direction increases. The combination of increasing the average distance an electron travels before it is knocked off course, and reducing the effective mass results in electron mobility enhancements [Lim04, Tho04a, Tho05, Tho04c] Hole mobility transport is more complex. The valence band consists of three bands that are all centered at the gamma point, and from lowest to highest energies are the heavy-hole, light-hole, and spin-orbit bands. When strain is applied, the degeneracy is

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14 lifted between the light and heavy hole bands, and holes fill the light hole-like band, thus reducing the effective mass and increasing hole mobility [Moh04]. Under no strain, the bands have mirror symmetry about the k=0 point. Applying a uniaxial or biaxial strain in the [110] direction results in severe band warping. For biaxial tensile strain, the warping remains symmetrical; meaning that the electrons repopulate the lowest energy levels equally. However for uniaxial strain, the warpage is no longer mirror symmetrical and the holes will still repopulate the lowest energy states first. The breaking of the symmetry is caused by a shear stress component that does not affect the conduction band and is not present for biaxial stress [Gha04]. A key advantage to uniaxial compressive strain for PMOS devices is that the hole mobility enhancements do not degrade at high vertical fields. This is because the large out-of-plane mass causes further band splitting with confinement in the inversion layer of a MOSFET [Fis03]. On the contrary, biaxial stress does not maintain the hole mobility enhancements at higher vertical fields because unlike uniaxial stress, at high fields the bands splitting reduces because of the lighter out-of-plane mass. At approximately 1 MV/cm, the mobility decreases to that of the universal hole mobility, and all gains from straining are lost [Gha05, Tho04a, Tho05, Tho04c]. The mobility vs. effective field data for biaxial and different applications of uniaxial stress are shown below. Note that only the uniaxial stress applied by silicon germanium in the source/drain region resulted in mobility enhancements at high vertical fields.

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15 Figure 1-7: Strained silicon hole mobility enhancement vs. vertical electric field (wafer bending, SiGe S/D, biaxial substrate stress [Tho04c]. 1.4.1.1 Biaxially Strained MOSFETS Applying stress in the channel region of a device allows for higher carrier mobility. Tensile strain increases the interatomic distances in the silicon crystal, thus increasing the mobility of electrons. The same effect is observed with holes and compressive strain. Although this method of introducing strain enhances both hole and electron mobility, a large mobility loss is evident at high vertical fields [Tho05]. Tensile strain G Figure 1-8: Formation of biaxially strained NMOS transistor p Si Substrate p SiGe graded buffer layer p Relaxed Si 1-x Ge x n+ n+ Strained Si SiO 2 D n+ poly-Si S

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16 Biaxial strain occurs in both the x and y directions of the deposited silicon layer. The formation of biaxially strained NMOS transistors begins with a silicon wafer and a grown SiGe graded buffer layer. The buffer layer is formed by linearly increasing the Ge content as the layer thickness is increased. As the Ge content becomes larger, relaxation occurs in the layer by generating misfit dislocations. When a lattice constant approximately 1% greater than that of silicon is formed, a relaxed Si 1-x Ge x is grown on top of the graded layer to set the lattice constant of the material [Tho04a]. Finally, a defect-free thin silicon layer is grown on top of the relaxed structure and the layer remains strained as long as the thickness is below a critical value [Cro04, Peo85]. The critical thickness decreases as the lattice mismatch (% Ge) increases. This is illustrated in Figure 1-9 below. Figure 1-9: Critical thickness as a function of Ge composition for SiGe on Si [Peo85]. Fiorenza et al. studied strained silicon MOSFETS with silicon thicknesses below and above the critical thickness value to understand the effects of exceeding the critical

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17 thickness on device performance [Fio04]. Although increasing the strained silicon thickness far beyond its critical value had little effect on mobility loss, a significant off-state leakage current was observed, which is deleterious to device performance. The leakage current was attributed to misfit dislocations that form at the silicon/SiGe interface and can cross between the MOSFET source and drain. The increased leakage was only observed when transistor gate lengths were less than the diffusion lengths. Figure 1-10: Drain current leakage mechanism in strained silicon films with misfit dislocations [Fio04]. Figure 1-11: Subthreshold characteristics of strained silicon MOSFETS with strained silicon thicknesses above the critical thickness. Devices above the critical thickness (14.5 nm, 20 nm, and 100 nm) show increased off-state leakage current [Fio04].

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18 1.4.1.2 Uniaxially Strained MOSFETS The Intel Corporation recently developed a process flow that uses two different approaches to introduce uniaxial channel strain in both NMOS and PMOS devices. With this new process, strain is independently introduced into the channel of both devices with minimal integration challenges or major increased in manufacturing cost. NMOS devices are fabricated with the standard process flow, and at the end of the process, a highly tensile nitride capping layer is deposited over the source, gate and drain regions. The high tensile stress, approximately 1.8x10 10 dyne/cm 2 in the capping layer creates compressive stress in the source and drain regions, which in turn induces longitudinal tensile stress and out of plane compressive stress in the channel area. [Tho04a]. Figure 1-12: Stress along the channel in a strained silicon NMOS transistor [ISE04] Uniaxial strain is introduced into PMOS transistors by depositing Si 1-x Ge x in a recessed etched trench (source and drain regions) on each side of the channel. Boron has a higher solid solubility limit in silicon germanium, thus allowing for higher boron activation [Sad02]. Since the Si 1-x Ge x has a larger lattice constant than Si, it compresses

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19 the channel from both sides and induces compressive stress in the channel region. For a PMOS device of Si 0.83 Ge 0.17 source/drain regions, 1.4 GPa of compressive stress simulation results show approximately 500 MPa of uniaxial compression in the channel [Tho05]. This technique of applying strain in the channel however is only applicable for nanometer channel lengths; in longer devices the compressive force would not have penetrated far enough to strain the entire channel. A large benefit to introducing strain in this technique is that integration issues are kept to a minimum because the strain is applied late in the process flow. Because the Si 1-x Ge x is confined to the source/drain regions, self-heating and leakage currents are not observed [ISE04]. Compressive stress from is shallow trench isolation structures has also demonstrated enhancements in PMOS device performance, which was discussed above in Section 1.3. Figure 1-13: Stress along the channel in a strained silicon PMOS transistor [ISE04] 1.4.2 Stress effects on electrical characteristics In 1954, Charles S. Smith discovered that bulk silicon and germanium demonstrate a change in electrical resistance with strain [Smi54]. This is known as the piezoresistive effect, and it can be used as a strain measurement tool for in strained silicon devices.

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20 Since there is a lack of data for many thin film materials used in semiconductor processing, the bulk coefficients are used for simplicity. For small strains, piezoresistance varies linearly with stress, and by analyzing the piezoresistive coefficients, it was observed that the most effective stress for PMOS devices is longitudinal compressive stress, but is longitudinal tensile and out-of-plane compressive for NMOS devices [Tho04a]. Thompson et al. studied mobility enhancements in MOSFETs at low strain and high vertical electric field [Tho04a]. For PMOS devices, the piezoresistance coefficients predicted that for 500 MPa of stress, a 40% increase in hole mobility for uniaxial compressive stress, and a 5% decrease in hole mobility for biaxial tensile stress resulted. Longitudinal uniaxial compressive strain introduced by Si 0.83 Ge 0.17 in the source/drain of a PMOS increased the hole mobility by 50% for a 45 nm gate length, and the NMOS devices showed a 10% mobility enhancement from a 75 nm capping layer [Tho04a]. The electron mobility enhancement is less than the PMOS because the strain induced from the nitride capping layer is less than the strain from growing Si 0.83 Ge 0.17 into the source/drain regions. However, the strain from the capping layer increases as the nitride capping layer is increased. Wafer bending techniques performed by Uchida et al. investigated the hole and electron mobility enhancement in biaxial and uniaxial stressed bulk and SOI MOSFETs. For both carriers, the appropriate uniaxial stress showed the largest enhancements in the [110] direction at high vertical fields. For 3.5 nm SOI NMOS devices, the electron mobility enhancements under biaxial and uniaxial strains were almost equivalent. In

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21 addition, the electron mobility enhancement in the [110] direction under uniaxial tensile strain was comparable in both SOI and bulk devices. Lim et al. and Thompson et al. demonstrated through wafer bending, a favorably small threshold voltage shift was found for uniaxially strained NMOS devices. Biaxially strained NMOS devices exhibited a four times greater threshold voltage shift than uniaxially strained silicon NMOS transistors. Simulations show that when correcting for the large biaxial threshold voltage shift, much of the performance gain is lost [Lim04]. The small threshold shift for uniaxial strain, however, is a result of lower bandgap narrowing and the strain of the n+ poly gate [Tho04c]. Figure 1-14: Calculated and measured threshold voltage shift for NMOS under biaxial and uniaxial stress (4x shift for biaxial stress) [Lim04, Tho04c]. 1.5 Organization The purpose of this work is to understand the unintentional stress sources that arise during integrated circuit (IC) fabrication process and provide more accurate process models. By understanding how the stresses affect device operation, the stresses and strains can be engineered to improve device performance and avoid high leakage currents. In this work, C++ code was implemented in Florida Object Oriented Processing Simulator (FLOOPS) to study stress in the silicon substrate due to boron doping and

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22 nitride deposition. Simulations were performed for software validation and results were presented. This chapter provided a literature review describing many applications of stress in silicon technology. In the first section, stress induced dislocations were discussed for various structures. Next, the effects of STI stress on device performance were addressed. In the following section, the strained silicon concept was introduced and the effects of the advantageous and unintentional stresses on device performance were presented. In Chapter II, the concepts of stress and strain are defined, examples of the normal and shear components are given, and a stress-strain relationship for linear elastic materials also described. In Chapter III, various stress and strain sources that arise during the semiconductor fabrication process are addressed, including sources from LOCOS, STI, thin film deposition, and dopant induced strains. Chapter IV focuses on the software implementation in FLOOPS to calculate the displacement and stress in the silicon substrate due to boron doping and nitride deposition. Chapter V provides applications and results of the displacements and stresses computed from beam bending, nitride deposition, and PMOS-like structure simulations. Chapter VI provides a summary and recommendations for future work.

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CHAPTER 2 LINEAR ELASTICITY, STRESS, AND STRAIN 2.1 Linear Elastic Materials Linear elasticity is a property that all materials possess to an extent. Solids respond to externally applied loads by developing internal forces, and stress is the distribution of those forces over a unit area. A solid deforms from its natural state due to stress, and if the deformation is small enough, the solid will return to its original shape once the load has been removed. The relationship between stress and strain for linear elastic materials is shown in Figure 2-1. Figure 2-1: Linear elastic deformation A simple example to illustrate linear elasticity is an ideal spring. One end of the spring is fixed and the other end is free to move. F x x Figure 2-2: Deformation of a spring with an applied force 23

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24 When an external force is applied to the spring, an equal but opposite counter force is generated. A deformation x, or strain results due to the force applied. The internal force and deformation is related by kxf where f is the force, x is the length of the spring, and k is the stiffness of the spring. Stiffness is a measure of how resistant the body is to external forces. If too much stress is applied, the spring will not return to its original position and will become plastically deformed. A measure of how much stress can be applied before plastic deformation occurs is called the yield strength. Under the temperatures ranges and processing conditions that will be considered in this work, silicon acts as a linear elastic material. Understanding how stress affects the fabrication process is very important because proper strain engineering can enhance device performance, while unintentional strain can be deleterious. In this section, stress, strain, plane stress, plane strain, and the stress-strain relationship will be discussed. 2.2 The Stress Tensor Stress () is defined as the force per unit area acting on the surface of a solid. AFA0lim (2-1) Stresses have two components, normal and shear forces. Normal forces act perpendicular to a face and tend to stretch or compress a body, while shear forces () act along the face of a body and exhibit a tearing motion. Tensile forces are positive, while compressive forces are negative. An example illustrating a normal force is a weight hanging from the bottom of a cube by a string. The force of the weight acts perpendicular to the bottom of the cube and pulls the box downward to create a tensile force. To illustrate shear stress imagine a metal rod permanently attached by a bolt to a sheet of metal. If the rod was pushed parallel to the metal sheet, the ripping forces that develop in the bolt represent the shear stresses.

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25 To illustrate all of the stress components, consider an infinitesimal cube with normal ( ij ) and shear ( ij ) stress components stress components in the x, y, and z directions. The first subscript identifies the face on which the stress is acting, and the second subscript identifies the direction. x y xz +y xx y z yy z y zz +z y x zx +x Figure 2-3: Stress components of an infinitesimal cubic element. For example, to evaluate the stress acting on the y-plane of the cube in figure 2-3, with area, the stress vector T on that plane is: zxAy zyxyzyyyxT (2-2) where x, y, and z are unit vectors in the x, y, and z directions, and the normal and shear stress components acting on the y-plane are: xxAyxAFy0lim (2-3) yyAyyAFy0lim (2-4)

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26 yzAyzAFy0lim (2-5) Nine stress components from three planes are needed to describe the stress state at an arbitrary point on the continuous body. The grouping of these terms in matrix form is called the stress tensor ij: (2-6) zzyzxzzyyyxyzxyxxxij In static equilibrium, some of the shear stresses are equal xy= yx, yz= zy, and xz= zx, and by symmetry, the stress matrix can be reduced to six components: zxyzxyzzyyxxtotal (2-7) 2.3 The Strain Tensor When forces are applied to a solid body it will deform. Strain () is a unitless parameter that quantifies the amount of deformation, and is equal to a change in length in a given direction divided by the initial length. To illustrate normal strain, consider an infinitesimal element with possible displacements u(x,y,z), v(x,y.z), and w(x,y,z). The variables u, v, and w are the displacements in the x, y, and z directions respectively. Assume the element in figure 2-4 experiences deformation in all three directions, and the dashed lines represent the element after deformation. The change in length in the x and z

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27 directions are negative, which represents a compressive, or negative strain. The change in length in the y direction is positive, which represents a tensile or positive strain. Figure 2-4: Normal strain in the x, y, and z directions. du/dx<0, dv/dy>0, and dw/dz<0 Silicon, like all linear elastic materials, becomes narrower in the cross section when it is stretched. A measure of the transverse to longitudinal strain is know as Poissons ratio, where a positive ratio is considered tensile and a negative ratio is considered compressive. allongitudintransverse (2-8) Shear strain () is the displacement in x direction with respect to a change in the length of y, plus the displacement in the y direction with respect to a change in length of x: )()(xuyuxuyuyxyxxy (2-9) To illustrate shear strain, consider the differential element experiencing deformation in the x and y directions where 1 and 2 are the change in angle from the original shape, and u x and u y are the direction of the displacements. dz+dw/dz dx+du/dx dy+dv/dy +x +y dy dz dx +z

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28 u x Figure 2-5: Example of shear strain in the x-y direction For small displacements, referred to as micro-strain (), the shear strain can be approximated as the angle itself, tan ~ and the total strain is equal to the sum of the angles 1 and 2. [Sen01] To illustrate the strain components, consider the cube from figure 2-4. There are nine normal and shear strain components that are related to the displacements by: : zwywzvxwzuzvywyvxvyuzuxwyuxvxuzzzyzxyzyyyxxzxyxx (2-10) Combining these terms in matrix is called the strain tensor, ij: zzyzxzzyyyxyzxyxxxij (2-11) In static equilibrium, the shear components are equal: )(21),(21),(21xwzuywzvxvyuzxxzzyyzyxxy (2-12) By symmetry of the matrix, the strain tensor can be condensed into six components: 1 x 2 y u y

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29 xzyzxyzzyyxxtotal (2-13) 2.4 Plane Stress Plane stress is defined as a state of stress in which the normal stress and shear stresses directed perpendicular to the plane are assumed to be zero: z = xz = yz = 0. Thin films exhibit plane stress because the z direction dimension is very small in comparison to the x and y dimensions, and the forces only act in the xy plane. A significant source of plane stress in thin films arises from the deposition process. Stress from thin films will be discussed in more detail in Chapter III. Consider a thin film attached to a substrate to illustrate plane stress. The regions of the plane that are about three times the film thickness from the edge exhibit plane stress because the top surface is stress free. The behavior in the edge regions is more complex, and is dominated by peel forces that tend to detach the film from the substrate. [Sen01] Figure 2-6: Plane stress in a thin film For an isotropic linear solid under plane stress, the in-plane strain () and shear strain () values are defined as: x = )(1yxE (2-14) Edge Region Thin Film Plane Stress Region Substrate

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30 y = )(1xyE (2-15) xy = xyE )1(2 (2-16) The only non-zero out of plane strain is: z = )(yxE (2-17) 2.5 Plane Strain Plane strain is defined as a state of strain in which the normal strain z and shear strains xz and yz = 0: y yx x y x x x y yx y Figure 2-7: Example of plane strain in the x-y direction The plane strain assumption is used for long bodies with constant cross-sectional area whose forces only acts in the xy plane, and used when the strain in the z direction is significantly less than in the other two orthogonal directions. Under this assumption, yxxy and the strain matrix reduces to: yyxyyxxxxy (2-18)

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31 2.6 The Stress-Strain Relationship The relationship between stress and strain is described by Hookes Law, and it is used to calculate the deformation in a material due to stress. The ratio of stress to strain is known as Youngs Modulus of Elasticity, E, and the ratio of shear stress to shear strain is known as the Shear Modulus of Elasticity, G. For a linearly elastic material, the normal stress is linearly proportional to normal strain by: E (2-19) and the normal forces are resisted by the bodys bulk modulus, which determines how much a solid will compress under external pressure: )21(3EK (2-20) Shear stress is linearly proportional to shear strain by: G (2-21), and shear forces are resisted by the bodys shear modulus: )1(2EG (2-25) The Hookean Model For linear elastic materials stress is linearly proportional to the strain and is described by: ijijklijC (2-26) where Cijkk is the fourth order elastic stiffness tensor of 81 material constants, ij is the equilibrium stress values from (2-7) and ij is the equilibrium strain from (2-13).Silicon is an anisotropic material with diamond cubic crystal symmetry and the matrix reduces to 36 components with three elastic constants c11, c12, and c44: ijklC

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32 444444111212121112121211000000000000000000000000ccccccccccccCijkl (6-2) C11 = 166 GPa, C12 = 64 GPa and C44 = 80 GPa [Str05]. Although silicon is an anisotropic material, it can be approximated with isotropic elastic properties for simplicity, meaning that the elastic properties in all directions are equal. For isotropic material, the elastic constants c11, c12, and c44 are [Sen01, Zie89] )21)(1()1(11 Ec (6-3) )21)(1(12vvEc (6-4) )1(44Ec (6-5) The elasticity constants for the crystal directions are E[100] = 129 GPa, E[110] = 168 GPa, and E[111] = 186 GPa [Str05]. Hookes Law states that strain can exist without stress. To illustrate this, consider an elastic band that experiences a force in the y direction, creating a stress in the y direction. The strain in the x direction however is not equal to zero. As the rubber band is pulled outward in the y direction, it moves inward in the x direction to fill the original space. The x plane does not have any external forces acting upon it, but a change in length is experienced. This demonstrates that strain can exist in a particular plane without any stresses present. When the forces are removed, the elastic band returns to its original shape.

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33 2.7 Summary This chapter discusses the mechanics behind linear elastic materials and definitions of stress and strain. First, linear elastic materials are defined as materials that return to their original form after an applied force is removed, and a spring is used to demonstrate this behavior. When to much force is applied, the spring will leave the elastic regime and experience plastic deformation. Next the stress and strain tensors are defined by the normal and shear components. Stress is the force per unit area, and strain is the change in length divided by the original length. In static equilibrium, both the stress and strain tensors can be reduced to six components compared to nine because the shear stresses and shear strains are equal. Next, the two-dimensional plane stress and plane strain assumptions are discussed. Finally, the stress-strain relationship is described by Hookes Laws, which relates Youngs Modulus, the Shear Modulus and the Bulk Modulus to stress and strain, and the laws explain how strain can exist without stress. In Chapter III, stress and strain sources that arise during the IC fabrication process will be discussed in detail. Different sources of stress and strain that will be explored are: non-planar oxidation, thin film deposition, STI formation, and dopant induced strains.

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CHAPTER 3 STRAIN SOURCES While scaling devices to nanometer dimensions improves performance, it also strongly magnifies the mechanical forces that arise during fabrication. Stress and strain are unintentionally introduced into the silicon substrate after various stages of the fabrication process, and are becoming increasingly difficult and expensive to cope with. Stress from thermal expansion mismatch, ion implantation and lattice mismatch can all result in thin film stress. This chapter will discuss the main factors influencing stress and strain from the IC fabrication process and measures to control them. Oxidation induced stress, thin film stresses, STI stress, and dopant induced strains will be discussed. Finally, a brief discussion of boron diffusion in silicon and silicon germanium (SiGe) will be provided. 3.1 Oxidation Induced Stress Silicon dioxide (SiO 2 ) formation is a critical process step for device fabrication, and exposing a silicon wafer to oxygen at high temperatures forms an excellent electrical isolator. In addition to its isolation properties, SiO 2 also acts as a barrier to impurities during deposition and implantation. [Jae02] During thermal oxidation, Si-Si bonds are broken to accommodate the oxygen atoms, and the oxide reacts with the Si at the Si-SiO 2 interface. The forming oxide consumes the silicon as it expands upwards at a rate of 2.2 times the volume of oxidized silicon. The interface moves into the Si bulk and leaves behind a compressively stressed region. The coefficient of thermal expansion for SiO 2 is less than that of Si, resulting in a negative strain value. In non-planar regions, the 34

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35 behavior is more complex because the oxide can no longer freely expand upward. On convex surfaces such as the top corner of an isolation trench, the oxide becomes stretched around the corner in tension. On concave surfaces such as the bottom corner of an isolation trench, the growing oxide squeezes together and becomes compressed. The stress from oxide growth relaxes depending on the oxide viscosity and as the temperature increases, the oxide flow increases and permits faster relaxation of the structural strains. [Yen00, Yen01] Oxide viscosity determines the oxide growth on shaped surfaces, and is described by: )2/sinh(2/)()(kTVckTVcTstressss (2-1) where )(T is the stress free temperature dependent oxide viscosity, s is the shear stress in the oxide, and Vc is a fitting parameter [Yen00, Yen01]. Yen et al [Yen01] showed that external mechanical stress affects the kinetics of silicon thermal oxidation. It had been previously understood that the oxidation rate constants were only temperature dependent, but recent studies show that stress also plays a large role in the rate. In the experiment conducted, two wafers were bent, one in tension and the other in compression and the oxide thickness and stress distribution across the wafer was observed over time. The tensile wafer exhibited an increase in oxide growth, while the wafer in compression showed little to no effect. The increase in oxide growth can be explained by the enlarged atom spacing of the silicon wafer under tensile stress. LOCOS Formation Local Oxidation of Silicon (LOCOS) is an obsolete technique used to isolate active regions of ICs. Selected areas of the wafer are oxidized by masking the non-oxidized

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36 region with silicon nitride (Si3N4). Beginning with a clean wafer, a uniformly thin layer of SiO2 is grown, and a layer of Si3N4 is deposited. The thin SiO2 layer is present to alleviate the mismatch stress between the silicon and the nitride layer. After the nitride is patterned, the wafer is exposed and all areas not covered by the nitride form a thick layer of SiO2. Compared to a planar surface, the stress from LOCOS formation is significantly higher because the volume expansion is dimensionally confined. [Sar04] The main forces that arise in the formation of LOCOS structures are illustrated in Figure 3-1: F1 represents the intrinsic stresses from the pad oxide and nitride layer, F2 represents the tensile bending stresses from the nitride deposition, F3 represents the compressive stresses from the non-planar field oxide growth into confined areas, and F4 represents the thermal expansion mismatch stress from the difference in thermal expansion coefficients between Si and SiO 2 F2 F3 F1 F1 F4 Figure 3-1: Forces present in LOCOS formation [Sar04] Due to the high stresses encountered in LOCOS formation, alternate isolation techniques such as shallow and deep trench isolation were developed.

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37 3.2 Thin Film Stress Thin films are a layer with high surface-to-volume ratio and are commonly used in IC fabrication for masking, passivation, isolation, and conduction [Hu91]. All stresses present in thin films after deposition are referred to as residual stresses and can be broken down into two components: 1) thermal mismatch stress and 2) intrinsic stresses. Thin films can be deposited or thermally grown, but depending on the deposition process, temperatures, and dopant concentration, tensile or compressive residual stresses will be obtained [Hu91]. The regions of highest intrinsic stress in thin films are at the film edges or in non-planar regions. Residual stresses will cause device failure due to instability and buckling if the deposition process is not properly controlled. 3.2.1 Thermal Mismatch Stress Thermal mismatch stress occurs when two materials with different coefficients of thermal expansion are heated and expand at different rates. During thermal processing, thin film materials such as polysilicon, SiO 2 and Si 3 N 4 expand when exposed to high temperatures and contract when cooled to lower temperatures according to their coefficient of thermal expansion. The thermal expansion coefficient for small strains such as those encountered in IC processing is defined as the rate of change of strain with temperature and is measured in microstrain/Kelvin (/K) [Sen01]: dTdT (2-2) Although T is temperature dependent, it can be treated as a constant over a wide range of temperatures. For example, Si ~ polysilicon has an T ranging from 2.6-4.5 over the temperature ranges of 20-900C [Fre03] and SiO 2 has an T of 0.5

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38 Consider the strain when a thin Si 3 N 4 layer is deposited onto a Si wafer at temperature T d and cooled to room temperature T r and T =. T d T r. The thermal mismatch strain of the substrate is [Sen01]: TTsubsub (2-3) If the film was not attached to the substrate, it would experience a thermal strain: TTff (2-4), Thin films that are attached to a substrate experience more complex behavior. Given that the Si wafer is much thicker than the Si 3 N 4 layer, the nitride will contract according to the Si substrate and the thermal mismatch strain that results is [Fre03]: TTsTfmismatchf)(, (2-5) where Tf and Ts are the thermal expansion coefficients of the film and substrate respectively. Positive strain is denoted as tensile and negative strain as compressive. Thermal mismatch stress and strain are related through Youngs modulus E, and Poissons ratio, by: mismatchffmismatchfE,,)1( (2-6) where Ef is Youngs Modulus for the film, and f, mismatch is the thermal mismatch strain described in ( 2-5). 3.2.2 Intrinsic Stress Intrinsic stress is the component of residual stress due to variations in the deposition process and is dependent on factors such as: deposition rate, thickness and temperature. It is important to minimize the intrinsic stresses generated because their magnitudes can amount to stresses greater than those of thermal mismatch. After a thin

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39 film is deposited, it will lie in either tension or compression. Tensile intrinsic stress is the result of a film wanting to be smaller than the substrate because it was stretched to fit it. Compressive stress results when a film wants to be larger than the substrate because it was compressed to fit. A technique commonly used to quantify the intrinsic stress is measuring the substrate curvature. In 1909 Stoney observed that a metal film deposited on a substrate was in tension or compression when no external loads were applied to it [Fre03]. Through this observation, Stoney created a simple analysis to relate the stress in the film to the amount of substrate curvature. This is known as the Stoney formula [Fre03]: fsiSisifhhRE)1(6 (2-7) where ESi and, Si are Youngs Modulus and Poissons Ratio for Si, hf and hSi are the film and Si thicknesses, and R is the radius of curvature of the substrate. Annealing can be performed to alter the residual stresses in thin films, however the large thermal budgets necessary to achieve stress relaxation is inconvenient for standard silicon processing. Zhang et al. [Zha98] showed that compared to conventional heat treatments, high temperature rapid thermal annealing (RTA) can effectively reduce the residual stress within a few seconds. 3.3 Stress from STI Shallow trench isolation (STI) is a technique used to electrically isolate transistors. While allowing a higher packing density, STI structures are becoming major contributors to the mechanical stresses present in the silicon substrate. To create an STI structure a trench is etched into the silicon using reactive ion etching (RIE). Next the trench walls are lined with a thin layer of SiO 2 by thermal oxidation. The trench is then filled with

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40 chemical vapor deposition (CVD) SiO 2 another CVD dielectric or CVD polysilicon. Finally, the structure is chemical mechanical polished (CMP), and a planar STI structure is created [Chi91]. The stress that results from this process comes from three areas: 1) thermal oxidation of a non-planar surface, 2) thermal mismatch stress from the different materials, and 3) intrinsic stress from the CVD fill deposition. For SOI devices, the silicon can re-oxidize at the buried oxide/Si interface at the STI edge which bends the silicon and adds an additional compressive stress component in the channel of the transistor [Gal04]. These stress sources act cumulatively and result in increased stress levels in the silicon substrate. If the stress levels become significant enough device failure is likely to occur. Thermal oxidation of non-planar surfaces leaves a compressive stress in the silicon substrate. After etching a trench in the silicon a SiO 2 sidewall liner is thermally grown which creates a large stress in the trench corners due to the oxide growth. In the top corners of the trench, the stress is tensile in the oxide and compressive in the silicon, and in the bottom corners of the trench, the silicon is in tension while the oxide is in compression [Law03]. This corner-induced stress is relaxed by the viscous flow of oxide which was described in section 2.1.

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41 Figure 3-2: Top corner of an STI structure The second source of stress is the thermal mismatch that arises during the STI process. Before thermal oxidation occurs, the silicon is considered to be in a zero-stress state. After thermally growing the oxide, the wafer is cooled from the oxidation temperature to an intermediate temperature causing a thermal mismatch stress between the Si and SiO 2 Since the coefficients of thermal expansion are almost equivalent for Si and polysilicon, no thermal mismatch strain results for any change in temperature [Chi91]. The final source of stress is a result of the intrinsic stress of CVD fill deposition. Depending on the fill material used and the process conditions, the thin film can have a tensile or compressive intrinsic stress [Chi91]. Films of this nature exhibit biaxial stress, however, when considering an entire trench structure, the biaxial plane changes around the rounded corners of the trench. Hu performed many isolation trench studies to investigate the effects of varying trench geometry on the stress distribution. His studies showed that for an oxide-filled trench, a compressive stress existed perpendicular to the trench sidewall, localized near

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42 the bottom of the trench and at the surface. In addition, there was a tensile component parallel to the trench near the center of the side wall. The shear stresses were dominant near the trench ends, but vanished at the mid-length of the trench. [Chi91, Hu91]. Stress cancellation can be desirable for increasing the density of transistors on a wafer. For NMOS devices, where compressive channel stress degrades device performance, stress reducing techniques can be employed to return the substrate to a zero stress state. Some mechanisms to alleviate the stress generated during the STI process are counter doping and corner rounding. Boron introduces a local tensile strain into the silicon substrate when it sits in a substitutional lattice site. In areas of larger compression, boron can be introduced by ion implantation or diffusion to even out stresses. By altering the processing conditions, different magnitudes of stress can be achieved to cancel out stresses of opposite magnitudes. Oxide growth stress is significant in the corner regions of isolation trenches and can be reduced by corner rounding. After an oxide is grown it is isotropically etched and the new oxide regrows around a more rounded corner, lowering the total stress from the growth process. 3.4 Dopant Induced Stress It is well known that introducing dopants into silicon will induce a mechanical stress in the substrate and change the lattice structure. As dopants are introduced in silicon through ion implantation or diffusion, a local lattice expansion or contraction will occur due to the varying atomic sizes and bond lengths of the dopants. Boron is smaller in size than silicon and when it sits on a substitutional lattice site, a local lattice contraction occurs because the bond length for Si-B is shorter than for Si-Si. Horn et al [Hor55] discovered that a single boron atom exerts a 0.0141 lattice contraction per atomic percentage of boron in silicon at room temperature. Germanium on the other

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43 hand is larger than silicon and when it sits on a substitutional lattice site, a local lattice expansion occurs. At high concentrations significant strain values can result due to a lattice mismatch between the silicon substrate and the dopants [Avc02]. The lattice contraction and expansion for boron and germanium are illustrated in figure 3-3. Lattice Expansion from Germanium Lattice Contraction from Boron Figure 3-3: Lattice contraction due to boron atom, and lattice expansion due to germanium atom Stress has demonstrated enhancements in the solid solubility limit of boron in silicon. As we move towards smaller, faster transistors, higher concentrations of dopants have to be packed into smaller regions of the silicon substrate [Sad02]. A critical threat to the future development of ICs is that the electrical solubility limit of boron is being reached. For operational devices, dopants must be electrically activated by annealing to repair the crystal damage from ion-implantation, allowing dopants to sit on substitutional lattice sites. It is important to investigate methods to enhance the solubility of boron in

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44 silicon because it is the most commonly used p-type dopants. Sadigh et al. suggested from calculations that the proper stresses can double the solubility of dopants such as boron in silicon at an annealing temperature of 1000C for 1% biaxial compressive strain [Sad02]. He observed that negatively charged dopants, such as boron become more soluble under compressive stress, and positively charged dopants such as arsenic prefer tensile stress. The size mismatch of the dopant compared to silicon also plays a large role in the solubility enhancement. The maximum solubility enhancement occurs when the charge and size mismatch with silicon favor the same type of strain. Stress from Dislocation Loops Dislocations are a break in the regular lattice spacing, and when too much stress is applied, the silicon substrate will yield by generating dislocations to relax the stress in the material. The presence of many dislocations forms loops, and the growth rate of these loops is dependent on point defect concentration. When combined with ion implantation or oxidation, dislocation loops will nucleate below the substrate's yielding point [Avc02]. The regions of highest stress typically exist on non-planar topologies and at film edges. During several process steps in the fabrication process, a nitride layer is used to mask the oxidation of silicon in active regions. A high shear stress develops at the nitride edge and if the stress becomes too significant, dislocation loops are generated and can glide [Avc02]. To alleviate some of the stress around the nitride edge, a pad oxide can be inserted between the nitride edge and the substrate. Dislocation loops are also generated from STI formation. Fahey et al. [Fah92] demonstrated that minimizing the stress from the STI process such by changing the nitride thickness or using different fill materials

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45 with less intrinsic stress, will help reduce the dislocation density in the substrate. A more in depth explanation of stress from dislocation loops can be found in Chapter I. 3.5 Dopant Diffusion in Silicon and Silicon Germanium (SiGe) As we move towards the next technology node in the ITRS Roadmap, shallow source/drain junctions requiring high concentrations of active dopants are packed into smaller regions of the substrate. Achieving shallow junctions with active dopants is becoming increasingly difficult due to excessive dopant diffusion. Phosphorus, boron and indium are considered "fast" diffusers, where arsenic and antimony are "slow" diffusers. Arsenic has been the dopant of choice to fabricate NMOS transistors, however PMOS transistors encounter more problems because boron is the only dopant with a high enough solid solubility for the processing temperatures required. Effects such as transient enhanced diffusion (TED) cause the dopant profile to move significantly during annealing, resulting in deeper junction regions. Ion implantation is used to introduce dopants into the substrate but it creates significant crystal damage. Annealing is used to remove the damage from the implant, return the silicon lattice to a crystalline configuration, and place dopants on substitutional sites to become electrically active. During the early stages of the annealing process, excess interstitials react with dopants resulting in TED; boron is a dopant that strongly exhibits this behavior. Boron interacts with excess interstitials to form BI pairs and they diffuse by breaking atomic bonds and moving the BI pair throughout the lattice. At lower temperatures the damage is not repaired and enhances the dopant diffusion, while at higher temperatures the damage annihilates faster and a transient diffusion is not as significant [Plu00].

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46 Ficks Laws describe dopant diffusion, and the first law relates dopant diffusion to the concentration gradient by [Plu00]: xCDF (2-8) where F is the flux, D is the diffusivity, and xC is the concentration gradient. Ficks second law of diffusion states that the rate of change of concentration is proportional to the second derivative of the concentration: )(22CDF x CDtC (2-9) In a zero stress-state, dopants diffusivity is characterized by: )exp(0kTEDDA (2-10) where D is the diffusivity, D 0 is the exponential prefactor, E A is the activation energy, k is Boltzman's constant, and T is the temperature. When compressive and tensile strain is introduced, dopants diffusivities change. Boron for example has an enhanced diffusivity under tensile stress, and a decreased diffusivity under compressive stress. Thus, compressive stress is applied to retard boron diffusion when forming shallow junctions. Boron is a known interstitial diffuser, and the diffusion coefficient is composed of two parts: the neutral and positive charged state of the interstitial [Zan03]: )(0iIBIBBnpDDD (2-11) where ni is the intrinsic carrier concentration and p is the hole concentration. In equilibrium, ni=p. The DBI terms can be expressed in Arrhenius form as: )/exp(0kTQDDBIBIBI (2-12)

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47 where D 0 BI is the prefactor and Q BI is the enthalpy. Diffusion in alloys such as Si 1-x Ge x is different that in pure silicon due to a lattice mismatch between the two materials. There is a 4.2% difference in the lattice constant s of Si and Ge; Si has a lattice constant of ~ 5.43 while Ge has a lattice constant of ~ 5.65. When a layer of Si 1-x Ge x is grown on top of Si, it has a bulk relaxed lattice constant which is larger than Si. Layers grown below the critical thickness become strained, but once the critical thickness is exceeded, misfit dislocations are released to relieve the strain of the layer. Impurity diffusion in SiGe is a debated topic, and many researchers have observed the diffusivity of boron in SiGe. Aziz et al [Raj03] looked at diffusion under biaxial strain with a strain-induced activation enthalpy term. Kuo et al found that increasing Ge content from 0-60% decreased B diffusion and that strain was not a significant factor. He attributed the decrease in B diffusion to the binding between B and Ge atoms which immobilized the B [Kou95]. Rajendran et al found results similar to Kuo and modeled the diffusion of B in Si1-xGex as a result of GeBclusters. This behavior can be attributed to the fact that B creates a local tensile strain around a B atom, and Ge provides a local compressive strain around a Ge atom. The positive and negative strains are attracted to each other and form a complex to release the stress energy. The total strain from Ge incorporation is [Raj03]: SiSiGeSiGeaaaS/)( (2-13) xaaaaSiGeSiGeSi)( (2-14) where a is the lattice constant and x is the atomic fractions of Ge, and substitution the in the lattice constants for Ge and Si gives the strain S = 0.0425x.

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48 The boron diffusivity is modeled as (2-10) in silicon. However, in SiGe the incorporation of Ge atoms changes the overall B diffusivity to [Raj03]: )/exp()/exp(0kTQSkTEDDBeffB (2-15) where S is the local strain from Ge, and Q is the rate of change of activation energy per unit strain. 3.6 Summary This chapter discussed the multiple stress and strain sources that arise during the fabrication process Oxidation-induced stress was described and issues such as the oxidation of non-planar surfaces were addressed. To go into more depth, stress from LOCOS formation such as intrinsic stresses, bending stresses, non-planar oxidation stresses, and thermal expansion stresses between the Si and SiO2 were discussed. In the next section, thin film stresses were described. Thin films exhibit residual stresses and are composed of two components: thermal mismatch strains as a result of materials having different thermal expansion coefficients, and intrinsic stresses as a result of varying conditions during the deposition process. The next section introduced stress from STI structures. The formation of an STI was described and the stress as a result of non-planar oxidation, thermal mismatch strain, and intrinsic stresses were explained. When accounting for stress from an STI, all of the sources are necessary and none can be ignored in computations. Methods to alleviate STI stress such as strain compensation and corner rounding were also touched on. The next section discussed dopant induced stress due to lattice mismatch between different dopants and stress from dislocation loops. Finally, boron diffusion in silicon and silicon germanium under was explored. Chapter IV

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49 focuses on the software implementation in the process simulator FLOOPS, and their applications for boron doping and nitride deposition.

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CHAPTER 4 SOFTWARE ENHANCEMENTS TO FLOOPS Mechanical stresses from process steps such as trench isolation, doping, and epitaxial regrowth play a large role in the scaling of semiconductor devices. Understanding how these stresses affect phenomenon such as dopant diffusion and defect evolution is critical for understanding the limitations of each process technology. Continuum mechanics, which is a branch of mechanics that deals with continuous matter, is used to study these behaviors. More specifically, solid mechanics is the study of the physics of continuous solids. Differential equations are used to solve problems in continuum mechanics, and the equations are specific to the materials under investigation. For example linear elasticity in silicon is described using the constitutive equation known as Hookes Law that was described in Chapter II. Most of the materials used in silicon processing are modeled as simple elastic materials which make process modeling simpler. This chapter focuses on the software implementation in the process simulator, FLOOPS (Florida Object Oriented Process Simulator). The elastic, bodyforce, stress and strain operators were developed in FLOOPS to calculate the displacement and stress in the silicon substrate due to boron doping and nitride deposition. The Finite Element Method was implemented using the 2-D plane strain approximation to discretize the region and solve the equations. Simulations were performed to verify the software functionality. The model that FLOOPS currently utilizes to compute stress is a viscoelastic model that was developed for LOCOS; an outdated process. This model 50

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51 utilizes nonlinear and stress dependent viscosities to describe the behavior of the material, which is no longer an accurate assumption. First, the viscous flow of the oxide is computed in response to the growth forces and then changing forces are calculated as a result of the growth rate [Sim04]. For current fabrication processes, however, the material model that most accurately describes the behavior of materials is the linear elastic model. Unlike the current viscoelastic model that is used, the linear elastic model will couple the mechanical equations with the diffusion solution. In addition, the operators listed above were integrated with the property database and process commands [Law02]. As discussed in Chapter III, the introduction of different dopants into the silicon substrate causes change in the mechanical state of the lattice. Dopants come in a variety of sizes and cause a local tensile or compressive strain in the lattice due to the size mismatch between the dopants and silicon. Boron is a substitutional dopant that is smaller than silicon, and it introduces a local tensile strain in the lattice. Chu et al., Rueda et al., and Yang et al. demonstrated that bending occurs in boron doped cantilever beams, and the amount and direction of bending are dependent on the beam length, width, and doping profile into the depth of the beam [Chu93, Rue98, Yan95]. The strain from boron doping was used to calculate the deflection of the cantilever beam, and results were compared with those of Rueda. Other structures such as a strip of nitride on silicon, and silicon doped with boron source/drain regions were simulated and the stresses were observed. The results will be discussed in Section Chapter V. 4.1 FLOOPS Background FLOOPS is a C ++ based simulation program which uses physical models to describe various process steps such as ion implantation, oxidation and diffusion.

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52 Furthermore, FLOOPS uses the Alagator scripting language to define partial differential equations to solve these models by reading in material properties from the parameter database. To arrive at a solution, the program solves a series of differential equations and utilizes matrix mathematics to generate a solution. An internal Newtonian solver is used to converge to a solution. Newtons Method is defined as [Adl04]: )(')(1nnnnxfxfxx (4-1) Equation 4-1 states that the next solution is equal to the previous solution minus the value of the function at the previous solution divided by the value of the functions derivative at the previous solution. Operators such as gradients and time derivatives are needed when solving partial differential equations. FLOOPS currently has five operators ddt, grad, sgrad, diff, and trans. The elastic, bodyforce, stress, and strain are the new operators created in this work. The ddt operator computes time derivatives and the grad and sgrad operators take spatial derivatives. These operators are necessary when performing a diffusion simulation. The diff and trans operators can be used to compute the parallel and perpendicular electric field components needed to evaluate device mobility [Law02]. The elastic, bodyforce, stress and strain operators calculate the stiffness, displacement, stress and strain in the silicon substrate respectively, and will be used to couple the mechanical stress equations with the diffusion process step. 4.2 The Finite Element Method The Finite Element Method (FEM) is a numerical technique used for solving differential equations that describes a variety of problems, such as the solution to

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53 displacement in an elastic continuum The principle of this method allows a complicated region to be sub-divided into elements in a process called discretization. By solving the differential equations of each region, the behavior of the complete domain is determined. First, the geometry of the solid was identified as a three-noded triangle and a 2-D finite element mesh was generated. Each node in the mesh was assigned a number and a set of coordinates (x, y) which specified the position of the node, and as forces were applied, nodes of the solid moves accordingly. Lets revisit the mechanical equation to be solved is f=kx, where f is the force applied, k is the material stiffness, and x is the unknown, displacement. For this notation, the f term (and any force discussed from here on) is referred to as the right hand side, and the k term, or stiffness, is referred to as the left hand side. The first step in solving the mechanical problem is finding the element stiffness matrix (left hand side), which describes the how each element will respond to forces. The element stiffness matrix for each element is then assembled into a global stiffness matrix that describes the behavior of the entire material region. Next, the right hand side needs to be constructed, which consists of the force, specifically the force from boron doping. Reflecting boundary conditions were applied and the unknown was solved for, in this case, displacement. From the calculated displacements, other parameters of interest such as stress were computed. Silicon was modeled as an isotropic elastic material and the two-dimensional plane strain approximation was used to implement the operators into FLOOPS.

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54 4.2.1 Constructing FEM Elements for the Elastic, Bodyforce, Stress, and Strain Operators Consider a three-noded triangle e, defined by nodes i, j, and k numbered in the counter-clockwise direction with an area and displacements in the x and y directions. Node k (x k y k ) Element e with area Node j (x j y j ) Figure 4-1: Triangular element in coordinate system There are two degrees of freedom (x, y) for each node and three nodes per triangle, creating six degrees of freedom per element. The stiffness of a finite element describes how the element responds to external forces. The stiffer a material, the less deformation it will experience, whereas a flexible material will deform more. Under mechanical equilibrium, all of the nodal forces are equal to zero, q e = 0. Integrating over the triangular element gives the stiffness matrix: )(voldBDBkTe (4-2) or in discretized form [Zie89]: BDBkTe (4-3) Node i (x i y i )

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55 where k is the element stiffness, is the element area in two dimensions, and the element volume in three dimensions. The B matrix is a constant matrix dependent on nodal coordinates and [Zie89]: jiijikkikjjkijkijkjiikkjyyxxyyxxyyxxxxxxxxyyyyyyB 00000021 (4-4) where is twice the area of the triangle and is equal to: 2 )]()()[(2ijjiikkijkkjyxyxyxyxyxyx (4-5) The B matrix is used to relate the strain to the displacements, which will be discussed more in Section 4.2.2. The D matrix contains the material properties E and For plane strain, the D matrix is equal to: )1(2)21(00011011)21()1()1( ED (4-6) To find the displacements due to external forces, a matrix mathematics solver called UMF is used to solve the equation Ax=b, where A represents the stiffness, b represents the external forces, and x represents the nodal displacements. Below is a portion of the code developed to build the stiffness matrix for a single element. The B matrix routine takes the six coordinates of a triangle as arguments (three nodes two displacements x, y per node) and returns the [3x6] matrix that was illustrated in (4-4). From the B matrix, the transpose of the B matrix is easily obtained. The D matrix contains the material properties such as Youngs Modulus and Poissons Ratio and returns a [3x3] matrix. As illustrated in (4-4), the stiffness routine multiplies the B

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56 matrix, transpose of the B matrix, and the D matrix together and returns the [6x6] stiffness matrix for a single element. B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] ); BT_Matrix(Bmatrix, BTmatrix); D_Matrix(Dmatrix, E, nu); Stiffness(BTmatrix, Dmatrix, Bmatrix, C, stiffness); The sum of all element stiffness matrices is known as the global stiffness matrix, which determines the stiffness of the each material region in the mesh. The flowchart below in figure 4-2 demonstrates the step-by-step procedure to create the stiffness matrix for an element. Figure 4-2: Flowchart to create element stiffness matrix 4.2.1.1 Plane Strain Assumption The plane strain approximation assumes that 0 zzyzxz ; however stress in the z-direction is not equal to zero. This assumption can be used to solve problems with infinitely long dimensions in the z-direction; therefore the strain in the z-direction will approach zero [Rue97]. A problem with the plane strain assumption arises with dopant

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57 and thermal mismatch strain because both dopant and thermal mismatch strains have stress components in the z-direction. To compensate for the 3-D behavior in a 2-D domain, the 2-D strain must be multiplied by a factor of (1+v): 0)1(zzyyxx (4-7) 4.2.1.2 Boundary Conditions Reflecting boundaries require that the normal component of the velocity and displacement field is set to zero across the interface, which corresponds to a mirror-reflected symmetry across the boundary [Rue97]. To verify the boundary conditions was working, simple simulations were performed that fixed one side of the mesh to zero with the boundary condition, and displaced the other side to a specified distance. The proper displacements were observed across the mesh, verifying the boundary functioned correctly. Figure 4-3: Verification of boundary conditions displacements due to external forces

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58 4.2.2 Forces from Boron Doping The equivalent nodal force at node i due to element e must have the same number of components as the nodal displacements, six values two for each node. This force is described by: eiq eVebTefvoldBq)( (4-8) where B T is the transpose of the vector relating strain to nodal displacements, f b is the distributed body forces of the element, and is the stress tensor. The bodyforce operator was created to model the force from boron and is modeled by [Zie89] eVeBTbevoldDBf)( (4-9) Integrating over the volume of the element gives the body force in discretized form: (4-10) BeTbeDBf The general stress-strain relationship of linear elastic materials is given by: 00)( D (4-11) where D is the elasticity matrix, and 0 and 0 and are the initial stress and strain tensors. The elemental strain is related to the elemental displacements by: eeaB (4-12) where a is the displacements and B is the constant matrix given in (4-4). By substituting equation (4-11) into (4-8), the expression for nodal forces becomes: eeeVebeTVeTVeTefvoldDBvoldDBvoldDBq)()()(00 (4-13) The bodyforce operator was developed to model the elemental strain ( B ) from boron doping, and is modeled by [Cha96, Rue97]: )100(SiBoronSiBeBCCA (4-14)

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59 Where B is the lattice contraction parameter for boron in silicon, is the boron concentration, (=5x10 BoronC SiC 22 cm -3 ) is the atomic density of silicon, and (=5.4295) is the lattice constant of silicon. Horn et al found that the silicon lattice contracts 0.0141 per atomic percentage of boron concentration [Hor55]. Since the boron concentration is a nodal quantity, the elemental boron concentration must be calculated from the nodal concentrations. To obtain the elemental values of boron strain from the nodal values, the boron concentration is first divided by the atomic density of silicon ( SiA SiBoronCC ). The lattice displacement is equal to ( SiBoronCC ) times the lattice contraction parameter ( B ). Then the strain is computed by dividing the lattice displacement by the lattice constant of silicon (A Si ) [Rue98]. The average elemental strain is then computed as the average of the strain value at each of the nodes. Below is part of the code to calculate the nodal displacements and a flowchart for the procedure: double s1 = a.Val(0).get(k); //evaluate the strain at each node double s2 = a.Val(2).get(k); double s3 = a.Val(4).get(k); //compute the average elemental strain by taking the average of all nodal values. Strain[0] = sqrt(2.0) (s1+s2+s3) / 6.0; strain[1] = sqrt(2.0) (s1+s2+s3) / 6.0; //assume no shear component for dopant-induced stress strain[2] = 0.0; B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] ); BT_Matrix(Bmatrix, Btmatrix); //create B transpose from B matrix D_Matrix(Dmatrix, E, nu); //create D matrix BTMultD(Btmatrix, Dmatrix, C); //multiply B transpose[6x3] *D[3x3]=C [6x3] MultBtDBF(C, strain, fx); //multiply C [6x3] elemental strain [3x1]= nodal displacements [6x1]

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60 Figure 4-4: Flowchart to solve for forces from boron doping 4.2.3 Strain and Stress Computation The strains and stresses were calculated from the displacements described in section 4.2.2. The strain is related to the nodal displacements by (4-12) and is equal to the B matrix times the nodal displacements that were calculated in 4.2.2. The strain is a [3x1] column vector containing the normal xx, yy and the shear xy values: xyyyxx (4-15) The stress is related to the strain by the D matrix as defined in (4-11), and by multiplying the strain values above by the D matrix, another [3x1] column vector of the stresses is obtained: xyyyxxD (4-16) Once the displacements in the silicon were solved for, the function on the command line to solve for stress or strain is: select z= Stress/Strain(xx/yy/xy, displacement), which calls the stress or strain operators and calculates their values based on the displacements. The xx, yy, or xy stress or strain values can be obtained with this function. As noted in (4-15) and (4-16), the column array of stress and strain represent

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61 the xx, yy, and xy directions respectively; all of the strain or stress components are initially solved for, and additional code will determine which direction of stress is desired. Contours of the stress fields were plotted, and will be illustrated in chapter V. Below is part of the code and the flowchart to calculate the strains and stresses from the nodal displacements: B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] ); //multiply [3x6]B*[6x1]displacement=elestrain[3x1] strain[xx, yy, xy] MultiplyStrain(Bmatrix, elestrain, displacement); // find tt to determine if want xx, yy, or xy direction if (tt==Dir_XX) val = elestrain[0]; else if (tt==Dir_YY) val = elestrain[1]; else val = elestrain[2]; //now calculate the stresses from the strains MultiplyStress(Dmatrix, elestrain, stress); //elestrain [3x1]*Dmatrix[3x3]=stress[3x1] Figure 4-5: Flowchart to calculate strain and stress 4.3 Summary This chapter began by introducing continuum mechanics and the finite element method. Large areas were sub-divided into smaller regions in a process called discretization to create elements. The stiffness of a region describes how it responds to external forces, and the procedure to create the stiffness matrix for a single element was described. Next, the bodyforce operator defined as representing the forces due to boron doping. The mechanical equation f=kx was solved for, and from the calculated displacements, the stresses in the silicon substrate were calculated. In the next chapter,

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62 applications such as beam bending, nitride deposition, and channel stress from boron doping will be explored.

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CHAPTER 5 APPLICATIONS AND COMPARISONS OF TWO-DIMENSIONAL SIMULATIONS As device channel lengths are scaled into the deep submicron realm, stress components that once could be ignored are now significant. A few examples of how stress is introduced during different process steps is by creating STI structures, doping the source and drain regions, and depositing thin films. At channel lengths as short as 0.1 um, these stress sources can create enough undesirable stress in the channel to alter the carrier mobility and decrease overall device performance. Methods to either suppress the undesirable stress, or enhance the advantageous stress are under research. The software operators, discussed in Chapter IV, were used to calculate stress from various process steps, and the results were compared with experiments from literature and simulations from the commercial version of ISE FLOOPS for software validation. This chapter presents finite element based models that calculate the residual stresses in various structures. To illustrate the effect of strain from boron doping, a silicon cantilever beam was simulated and the beam length, width, and concentration gradient were varied to observe the bending behavior from a particular boron diffusion process. Next, the stress caused by depositing a strip of nitride on silicon was simulated, and the stress around the corner of the nitride/silicon interface was compared with the values simulated from the ISE version of FLOOPS. Lastly, the stress from doping the source drain regions with boron was observed, and the effects of scaling the channel length, source/drain length, and boron concentration were quantified. 63

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64 5.1 Boron-Doped Beam Bending Cantilever beams are used in silicon fabrication technology to create sensors and other MEMS devices. Beam structures are fabricated by thermally diffusing or implanting boron on one side of the silicon wafer, and etching through a mask on the other side of the wafer. sing etchants such as KOH, silicon layers with boron concentrations greater than 7x10 19 cm -3 (p + Si) show significant slower etching rates than compared to undoped silicon [Yan95]. Since boron is a substitutional atom in silicon, the silicon lattice will contract in the boron diffused layer, and layers with different concentrations of boron will be subjected to different tensile stresses. The wafers bend up or downwards after the cantilever beams are released due to the stress gradient through the depth of the beam [Jae02, Nin96, Rue98,Yan95]. Yang and Chu et al. demonstrated that as-implanted cantilever beams with tensile residual stresses bend upwards to maintain equilibrium. However, subsequent processing steps such as oxidation or annealing can change the residual stress state from tensile to compressive [Yan95]. The results of these experiments however are not comparable because of the difference in experimental conditions. For a cantilever beam made of linear elastic material such as silicon, the beam deflection is [Nin96] EIMlvdef22 (5-1) where M is the bending moment, I is the moment of inertia of the beam, and E is Youngs Modulus. For cantilever beams of different lengths, but identical M, E, and I, the deflection curves are the same.

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65 Beams with a uniform dopant profile, or a profile that is symmetric to the center of the beam, do not exhibit bending due to equal distribution of forces from boron through the thickness of the beam. C B +y +x x=0 x=0 x=0 Figure 5-1: A uniform or symmetric doping profile about the center of the cantilever beam thickness results in no bending However, under a concentration gradient, the beam will bend towards the more heavily doped boron side with respect to the center of the beam thickness to relieve the tension. This is a similar concept to applying a nitride strip on top of silicon, and it will be explored in the next section. For example, a doping profile located near the surface of the beam will bend upwards, while a profile located towards the bottom of the beam will bend downwards. C B C B +y +y +x +x x=0 x=0 x=0 x=0 Figure 5-2: The strain from boron causes bending towards the more heavily doped boron side of the beam (a) downwards bending (b) upwards bending

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66 5.1.1 Beam Bending Simulation Results Simulations in FLOOPS were performed to observe how varying the length, width, and concentration gradient affected the deflection of the cantilever beam. The experimental conditions of Rueda et al. [Rue98] were replicated to obtain accurate results. A boron profile with a peak concentration of 8x10 19 cm -3 was implanted into silicon. The initial beam dimensions were 50um long by 0.6um thick. The grid spacing was 0.05 um in the x-direction to resolve the boron profile, and 0.5um in the y-direction. The material properties used for silicon were: Youngs Modulus =1.22x10 12 dyn/cm 2 and Poissons Ratio=0.3 [Rue98]. The boundary condition requirement for cantilever beams is the displacement and the first derivative of the displacement (velocity) is equal to zero. To achieve this, the left side of the boundary was fixed. 5.1.2 Effect of Varying Beam Length Figure 5-3 demonstrates the beam deflection versus beam lengths for a 0.6 um thick beam. As stated in equation (5-1), a beam with identical material properties will follow the same deflection curve. As the beam length was increased from 25 um to 50 um, the deflection increased accordingly and fit a parabolic curve. These results agree with those of Rueda et al. and Chu et al.

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67 Deflection vs distance for various beam lengths, width=0.6um00.020.040.060.080.10.120102030405060beam lengthdeflection (um) 50 um 45 um 40 um 30 um 25 um Figure 5-3: Beam deflection vs. beam length 5.1.3 Effect of Varying Beam Width The next figure illustrates the effect of varying the beam width on the beam deflection. Notice the cantilever beams deflect in the negative-x direction, equating to an upwards bending as in Figure 5-2 (b). The beam width is varied from 0.6 um to 1.15 um and the deflection is observed. As anticipated, narrower beams deflect more than thicker beams. The deflections observed were in agreement with those of Rueda et al. Deflection vs distance for various beam widths-0.07-0.06-0.05-0.04-0.03-0.02-0.01001020304050beam length (um)deflection (um) 0.6 um 0.8 um 1.0 um 1.15 um Figure 5-4: Beam deflection vs. beam length for varying beam widths

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68 5.1.4 Effect of Varying Dopant Profile The diffusion of boron in silicon is concentration dependent and is modeled by [Jae02]: 2)2(exp),(DtxNtxNp (5-2) where N p is the peak concentration in cm -3 x is the distance in cm into the bulk of the wafer, D is the diffusivity of boron in silicon in cm 2 /sec, and t is the time in seconds. The effect of varying the concentration gradient on beam deflection is shown below in Figure 5-5. For simulation purposes, the Dt factor was varied and the deflection of the beam was observed for a beam length of 50 um and width of 0.6 um. The beam with a larger boron distribution resulted in greater beam deflection. Defleciton for various doping profiles, length=50 um, thickness=0.6 um-0.5-0.4-0.3-0.2-0.100.101020304050beam length (um)deflection (um) N(x)=8e19exp(-x^2/.01) N(x)=8e19exp(-x^2/.001) N(x)=8e19exp(-x^2/.0001) N(x)=8e19exp(-x^2/.1) Figure 5-5: Beam deflection vs. beam length for varying doping profiles 5.2 Multiple Material Layer Bending Simulations Due to its excellent mechanical properties, silicon nitride can be used for a variety of applications such as: a structural material to fabricate MEMS devices, isolation layers between transistors, masks for diffusion and etching, and recently, to induce uniaxial

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69 tensile strain in the channel of NMOS transistors. Nitride is deposited by chemical vapor deposition typically around 700C, and has a higher thermal expansion coefficient than silicon. If the resulting stress is below a certain threshold, the structure relaxes by distorting, and above the threshold it will generate dislocations. In equilibrium, the forces and moments between the silicon and silicon nitride must balance, creating a bending in the materials. The tensile residual stress in the nitride causes it to curl up at the edges, creating a pocket of tension near the edges of the silicon nitride/silicon interface, and compressive stress underneath the nitride. The bending behavior is illustrated in Figure 5-6 below: Figure 5-6: Nitride curling up at edges due to tensile residual stress A functionality test was performed to ensure the multiple material layer structure behaved as expected. In FLOOPS, a region of silicon nitride was defined on top of a silicon region. The material properties used for each material were [Jae02]:

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70 Table 1: Material parameters used for nitride on silicon simulations Youngs Modulus Poissons Ratio Silicon Nitride 3x10 12 dyn/cm 2 .25 Silicon 1.22x10 12 .3 In the first set of simulations, the nitride thickness was varied while the silicon thickness was kept constant at 10 um. Fixed boundary conditions were set at the bottom of the wafer, so a relatively thick substrate was selected to ensure that a small structure would not interfere with the bottom boundary. An intrinsic stress, approximately 1.6x10 10 dyn/cm 2 was defined in the yy (channel direction) direction of the nitride. The bodyforce operator, discussed in Chapter IV, was used to provide the intrinsic stress in the nitride. By varying the elemental strain in the silicon nitride layer, an approximate value of the intrinsic stress can be computed. These stress values were compared with results from the ISE version of FLOOPS for the same simulation. When the stresses were equal, the elemental strain in the nitride was approximately equal to the intrinsic stress of 1.6x10 10 dyn/cm 2 This is an unpractical way to provide intrinsic stress in a material layer and is discussed in the future work section of Chapter VI. The effect of varying the nitride thickness, while maintaining a constant silicon thickness, on wafer bending is illustrated in Figure 5-7. As the nitride thickness is increased, the structure curls up more appreciably due to a greater constant force distributed through the nitride layer.

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71 Deflection vs distance for varying nitride thickness, silicon thickness=10um-0.00200.0020.0040.0060.0080.010.0121.62.12.63.13.64.1distance (um)deflection (um) Nitride=0.1 um Nitride=0.2 um Nitride=0.25 um Figure 5-7: Deflection vs. distance for varying nitride thicknesses Next, the effect of varying the silicon substrate thickness on wafer bending was observed. The nitride thickness was kept constant at 0.1 um, while the silicon thickness was varied. As the silicon thickness was decreased from 15 to 5 um, an increase in wafer curvature was observed as expected. Deflection for varying silicon thickness, nitride thickness= 0.1 um-0.002-0.00100.0010.0020.0030.0040.0050.0061.522.533.54distance (um)deflection (um) Silicon=15 um Silicon=10 um Silicon=8 um Silicon=5 um Figure 5-8: Deflection vs. distance for varying silicon thicknesses

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72 The stress fields from the structure in Figure 5-6 are illustrated in Figures 5-9, 5-10, and 5-11. The lateral edges are not constrained and bottom boundary condition is used. The substrate is 20 um thick and the nitride is 0.1 um thick. The deposited nitride is assumed to be in tension. If the nitride extends over the entire substrate, minimal stress in the substrate would result since the substrate several orders of magnitude larger than the nitride. However the nitride is patterned and large stresses are generated in regions close to the edge, which is known as the lift-off effect, causing the edges to go into tension [Sen01]. The region below the nitride is pushed down in compression. The stress in the yy (channel) direction is larger than the xx (bulk) direction because the intrinsic stress in the nitride is defined in the yy direction. These results are in accordance with a similar simulation performed by Chaudhry [Cha96]. Figure 5-9: Stress.yy from silicon nitride on silicon

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73 Figure 5-10: Stress.xx from silicon nitride on silicon Figure 5-11: Stress.xy from silicon nitride on silicon

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74 The shear components of stress have implications on bulk processing (dislocation loop glide and substrate yielding), thus it is of use to explore these stresses. The slip pattern in silicon for the <111> plane is the [110] direction, which corresponds to shear stresses. The contours of the xy simulations indicate that the shear stress lobes peak at approximately 45 and represent the area for dislocation loop glide. The contour is a double lobe because the shear stress is related to the polar coordinates as [Cha96]: 2sin2cos2sin)(rrrz (5-3) In the experiments performed by Ross, dislocation loops from a nitride strip on silicon formed in the same region indicated by the stress contours. In simulation, Chaudhry also found lobes of the same shape to form on nitride strips in silicon. Effect of Boundary Conditions on Stress Fields Two different reflecting boundary conditions were simulated for the nitride on silicon structure to observe the overall shape of the stress contours. The reflecting bottom boundary condition and reflecting left and reflecting right boundary conditions were applied and the stress in the xx, yy, and xy directions are illustrated: Figure 5-12: Stress xx for reflecting bottom (left) and reflecting left and right (right) boundary conditions

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75 Figure 5-13: Stress yy for reflecting bottom (left) and reflecting left and right (right) boundary conditions Figure 5-14: Stress xy for reflecting bottom (left) and reflecting left and right (right) boundary conditions For the xx and yy stress simulations, stresses build up near the edges for the reflecting left and right boundary conditions. This would be expected because the left and right hand sides are fixed and there is no free surface for the stresses to relax. For the reflecting bottom xx and yy simulations, the compressive region underneath the nitride extends slightly lower than for the reflecting left and right boundary conditions. Overall, although the stress distribution for each simulation varies somewhat throughout the complete structure, the local stresses around the nitride/silicon interface are well-represented.

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76 5.3 Channel Stress from Boron Source/Drain Doping As discussed in Chapter IV and demonstrated in Section 5.1, boron doping introduces a local tensile strain in the substrate due to its size mismatch with silicon. The strain from the boron doping causes the silicon to warp and the deformations are used to calculate the resulting stresses in the substrate. While this phenomenon is beneficial for fabricating MEMS devices such as sensors and membranes, it can be deleterious to device operation as channel lengths are decreased below 100 nm. Stress in the channel from doping the source and drain regions was a relatively insignificant factor until CMOS transistor channel lengths entered the nanometer realm. Consider a PMOS transistor doped with boron source drains. Boron is the p-type dopant of choice due to its high solubility limit in silicon; at 1100C, boron has a solubility limit in silicon of 3.3x10 20 /cm -3 [Jae02]. Negatively charged dopants, such as boron, become more soluble under compressive stress, but the tensile stress induced from boron doping can counteract the desired compressive channel stress applied to increase hole mobility [Sad02]. For PMOS devices, tensile stress from boron incorporation as low as 100 MPa can compensate the intentional compressive stress engineered into the channel, resulting in a net close to zero stress. This example could be applicable for the compressive stress introduced from STI structures. The bending behavior of a boron-doped silicon beam was properly calculated and compared with experimental data in Section 5.1. This technique is taken one step further and applied to a PMOS-like device; a silicon substrate and source/drain regions doped with boron. To observe the channel stress under varying process parameters, the stress at the center of the channel from boron doping in the source/drain region was observed. The channel length, source drain length, and boron concentration were varied to observe

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77 scaling trends for different technology nodes. The finite element structure showing the parameters to be varied is illustrated in Figure 5-15. S/D Length Figure 5-15: Silicon doped with boron source drain regions general structure Boron Boron Channel Length Silicon 5.3.1 Effects of Channel Length Scaling The channel is used for carrier conduction and is defined as the region between the source and the drain; approximately 100 below the surface. The first structure simulated had a peak boron concentration of 2x10 20 /cm 3 in the source/drain regions, source/drain lengths of 1 um, and a junction depth of 0.12um. As the channel lengths were varied from 1 um to 45 nm, the stress at the center of the channel was observed. The results illustrate that as channel lengths decreased, the increased stress in the center of the channel approached exponentially. At a 45 nm channel length, approximately 80 MPa of stress exists from source drain doping alone. Due to the free surface at the top of the structure, the structure relaxes and deformed more than if a realistic PMOS device with a gate and spacers were present.

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78 Stress vs Channel Length0.00E+001.00E+072.00E+073.00E+074.00E+075.00E+076.00E+077.00E+078.00E+079.00E+0700.20.40.60.811.2Channel Length (um)Stress (Pa) Figure 5-16: The effect of scaling channel length on stress from boron doping 5.3.2 Effect of Source/Drain Length Scaling The length of the source and drain is determined by design rules specific to each technology, and is equal to 6 lambda, where lambda is half of the minimum feature size. The simulated structure had a peak boron concentration of 2x10 20 /cm 3 in the source/drain regions and a junction depth of 0.12um. As the source/drain lengths were varied from 0.3 um to 1 um, the stress at the center of the channel was observed. This was performed for both 45 nm and 100 nm channel lengths. For longer source/drain lengths, larger amounts of boron are available to pull on the channel, thus increasing the stress. This trend is shown in Figure 5-17.

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79 Stress vs Source/Drain Length0.00E+001.00E+072.00E+073.00E+074.00E+075.00E+076.00E+077.00E+078.00E+079.00E+0700.511.5Source/Drain Length (um)Stress(Pa) 100 nm channel 45 nm channel Figure 5-17: The effect of scaling the source/drain length on channel stress for 100 nm and 45 nm channel lengths 5.3.3 Effect of Boron Concentration Scaling The effect of varying the boron concentration in the source/drain regions on channel stress was explored. Of all the factors affecting the stress in the channel, the boron concentration appears to have the largest influence on the channel stress. The simulated structure had a source/drain length of 1 um and a junction depth at 0.12 um. The boron concentration was varied from 6x10 19 to 5x10 20 /cm 3 and the stress at the center of the channel was observed. Although boron is soluble in silicon up to approximately ~3.3x10 20 /cm 3 it is soluble at larger concentrations in silicon germanium. For 45 nm and 100 nm devices, the stress in the channel approaches 100 MPa at concentrations above 2.5x10 20 /cm 3 and 3x10 20 /cm 3 respectively.

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80 Stress vs Boron Concentration0.00E+005.00E+071.00E+081.50E+082.00E+082.50E+080.00E+001.00E+202.00E+203.00E+204.00E+205.00E+206.00E+20 Boron Concentration /cm^3Stress(Pa) 100 nm channel 45nm channel Figure 5-18: The effect of scaling the source/drain length on channel stress for 100 nm and 45 nm channel lengths 5.4 Summary As the semiconductor industry enters the nanometer realm, stress from sources that were given little recognition in the past are becoming significant such as: stresses from STI structures, film deposition, and dopants. This chapter provided results regarding the stress from boron doping and the stress from nitride deposition. Boron is the main dopant for PMOS transistors due to it high solid solubility limit in silicon, however at large concentrations and small device dimensions, the presence of boron can alter intentional stress placed in the channel for carrier mobility enhancement, as well as introducing unintentional stress in the wafer. Boron-doped cantilever beams were simulated to demonstrate the effect of boron doping on beam deflection that resulted from a non-uniform doping profile. The simulation setup was identical to that of Rueda et al., and the bending behavior results were in accordance. The beam length and width dictated the amount of beam deflection. Shorter, thicker beams deflected less than longer, thinner beams with identical boron

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81 diffusion profiles. Beams with larger boron concentrations or wider diffusion profiles deflected more than beams with lower concentrations, or steeper diffusion profiles. Next, the stress from depositing a strip of nitride on silicon was observed. The intrinsic stress of approximately 1.6x10 10 dyn/cm 2 in the longitudinal direction is the main source of stress in nitride. As the edge regions of the nitride curl up, the silicon to curls up as well. This known behavior creates significant stress in the [110] direction. Tensile lobes are observed at the silicon nitride/silicon interface, and large compressive stresses are observed underneath the nitride film. Different boundary conditions were also simulated to investigate how the stress distributions differ throughout the structure. Although the stress distribution throughout the entire structure varied slightly, the local stresses around the nitride on silicon structure were approximately equal. Stresses built up more along the sides of the structure with fixed left and right hand side boundary conditions, as expected. Table 2: Results summarizing the effect of boron doping on channel stress Parameters varied Effect on Stress Channel Length As channel length decreased, stress in the center of the channel increased Source/Drain Length As source/drain length decreased, stress in the center of the channel decreased Boron Concentration As the boron concentration increased, the stress in the center of the channel increased

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82 Lastly, the effect of stress in the channel from boron doping was examined. The channel length, source/drain length, and boron concentration were varied and the stress at the center of the channel was quantified. Above is a table summarizing the results: Increasing the boron concentration appeared to have the most significant effect on increasing the stress in the channel. For concentrations greater than 2.5x10 20 /cm 3 for 45 nm channel lengths and 3x10 20 /cm 3 for 100 nm channel lengths, the stress in the channel was greater than 100 MPa. In chapter IV, a summary of each chapter will be presented, and future work will be discussed.

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CHAPTER 6 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE WORK 6.1 Summary and Conclusions In this thesis, many important sources of stress in silicon technology have been investigated. Finite element code was implemented in FLOOPS to develop a two-dimensional model for dopant induced stress in the silicon substrate. The model was verified with experimental data when possible, and was compared to simulation data otherwise. In Chapter I, a survey of existing literature on stress applications in silicon technology and driving motivations for studying stress was discussed. Stress-induced defect formation from patterned structures was quantified by experimentation and through simulation. Next, strained silicon was introduced because this work will have many future implications in this area of research. Applications of how the advantageous stress enhances device performance and how the unintentional stress hinders device performance were exemplified. Chapter II introduced the concepts of stress, strain, and linear elasticity. Examples of normal and shear stresses were presented. Stress from patterned films are commonly encountered in IC fabrication, and understanding the stresses generated as a result of deposition are important. Examples are provided to describe the plane stress that results due to a thin film on a thick substrate. Chapter III discusses various unintentional stress sources that arise during semiconductor fabrication processes such as STI formation, film deposition, and dopant 83

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84 induced stresses. Non-planar oxidation, thermal mismatch, and intrinsic stresses all accumulate in and around the STI structure to contribute to the total stresses. In addition to STI formation, variations in the deposition process of thin films can affect the magnitude and amount of residual stress in the film and substrate. Next, stress from dopants and dislocation loops, and stress assisted diffusion was discussed. Since boron is smaller than silicon, it contracts the silicon lattice and creates a local tensile region. Germanium, on the other hand, is larger than silicon and creates a lattice expansion. Due to dopant incorporation, the silicon will distort to relax the stress. This was demonstrated in Chapter V in the beam bending simulations. If the stress in the substrate is too high, it will yield by generating dislocations. Dislocation loops form as a result of high shear stresses in the {111} plane and can glide in the [110] plane if the critical glide stress is exceeded. Lastly, stress assisted diffusion of boron in silicon and silicon germanium was discussed. A possible explanation to boron diffusion retardation in silicon germanium is attributed to the boron-germanium binding. Chapter IV focuses on the software enhancements in FLOOPS to calculate the displacements and stresses in the silicon substrate due to boron doping. The finite element method was implemented using the 2-D plane strain equation to create the elastic, bodyforce, strain, and stress operators. The equation to be solved is essentially f=kx, where f is the force from the dopants, k is the stiffness, and x is the resulting displacements. The elastic operator was developed to find the stiffness (k) of the silicon mesh, and the bodyforce operator equated the strain from boron doping into an elemental force (f). The matrix equation was solved, and the resulting displacements were transformed into strains and stresses through the strain and stress operators.

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85 The linear elastic model was also integrated with the property database and process commands. Chapter V provided applications and results to the beam bending, nitride deposition, and PMOS-like structure simulations. A beam bending experiment was performed to observe the effect of strain from boron doping. The beam length, thickness, and doping profile were adjusted independently and the bending behavior was observed. Due to the non-uniform boron doping profile in the beam, the beam will bend upwards towards the tensile region to relieve the stress. Larger deflections resulted from longer beam lengths, thinner beams, and wider diffusion profiles. The simulation values agreed with those of Rueda. Next the stress from a nitride deposition was simulated by applying a constant force to the nitride layer and equating the force to an intrinsic stress. Stress contours were compared with ISE FLOOPS, and when the substrate stresses were equivalent, the proper intrinsic stress of 1.6x1010 dyne/cm2 was defined in the nitride. These results were comparable to the simulation of Chaudhry as well. Two different boundary conditions reflecting bottom, and reflecting left and right were simulated to observe the xx, yy, and xy stress in the silicon substrate from nitride deposition. Although the stress contours varied slightly throughout the structure, the local stresses around the nitride/silicon interface were approximately equal for both boundary conditions. It was concluded that the different boundary conditions did not have significant effect on the stress simulation results. Finally, the stress in the center of the channel due to boron doping in the source drain was investigated. Since the boron atom is smaller than the silicon atom, it exerts a

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86 local tensile stress in the substrate which is transferred to the channel. In PMOS transistors, where boron is used as the source/drain dopant, enough tensile stress could counteract the advantageous compressive stress that is engineered into the channel for mobility and overall performance enhancements. To calculate these stresses from boron doping, a PMOS-like structure that consisted of bulk silicon with boron source/drain regions was simulated. Factors such as channel length, source/drain length, and boron concentration were varied to assess the channel stress. The results showed that decreasing the channel length, increasing the source/drain length, and increasing the boron concentration all resulted in larger stresses in the channel region. Increasing the boron concentration appeared have the largest effect in generating larger stresses. In a real device however, the resulting stress most likely will be larger due to all factors scaling together. 6.2 Recommendations of Future Work Some of the important sources of stress in semiconductor fabrication technology have been analyzed and modeled as part of this thesis. The emphasis of this work was to develop a more accurate method to calculate stresses in the silicon substrate due to dopant incorporation using software, and to demonstrate functionality through simulations. As each technology node demands smaller feature sizes, very precise models will be necessary to predict device behavior. The work described below provides recommendations that will further enhance the capabilities that were implemented into FLOOPS. 6.2.1 Additions to Software The software operators that were implemented into FLOOPS accurately simulate the stress from dopant incorporation. However, to quantify the total stress in a CMOS

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87 structure, multiple stress sources must be accounted for. After the stress sources are properly modeled, boundary conditions need to be optimized for each stress source. The first work to be completed is to link the mechanical stress code with the solution to the diffusion equation. To solve the diffusion equation, derivatives with respect to the solution (displacement) must be computed. This entails developing code to calculate the derivatives of the bodyforce, strain, and stress operators. Next, stress sources such as stress from dislocation loops, thin film deposition, thermal mismatch, oxide growth, and STI stress must be taken into account. These additional stress sources are right hand side components, like the stress from boron doping and represent the force components (f) in the elastic equation f=kx. Since each type of stress is unique, an operator to compute each stress source is required. After the operators are developed, adding the stress sources together to calculate the total stress of the system can be performed using tcl scripts. The stress from dislocation loops should be relatively easy to incorporate because it is the same principle used in the stress from boron doping. The dislocation loops are treated as a strain induced by a change in the lattice parameter from introducing extra atoms into the lattice. The relationship describing the depth dependent number of atoms due to loops of radius, R, is [Cha96]: max22110)(2)(RXDALLdXXRRfDxN (6-1) where D110 is the density of silicon atoms in the {110} plane and X is the distance from the center of the loops. The finite element method computes the strain due to the loops as:

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88 2201002.5)( x xNAllxx (6-2) This strain is converted into a force, and subsequently into a stress using the same method performed from boron doping in silicon. In Chapter V, the stress from a thin strip of nitride deposited on a thick silicon substrate was calculated and the stress contours were compared with simulation values from ISE FLOOPS. However, the intrinsic stress in the nitride was modeled by applying a constant strain using the bodyforce operator, which converts a strain (application was for strain from boron doping), into a force. Next the stress operators converted the constant force into a constant stress value (the intrinsic stress of nitride). Though it provided the correct solution, it was a complicated method to model the intrinsic stress. The main purpose of this simulation was to further verify that the software had the ability to accurately calculate stress from a force. For an initial implementation, only the yy stress component will be included. For planar thin films, intrinsic stress is specified at the nodes parallel to the deposition direction. However over non-planar surfaces, simulating the deposition process is more complicated, which makes calculating stresses more difficult. Around the non-planar surface, the stresses are translated from the planar system axis to the axis perpendicular to the normal of the growing film. The stresses at the non-planar nodes then must be averaged with their neighboring elements [Rue97]. This is illustrated below in Figure 6-1.

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89 yy and xx components yy yy at all nodes +y +x xx Figure 6-1: Intrinsic stresses are oriented parallel to the interface on which the film is grown or deposited (left) planar film, (middle) non-planar film [Rue97]. Computing the thermal mismatch stress can be invoked on the command line, or using tcl scripts. The thermal mismatch stress is calculated by multiplying the difference in thermal expansion coefficients of the two materials by the temperature difference (i.e., deposition temperature and room temperature). Oxide growth is currently treated as a viscoelastic material that flows at high stresses and temperatures. This is valid for large amounts or long oxide growth steps, which are typically not employed for current fabrication processes. Large oxide growth was once important for LOCOS formation, but trench isolation has taken over due to the lower stresses generated. For process steps such as trench isolation, oxide is typically deposited in thin layers, and acts more like an elastic material. Adding this stress source is not as straight forward because the growth kinetics of oxide under stress is different than in an unstressed material. In addition, computing the oxide growth forces in non-planar topology must be accounted for. Boundary conditions are defined on the external edges of each material, and different boundary conditions will finite element simulations. Chaudhry demonstrated the effect of different boundary conditions on dislocation loop stress [Cha96]. In the work presented in this thesis, reflecting boundary conditions were implemented to

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90 investigate the effect of fixing the left and right, or bottom side of the finite element mesh. A reflecting boundary simulates mirror symmetry by setting the normal velocity and displacement field equal to zero at the boundary. Reflecting boundary conditions are illustrated in Figure 6-2 for all edges except for the top surface which is free to relax. Top Free Surface x = dx/dt = 0 perpendicular to interface Figure 6-2: Reflecting boundary condition displacement and velocity perpendicular to the interface is set to zero, but can have vertical movement. Top surface is free to relax. For a diffusion simulation, this would imply that no diffusion can occur across the interface, or for a stress simulation, the forces across the interface are equal to zero. In this work the displacement solution is two-dimensional, having x and y displacement values. Currently, when a reflecting boundary condition is applied, both the x and y values are simultaneously fixed at the same node. Future enhancements could include decoupling the x and y coordinates by allowing one coordinate to deform while the other remains fixed. Other boundary conditions, such as Dirichlet and periodic boundary conditions can be tested to obtain more accurate stress simulation results. The Dirichlet boundary conditions states that the value of the solution is defined on the boundary of the solution domain. The periodic boundary condition is similar to the reflecting boundary condition in that one lateral edge demonstrates mirror symmetry by setting the normal component of the displacement and velocity to zero along the boundary, while the other

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91 lateral edge is allowed to move by a constant distance, thus restricting all nodes to the same value of normal displacement [Cha96]. Before simulating an entire transistor structure, stresses after each process step need to be calibrated with experimental data and model parameter fitting. In conjunction with properly modeling all of the stress sources, optimization of boundary conditions will allow for more accurate MOSFETs models in the future. 6.2.2 Stress-Dependent Diffusivity Model SiGe and strained silicon have been identified as alternative materials to help extend Moores Law for years to come. To update and incorporate new models, knowledge of how stress will affect dopant diffusion is essential. It is known that boron diffusion is enhanced under tensile stress and retarded under compressive stress. The exact mechanisms governing boron diffusion in SiGe have been speculated, but are still unknown. Zangenbeg et al. confirmed that macroscopic strain does contribute to dopant diffusion. His studies showed that boron diffusion was enhanced by a factor of 2 in strained silicon, and decreased by a factor of 2 in Si0.88Ge.12 and by a factor of 4 in Si0.76Ge0.24 [Zan03]. Another theory of retarded boron diffusion in SiGe is the Ge-B pairing. The local tensile strain from boron and local compressive strain from Ge will attract one another to relieve the stress [Cro04, Kuo95]. The diffusivity enhancement and retardation of boron under relaxed, tensile, compressive stress is shown in Figure 6-3.

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92 Figure 6-3: Diffusion of B in (left) relaxed Si, tensile Si, and Si 0.99 Ge 0.01 and (right) diffusion of B in strained and relaxed Si 0.76 Ge 0.24 [Zan03]. 6.2.3 STI Induced Stress Modeling As channel lengths decrease, stress sources such as STI have demonstrated a uniaxial compressive stress in the [110], or channel direction of MOSFETs. As a result, scaling devices introduces another method of channel engineering without having to modify the existing fabrication process. However, the source/drain regions are also in closer proximity to the channel, and for bulk silicon PMOS devices, the tensile strain from boron (without SiGe source/drains) can counteract the advantageous compressive stress from the STI, reducing the performance enhancement. It was demonstrated in Chapter V through simulation, that the strain from boron doping in silicon is significant enough to affect the channel stress for both 100 nm and 45 nm channel lengths. The STI-induced stress can be tailored by the geometry of the structure. Shah demonstrated through simulation the effect of transverse stress on STI width, depth, active area width, and STI topology. Wider trenches for the same active area length exhibited higher channel stress. For STI depth, he observed that there was an optimal depth at which the maximum compressive stress in the channel could be achieved. Depths greater or shallower than this critical value resulted in a sharper roll-off of the

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93 stress in the channel. Raised STI structures demonstrated larger stresses than recessed structures due to the enhanced stresses associated with non-planar surface topology. A caveat with these finding is that the STI stress was only defined in the transverse region, however the intrinsic stress is defined in both the transverse {1-10} and out-of-plane {001} regions. Though simulations need to be performed which take into account the intrinsic stress in both directions, these results are very promising to bringing us one step closer in understanding STI stress affects at nanometer channel lengths. It has been long known that longitudinal uniaxial compressive stress enhances hole mobility, but degrades electron mobility, whereas transverse tensile stress improves both types [Smi54, Tho04a]. A technique that is currently being explored to improve CMOS devices is the HARP STI process. After a standard STI is fabricated, the HARP process densifies the trench structure, creating a moderate to high transverse tensile stress [Tho05b]. The mechanisms governing the stress magnification are not completely understood, thus methods to properly model this behavior would enable a more fundamental understanding of this phenomenon. An example application would be to investigate the effect of stress superposition for enhanced device performance. A tensile nitride capping that induces a uniaxial tensile stress in the channel is incorporated into NMOS devices to increase electron mobility. Intel uses SiGe source/drains and IBM uses compressive nitride capping layers to induce a uniaxial compressive stress in the channel to increase hole mobility. Could the transverse tensile stress induced from the HARP process that enhances mobility in both devices be added to the advantageous longitudinal stresses to enhance device performance further [Tho05b]?

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94 6.2.4 Modeling Silicon at the Elastic/Plastic Limit As we continue to decrease the physical dimensions of semiconductor devices, many different processing techniques are being explored to meet the requirements of the International Technology Roadmap for Semiconductors (ITRS). An area of active research is how stress affects material properties and device performance. Phen investigated this phenomenon with a wafer bending experiment by placing ultra-thin silicon wafers preamorphized with Ge and implanted with boron in tension, compression, and under no stress. The samples were annealed and the activation and defect densities were observed under each condition. Hall measurements indicated there was little difference in activation at low temperatures, and TEM indicated larger defect densities for the compressed layers [Phe04]. However, to successfully conduct theses studies, it is critical that the stress at the surface of the samples is below the yield strength of silicon to avoid plastic deformation. Yield strength of a material is dependent on the amount of stress applied, the processing temperature, and the amount of time the sample is stressed. Thus, to increase the stress that a sample is subjected to, one of the other parameters will have to be decreased to avoid deforming the material by slip.

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95 Figure 6-4: Yield point reduction as a function of temperature. The yield strength of silicon is over 100 MPa at 500C, but drops to approximately 10 MPa at 1000C. Rabier et al. found the limit of elasticity in silicon is limited by a thermal budget of 750C for 10 min at a stress of 100 MPa [Rab00]. This creates large challenge for performing high temperature studies below the plastic deformation limit. Phens results of the elastic/plastic limit for silicon under various temperatures are illustrated in Figure 6-5.

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96 5005506006507007508008509009501000050100150200250300350Time (s)Temperature (C) No Slip Slip Future Work Figure 6-5: Regime of elastic/plastic deformation of silicon for various temperatures and times under 110 MPa stress [Phe04]. The work presented in this thesis allows silicon to be modeled in the elastic regime, but the elasticity of silicon ceases to exist at higher temperatures under a given stress, as described above. Thus, modeling silicon in the non-linear plastic regime would be beneficial because it will cut down on the technology development time and cost of running many experiments. In addition, experimental data for silicon that has undergone plastic deformation is readily available for instant calibration.

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97 APPENDIX A CODE APPENDIX The code in this appendix was either modified from its original author, Dr. Mark E. Law, or written by Heather E. Randell. Each file will specify if the code was written or modified. EleInfo.h The Nind and Sind functions are used to access the node numbers (0-2) and the solution number (0-1) respectively For the Sind function 0 represents the x solutions, while 1 represents the y solution. Each function takes in an integer (0-5) to represent 3 nodes 2 positions per node. The output of Nind and Sind are shown below. Node Number Nind Sind 0 0 0 1 0 1 2 1 0 3 1 1 4 2 0 5 2 1 int Nind(const int i) const { return i / ns; } int Sind(const int i) const { return i % ns; } Expr.cc The Expr class is the base class for all types of expressions. A few examples are: SumExpr which performs the addition and subtraction function, PrdExpr which performs the multiply and divide function, SolExpr which is a solution reference, PowExpr which handles exponents, and DiscExpr which handles discritizable functions. The functions below are defined for many of the expressions, in addition to the expressions listed above. They will be defined in more detail in Spatial.cc, where the body of the function originates. After the function is evaluated in Spatial.cc, if the values of the stiffness matrix are not already stored, it is passed in as an argument and the location of its values are stored. StaticColumn &Expr::EleEvaluate( ElementInfo &ev ) { int i, k; if ( !nodestore ) FLPS_panic("retrieving cached answers when they are unavailable"); int cached = this->Column0Cached(ev); if ( !cached && nodestore ) { for(i = 0; i < ev.Size(); i++) { VectorStatic &v0( se0->Val(i) ); for(int k = 0; k < ev.VecLen(); k++) v0[k] = v[ev.node(i,k)->Index()];

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98 } } return *se0; } StaticColumn &Expr::EleInside( ElementInfo &ev ) { int i, k; if ( !nodestore ) FLPS_panic("retrieving cached answers when they are unavailable"); int cached = this->Column1Cached(ev); if ( !cached && nodestore ) { for(i = 0; i < ev.Size(); i++) { VectorStatic &v0( se1->Val(i) ); for(int k = 0; k < ev.VecLen(); k++) v0[k] = v[ev.node(i,k)->Index()]; } } return *se1; } StaticMatrix &Expr::EleDeriv( ElementInfo &ev ) { int i,j,k; FLPS_panic("retrieving cached answers when they are unavailable"); int cached = this->MatrixCached(ev); if ( !cached && nodestore ) { for(i = 0; i < ev.Size(); i++) { for(j = 0; j < ev.Size(); j++) { VectorStatic &v0( sd->Val(i,j) ); if ( i == j ) for(int k = 0; k < ev.VecLen(); k++) v0[k] = v[ev.node(i,k)->Index()]; else v0 = 0.0; } } } return *sd; } Genpde.cc Genpde.cc contains the routines that allocate space, and numbers the nodes for the multidimensional displacement solution. This code was modified from its original Author, Dr. Mark E. Law.

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99 void GenericPDE::SetEqnMap( ElementInfo &ev, EqnMap &stf ) { if ( sid->isDimension() ) ev.SetSolDim( m->dimension() ); //get and set equation numbers.... IntData &e = sol->EqnNum(); IntBlock e1; e1.ReSize(ev.VecLen()); //for each node, initialize the equation numbers for(int j = 0; j < ev.Size(); j++) { ev.SetCur(j); for(int i = 0; i < ev.VecLen(); i++) e1[i] = sol->EqnNum( ev.Sind(j) ).get( *ev.node(j,i) ); stf.SetIntRow( off, j, e1 ); } } void GenericPDE::VectorElement( ElementInfo &ev, EqnMap &stf ){ int i, j; if ( sid->isDimension() ){ ev.SetSolDim( m->dimension() ); else ev.SetSolDim(1); } if ( ev.type() == NODE ) { FLPS_panic("GenericPDE::VectorEdge called with non-edges"); } if ( Eeq->IsEmpty() ) return; stf.SetSteady(); StaticColumn &r = Eeq->EleEvaluate( ev ); for(i = 0; i < ev.Size(); i++){ stf.Sumrhs( off, i, r.Val(i) ); } //get derivatives... ExprIter ei( Eder ); while( ei++ ) { int oa = ei.cursign(); StaticMatrix &r = ei.current().EleDeriv( ev ); for(i = 0; i < ev.Size(); i++) { for( j= 0; j< ev.Size(); j++) { stf.SumBlock( r.Val(i,j), off, oa, i, j ); VectorStatic &ref = r.Val(i,j); } } }

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100 } int GenericPDE::NumberNode( Node &n, const int ne ) { int i; int length = 1; int nodecount=0; if ( sid->isDimension() ) { length = m->fieldserver().dimension(); } int assign = ne; for( i = 0; i < length; i++ ) { if ( sol->EqnNum(i).get(n) != 0 ) continue; assign += 1; NodeIter ni( n.location().nodes() ); while( ni++ ) { if ( sid->isContinuous() ){ sol->EqnNum(i).set( ni.current(), assign ); } //sets equation number at each node if ( ni.current().mesh().mater() == m->mater() ){ sol->EqnNum(i).set( ni.current(), assign ); } //sets equation number at each node } Coordinate &c=n.location(); cout << "Node location" << "<<"x=" << c.x() << " <<"y=" << c.y() <<" << "equation number = << solEqnNum(i).get(n) << endl; } return assign; }

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101 Spatial.cc The file contains the routines for the elastic, bodyforce, stress, and strain computations to compute the displacements and stress due to boron doping. This code was developed by Heather E. Randell. DiscExpr::ElasticEval computes the stiffness matrix of an element. DiscExpr::BodyForceEval computes the forces from boron doping. DiscExpr::StrainEval converts the forces from boron doping into strain values, and DiscExpr::StressEval converts the forces strains into a stress component. void DiscExpr::ElasticEval( ElementInfo &ev ) { double x0; double y0; double x1; double y1; double x2; double y2; double C[6][3]; double stiffness[6][6]; double Bmatrix[3][6]; double BTmatrix[6][3]; double Dmatrix[3][3]; double fx[6]; double displacement[6]; double x[3]; double y[3]; if ( oar != NULL ) FLPS_panic("fubar"); StaticColumn &a = arg->EleInside(ev); for (int k=0; klocation(); //find location of //nodes x[ev.Nind(l)]=chead.x(); y[ev.Nind(l)]=chead.y(); } //finishes NodeLen for loop B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] );

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102 BT_Matrix(Bmatrix, BTmatrix); D_Matrix(Dmatrix, E, nu); Stiffness(BTmatrix, Dmatrix, Bmatrix, C, stiffness); //multiply stiffness matrix by column vector Multiply(stiffness, displacement, fx); for (int i=0; i<6; i++){ //store info at Val(i) VectorStatic &v = se0->Val(i); v[k] = fx[i]; cout << "fx = << " << v[k] << endl; } }//finishes VecLen for loop } StaticColumn &DiscExpr::EleInside( ElementInfo &ev ) { FLPS_panic("DiscExpr inside another discexpr") } void DiscExpr::ElasticDeriv( ElementInfo &ev) { double x0; double y0; double x1; double y1; double x2; double y2; double C[6][3]; double stiffness[6][6]; double Bmatrix[3][6]; double BTmatrix[6][3]; double Dmatrix[3][3]; double fx[6]; double displacement[6]; //Print out nodes of all faces & create storage for the nodes double x[3]; double y[3]; for (int k=0; klocation(); //find //location of nodes cout << "x = <
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103 B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] ); BT_Matrix(Bmatrix, BTmatrix); D_Matrix(Dmatrix, E, nu); Stiffness(BTmatrix, Dmatrix, Bmatrix, C, stiffness); for (int i=0; i<6; i++){ for (int j=0; j<6; j++){ VectorStatic &v = sd->Val(i,j); v[k] = stiffness[i][j]; } } }//finishes VecLen for loop } //This function calculates the strain from boron doping void DiscExpr::BodyForceEval( ElementInfo &ev ) { double x0; double y0; double x1; double y1; double x2; double y2; double C[6][3]; double stiffness[6][6]; double Bmatrix[3][6]; double BTmatrix[6][3]; double Dmatrix[3][3]; double fx[6]; double displacement[6]; double x[3]; double y[3]; double strain[3]; if ( oar != NULL ) FLPS_panic("fubar"); StaticColumn &a = arg->EleInside(ev); for (int k=0; k
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104 strain[0] = sqrt(2.0) (s1+s2+s3) / 6.0; strain[1] = sqrt(2.0) (s1+s2+s3) / 6.0; //assume no shear component strain[2] = 0.0; for (int l=0; l<6; l+=2) { //loop over 3 nodes of each face NOTE:should be less than ev.Size() for an arbitrary //element, but triangles is 3 Coordinate &chead = ev.node(l,k)->location(); //find //location of nodes x[ev.Nind(l)]=chead.x(); y[ev.Nind(l)]=chead.y(); } //finishes NodeLen for loop B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] ); BT_Matrix(Bmatrix, BTmatrix); D_Matrix(Dmatrix, E, nu); BTMultD(BTmatrix, Dmatrix, C); //multiply [6x3]C*nodal //strain[3x1]=(displacements) forces [6x1] MultBtDBF(C, strain, fx); for (int i=0; i<6; i++){ //store info at Val(i) VectorStatic &v = se0->Val(i); v[k] = fx[i]; //store away the displacements cout << "fx = << " << v[k] << endl; } }//finishes VecLen for loop } void DiscExpr::BodyForceDeriv( ElementInfo &ev ) { for (int k=0; kVal(i,j); v[k] = 0.0; } } }//finishes VecLen for loop } //this is not general

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105 void DiscExpr::StrainEval( TensorType tt, ElementInfo &ev ) { double x0; double y0; double x1; double y1; double x2; double y2; double C[6][3]; double stiffness[6][6]; double Bmatrix[3][6]; double BTmatrix[6][3]; double Dmatrix[3][3]; double fx[6]; double displacement[6]; double x[3]; double y[3]; double strain[3]; double elestrain[3]; double val; if ( oar != NULL ) FLPS_panic("fubar"); StaticColumn &a = arg->EleInside(ev); for (int k=0; klocation(); //find location of //nodes x[ev.Nind(l)]=chead.x(); y[ev.Nind(l)]=chead.y(); } //finishes NodeLen for loop B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] ); //multiply //3x6]B*[6x1]=elestrain[3x1] strain[xx, yy, xy] MultiplyStrain(Bmatrix, elestrain, displacement); // find tt to determine if //want strain_xx, strain_yy, or strain_xy if (tt==Dir_XX) val = elestrain[0]; else if (tt==Dir_YY) val = elestrain[1]; else val = elestrain[2];

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106 for (int i=0; i<3; i++){ //store info at Val(i) //store away the elemental strain values at //each node (strain_xx, yy, or xy) VectorStatic &v = se0->Val(i); v[k] = val; cout << "strain = << " << v[k] << endl; } }//finishes VecLen for loop } void DiscExpr::StrainDeriv(TensorType tt, ElementInfo &ev ) {FLPS_panic("Calling StrainEval"); } void DiscExpr::StressEval( TensorType tt, ElementInfo &ev ) { double x0; double y0; double x1; double y1; double x2; double y2; double C[6][3]; double stiffness[6][6]; double Bmatrix[3][6]; double BTmatrix[6][3]; double Dmatrix[3][3]; double fx[6]; double displacement[6]; double x[3]; double y[3]; double strain[3]; double elestrain[3]; double stress[3]; double val; if ( oar != NULL ) FLPS_panic("fubar"); StaticColumn &a = arg->EleInside(ev); for (int k=0; k
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107 Coordinate &chead = ev.node(l,k)->location(); //find location of //nodes x[ev.Nind(l)]=chead.x(); y[ev.Nind(l)]=chead.y(); } //finishes NodeLen for loop B_Matrix( Bmatrix, x[0], y[0], x[1], y[1], x[2], y[2] ); D_Matrix(Dmatrix, E, nu); //multiply [3x6]B*[6x1]=elestrain[3x1] strain[xx, yy, xy] MultiplyStrain(Bmatrix, elestrain, displacement); MultiplyStress(Dmatrix, elestrain, stress); // find tt to determine if want //strain_xx, strain_yy, or strain_xy if (tt==Dir_XX) val = stress[0]; else if (tt==Dir_YY) val = stress[1]; else val = stress[2]; for (int i=0; iVal(i); v[k] = val; //store away the stress values at each node //(xx, yy, or xy) cout << "stress = << " << v[k] << endl; } }//finishes VecLen for loop } void DiscExpr::StressDeriv(TensorType tt, ElementInfo &ev ) {FLPS_panic("Calling StressEval");} double Delta (double x0, double y0, double x1, double y1, double x2, double y2) { double ans = (((x1*y2) (x2*y1)) ((x0*y2) (x2*y0)) + ((x0*y1) (x1*y0))); cout << "two_delta =" << ans << "\n"; return ans; } //BT*D*B=stiffness matrix, start here with B matrix void B_Matrix( double Bmatrix[3][6], double x0, double y0, double x1, double y1, double x2, double y2 ) { Bmatrix[0][0] = y1 y2; Bmatrix[1][0] = 0; Bmatrix[2][0] = x2 x1; Bmatrix[0][1] = 0; Bmatrix[1][1] = x2 x1; Bmatrix[2][1] = y1 y2;

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108 Bmatrix[0][2] = y2 y0; Bmatrix[1][2] = 0; Bmatrix[2][2] = x0 x2; Bmatrix[0][3] = 0; Bmatrix[1][3] = x0 x2; Bmatrix[2][3] = y2 y0; Bmatrix[0][4] = y0 y1; Bmatrix[1][4] = 0; Bmatrix[2][4] = x1 x0; Bmatrix[0][5] = 0; Bmatrix[1][5] = x1 x0; Bmatrix[2][5] = y0 y1; double two_delta = Delta (x0, y0, x1, y1, x2, y2); cout <<"Bmatrix is...\n"; for (int i=0;i<3; i++) { for (int j=0; j<6; j++) { Bmatrix[i][j] = (Bmatrix[i][j] / two_delta); cout << Bmatrix[i][j]<< ","; } cout<< "\n\n\n"; } } //Compute BT matrix void BT_Matrix (double Bmatrix[3][6], double BTmatrix[6][3]) { for (int i=0;i<6; i++) { for (int j=0; j<3; j++) { BTmatrix[i][j]=Bmatrix[j][i]; } } } //Compute D matrix void D_Matrix (double Dmatrix[3][3], double E, double nu) { /* Dmatrix[0][0] = 1; //This is the plane stress approximation Dmatrix[1][0] = nu; Dmatrix[2][0] = 0; Dmatrix[0][1] = nu; Dmatrix[1][1] = 1;

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109 Dmatrix[2][1] = 0; Dmatrix[0][2] = 0; Dmatrix[1][2] = 0; Dmatrix[2][2] = (1-nu)*0.5; cout << "Dmatrix is...\n"; for (int i=0;i<3; i++) { for(int j=0;j<3; j++) { Dmatrix[i][j] = Dmatrix[i][j] (E/(1-(nu*nu))); cout << Dmatrix[i][j]<< ","; } cout<< "\n\n\n"; } */ Dmatrix[0][0] = 1; //This is the plane strain approximation Dmatrix[1][0] = (nu/(1-nu)); Dmatrix[2][0] = 0; Dmatrix[0][1] = (nu/(1-nu)); Dmatrix[1][1] = 1; Dmatrix[2][1] = 0; Dmatrix[0][2] = 0; Dmatrix[1][2] = 0; Dmatrix[2][2] = ((1-(2*nu))/(2*(1-nu))); cout << "Dmatrix is...\n"; for (int i=0;i<3; i++) { for(int j=0;j<3; j++) { Dmatrix[i][j] = Dmatrix[i][j] ((E*(1-nu))/((1+nu)*(1-(2*nu)))); cout << Dmatrix[i][j]<< ","; } cout<< "\n\n\n"; } } //multiply BT*D*B to get a 6 by 6 stiffness matrix void Stiffness(double BTmatrix[6][3], double Dmatrix[3][3], double Bmatrix[3][6], double C[6][3], double stiffness[6][6]) { for (int i=0;i<6; i++) { for (int j=0; j<3; j++) { C[i][j]=0; for (int z=0; z<3; z++){

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110 C[i][j] += BTmatrix[i][z] Dmatrix[z][j]; } } } //multiply stiffness = C*B for (int i=0;i<6; i++) { for (int j=0; j<6; j++) { stiffness[i][j]=0; for (int z=0; z<3; z++){ stiffness[i][j] += C[i][z] Bmatrix[z][j]; } } } } //multiply BT* D to compute body forces void BTMultD(double BTmatrix[6][3], double Dmatrix[3][3], double C[6][3]) { for (int i=0;i<6; i++) { for (int j=0; j<3; j++) { C[i][j]=0; for (int z=0; z<3; z++){ C[i][j] += BTmatrix[i][z] Dmatrix[z][j]; } } } } //multiply stiffness (derivative matrix) fx void Multiply(double stiffness[6][6], double displacement[6], double fx[6]) { for (int i=0; i<6; i++){ fx[i]=0; for(int j=0; j<6; j++){ fx[i] += stiffness[i][j] displacement[j]; } } } void MultBtDBF(double C[6][3], double strain[3], double fx[6]) //f[x] is the 6 displacement values { for (int i=0; i<6; i++){ fx[i]=0;

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111 for(int j=0; j<3; j++){ fx[i] += C[i][j] strain[j]; } } }

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APPENDIX B SIMULATION FILES This appendix contains the simulation files for the results presented in Chapter 5. #This simulation computes the displacement in the silicon beam due to boron doping. #The grid is adjusted in the x and y directions to accommodate changes in the length and #width. The doping profile is adjusted by commenting out the line profile name=Bar #infile=bartop1p4u.prof, and uncommenting the line sel z=8.0e19*exp(-x*x/0.01) #name=Bar. math diffuse dim=2 umf none col !scale solution name=Potential nosolve pdbSetBoolean Silicon displacement Negative 1 pdbSetBoolean ReflectLeft displacement Negative 1 pdbSetDouble Silicon displacement Abs.Error 1.0e-8 pdbSetDouble ReflectLeft displacement Abs.Error 1.0e-8 #Set up grid line x loc=0.2 tag=top spa=0.05 line x loc=1.4 tag=bot spa=0.05 line y loc=0.0 tag=left spa=0.5 line y loc=50 tag=right spa=.5 #Define silicon region region silicon xlo=top xhi=bot ylo=left yhi=right init #Import doping profile, uncomment the second line to adjust the doping # profile profile name=Bar infile=bartop1p4u.prof #Set up solution for displacement solution name = displacement add solve dim continuous solution name = Temp const val = 1000 add solve #Fix left boundary pdbSetBoolean ReflectLeft displacement Fixed 1 pdbSetString ReflectLeft displacement Equation "displacement" 112

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113 #Set Youngs Modulus and Poissons Ratio pdbSetDouble Silicon YoungsModulus 1.80E12 pdbSetDouble Silicon PoissonRatio 0.28 #Evaluate the equation the argument of the bodyforce operator is the strain from boron doping pdbSetString Silicon displacement Equation "elastic(displacement)-BodyForce((1+.3)*5.19e-24*Bar)" #Initiate Alagator diffuse time = 1e-6 temp=1000 init=1.0e-5 plot.2d grid pos=displacement #Solve for Stress/Strain in the xx, yy, or xy directions select z = "Stress(xy, displacement)" #This simulation computes the displacement and stress in the silicon due to an intrinsic #force (stress) in the nitride layer. NOTE: This is an unpractical method to apply an #intrinsic stress in a nitride layer. math diffuse dim=2 umf none col !scale solution name=Potential nosolve pdbSetBoolean Silicon displacement Negative 1 pdbSetBoolean ReflectLeft displacement Negative 1 pdbSetDouble Silicon displacement Abs.Error 1.0e-8 pdbSetDouble ReflectLeft displacement Abs.Error 1.0e-8 pdbSetBoolean nitride displacement Negative 1 pdbSetBoolean ReflectLeft displacement Negative 1 pdbSetDouble nitride displacement Abs.Error 1.0e-8 pdbSetDouble ReflectLeft displacement Abs.Error 1.0e-8 #Set Youngs Modulus and Poissons Ratio pdbSetDouble Silicon YoungsModulus 1.22e12 pdbSetDouble Silicon PoissonRatio 0.3 pdbSetDouble nitride YoungsModulus 3e12 pdbSetDouble nitride PoissonRatio 0.25 #Set up grid line x loc=-0.02 tag=nit spa=0.05 line x loc=0.0 tag=top spa=0.05 line x loc=10 tag=bot spa=0.5 line y loc=0.0 tag=left spa=0.5

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114 line y loc=5 tag=side spa=.1 line y loc=10 tag=mid spa=.1 line y loc=15 tag=right spa=.5 #Define silicon, nitride, and gas region region gas xlo=nit xhi=top ylo=left yhi=side region gas xlo=nit xhi=top ylo=mid yhi=right region nitride xlo=nit xhi=top ylo=side yhi=mid region silicon xlo=top xhi=bot ylo=left yhi=right init # Apply a constant force (intrinsic stress) in the nitride material select z=0.6e20*(Material(nitride)) name=Bar #Set up solution for displacement solution name = displacement add solve dim continuous solution name = Temp const val = 1000 add solve #Fix left boundary pdbSetBoolean ReflectBottom displacement Fixed 1 pdbSetString ReflectBottom displacement Equation "displacement" #Evaluate the matrix pdbSetString Silicon displacement Equation "elastic(displacement)" pdbSetString nitride displacement Equation "elastic(displacement)+BodyForce(Bar*5.19e-22)" #Initiate Alagator diffuse time = 1e-6 temp=1000 init=1.0e-5 plot.2d grid pos=displacement #Solve for Stress/Strain in the xx, yy, or xy directions select z = "Stress(xy, displacement)" #This simulation computes the stress in the silicon due to boron doping. The channel length and source/drain length can be adjusted in the grid. The boron concentration can be manually adjusted on the sel z=2e20*exp(-x*x/0.0013)*((y<1.0)||(y>1.1)) name=Bar line math diffuse dim=2 umf none col !scale solution name=Potential nosolve

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115 pdbSetBoolean Silicon displacement Negative 1 pdbSetDouble Silicon displacement Abs.Error 1.0e-8 pdbSetBoolean nitride displacement Negative 1 pdbSetDouble nitride displacement Abs.Error 1.0e-8 pdbSetBoolean ReflectBottom displacement Negative 1 pdbSetDouble ReflectBottom displacement Abs.Error 1.0e-8 #Fix bottom boundary pdbSetBoolean ReflectBottom displacement Fixed 1 pdbSetString ReflectBottom displacement Equation "displacement" #Set Youngs Modulus and Poissons Ratio pdbSetDouble Silicon YoungsModulus 1.80E12 pdbSetDouble Silicon PoissonRatio 0.28 pdbSetDouble nitride YoungsModulus 3E12 pdbSetDouble nitride PoissonRatio 0.25 #Set up Grid line x loc= 0.0 tag=SiTop spacing=0.01 line x loc = 0.12 tag=BorBottom spacing=0.005 line x loc = 0.5 spacing=0.1 line x loc=5.0 tag=SiBottom spacing=0.2 line y loc=0.0 tag=Mid spac=0.01 line y loc=1.0 tag=BorRight spac=0.05 line y loc=1.1 tag=BorLeft spac=0.05 line y loc=2.1 tag=Right spac=0.01 #Define silicon region region silicon xlo=SiTop xhi=SiBottom ylo=Mid yhi=Right init #Set up solution for displacement solution name = displacement add solve dim continuous solution name = Temp const val = 1000 add solve #Selectively implant the channel region with species Bar (boron) sel z=2e20*exp(-x*x/0.0013)*((y<1.0)||(y>1.1)) name=Bar #Evaluate the matrix pdbSetString Silicon displacement Equation "elastic(displacement)+bodyforce((1+.28)*Bar*5.19e-24)" #Initiate Alagator

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116 diffuse time = 1.0e-6 temp=1000 init=1.0e-5 #Solve for Stress/Strain in the xx, yy, or xy directions select z= "Stress(yy, displacement)" print.1d x=.01

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LIST OF REFERENCES [Adl04] Adler, A, Newton-Rhapson Method, University of British Columbia, Course Notes, Math 104/184: Differential Calculus, Fall 2004. [Avc02] I. Avci Loop Nucleation and Stress Effects in Ion-Implanted Silicon. Doctoral Dissertation. University of Florida, 2002. [Azi01] M. J. Aziz, Stress Effects on Defects and Dopant Diffusion in Si, Materials Science in Semiconductor Processing, Vol.4, pp. 397-403, 2001. [Azi03] M. J. Aziz, Dopant Diffusion Under Pressure and Stress, IEDM, Washington, D.C., pp. 137-142, December 2003. [Bon01] J.M. Bonar, A.F.W. Willoughby, A.H. Dan, B.M. McGregor, W. Lerch, D. Loeffelmacher, G.A. Cooke, and M.G. Dowsett, Antimony and Boron Diffusion in SiGe and Si Under the Influence of Injected Point Defects, J. Materials Science: Materials in Electronics, Vol.12, No.4, June 2001. [Cea96] S.M.Cea, Multidimensional Viscoelastic Modeling of Silicon Oxidation and Titanium Silicidation, Doctoral Dissertation. University of Florida. 1996. [Cea04] S.M. Cea, M. Armstrong, C. Auth, T. Ghani, M.D. Giles, T. Hoffman, R. Kotlyar, P. Matagne, K. Mistry, R. Nagisetty, B. Obra,dovic, R. Shaheed, L. Shifren, M. Stettler, S. Tyagi, X. Wang, C. Weber, K. Zawadzki, Front End Stress Modeling for Advanced Logic Technologies, IEDM, pp.963-966, San Francisco, CA, 2004. [Cha96] S. Chaudhry, "Analysis and Modeling of Stress Related Effects in Scaled Silicon Technology," Doctoral Dissertation. University of Florida. 1996. [Chi91] D. Chidambarrao, J.P. Peng, and G.R. Srinivasan, Stresses in Silicon Substrates Near Isolation Trenches, Journal of Applied Physics, Vol.70, No.9, pp. 4816-4822, November 1, 1991. [Chu93] W.H. Chu and M. Mehregany, A Study of Residual Stress Distribution Through the Thickness of p + Silicon Fioms, IEEE Transactions on Electron Devices, Vol. 40, No.7, pp. 1245-1250, July 1993. 117

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118 [Col03] L. Collins, Silicon Takest, IEE Review, pp. 46-49, December 2005. [Cow94] N.E.B. Cowern, P.C. Zalm, P. van der Sluis, D.J Gravesteign, and W.B. de Boer, Diffusion in Strained Si(Ge), Physical Review Letters, Vol.72, No.16, pp. 2585-2588, April 18, 1994. [Cro04a] R. Crosby, Evolution of Si Interstitials Induced by Si + -Implantation in Silicon Germanium (SiGe). Doctoral Dissertation. University of Florida, 2004. [Cro04b] R.T. Crosby, K.S Jones, M.E. Law, A.F. Saavedra, J.L. Hansen, A.N. Larsen, and J. Liu, Strain Relaxation of Ion-Implanted Strained Silicon on Relaxed SiGe, Materials Research Society Symposium Proceedings, Vol.810, 2004. [Dei02] H.M. Deitel and P.J. Deitel. C ++ How to Program: Third Edition, Pearson Education, Patparganj, Delhi, India, 2002. [Fah92] P.M. Fahey, S.R. Mader, S.R. Stiffler, R.L. Mohler, J.D. Mis, J.A. Slinkman, Stress-Induced Dislocations in Silicon Integrated Circuits, IBM Journal of Research and Development, Vol.36, No.2, pp. 158-182, March 1992. [Fio04] J.G. Fiorenza, G. Braithwaithe, C.W. Leitz, M.T. Currie, J. Yap, F. Singaporewala, V.K. Yang, T.A. Langdo, J. Carlin, M. Somerville, A. Lochtefled, H. Badawi, and M.T. Bulsara, Film Thickness Constraints for Manufacturable Strained Silicon CMOS, Semiconductor Science and Technology, Vol.19, pp. L4-L8, 2004. [Fis03] M.V. Fischetti,Six-Bank kp Calculation of the Hole Mobility in Silicon Inversion Layers, Journal of Applied Physics, Vol.94, pp.1079-1095, 2003. [Fre03] L.B. Freund and S. Suresh Thin Film Materials: Stress,Defect Formation and Surface Evolution, Cambridge University Press, Cambridge United Kingdom, 2003. [Gal04] C. Gallon, G. Reimbold, G. Ghibaudo, R.A. Bianchi, R. Gwoziiecki, S. Orain, E. Robilliart, C. Raynaud, H. Dansas, Electrical Analysis of Mechanical Stress Induced by STI in Short MOSFETs Using Externally Applied Stress, IEEE Transactions on Electron Devices, Vol.51, No.8, pp. 1254-1261, August 2004.

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119 [Gha04] T. Ghani, M. Armstrong, C. Auth, M.D. Giles, K.Mistry, A. Murthy, L. Shifren, S. Thompson, and M. Bohr, Uniaxial Strained Silicon CMOS Devices for High Performance Logic Nanotechnology, Electrochemical Society Fall Meeting, Honolulu, Hawaii, October 2004. [Gud04] P. Guduru, Brown University. Course Notes, EN175: Advanced Mechanics of Solids, Fall 2004. [Hor55] F. H. Horn, Densitometric and Electrical Investigation of Boron in Silicon, Physical Review, Vol.97, No.6, pp. 1521-1525, March 1, 1955. [Hoy02] J.L. Hoyt, H.M. Nayfeh, S. Eguchi, I. Aberg, G. Xia, T. Drake, E.A. Fitzgerald, D.A. Antoniadis, Strained Silicon MOSFET Technology, IEDM, p. 23, 2002. [Hu91] S.M. Hu, Stress-Related Problems in Silicon Technology, J. Appl. Phys, Vol.70, No.6, pp. R53-R80, September 15, 1991. [ISE04] Integrated Systems Engineering, Simulations of Strained Silicon CMOS Devices, September 2004, www.ise.ch/appex/strain_si_www.pdf April 2005. [Jae02] Richard C. Jaeger Introduction to Microelectronic Fabrication, Volume V, Prentice Hall, Upper Saddle River, NJ 2002. [Jeo03] Y. Jeon, G.C. F. Yeap, P. Grudowski, T. Van Gompel, J. Schmidt, M. Hall, B. Melnick, M. Mendicino, S. Venkatesan, The Impact of STI Mechanical Stress on the Device Performance of 90nm Technology Node with Different Substrates and Isolation Processes, SOI Conference, Newport Beach, CA, 2003. [Jon03] K.S. Jones, C.E. Ross, D.Zeenberg, Semiconductor Research Corporation Annual Review, Raleigh, NC., 2002. [Kuo95] P. Kuo, J.L. Hoyt, and J.F. Gibbons, The Effects of Strain on Boron Diffusion in Si and Si 1-x Ge x , Applied Physics Letters, Vol.66, pp. 580, 1995. [Law02a] M.E. Law FLOOPS 2002 Release Manual, Gainesville, FL, 2002. [Law02b] M.E. Law, Simulation and Verification of Advanced Technologies. Semiconductor Research Corporation Proposal Task 1017, 2002. [Law03] M.E. Law, University of Florida, Course Notes, EEL 6324: Silicon Fabrication Technology, Spring 2003.

PAGE 135

120 [Lim04] J.S. Lim, S.E. Thompson, and J.G. Fossum, Comparison of Threshold-Voltage Shifts for Uniaxial and Biaxial Tensile-Stressed m-MOSFETs, IEEE Electron Device Letters, Vol.25, No.11, pp. 731-733, November 2004. [Moh04] N. Mohta and S.E. Thompson, Strained Si-The Next Vector to Extend Moores Law, To be published in IEEE Circuits and Devices Magazine, 2005. [Moo65] G. E. Moore, Cramming More Components Onto Integrated Circuits, Electronics, Vol. 38, No.8, pp. 114-117, April 19, 1965. [Nin96] X.J. Ning, Distribution of Residual Stresses in Boron Doped p + Silicon Films, Journal Electrochemical Society, Vol.143, No.10, pp. 3389-3393, October 10,1996. [Par93] H. Park, K.S. Jones, J.A. Slinkman, and M.E. Law, The Effects of Strain on Dopant Diffusion in Silicon, IEDM 1993. [Par95] H. Park, K.S. Jones, M.E. Law, Effects of Hydrostatic Pressure on Dopant Diffusion in Silicon, J. Appl. Phys, Vol. 78, No.6, pp. 3664-3670, September 15, 1995. [Pbs47] ScienCentral, Inc. and The American Institute of Physics, Miracle Month, the Invention of the First Transistor, 1999, http://www.pbs.org/transistor/background1/events/miraclemo.html April 2005. [Peo85] R. People and J.C. Bean, Calculation of Critical Thickness Versus Lattice Mismatch For Ge x Si 1-x /Si Strained-Layer Heterostructures, Applied Physics Letters, Vol.47, No.3, pp. 322-324, August 1, 1985. [Phe04] M.S. Phen, The Effects of Stress on Dopant Activation and Defect Morphoogy, Semiconductor Research Corporation Annual Review, Raleigh, NC, 2004. [Plu00] J. Plummer, M. Deal, and P. Griffen, Silicon VLSI Technology: Fundamentals, Practice, and Modeling, Prentice Hall, Upper Saddle River, New Jersey, 2000. [Rab00] J. Rabier, J.L Dement, Heteroepitaxy of GaN on Silicon: In Situ Measurements. Phys. Stat. Sol, Vol. 222, No.63, 2000. [Raj01] K. Rajendran and W. Schoenmaker, Modeling of Complete Supression of Boron Out-Diffusion in Si 1-x Ge x by Carbon Incorporation, Solid State Electronics, Vol.45, pp.229-233, 2001.

PAGE 136

121 [Raj03] K. Rajendran, D. Villaneuva, P. Moens, W. Schoenmaker, Modeling of Clustering Reaction and Diffusi on of Boron in Strained Si1-xGex Epitaxial Layers, Solid State Electronics, Vol.47, pp. 835-835, 2003. [Ran04] H. Randell, L. Radic, I. Avci, and M.E. Law, Strain Simulations in FLOOPS, ISE Newsletter, September 2004. [Rim04] K. Rim, L. Shi, K. Chan, J. Ott, J. Chu, D. Boyd, K. Jenkins, D. Lacey, P.M. Mooney, M. Cobb, N. Klymko, F. Jamin, S. Koester, B.H. Lee, M. Gribelyuk, and T. Kanarsky, Strained Si for Sub-100 nm MOSFETs, Solid State Electronics, Vo l.48, No.2, pp. 239-243, February 2004. [Ros03] C.E. Ross and K.S. Jones, The Effect of a Patterned Nitride Layer on the Evolution of Implant-Related Dama ge in Silicon, Ultra Shallow Junctions Conference, Santa Cruz, CA, September 2003. [Ros04] C.E. Ross and K.S. Jones, The Role of Stress on the Shape of the Amorphous-Crystalline Interface and Ma sk-Edge Defect Formation in Ion-Implanted Silicon, Material s Research Society Symposium Proceedings, Vol. 810, pp. C10.4, Warrendale, PA, 2004. [Rue97] H. Rueda, Modeling of Mechanical Stress in Silicon Isolation Technology and its Influence on Device Characteristics , Doctoral Dissertation. Universi ty of Florida, 1997. [Rue98] H. Rueda, and M.E. Law, Modeling of Strain in Boron-Doped Silicon Cantilevers, MSM Proceedings, pp. 94-99, August 1998. [Sar04] K. Saraswat, Int egrated Circuit Isolation Technologies, Stanford University. Integrated Circuit Fa brication Laboratory, EE410 Course Notes, Spring 2004. [Sad02] B. Sadigh, T. J. Lenosky, M.J. Ca turla, A.A. Quong, L.X. Benedict, and T.D. de la Rubia, Large Enhancement of Boron Solubility in Silicon Due to Biaxial Stress, Applied Phys ics Letters, Vol.80, No.25, pp.4738-4740, June 24, 2002. [Sco99] G. Scott, J. Lutze, M. Rubin, F. Nouri, and M. Manley, NMOS Drive Current Reduciton Caused by Transi stor Layout and Trench Isolation Induced Stress, IEEE 1999. [Sen01] S. D. Senturia. Microsystem Design, Kluwer Academic Publishers, Norwell, MA, 2001.

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122 [She05] Y.M. Sheu, S.J. Yang, C.C. Wang, C.S. Chang, L.P. Huang, T.Y. Huang, M.J. Chen, and C.H. Diaz, Modeling Mechanical Stress Effect on Dopant Diffusion in Scaled MOSFETs, IEEE Transactions on Electron Devices, Vol.52, No.1, pp. 30-28, January 1, 2005. [SIA03] Semiconductor Industry Associat ions (SIA), International Technology Roadmap for Semiconductors (ITRS), 2003. [Smi54] C.S. Smith, Piezoresistance Effect in Germanium and Silicon, Physical Review, Vol.94, No.1, pp. 42-49, April 1, 1954. [Tho04a] S.E. Thompson, M. Armstrong, C. Auth, M. Alavi, M. Buehler, R. Chau, S. Cea, T. Ghani, G. Glass, T. Hoffman, C. H. Jan, C. Kenyon, J. Klaus, K. Kuhn, Z. Ma, B. McIntyre, K. Mistry, A. Murthy, B. Obradovic, R. Nagisetty, P. Nguyen, S. Sivakumar, R. Shaheed, L. Shifren, B. Tufts, S. Tyagi, M. Bohr, and Y. El-M ansy, A 90-nm Logic Nanotechnology Featuring Strained-Silicon, IEEE El ectron Device Letters, Vo.25, No.4, pp. 191-193, April 4, 2004. [Tho04b] S.E. Thompson, M. Armstrong, C. Auth, S. Cea, R. Chau, G. Glass, T. Hoffman, J. Klaus, Z. Ma, B. McIntyre, A. Murthy, B. Obradovic, L. Shifren, S. Sivakumar, S. Tyagni, T. Ghani, K. Mistry, M. Bohr, and Y. El-Mansy, A Logic Nanotechnology Featuring Strained-Silicon, IEEE Electron Device Letters, V o.25, No.4, pp. 191-193, April 4, 2004. [Tho04c] S.E. Thompson, G. Sun, K. Wu, J. Lim, and T. Nishida, Key Differences For Process-Induced Uniaxial vs. S ubstrate-Induced Biaxial Stressed Si and GE Channel MOSFETs, IEDM 2004. [Tho04d] S.E. Thompson, No Exponential is Forever, University of Florida, Course Notes, EEL 6935: From Leading Edge CMOS to Nanotechnology Devices, Fall 2004. [Tho05] S.E. Thompson, R. Chau, T. Ghani, K. Mistry, S. Tyagi, and M. Bohr, In Search of Forever, Continued Transi stor Scaling One New Material at a Time, IEEE Transactions on Semiconductor Manufacturing, Vol.18, No.1, pp. 1-11, February 1, 2005. [Tho05b] S.E. Thompson, N. Shah, Harp Presentation to Applied Materials, April 2005. [Uch04] K. Uchida, R. Zednik, C.H. L u, H. Jagannathan, J. McVittie, P.C. McIntyre, and Y. Nishi, Experiment al Study of Biaxial and Uniaxial Strain Effects on Carrier Mobility in Bulk and Ultrathin-body SOI MOSFETs, IEEE 2004.

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123 [Wei04] P. Weiss, Straining For Speed, Science News Online, Vol.165, No.9 pp. 136, February 28, 2004. [Wit93] A. Witvrouw and F. Spaepen, Viscosity and elastic constant of amorphous Si and Ge, Journal of Applied Physics, Vol.74, pp.7144-7161, 1993. [Wol05] S. Wolf, The Top 10 Enabling Silicon Processing Technologies of 2005, Lattice Press, http://www.latticepress.com/spreport1net.html April 2005. [Yan95] E.H. Yang, and S.S. Yang, The Quantitative Determination of the Residual Stress Profile in Oxidized p+ Silicon Films, Sensors and Actuators A, Vo.54, pp. 684-689, 1996. [Yen00] J.Y. Yen and J.G. Hwu, Enhancement of Silicon Oxidation Rate Due to Tensile Mechanical Stress, Applie d Physics Letters, Vol.76, No.14, pp. 1834-1835, April 3, 2000. [Yen01] J.Y. Yen and J.G. Hwu, Stress E ffect on the Kinetics of Silicon Thermal Oxidation, Journal of Applied Physics, Vol.89, No.5, pp.3027-3032, April 2001. [Yer94] D.W. Yergeau, R. W. Dutton, A General OO-PDE Solver for TCAD Applications, 1994, www-tcad.stanford.edu/tcad /pubs/framework/oonski94.pdf April 2005. [Zab01] N. Zabras, Small Strain and Loga rithmic Strain Defin itions, Plane Strain Conditions, Strain Transformations and Linear Elasticity, MAE 612:Spring 2001. [Zan03] N. R. Zangenberg, J. Fage-Ped ersen, J. Lundsgaard Hansen, and A. Nylandsted, Boron and Phosphorus Diffu sion in Strained and Relaxed Si and SiGe, Journal of Applied Physics, Vol. 94, No. 6, pp. 3883-3890, September 15, 2003. [Zha98] X. Zhang, T.Y. Zhang, M.Wong, Y. Zohar, Rapid Thermal Annealing of Polysilicon Thin Films, Journal of Microelectromechanical Systems, Vol.7, No.4, December 1998. [Zie89] O.C. Zienkiewicz and R.L. Taylor Silicon The Finite Element Method Fourth Edition, Volume 1, Basice Formulation and Linear Problems, McGraw-Hill Book Company, London, 1989.

PAGE 139

BIOGRAPHICAL SKETCH Heather Eve Randell was born on April 26, 1979, in Dover, New Jersey. She has a younger brother, Aaron Randell, and two loving parents Susan and Arthur Randell. She received her B.S. in Electrical Engineering in 2003 at the University of Florida. Her hobbies include belly dancing, traveling, sports, outdoor activities, and reading. 124


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APPLICATIONS OF STRESS FROM BORON DOPING AND OTHER
CHALLENGES IN SILICON TECHNOLOGY















By

HEATHER EVE RANDELL


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Heather Eve Randell

































This document is dedicated to my mom, dad, and brother Aaron.















ACKNOWLEDGMENTS

First and foremost, I would like to thank my advisor, Dr. Mark E. Law, for all the

support, encouragement, and assistance he has given me throughout my graduate studies,

and for the opportunity to do research in the SWAMP group. No matter how busy Dr.

Law is, even as the department chairman, he always has the time to discuss research and

sports with his students. During our research conferences to San Francisco, California,

he was a great tour guide, brought his students to excellent restaurants, and had great

recommendations for wineries in Napa Valley. I am also very grateful to Dr. Kevin S.

Jones and Dr. Scott E. Thompson for supporting my research activities and for their

guidance and support as my supervisory committee.

This research could not have been completed without the financial support of the

Semiconductor Research Corporation. Ginny Wiggins always made sure that all of the

SRC Scholars and Fellows were properly accommodated. From IBM, I would like to

thank Rick Wachnik for being a great industry mentor and for all of our stimulating

conversations. I would like to thank Ana Cargile for her making sure that IBM had a

close correspondence with their scholars. I would like to thank the University of

Florida's Department of Electrical and Computer Engineering for funding me in the

beginning of my master's studies.

During the research process, it was beneficial to have previous SWAMPies in

industry to consult as resources. I would like to thank Steve Cea and Hernan Rueda for

the time and support in my research activities. There are also some current SWAMPies









who I would like to specifically thank. Sharon Carter and Teresa Stevens have been

fantastic program assistants at the SWAMP Center. I thank them for all of their

assistance. I am very grateful to Ljubo Radic for providing patience and assistance since

my first day in the group. Whenever I had FLOOPS or coding questions, I could always

turn to Ljubo for help. I will miss being enlightened with all of his online Ph.D. comics

and jokes. I would like to thank Renata Camillo-Castillo and Jeanette Jacques for being

helpful people over the years. They were both a part of the research group before I

joined, and have been valuable resources over the years. I wish Renata the best of luck

with little Naysan Victor, he is such a precious baby boy! I would like to thank Michelle

Phen, Nina Burbure, and Nirav Shah for being available for research related discussions.

I will really miss having Nicole Staszkiewicz around as a great friend and inspiration

over the last two years. I owe a lot of my good health habits to her. I would also like to

thank all the old and new SWAMPies who have been around for Friday lunches, good

conversations, and for creating an enjoyable work environment over the years.

My time at the University would not be complete without the late nights at NEB

crew: Xavier Bellarmine (and research colleague), Sid Pandey, DaeVi Hwang, and Seth

Lakritz. I will try to, but will never forget the many long nights we spent in that building

doing homework and studying for exams. Occasionally we were treated with a beautiful

sunrise. I thank them all for being great colleagues and even better friends. I thank my

roommate, Jennifer Lavery, for all her support during this process, for being a great

friend, and for watching after my kitties whenever I left town.









To my mom, dad, brother Aaron, and the rest of my family, I love them so much.

None of this would be possible without them. I thank them so much for their

unconditional love and support my entire life.

Last, but definitely not least, I am ever grateful to Ryan Smith. He has been an

everlasting source of love, encouragement, and support. I thank him for always believing

in me like I believe in him.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ......... .................................................................................... iv

LIST OF TABLES ......... ...... ............................. ...................... .. x

LIST OF FIGURES ......... ......................... ...... ........ ............ xi

ABSTRACT ........ .............. ............. .. ...... ..................... xiv

CHAPTER

1 IN TR OD U CTION ............................................... .. ......................... ..

1 .1 M o tiv atio n ................. ...... .. .... ............................................................. .. 2
1.2 Stress Induced D effects in Patterned Structures ....................................................4
1.3 Mechanically Induced Channel Stress from Shallow Trench Isolation...............7
1.4 Strained Silicon ................................................................................. 12
1.4.1 Strained Silicon Physics ..................................... ......................... ......... 13
1.4.1.1 Biaxially Strained M OSFETS .....................................................15
1.4.1.2 Uniaxially Strained M OSFETS ............. .......................................18
1.4.2 Stress effects on electrical characteristics .............. ..................................19
1.5 O rg an izatio n ..................................................... ................ 2 1

2 LINEAR ELASTICITY, STRESS, AND STRAIN.................. ............... 23

2 .1 L inear E plastic M materials ............................................................. .....................23
2 .2 T he Stress T ensor .............................. ......................... ... ...... .... ..... ...... 24
2 .3 T he Strain T ensor .............................. ......................... ... ...... .... ..... ...... 26
2 .4 P lan e Stress ...................................... ............................. ................ 2 9
2 .5 P lan e Strain .................. ................................................ ................ 3 0
2.6 The Stress-Strain R relationship ........................................ ......... ............... 31
2 .7 S u m m ary ...................................... ............................... ................ 3 3

3 ST R A IN SO U R C E S ................................................................. ......... ...................34

3.1 O xidation Induced Stress ......................................................................... .... ... 34
3 .2 T h in F ilm Stress............ .............................................................. .. .... .... ... .. 3 7
3.2.1 Therm al M ism atch Stress ...................................................... ..... .......... 37
3 .2 .2 Intrin sic Stress .................... .......................... .... ........ ......... .. .... 38









3.3 Stress from ST I .......... .... ................ .............................. .... ...... 39
3.4 D opant Induced Stress .................... ... ............. ..........................................42
3.5 Dopant Diffusion in Silicon and Silicon Germanium (SiGe)............................45
3 .6 S u m m a ry .............................................................. ....... ........................................4 8

4 SOFTWARE ENHANCEMENTS TO FLOOPS.................................................50

4 .1 F L O O P S B background ................................................................ .....................5 1
4.2 The Finite Elem ent M ethod .................................. .............. .. ..... .. ............. 52
4.2.1 Constructing FEM Elements for the Elastic, Bodyforce, Stress, and
Strain O operators .......................................... .......................... ......... 54
4.2.1.1 Plane Strain A ssum ption ...................................... ............... 56
4.2.1.2 B oundary Conditions.................................... ........................ 57
4.2.2 Forces from B oron D oping...................................... ........ ............... 58
4.2.3 Strain and Stress Com putation ....................................... ............... 60
4.3 Sum m ary ..................................... ................................ ........... 61

5 APPLICATIONS AND COMPARISONS OF TWO-DIMENSIONAL
SIM U LA TION S ........................................ ... .. .. .. ...... .... ....... 63

5.1 Boron-D oped Beam Bending ........................................ .......................... 64
5.1.1 Beam Bending Simulation Results.........................................................66
5.1.2 Effect of Varying Beam Length ................................................66
5.1.3 Effect of Varying Beam W idth ................................. ............... 67
5.1.4 Effect of Varying Dopant Profile ...............................................68
5.2 Multiple Material Layer Bending Simulations................... ................................68
5.3 Channel Stress from Boron Source/Drain Doping ............................................76
5.3.1 Effects of Channel Length Scaling.........................................................77
5.3.2 Effect of Source/Drain Length Scaling ............................................... 78
5.3.3 Effect of Boron Concentration Scaling ................................. ............... 79
5.4 Sum m ary ............................................................... ... .... ......... 80

6 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE
W O R K .........................................................................................................8 3

6.1 Sum m ary and Conclusions ............................................................................83
6.2 Recommendations of Future Work.............................................. ...............86
6.2.1 A dditions to Softw are .............................................. ........................... 86
6.2.2 Stress-Dependent Diffusivity Model...................................................91
6.2.3 STI Induced Stress Modeling ................................................................92
6.2.4 Modeling Silicon at the Elastic/Plastic Limit...........................................94

APPENDIX

A C O D E ...................................................................................... 9 7

B SIM U L A TIO N FILE S ........... ........................................................ ............... 112









L IST O F R E FE R E N C E S ......................................................................... ................... 117

BIOGRAPHICAL SKETCH ............................................................. ..................124
















LIST OF TABLES


Table page

1 Material parameters used for nitride on silicon simulations ..................................70

2 Results summarizing the effect of boron doping on channel stress.......................81
















LIST OF FIGURES


Figure p

1-1 Evolution of transistor minimum feature size and transistor cost vs. year...............3

1-2 Evolution of the M OSFET from 1947 to 2002 ........................................ ..............3

1-3 Dislocation formation at the edge of a nitride strip after solid-phase epitaxial
regrowth (left) before annealing and (right) after annealing............... ................5

1-4 Application of stress to patterned wafers prevented line defects from forming ........6

1-5 Linear variation of mobility enhancement for a bulk NMOS transistors .................

1-6 Dopant profiles, vertical profiles are taken at the gate edge and lateral profiles are
taken 15 nm below the device surface ........................................ ............... 12

1-7 Strained silicon hole mobility enhancement vs. vertical electric field ..................15

1-8: Formation of biaxially strained NM OS transistors ...................................................15

1-9 Critical thickness as a function of Ge composition for SiGe on Si..........................16

1-10 Drain current leakage mechanism in strained silicon films ..................................17

1-11 Subthreshold characteristics of strained silicon MOSFETS with strained silicon
thicknesses above the critical thickness. ...................................... ............... 17

1-12 Stress along the channel in a strained silicon NMOS transistor ...........................18

1-13 Stress along the channel in a strained silicon PMOS transistor............................19

1-14 Calculated and measured threshold voltage shift for NMOS under biaxial and
u n iax ial store ss ..................................................................... .. 2 1

2-1 Linear elastic deformation...................... ...... .............................. 23

2-2 Deformation of a spring with an applied force ................................ ............... 23

2-3 Stress components of an infinitesimal cubic element. ...........................................25

2-4 Normal Strain in the x, y, and z directions..........................................................27









2-5 Example of shear strain in the x-y direction .................................... ............... 28

2-6 P lane stress in a thin film .............................................................. .....................29

2-7 Example of plane strain in the x-y direction ....................................................30

3-1 Forces present in LOCOS form ation .............. ................................. ............... 36

3-2 Top corner of an STI structure ........................................ ........................... 41

3-3 Lattice contraction due to boron atom, and lattice expansion due to germanium
ato m ...............................................................................................4 3

4-1 Triangular element in coordinate system ...................................... ............... 54

4-2 Flowchart to create elem ent stiffness matrix................................. ............... 56

4-3 Verification of boundary conditions ............................................. ............... 57

4-4 Flowchart to solve for forces from boron doping ......................................... 60

4-5 Flowchart to calculate strain and stress ..........................................................61

5-1 A uniform or symmetric doping profile about the center of the cantilever beam
thickness results in no bending........................................... .......................... 65

5-2 The strain from boron causes bending towards the more heavily doped boron side
of the beam (a) downwards bending (b) upwards bending ................................65

5-3 B eam deflection vs. beam length .................................................. .....................67

5-4 Beam deflection vs. beam length for varying beam widths ...................................67

5-5 Beam deflection vs. beam length for varying doping profiles ..............................68

5-6 Nitride curling up at edges due to tensile residual stress ......................................69

5-7 Deflection vs. distance for varying nitride thicknesses................ .............. ....71

5-8 Deflection vs. distance for varying silicon thicknesses.............................71

5-9 Stress.yy from silicon nitride on silicon ............................. .....................72

5-10 Stress.xx from silicon nitride on silicon ............... ...........................................73

5-11 Stress.xy from silicon nitride on silicon ............ .............................................73

5-12 Stress.xx for reflecting bottom and reflecting left and right boundary ...................74









5-13 Stress.yy for reflecting bottom and reflecting left and right boundary ...................75

5-14 Stress.xy for reflecting bottom and reflecting left and right boundary ...................75

5-15 Silicon doped with boron source drain regions general structure .......................77

5-16 The effect of scaling channel length on stress from boron doping ........................78

5-17 The effect of scaling the source/drain length on channel stress for 100 nm and 45
n m ch an n el len gth s ........................................................... ...... ............ .... 7 9

5-18 The effect of scaling the source/drain length on channel stress for 100 nm and 45
nm ch ann el length s ................................................................. ................ 80

6-1 Intrinsic stresses are oriented parallel to the interface on which the film is grown or
deposited (left) planar film, (middle) non-planar film ..........................................89

6-2 Reflecting boundary condition displacement and velocity perpendicular to the
interface is set to zero, but can have vertical movement ......................................90

6-3 Diffusion of B in (left) relaxed Si, tensile Si, and Si0.99Geo.01 and (right) diffusion of
B in strained and relaxed Si0.76G e .24............................................. ............... 92















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

APPLICATIONS OF STRESS FROM BORON DOPING AND OTHER
CHALLENGES IN SILICON TECHNOLOGY

By

Heather Eve Randell

May 2005

Chair: Mark E. Law
Major Department: Electrical and Computer Engineering

Semiconductor device performance has been improving at a dramatic rate due to

scaling to nanometer dimensions. Strain engineering of the substrate has also proven to

increase drive currents in MOSFETS and other advanced devices. An active area of

research and development is focused on intentionally straining the channel of MOSFETS

to enhance mobility. However, increased scaling can also magnify the mechanical forces

that arise during IC fabrication.

Multiple material layers with differing thermal expansion coefficients and

deposited stress levels become closer in proximity to one another and to the device

channel. Shallow trench isolation (STI) can create large stresses due to thermal

mismatch, oxide growth, and trench fill, and the sharp corners at the top and bottom of

the trenches are major contributors to the stress behavior. Stress will influence dopant

and defect behavior in unexpected ways. It has been predicted that the proper stress can

double the solubility of dopants such as boron in silicon. Thus, accurate process models









need to be developed to incorporate both the intentional and unintentional stress sources

in order to maximize device performance. This work focuses on the unintentional stress

source from dopant incorporation.

The model that FLorida Object Oriented Device and Process Simulator (FLOOPS)

currently utilizes to compute stress and strain was developed for LOCOS processes,

which are largely no longer employed. In addition, these computations are decoupled

from the solution of the diffusion equations. Most of the materials used in silicon

processing can be modeled as simple elastic materials, which makes process modeling

easier. New models must be developed to more accurately calculate the stresses in the

silicon substrate.

To achieve this goal, new software operators were developed in FLOOPS to

calculate the displacements and stresses in the silicon substrate due to boron doping. This

elastic stress solver was integrated into the Alagator scripting language, and the

simulation results provide a more accurate description of the stress evolution. Part of the

future work is to enable the elastic stress solver to be coupled to defect and dopant

evolution.














CHAPTER 1
INTRODUCTION

Strain engineering has become a key component of emerging technologies,

however due to the great complexity and cost in IC fabrication, it is difficult to physically

develop new processes. Technology Computer Aided Design (TCAD) tools are

invaluable for shortening new technology development and for optimizing existing

processes [Cea96]. Front-end process modeling of stress effects from oxidation, thermal

mismatch, and intrinsic stress have been demonstrated over the last 15 years, beginning

with 2D and 3D modeling of oxide growth for viscous and viscoelastic materials [Cea96].

Recently stress simulations for strained silicon have been performed to understand the

effects of strain on device mobility and drive current enhancements, and threshold

voltage shifts [Lim04, Tho04a, Tho04c, Uch04].

While applying the proper strain has clearly demonstrated enhancements in

transistor performance, the effects of mechanical stress can also degrade device

characteristics. In the front-end process, shallow trench isolation (STI) is a major source

of stress in the MOSFET channel. The proximity and amount of the stress in the silicon

substrate limits the density of ICs, and when the too much stress is exerted in the silicon,

it will yield by releasing dislocations that lead to leakage currents and degraded device

performance. Thus, having an in depth understanding of how stress affects the

semiconductor fabrication processes is critical.

As we enter the nanometer regime, stress from standard process steps such as

source/drain doping introduce significant stress in the channel of MOSFETs. In PMOS









devices, the tensile stress generated in the channel from source/drain boron doping is

nearing values large enough to compensate the engineered strain engineered intended for

performance enhancement.

This focus of this chapter is to provide a survey of the existing literature on stress

applications in silicon technology. Section 1.1 provides a brief history of the transistor

and discusses scaling trends over the past 50 years. Section 1.2 presents work that

explored the effects of stress on defect evolution and regrowth velocities in patterned

structures. Section 1.3 discusses mechanically induced channel stress from shallow trench

isolation structures (STI). Section 1.4 introduces strained silicon and demonstrates

various methods of applying stress to enhance device performance. Section 1.5 will

provide a brief summary of each chapter of the thesis.

1.1 Motivation

The semiconductor industry is on an eternal hunt for methods to continue Moore's

Law. Since the invention of the transistor in 1947 by William Shockley, John Bardeen,

and Walter Brattain, and the fabrication of the first Metal Oxide Semiconductor Field

Effect Transistor (MOSFET) at Bell Labs in 1960, much innovation in the forms of

transistor scaling and new materials has led to the recent MOSFET [Tho04a,Tho05]. In

1965, Gordon Moore proposed that the number of transistors on an integrated circuit (IC)

will approximately double every 2 years [Moo65]. Since then, much work in the area of

transistor scaling has been accomplished. The goal of technology scaling is to create

faster, denser, low power circuits per chip for the same amount of money. For long

channel devices, dimensions and supply voltages scaled by the same factor in order to

maintain a constant electric field. The next trend in scaling was to maintain a fixed supply

voltage and scale only device dimensions. Modern short channel devices scale both the









supply voltage and device dimensions by different factors. Moore's prediction has held

over the last 4 decades and will continue as long as the price of a transistor continues to

drop in price [Tho04a]. The scaling of minimum feature size over the years and the

evolution of the transistor is illustrated in Figures 1-1 and 1-2.


1970 1980 1990 2000 2010 2020
Figure 1-1: Evolution of transistor minimum feature size and transistor cost vs. year
[Tho04a]


Figure 1-2: Evolution of the MOSFET from 1947 to 2002 [Pbs47].
Figure 1-2: Evolution of the MOSFET from 1947 to 2002 [Pbs47].









1.2 Stress Induced Defects in Patterned Structures

Thin films such as silicon nitride, silicon dioxide, and polysilicon are frequently

encountered in device fabrication; these films contain intrinsic stresses as a result of the

deposition process. Continuous films deposited over the entire silicon substrate produce

low levels of stress in the silicon because the substrate is generally a few orders of

magnitude thicker than the film. Large stresses occur when films are not planar or have

discontinuities, and silicon substrate yields by forming dislocations.

In MOSFET fabrication, high dose ion-implantation is used to accurately dope the

source/drain regions to desired junction depths. The implanted region becomes

amorphized and upon subsequent annealing dislocations form at the original amorphous-

crystalline interface. Dislocations have been known to affect dopant redistribution during

thermal cycling by capturing and emitting point defects, leading to variations in junction

depths. Calculations of the stress around a dislocation loop with observed density and

size shows that the pressure around the loop layer can locally be on the order of 109

dyne/cm2. This value is comparable to stresses induced from patterned nitride films and

isolation structures [Par95]. Thus, the control and understanding of dislocation loops

formation is critical.

The effect of multiple nitride stripes on stress and dislocation loop formation was

investigated by Chaudhry. His work demonstrated that the stress in the silicon substrate

is a strong function of the nitride stripe thickness and width. Narrow stripes resulted in

higher levels of stress than significantly wider stripes. Large shear stresses developed at

the nitride/silicon interface which can lead to slip in silicon. Hu reported the critical

shear stress slip in silicon to be 3x107 dyne/cm2. These dislocations lie on the { 111

plane and glide in the [110] direction [Fah92]. Dislocations in regions of shear stress









higher than this value will glide. Placing the nitride stripes in closer proximity offset the

shear stress components. The tensile component of one strip offset the compressive

component of the adjacent strip [Cha96].

Ross demonstrated the effect of stress on defect formation at the mask edge of

patterned structures and on the regrowth velocity [Ros03, Ros04]. Line and square

structures were formed by depositing 80A of SiO2 and 1540A of nitride on silicon. An

amorphizing silicon implant with a dose of lx1015 atoms/cm2 at 40keV was performed

after patterning the wafer, and samples were anneals between 550C and 750C. Cross-

sectional Transmission Electron Microscopy (XTEM) samples were prepared at different

stages of the solid-phase epitaxial regrowth process to observe the formation of half-loop

dislocations at the mask edge. The defects only occurred around the line edges and not

the square edges. When the square structures were etched and re-annealed, defects

formed around the mask edge. Dislocation loops migrate to regions of tension to relieve

stress, and FLOOPS simulations confirmed a tensile pocket at the nitride/silicon interface

where the defects formed. It was concluded that the stress from the nitride square

structure suppressed the defect formation.


Figure 1-3: Dislocation formation at the edge of a nitride strip after solid-phase epitaxial
regrowth (left) before annealing and (right) after annealing.









Low defects densities are required in the areas where devices are fabricated on

wafers because they lead to leakage current and performance degradation. In a study

performed by Phen [Phe04], a wafer bending study was performed in which the patterned

wafers aforementioned were bent to a stress of 86 MPa of tension and annealed at 7500C

for five minutes. Transmission electron microscopy micrographs confirmed that the

tensile mechanically-induced stress removed defects from the samples. This is further

proof that suggests stress affects defect formation and is worthwhile investigating.










Figure 1-4: Application of stress to patterned wafers prevented line defects from forming
[Phe04].

Isolation structures such as deep and shallow trench isolation are also known to

generate dislocations. After the formation of isolation structures, residual stresses are

present in the silicon and trench area; however they are not significant enough to generate

dislocations. These stresses will be addressed in Chapter III. After processing steps such

as ion implantation, point defects are introduced into the silicon and can serve as nuclei

for dislocation formation. Once the dislocations form, the stress in the silicon from the

trench formation can cause the dislocations to glide. The energy for dislocation glide is

much less than the energy for dislocation formation, thus the glide process can even

occur in materials with moderate stress [Fah92].

Fahey et al. observed the formation of dislocations in a deep trench isolation

structure filled with poly for a bipolar process. A phosphorus implant was performed to









make contact with the deep subcollector. After annealing to activate the dopant, defects

formed near the corners of the structure. The defects did not form in similar patterned

structures that did not receive the implant. In addition, no defects formed in unpatterned

wafers that received identical implantation implants and anneals. This phenomenon was

further investigated for a DRAM trench capacitor process, in which a deep trench filled

with poly, is fabricated next to a PMOS device. The source and drain are doped with

boron, and after the annealing step, gliding dislocations formed next to the trench on the

{ 111 } plane and glided in the [110] direction towards the PMOS transistor. Again, the

defects did not form in identical structures with no implantation. This study concluded

that the ion implantation can reduce the stress in silicon because it provides nuclei for

dislocations, and the dislocations glide due to the stress from forming the isolation

structures. However, if the dislocations glide out of the implanted area, they could

become deleterious to device performance [Fah92].

1.3 Mechanically Induced Channel Stress from Shallow Trench Isolation (STI)

Experimental data and simulations show that while the stress introduced by the STI

formation enhances PMOS drive current, it also demonstrates sensitivity to layout for

NMOS transistors [Jeo03, Gal04, Sco99, She05]. The STI process introduces a

compressive stress in the channel direction, which enhances hole mobility. The physics

behind this improvement in carrier mobility are discussed in Section 1.4. Scott et al.

observed a mobility reduction in NMOS devices due to stress from isolation trenches.

The proximity of the gate to the trench edge and the active area were critical factors that

made NMOS devices sensitive to layout. Linear current was reduced by as much as 13%

for diffusion lengths less than 2 um, and the extracted mobilities agreed with

piezoresistance calculations [Sco99]. Current reduction was also observed as the width









of the NMOS devices were decreased from 20 um to 0.5 um, where PMOS devices were

relatively insensitive to the width variation. Jeon et al. investigated the effects of

mechanical stress from STI formation on silicon-on-insulator wafers for a silicon

thickness of 50 nm and 90 nm. For the 50 nm wafers, he observed a 13.5% current

degradation in NMOS and a 23% current increase in PMOS current as the gate-edge-to-

STI distances were decreased from 2.69 um to 0.26 um [Jeo03]. Thus, it is critical to

compute the stresses throughout the IC fabrication process, and use those values as

parameters to for future technology development.

Gallon et al. performed wafer bending experiments to investigate the effect of STI

mechanical stress on 0.13 um bulk and SOI transistors. For both bulk and SOI devices,

an increase in PMOS and reduction in NMOS current was observed as the gate-to-STI

distance was decreased from 10 um to 0.34 um, which was in accordance with the

findings of both Scott and Jeon. For small stresses ranging from 10-1301 MPa, a linear

change in mobility enhancement/reduction was observed for NMOS and PMOS bulk

devices.












--
L-WffiW t











Figure 1-5: Linear variation of mobility enhancement for a bulk NMOS transistors
[Gal04].
[Gal04] .









Lower values of stress were applied because silicon yields for a mechanical stress

between 175-220 MPa. The modeling of silicon in the plastic regime will be addressed in

the future work Chapter IV. For both NMOS and PMOS devices, higher stresses were

observed in SOI vs. bulk transistors. This is because the silicon can reoxidize at the

buried-oxide/silicon interface at the STI edge, and the bending of the silicon adds to the

compressive stress in the channel from the STI formation [Gal04].

Gallon et al proposed that the enhanced performance for SOI PMOS and decreased

performance for NMOS devices is a result of the implantation, amorphization,

recrystallization process rather than from bandgap effects and reduction in conductivity

effective masses. Amorphous silicon relaxes by viscous flow under compressive stress

with a temperature dependence, which is driven by a decrease in concentration of defects

[Wit93]. When fabricating NMOS transistors, an arsenic implant of 2x1015/cm2 created

an amorphous layer approximately 50 nm below the surface. Simulations demonstrated

that due to the compressive stress from the STI, the amorphous layer was able to relax,

causing a reduction of internal stress from -1650 GPa to -750 MPa [Gal04]. The boron

implant for PMOS transistors however was non-amorphizing, and no initial stress

relaxation occurred. Bulk devices on the contrary did not show significant relaxation

after recrystallization because the stress from the STI formation is not large enough to

relax the amorphous layer (-400 MPa). As a result, bulk NMOS and PMOS transistors

retain their initial stress levels.

Strain relaxation of a SiGe layer upon regrowth was also observed by Crosby

[Cro04]. Fifty nm of strained silicon was grown on top of a graded SiGe buffer layer up

to 30% germanium incorporation. High Resolution X-ray Rocking Curves confirmed









that the strain varied from 0-2.4% throughout the structure. Low energy implants of 12

keV, creating at 30 nm amorphous layer, and high energy implants of 60 keV, creating a

100 nm amorphous layer were implanted with 1x1015/cm2 Si+ into the SiGe structure.

Both structures were annealed at 6000C and 6750C for up to 30 minutes. Similar to and

STI structure, SiGe creates a compressive stress due to the increased lattice constant of

germanium compared to silicon. For germanium contents exceeding a critical thickness,

the strained silicon layer will relax by emitting misfit dislocations at the Si/SiGe

interface. This will be described in more detail in Section 1.4. The strain relaxation

occurred in the structures for both implant conditions, but did not occur in unimplanted

samples. These finding further support the work of Gallon et al. suggesting that

compressive stress causes stress relaxation after amorphous regrowth.

Cowern et al. developed an Arrhenius relationship for dopant diffusion in a

biaxially strained SiGe layer to be [Cow94]:


Ds = DI exp[ ] (1-1)
kT

where Ds is the dopant diffusivity under strain, DI is the dopant diffusivity without strain,

s is the biaxial strain in the plane of the SiGe layer, and Q'is the activation energy per

strain. Similar to this relationship, Sheu et al. developed a sophisticated stress-dependent

dopant diffusivity model to calculate the mechanical stress from STI formation. The

model was calibrated to account for implant damage, dopant-point defect pairing

diffusion, silicon-oxide dopant segregation, oxidation-enhanced diffusion models, dopant

clustering models, dopant-defect clustering models, and intrinsic diffusion models. The

relationship for dopant diffusivity due to STI mechanical stress is [She05]:










Ds (T, x, y) = D, (T) exp[- AEs (T, xy) ] (1-2)
kT

where Ds is the dopant diffusivity under strain, Di is the dopant diffusivity without strain,

and AEs is the activation energy per volume change ratio (VCR) depending on dopant

species and temperature (T). The VCR is the volume change ratio due to stress, and for

small applied stresses, the VCR can be approximated as [She05]:

V, (T, x, y) s E, (T, x, y) E (T, x, y) + E (T, x, y)+ E (1-3)

where Exx is the strain in the direction of the channel, eyy is the strain perpendicular to the

channel, and ezz is the strain in the channel width direction. For simulations, a wide

width was chosen, so Ez is zero. Stress simulations involved the STI and other main

process steps, and the model was tested for MOSFETS with varying gate and active

lengths. Unsurprisingly, the compressive stress in the channel direction increased as the

active area decreased. Tensile stress was also observed in the bulk direction with

magnitudes significantly less than in the channel direction. For active areas = 0.6 um, the

stress and strain magnitudes were simulated to be -5x109 dyne/cm2 and -0.4%

respectively, which is equated to the strain from incorporating 10% germanium in silicon

[Cow94, Gal04]. It was concluded that the dopant distributions were properly computed

in the operating region of the device because device simulations matched subthreshold

NMOS I-V experimental data curves. Boron, a known interstitial diffuser, exhibited

retarded diffusion as a result of the compressive STI stress.




















"pth (~nm[ depul ';nrrq
1 a 6 --- b .. ----.---n--em l 1T-----'-

Y10 -r 1 (I dM

.c "c i! e e 1,',-lm
10 l.'
a AlptjB rn

ai i









0 0 1 0 0 30 30 63 ED
dil i Otspili i ( d (nmt r Dopi W ni In.rn
(aI) al dOt r id I ft It) .3p Wtalhl -1.dul-s prufO II r J

X.,Owi.i. MFEm T XA-rt'-ri 2AKlFETwn










Figure 1-6: Dopant profiles, vertical profiles are taken at the gate edge and lateral profiles
are taken 15 nm below the device surface [She05].

Threshold voltage increased with decreasing NMOS active areas, while PMOS

exhibited negligible voltage shift to the decreasing active area, which was also verified by
experimental data. This will be further explored in Section 1.4.


1.4 Strained Silicon

Two main factors that control the switching speed of an ideal transistor are the












channel length and the speed at which carriers move through the semiconductor material.
lo II -'




























and is described by the strained silicon concept. Strained silicon can be applied biaxially
-a -w -9 W a -3Do 1 D2 Sa a) w a -so -o9-s-D -so- -i o ip ;2 o 6 SO
d tain Iflf gale q4nte (no) dtrtaes lrni ^* ntlhif Inrt*l

..,.v %-o frl nMO$EtTS )'gIIIFET












Figuor uniaxially to improfies, vertical profiles are taken at the gate edge and lateral profiles














through mobility enhancements. An important and promising feature of strained silicon
are taken 15 nm below the device surface [SheOS].














for future technology nodes is that it increases device performance with decreasing NMOS active areas, while PMOS

exhibited negligible voltage shift to the decreasing the off-state leakage current. This is donealso verified by increasing the
experimental data. This will be further explored in Section 1.4.

1.4 Strained Silicon

Two main factors that control the switching speed of an ideal transistor are the

channel length and the speed at which carriers move through the semiconductor material.

In this section, the speed of the carrier through the semiconductor material is discussed,

and is described by the strained silicon concept. Strained silicon can be applied biaxially

or uniaxially to improve the drive currents in MOSFETs and other advanced devices

through mobility enhancements. An important and promising feature of strained silicon

for future technology nodes is that it increases device performance without decreasing the

channel length or increasing the off-state leakage current. This is done by increasing the









carrier mobility through the channel by reducing the conductivity effective mass, and/or

scattering rate [Moh04].

1.4.1 Strained Silicon Physics

Carrier mobility ([t) in semiconductors can be expressed as a linear relationship

between the velocity (v) and the external electric field (E) [Cro04]:

v = E (1-1)

The mobility is also function of transport scattering time (z) and effective mass (m*):


/U =e.- (1-2)
m

where e is the electron charge. Both effective mass and scattering reductions have

demonstrated mobility enhancements for electrons, while only effective mass reduction is

necessary for hole mobility enhancement. This is because the valence band splits less

than the conduction band under strain [Moh04].

For electron transport, the conduction band of silicon is sixfold degenerate. When

strain is applied, the degeneracy is lifted and lowest energy level of the band is split.

Two states drop to a lower energy level and the remaining four states occupy a higher

energy level. As a result of the band splitting, electron scattering is reduced, and the

average velocity in the conduction direction increases. The combination of increasing the

average distance an electron travels before it is knocked off course, and reducing the

effective mass results in electron mobility enhancements [Lim04, Tho04a, Tho05,

Tho04c]

Hole mobility transport is more complex. The valence band consists of three bands

that are all centered at the gamma point, and from lowest to highest energies are the

heavy-hole, light-hole, and spin-orbit bands. When strain is applied, the degeneracy is









lifted between the light and heavy hole bands, and holes fill the "light hole"-like band,

thus reducing the effective mass and increasing hole mobility [Moh04]. Under no strain,

the bands have mirror symmetry about the k=0 point. Applying a uniaxial or biaxial

strain in the [110] direction results in severe band warping. For biaxial tensile strain, the

warping remains symmetrical; meaning that the electrons repopulate the lowest energy

levels equally. However for uniaxial strain, the warpage is no longer mirror symmetrical

and the holes will still repopulate the lowest energy states first. The breaking of the

symmetry is caused by a shear stress component that does not affect the conduction band

and is not present for biaxial stress [Gha04].

A key advantage to uniaxial compressive strain for PMOS devices is that the hole

mobility enhancements do not degrade at high vertical fields. This is because the large

out-of-plane mass causes further band splitting with confinement in the inversion layer of

a MOSFET [Fis03]. On the contrary, biaxial stress does not maintain the hole mobility

enhancements at higher vertical fields because unlike uniaxial stress, at high fields the

bands splitting reduces because of the lighter out-of-plane mass. At approximately 1

MV/cm, the mobility decreases to that of the universal hole mobility, and all gains from

straining are lost [Gha05, Tho04a, Tho05, Tho04c]. The mobility vs. effective field data

for biaxial and different applications of uniaxial stress are shown below. Note that only

the uniaxial stress applied by silicon germanium in the source/drain region resulted in

mobility enhancements at high vertical fields.










140
Universal Biaxial Uriaxial SiGe SD
Mobility
t 120 Mo2lity 2$MPa Longitudinal
SUnlaxlal compression
Siwafer bending


go
0 e I Blaxlal dala Rim 1995, 20)02
60 L Uniexial SiGa S/D. Thompsan 2002
i Uniaxial wafer ibenlinn, this work

40
0.0 2.0 4.0 6.0 8.0 1.0 1.2
Effective Field / (MVcrn)
Figure 1-7: Strained silicon hole mobility enhancement vs. vertical electric field (wafer
bending, SiGe S/D, biaxial substrate stress [Tho04c].

1.4.1.1 Biaxially Strained MOSFETS

Applying stress in the channel region of a device allows for higher carrier mobility.

Tensile strain increases the interatomic distances in the silicon crystal, thus increasing the

mobility of electrons. The same effect is observed with holes and compressive strain.

Although this method of introducing strain enhances both hole and electron mobility, a

large mobility loss is evident at high vertical fields [Tho05].

Tensile strain

S D


p Si Substrate
Figure 1-8: Formation of biaxially strained NMOS transistor







16


Biaxial strain occurs in both the x and y directions of the deposited silicon layer.

The formation of biaxially strained NMOS transistors begins with a silicon wafer and a

grown SiGe graded buffer layer. The buffer layer is formed by linearly increasing the Ge

content as the layer thickness is increased. As the Ge content becomes larger, relaxation

occurs in the layer by generating misfit dislocations. When a lattice constant

approximately 1% greater than that of silicon is formed, a relaxed Sil-xGex is grown on

top of the graded layer to set the lattice constant of the material [Tho04a]. Finally, a

defect-free thin silicon layer is grown on top of the relaxed structure and the layer

remains strained as long as the thickness is below a critical value [Cro04, Peo85]. The

critical thickness decreases as the lattice mismatch (% Ge) increases. This is illustrated in

Figure 1-9 below.


t SFIT (%)
0 2 3 4



pm -,--, MPECANICA*L EQUILIBRIUM THEOiR
\ Mo thews and 8lakesleel
-- von der Merwe
SPWfSENT WORK
.04





t \ \







0 02 04 06 08 10
GERMANIUM FRACTION X
Figure 1-9: Critical thickness as a function of Ge composition for SiGe on Si [Peo85].

Fiorenza et al. studied strained silicon MOSFETS with silicon thicknesses below

and above the critical thickness value to understand the effects of exceeding the critical







17


thickness on device performance [Fio04]. Although increasing the strained silicon

thickness far beyond its critical value had little effect on mobility loss, a significant off-

state leakage current was observed, which is deleterious to device performance. The

leakage current was attributed to misfit dislocations that form at the silicon/SiGe interface

and can cross between the MOSFET source and drain. The increased leakage was only

observed when transistor gate lengths were less than the diffusion lengths.


Misfit
Strained i
SiliconDislocation
Silicon





SiGe

Figure 1-10: Drain current leakage mechanism in strained silicon films with misfit
dislocations [Fio04].

SV =2.5 V
L =0.8 Prn
0.1 LW = 200 pm
0.01
1 E-9 t increasing
E 1E-4
1 E-5
1O E-6 ta =100nm
St = 20 nm
IE-7
S1E-8ta = 12.5 nr
c 1E-9
1 E-10
1E-1 1 Drain current is line
1E-12 O Source current is squares
1E-13
-2 -1 0 1 2
Gate Voltage C')

Figure 1-11: Subthreshold characteristics of strained silicon MOSFETS with strained
silicon thicknesses above the critical thickness. Devices above the critical
thickness (14.5 nm, 20 nm, and 100 nm) show increased off-state leakage
current [Fio04].










1.4.1.2 Uniaxially Strained MOSFETS

The Intel Corporation recently developed a process flow that uses two different

approaches to introduce uniaxial channel strain in both NMOS and PMOS devices. With

this new process, strain is independently introduced into the channel of both devices with

minimal integration challenges or major increased in manufacturing cost. NMOS devices

are fabricated with the standard process flow, and at the end of the process, a highly

tensile nitride capping layer is deposited over the source, gate and drain regions. The

high tensile stress, approximately 1.8x1010 dyne/cm2, in the capping layer creates

compressive stress in the source and drain regions, which in turn induces longitudinal

tensile stress and out of plane compressive stress in the channel area. [Tho04a].






4.2saD0
t. +0
-1.96+ S










S .42 4. 02 M
Figure 1-12: Stress along the channel in a strained silicon NMOS transistor [ISE04]

Uniaxial strain is introduced into PMOS transistors by depositing Sil-xGex in a

recessed etched trench (source and drain regions) on each side of the channel. Boron has

a higher solid solubility limit in silicon germanium, thus allowing for higher boron

activation [Sad02]. Since the Sil-xGex has a larger lattice constant than Si, it compresses









the channel from both sides and induces compressive stress in the channel region. For a

PMOS device of Si0.83Geo.17 source/drain regions, 1.4 GPa of compressive stress

simulation results show approximately 500 MPa of uniaxial compression in the channel

[Tho05]. This technique of applying strain in the channel however is only applicable for

nanometer channel lengths; in longer devices the compressive force would not have

penetrated far enough to strain the entire channel. A large benefit to introducing strain in

this technique is that integration issues are kept to a minimum because the strain is

applied late in the process flow. Because the Sil-xGex is confined to the source/drain

regions, self-heating and leakage currents are not observed [ISE04]. Compressive stress

from is shallow trench isolation structures has also demonstrated enhancements in PMOS

device performance, which was discussed above in Section 1.3.

C. (Pal
-I .OE+09

03 .-0 -7.5E- 0 0-3










G,2
-0.3 --. i. 2 0 0. I 0.3
Figure 1-13: Stress along the channel in a strained silicon PMOS transistor [ISE04]

1.4.2 Stress effects on electrical characteristics

In 1954, Charles S. Smith discovered that bulk silicon and germanium demonstrate

a change in electrical resistance with strain [Smi54]. This is known as the piezoresistive

effect, and it can be used as a strain measurement tool for in strained silicon devices.









Since there is a lack of data for many thin film materials used in semiconductor

processing, the bulk coefficients are used for simplicity. For small strains,

piezoresistance varies linearly with stress, and by analyzing the piezoresistive

coefficients, it was observed that the most effective stress for PMOS devices is

longitudinal compressive stress, but is longitudinal tensile and out-of-plane compressive

for NMOS devices [Tho04a].

Thompson et al. studied mobility enhancements in MOSFETs at low strain and

high vertical electric field [Tho04a]. For PMOS devices, the piezoresistance coefficients

predicted that for 500 MPa of stress, a 40% increase in hole mobility for uniaxial

compressive stress, and a 5% decrease in hole mobility for biaxial tensile stress resulted.

Longitudinal uniaxial compressive strain introduced by Si0.83Geo.17 in the source/drain of

a PMOS increased the hole mobility by 50% for a 45 nm gate length, and the NMOS

devices showed a 10% mobility enhancement from a 75 nm capping layer [Tho04a]. The

electron mobility enhancement is less than the PMOS because the strain induced from the

nitride capping layer is less than the strain from growing Si0.83Geo.17 into the source/drain

regions. However, the strain from the capping layer increases as the nitride capping layer

is increased.

Wafer bending techniques performed by Uchida et al. investigated the hole and

electron mobility enhancement in biaxial and uniaxial stressed bulk and SOI MOSFETs.

For both carriers, the appropriate uniaxial stress showed the largest enhancements in the

[110] direction at high vertical fields. For 3.5 nm SOI NMOS devices, the electron

mobility enhancements under biaxial and uniaxial strains were almost equivalent. In









addition, the electron mobility enhancement in the [110] direction under uniaxial tensile

strain was comparable in both SOI and bulk devices.

Lim et al. and Thompson et al. demonstrated through wafer bending, a favorably

small threshold voltage shift was found for uniaxially strained NMOS devices. Biaxially

strained NMOS devices exhibited a four times greater threshold voltage shift than

uniaxially strained silicon NMOS transistors. Simulations show that when correcting for

the large biaxial threshold voltage shift, much of the performance gain is lost [Lim04].

The small threshold shift for uniaxial strain, however, is a result of lower bandgap

narrowing and the strain of the n+ poly gate [Tho04c].

-10D
Ulieial wavfwer banding rww.3







UStrn ll


Figure 1-14: Calculated and measured threshold voltage shift for NMOS under biaxial
and uniaxial stress (4x shift for biaxial stress) [Lim04, Tho04c].

1.5 Organization

The purpose of this work is to understand the unintentional stress sources that arise

during integrated circuit (IC) fabrication process and provide more accurate process

models. By understanding how the stresses affect device operation, the stresses and

strains can be engineered to improve device performance and avoid high leakage

currents. In this work, C++ code was implemented in Florida Object Oriented Processing

Simulator (FLOOPS) to study stress in the silicon substrate due to boron doping and
Simulator (FLOOPS) to study stress in the silicon substrate due to boron doping and









nitride deposition. Simulations were performed for software validation and results were

presented.

This chapter provided a literature review describing many applications of stress in

silicon technology. In the first section, stress induced dislocations were discussed for

various structures. Next, the effects of STI stress on device performance were addressed.

In the following section, the strained silicon concept was introduced and the effects of the

advantageous and unintentional stresses on device performance were presented. In

Chapter II, the concepts of stress and strain are defined, examples of the normal and shear

components are given, and a stress-strain relationship for linear elastic materials also

described. In Chapter III, various stress and strain sources that arise during the

semiconductor fabrication process are addressed, including sources from LOCOS, STI,

thin film deposition, and dopant induced strains. Chapter IV focuses on the software

implementation in FLOOPS to calculate the displacement and stress in the silicon

substrate due to boron doping and nitride deposition. Chapter V provides applications

and results of the displacements and stresses computed from beam bending, nitride

deposition, and PMOS-like structure simulations. Chapter VI provides a summary and

recommendations for future work.














CHAPTER 2
LINEAR ELASTICITY, STRESS, AND STRAIN

2.1 Linear Elastic Materials

Linear elasticity is a property that all materials possess to an extent. Solids respond

to externally applied loads by developing internal forces, and stress is the distribution of

those forces over a unit area. A solid deforms from its natural state due to stress, and if

the deformation is small enough, the solid will return to its original shape once the load

has been removed. The relationship between stress and strain for linear elastic materials

is shown in Figure 2-1.











Figure 2-1: Linear elastic deformation

A simple example to illustrate linear elasticity is an ideal spring. One end of the spring is

fixed and the other end is free to move.








x Ax

Figure 2-2: Deformation of a spring with an applied force









When an external force is applied to the spring, an equal but opposite counter force

is generated. A deformation Ax, or strain results due to the force applied. The internal

force and deformation is related by f = kx, wherefis the force, x is the length of the

spring, and k is the stiffness of the spring. Stiffness is a measure of how resistant the

body is to external forces. If too much stress is applied, the spring will not return to its

original position and will become plastically deformed. A measure of how much stress

can be applied before plastic deformation occurs is called the yield strength.

Under the temperatures ranges and processing conditions that will be considered in

this work, silicon acts as a linear elastic material. Understanding how stress affects the

fabrication process is very important because proper strain engineering can enhance

device performance, while unintentional strain can be deleterious. In this section, stress,

strain, plane stress, plane strain, and the stress-strain relationship will be discussed.

2.2 The Stress Tensor

Stress (o) is defined as the force per unit area acting on the surface of a solid.
AF
c = lim (2-1)

Stresses have two components, normal and shear forces. Normal forces act perpendicular

to a face and tend to stretch or compress a body, while shear forces (z) act along the face

of a body and exhibit a "tearing" motion. Tensile forces are positive, while compressive

forces are negative. An example illustrating a normal force is a weight hanging from the

bottom of a cube by a string. The force of the weight acts perpendicular to the bottom of

the cube and pulls the box downward to create a tensile force. To illustrate shear stress

imagine a metal rod permanently attached by a bolt to a sheet of metal. If the rod was

pushed parallel to the metal sheet, the ripping forces that develop in the bolt represent the

shear stresses.









To illustrate all of the stress components, consider an infinitesimal cube with

normal (oa) and shear (Ty) stress components stress components in the x, y, and z

directions. The first subscript identifies the face on which the stress is acting, and the

second subscript identifies the direction.


Txy
Txz
O'xx /- ^

T Tyz

+Z z Tyx
Tzx




+X

Figure 2-3: Stress components of an infinitesimal cubic element.

For example, to evaluate the stress acting on the y-plane of the cube in figure 2-3, with

AA = AxAz
area A' the stress vector T on that plane is:

T= r- x + c- y + rz z, (2-2)

where x, y, and z are unit vectors in the x, y, and z directions, and the normal and shear

stress components acting on the y-plane are:


S= lim AF (2-3)
yx AA~ xAA



AF
- = lim (2-4)
AAyo, 0y












Z li AF (2-5)
r = lim -
y AAO AAy


Nine stress components from three planes are needed to describe the stress state at an

arbitrary point on the continuous body. The grouping of these terms in matrix form is

called the stress tensor oij:


xx xy xz

S T x y yz Z (2-6)

I- zx T zy 7 zz


In static equilibrium, some of the shear stresses are equal zxy= zyx, zyz= Tzy, and Txz=

Tzx, and by symmetry, the stress matrix can be reduced to six components:



O'yy
CTY
O tota zz (2-7)



Z-
*xy
Tyz



2.3 The Strain Tensor

When forces are applied to a solid body it will deform. Strain (e) is a unitless

parameter that quantifies the amount of deformation, and is equal to a change in length in

a given direction divided by the initial length. To illustrate normal strain, consider an

infinitesimal element with possible displacements u(x,y,z), v(x,y.z), and w(x,y,z). The

variables u, v, andw are the displacements in the x, y, and z directions respectively.

Assume the element in figure 2-4 experiences deformation in all three directions, and the

dashed lines represent the element after deformation. The change in length in the x and z










directions are negative, which represents a compressive, or negative strain. The change

in length in the y direction is positive, which represents a tensile or positive strain.

dz+dw/dz
dz

dx+du/dx





dy dy+dv/dy
dy


+z + +y
Figure 2-4: Normal strain in the x, y, and z directions. du/dx<0, dv/dy>0, and dw/dz<0

Silicon, like all linear elastic materials, becomes narrower in the cross section when

it is stretched. A measure of the transverse to longitudinal strain is know as Poisson's

ratio, u, where a positive ratio is considered tensile and a negative ratio is considered

compressive.


U = transverse (2-8)
longitudinal

Shear strain (y) is the displacement in x direction with respect to a change in the length of

y, plus the displacement in they direction with respect to a change in length of x:

Au Auy au au
Y7 = ( + Y)=( X+ Y) (2-9)
Ay Ax ay dx

To illustrate shear strain, consider the differential element experiencing deformation in

the x andy directions where Oland 62 are the change in angle from the original shape, and

Aux and Auy are the direction of the displacements.


















Ax 01

Figure 2-5: Example of shear strain in the x-y direction

For small displacements, referred to as micro-strain (ts), the shear strain can be

approximated as the angle itself, tan 0 0 and the total strain is equal to the sum of the

angles 01 and 02. [SenOl] To illustrate the strain components, consider the cube from

figure 2-4. There are nine normal and shear strain components that are related to the

displacements by:

8u ov Ou Ow Ou
..XX Yxy + Yxz +-
ax Ox xay a +z
8u 8v 8v Qw vw
uy = -+- E= Y = + (2-10)
y Ox oy y z
ou Ow ov Ow Ow
2zx =-+ Yzy =-+ Ezz = -
dz a aOz Oy Oz

Combining these terms in matrix is called the strain tensor, sij:

= y/, Y,
S, = Y y 2yz (2-11)
Y- rZ y 2 = C

In static equilibrium, the shear components are equal:

1 O8u 8v 1 ov Qw 1 Ou Qw
Y = Y = + -), (Y = 7= ( + -), y = / = (- + -)
S 2 oy ox O 2 z Oy 2 Oz x (2-12)
By symmetry of the matrix, the strain tensor can be condensed into six components:











i yy

EtotalI E (2-13)
Y)y
YyZ



2.4 Plane Stress

Plane stress is defined as a state of stress in which the normal stress and shear

stresses directed perpendicular to the plane are assumed to be zero: oz = Txz = Tz= 0. Thin

films exhibit plane stress because the z direction dimension is very small in comparison

to the x andy dimensions, and the forces only act in the xy plane. A significant source of

plane stress in thin films arises from the deposition process. Stress from thin films will

be discussed in more detail in Chapter III.

Consider a thin film attached to a substrate to illustrate plane stress. The regions of

the plane that are about three times the film thickness from the edge exhibit plane stress

because the top surface is stress free. The behavior in the edge regions is more complex,

and is dominated by peel forces that tend to detach the film from the substrate. [SenOl]

Thin Film Plane Stress Regio Ede Reoion
Thin Film Ed

Substrate


Figure 2-6: Plane stress in a thin film

For an isotropic linear solid under plane stress, the in-plane strain (E) and shear

strain (y) values are defined as:

1


E


(2-14)










Sy (y vCx) (2-15)
E

2(1+ )(2-16)
Yxy E r (2-16)


The only non-zero out of plane strain is:

-U
z = -(x + ). (2-17)


2.5 Plane Strain


Plane strain is defined as a state of strain in which the normal strain Ez and shear strains

Yxz and yz = 0:



E Eyx



4-0

^xy


Eyx

Ey
Figure 2-7: Example of plane strain in the x-y direction

The plane strain assumption is used for long bodies with constant cross-sectional

area whose forces only acts in the xy plane, and used when the strain in the z direction is

significantly less than in the other two orthogonal directions. Under this assumption,

EX = EY and the strain matrix reduces to:


EX = YxY (2-18)
_/yX Eyy









2.6 The Stress-Strain Relationship

The relationship between stress and strain is described by Hooke's Law, and it is

used to calculate the deformation in a material due to stress. The ratio of stress to strain

is known as Young's Modulus of Elasticity, E, and the ratio of shear stress to shear strain

is known as the Shear Modulus of Elasticity, G. For a linearly elastic material, the

normal stress is linearly proportional to normal strain by:

S=E (2-19)

and the normal forces are resisted by the body's bulk modulus, which determines how

much a solid will compress under external pressure:

K = (2-20)
3(1- 2v)

Shear stress is linearly proportional to shear strain by:

r = Gy (2-21),
and shear forces are resisted by the body's shear modulus:
G = (2-25)
2(1 + v)



The Hookean Model

For linear elastic materials stress is linearly proportional to the strain and is described by:

- k = Cjklj (2-26)

where Cijkk is the fourth order elastic stiffness tensor of 81 material constants, cij is the

equilibrium stress values from (2-7) and eij is the equilibrium strain from (2-13). Silicon


is an anisotropic material with diamond cubic crystal symmetry and the Cjkl matrix

reduces to 36 components with three elastic constants cl1, c12, and c44:









c11 12 c12 0 0 0
c12 c c12 0 0 0
c,, c1, c,, 0 0 0
Ckl 2 2 (6-2)
0 0 0 c44 0 0
0 0 0 0 c44 0
0 0 0 0 0 c44

C11 = 166 GPa, C12 = 64 GPa and C44 = 80 GPa [Str05]. Although silicon is an

anisotropic material, it can be approximated with isotropic elastic properties for

simplicity, meaning that the elastic properties in all directions are equal. For isotropic

material, the elastic constants cl1, c12, and c44 are [SenOl, Zie89]

E(1- v)
c, = (6-3)
(1 + v)(1 2 v)

E-v
c12 (6-4)
(1 + v)( 2. v)

E
44 =- (6-5)
(1 + v)

The elasticity constants for the crystal directions are E[100] = 129 GPa, E[110] = 168

GPa, and E[ 11] = 186 GPa [Str05].

Hooke's Law states that strain can exist without stress. To illustrate this, consider

an elastic band that experiences a force in they direction, creating a stress in they

direction. The strain in the x direction however is not equal to zero. As the rubber band

is pulled outward in the y direction, it moves inward in the x direction to fill the original

space. The x plane does not have any external forces acting upon it, but a change in

length is experienced. This demonstrates that strain can exist in a particular plane

without any stresses present. When the forces are removed, the elastic band returns to its

original shape.









2.7 Summary


This chapter discusses the mechanics behind linear elastic materials and definitions

of stress and strain. First, linear elastic materials are defined as materials that return to

their original form after an applied force is removed, and a spring is used to demonstrate

this behavior. When to much force is applied, the spring will leave the elastic regime and

experience plastic deformation. Next the stress and strain tensors are defined by the

normal and shear components. Stress is the force per unit area, and strain is the change in

length divided by the original length. In static equilibrium, both the stress and strain

tensors can be reduced to six components compared to nine because the shear stresses

and shear strains are equal. Next, the two-dimensional plane stress and plane strain

assumptions are discussed. Finally, the stress-strain relationship is described by Hooke's

Laws, which relates Young's Modulus, the Shear Modulus and the Bulk Modulus to

stress and strain, and the laws explain how strain can exist without stress.

In Chapter III, stress and strain sources that arise during the IC fabrication process

will be discussed in detail. Different sources of stress and strain that will be explored are:

non-planar oxidation, thin film deposition, STI formation, and dopant induced strains.














CHAPTER 3
STRAIN SOURCES

While scaling devices to nanometer dimensions improves performance, it also

strongly magnifies the mechanical forces that arise during fabrication. Stress and strain

are unintentionally introduced into the silicon substrate after various stages of the

fabrication process, and are becoming increasingly difficult and expensive to cope with.

Stress from thermal expansion mismatch, ion implantation and lattice mismatch can all

result in thin film stress. This chapter will discuss the main factors influencing stress and

strain from the IC fabrication process and measures to control them. Oxidation induced

stress, thin film stresses, STI stress, and dopant induced strains will be discussed. Finally,

a brief discussion of boron diffusion in silicon and silicon germanium (SiGe) will be

provided.

3.1 Oxidation Induced Stress

Silicon dioxide (Si02) formation is a critical process step for device fabrication,

and exposing a silicon wafer to oxygen at high temperatures forms an excellent electrical

isolator. In addition to its isolation properties, Si02 also acts as a barrier to impurities

during deposition and implantation. [Jae02] During thermal oxidation, Si-Si bonds are

broken to accommodate the oxygen atoms, and the oxide reacts with the Si at the Si-Si02

interface. The forming oxide consumes the silicon as it expands upwards at a rate of 2.2

times the volume of oxidized silicon. The interface moves into the Si bulk and leaves

behind a compressively stressed region. The coefficient of thermal expansion for SiO2 is

less than that of Si, resulting in a negative strain value. In non-planar regions, the









behavior is more complex because the oxide can no longer freely expand upward. On

convex surfaces such as the top corner of an isolation trench, the oxide becomes stretched

around the corner in tension. On concave surfaces such as the bottom corer of an

isolation trench, the growing oxide squeezes together and becomes compressed. The

stress from oxide growth relaxes depending on the oxide viscosity and as the temperature

increases, the oxide flow increases and permits faster relaxation of the structural strains.

[YenOO, YenOl] Oxide viscosity determines the oxide growth on shaped surfaces, and is

described by:

,Vc / 2kT
r(stress) = q(T) sVc2kT(2-1)
sinh(o-Vc / 2kT)


where rq(T)is the stress free temperature dependent oxide viscosity, as is the shear stress

in the oxide, and Vc is a fitting parameter [YenOO, Yen01].

Yen et al [YenOl] showed that external mechanical stress affects the kinetics of

silicon thermal oxidation. It had been previously understood that the oxidation rate

constants were only temperature dependent, but recent studies show that stress also plays

a large role in the rate. In the experiment conducted, two wafers were bent, one in

tension and the other in compression and the oxide thickness and stress distribution

across the wafer was observed over time. The tensile wafer exhibited an increase in

oxide growth, while the wafer in compression showed little to no effect. The increase in

oxide growth can be explained by the enlarged atom spacing of the silicon wafer under

tensile stress.

LOCOS Formation

Local Oxidation of Silicon (LOCOS) is an obsolete technique used to isolate active

regions of ICs. Selected areas of the wafer are oxidized by masking the non-oxidized









region with silicon nitride (Si3N4). Beginning with a clean wafer, a uniformly thin layer

of SiO2 is grown, and a layer of Si3N4 is deposited. The thin SiO2 layer is present to

alleviate the mismatch stress between the silicon and the nitride layer. After the nitride is

patterned, the wafer is exposed and all areas not covered by the nitride form a thick layer

of SiO2. Compared to a planar surface, the stress from LOCOS formation is significantly

higher because the volume expansion is dimensionally confined. [Sar04] The main

forces that arise in the formation of LOCOS structures are illustrated in Figure 3-1: Fl

represents the intrinsic stresses from the pad oxide and nitride layer, F2 represents the

tensile bending stresses from the nitride deposition, F3 represents the compressive

stresses from the non-planar field oxide growth into confined areas, and F4 represents the

thermal expansion mismatch stress from the difference in thermal expansion coefficients

between Si and SiO2.

















Figure 3-1: Forces present in LOCOS formation [Sar04]

Due to the high stresses encountered in LOCOS formation, alternate isolation techniques

such as shallow and deep trench isolation were developed.









3.2 Thin Film Stress

Thin films are a layer with high surface-to-volume ratio and are commonly used in

IC fabrication for masking, passivation, isolation, and conduction [Hu91]. All stresses

present in thin films after deposition are referred to as residual stresses and can be broken

down into two components: 1) thermal mismatch stress and 2) intrinsic stresses. Thin

films can be deposited or thermally grown, but depending on the deposition process,

temperatures, and dopant concentration, tensile or compressive residual stresses will be

obtained [Hu91]. The regions of highest intrinsic stress in thin films are at the film edges

or in non-planar regions. Residual stresses will cause device failure due to instability and

buckling if the deposition process is not properly controlled.

3.2.1 Thermal Mismatch Stress

Thermal mismatch stress occurs when two materials with different coefficients of

thermal expansion are heated and expand at different rates. During thermal processing,

thin film materials such as polysilicon, SiO2, and Si3N4 expand when exposed to high

temperatures and contract when cooled to lower temperatures according to their

coefficient of thermal expansion. The thermal expansion coefficient for small strains

such as those encountered in IC processing is defined as the rate of change of strain with

temperature and is measured in microstrain/Kelvin (pE/K) [Sen01]:

de
aT =-- (2-2)
dT

Although aT is temperature dependent, it can be treated as a constant over a wide range of

temperatures. For example, Si polysilicon has an aT ranging from 2.6-4.5 ue, over the

temperature ranges of 20-9000C [Fre03] and SiO2 has an aT of 0.5 pe .









Consider the strain when a thin Si3N4 layer is deposited onto a Si wafer at temperature Td

and cooled to room temperature Tr and AT =. Td- Tr. The thermal mismatch strain of the

substrate is [SenOl]:

Esub = -subAT (2-3)

If the film was not attached to the substrate, it would experience a thermal strain:

Ef = -a fAT (2-4),

Thin films that are attached to a substrate experience more complex behavior. Given that

the Si wafer is much thicker than the Si3N4 layer, the nitride will contract according to the

Si substrate and the thermal mismatch strain that results is [Fre03]:

6f,mismatch = (aTf aT ) AT (2-5)

where aTf and aTs are the thermal expansion coefficients of the film and substrate

respectively. Positive strain is denoted as tensile and negative strain as compressive.

Thermal mismatch stress and strain are related through Young's modulus E, and

Poisson's ratio, v by:

Ef
f,msmatch f,mismatch (2-6)
l-

where Ef is Young's Modulus for the film, and ef, mismatch is the thermal mismatch

strain described in (2-5).

3.2.2 Intrinsic Stress

Intrinsic stress is the component of residual stress due to variations in the

deposition process and is dependent on factors such as: deposition rate, thickness and

temperature. It is important to minimize the intrinsic stresses generated because their

magnitudes can amount to stresses greater than those of thermal mismatch. After a thin









film is deposited, it will lie in either tension or compression. Tensile intrinsic stress is the

result of a film wanting to be "smaller" than the substrate because it was "stretched" to fit

it. Compressive stress results when a film wants to be "larger" than the substrate because

it was "compressed" to fit.

A technique commonly used to quantify the intrinsic stress is measuring the

substrate curvature. In 1909 Stoney observed that a metal film deposited on a substrate

was in tension or compression when no external loads were applied to it [Fre03].

Through this observation, Stoney created a simple analysis to relate the stress in the film

to the amount of substrate curvature. This is known as the Stoney formula [Fre03]:

E= =h,, (2-7)
S 6-.(1- v,)-R h,

where ESi and, vSi are Young's Modulus and Poisson's Ratio for Si, hf and hSi are the

film and Si thicknesses, and R is the radius of curvature of the substrate.

Annealing can be performed to alter the residual stresses in thin films, however the

large thermal budgets necessary to achieve stress relaxation is inconvenient for standard

silicon processing. Zhang et al. [Zha98] showed that compared to conventional heat

treatments, high temperature rapid thermal annealing (RTA) can effectively reduce the

residual stress within a few seconds.

3.3 Stress from STI

Shallow trench isolation (STI) is a technique used to electrically isolate transistors.

While allowing a higher packing density, STI structures are becoming major contributors

to the mechanical stresses present in the silicon substrate. To create an STI structure a

trench is etched into the silicon using reactive ion etching (RIE). Next the trench walls

are lined with a thin layer of Si02 by thermal oxidation. The trench is then filled with









chemical vapor deposition (CVD) SiO2, another CVD dielectric or CVD polysilicon.

Finally, the structure is chemical mechanical polished (CMP), and a planar STI structure

is created [Chi91].

The stress that results from this process comes from three areas: 1) thermal

oxidation of a non-planar surface, 2) thermal mismatch stress from the different

materials, and 3) intrinsic stress from the CVD fill deposition. For SOI devices, the

silicon can re-oxidize at the buried oxide/Si interface at the STI edge which bends the

silicon and adds an additional compressive stress component in the channel of the

transistor [Gal04]. These stress sources act cumulatively and result in increased stress

levels in the silicon substrate. If the stress levels become significant enough device

failure is likely to occur.

Thermal oxidation of non-planar surfaces leaves a compressive stress in the silicon

substrate. After etching a trench in the silicon a SiO2 sidewall liner is thermally grown

which creates a large stress in the trench corners due to the oxide growth. In the top

corners of the trench, the stress is tensile in the oxide and compressive in the silicon, and

in the bottom corners of the trench, the silicon is in tension while the oxide is in

compression [Law03]. This corer-induced stress is relaxed by the viscous flow of oxide

which was described in section 2.1.



























Figure 3-2: Top corner of an STI structure

The second source of stress is the thermal mismatch that arises during the STI

process. Before thermal oxidation occurs, the silicon is considered to be in a zero-stress

state. After thermally growing the oxide, the wafer is cooled from the oxidation

temperature to an intermediate temperature causing a thermal mismatch stress between

the Si and Si02. Since the coefficients of thermal expansion are almost equivalent for Si

and polysilicon, no thermal mismatch strain results for any change in temperature

[Chi91].

The final source of stress is a result of the intrinsic stress of CVD fill deposition.

Depending on the fill material used and the process conditions, the thin film can have a

tensile or compressive intrinsic stress [Chi91]. Films of this nature exhibit biaxial stress,

however, when considering an entire trench structure, the biaxial plane changes around

the rounded corners of the trench.

Hu performed many isolation trench studies to investigate the effects of varying

trench geometry on the stress distribution. His studies showed that for an oxide-filled

trench, a compressive stress existed perpendicular to the trench sidewall, localized near









the bottom of the trench and at the surface. In addition, there was a tensile component

parallel to the trench near the center of the side wall. The shear stresses were dominant

near the trench ends, but vanished at the mid-length of the trench. [Chi91, Hu91].

Stress cancellation can be desirable for increasing the density of transistors on a

wafer. For NMOS devices, where compressive channel stress degrades device

performance, stress reducing techniques can be employed to return the substrate to a zero

stress state. Some mechanisms to alleviate the stress generated during the STI process

are counter doping and corner rounding. Boron introduces a local tensile strain into the

silicon substrate when it sits in a substitutional lattice site. In areas of larger

compression, boron can be introduced by ion implantation or diffusion to even out

stresses. By altering the processing conditions, different magnitudes of stress can be

achieved to cancel out stresses of opposite magnitudes. Oxide growth stress is significant

in the corner regions of isolation trenches and can be reduced by corer rounding. After

an oxide is grown it is isotropically etched and the new oxide regrows around a more

rounded corer, lowering the total stress from the growth process.

3.4 Dopant Induced Stress

It is well known that introducing dopants into silicon will induce a mechanical

stress in the substrate and change the lattice structure. As dopants are introduced in

silicon through ion implantation or diffusion, a local lattice expansion or contraction will

occur due to the varying atomic sizes and bond lengths of the dopants. Boron is smaller

in size than silicon and when it sits on a substitutional lattice site, a local lattice

contraction occurs because the bond length for Si-B is shorter than for Si-Si. Horn et al

[Hor55] discovered that a single boron atom exerts a 0.0141A lattice contraction per

atomic percentage of boron in silicon at room temperature. Germanium on the other








hand is larger than silicon and when it sits on a substitutional lattice site, a local lattice

expansion occurs. At high concentrations significant strain values can result due to a

lattice mismatch between the silicon substrate and the dopants [Avc02]. The lattice

contraction and expansion for boron and germanium are illustrated in figure 3-3.


00000 00000
00000 00000
00000 oo0oo0
00000 O0000
00000 00000
Lattice Expansion from Germanium

00000 00000
00000 O0 000
00000 00 00
00000 00000

00000 00000
Lattice Contraction from Boron


Figure 3-3: Lattice contraction due to boron atom, and lattice expansion due to
germanium atom
Stress has demonstrated enhancements in the solid solubility limit of boron in

silicon. As we move towards smaller, faster transistors, higher concentrations of dopants

have to be packed into smaller regions of the silicon substrate [Sad02]. A critical threat

to the future development of ICs is that the electrical solubility limit of boron is being

reached. For operational devices, dopants must be electrically activated by annealing to

repair the crystal damage from ion-implantation, allowing dopants to sit on substitutional

lattice sites. It is important to investigate methods to enhance the solubility of boron in









silicon because it is the most commonly used p-type dopants. Sadigh et al. suggested

from calculations that the proper stresses can double the solubility of dopants such as

boron in silicon at an annealing temperature of 10000C for 1% biaxial compressive strain

[Sad02]. He observed that negatively charged dopants, such as boron become more

soluble under compressive stress, and positively charged dopants such as arsenic prefer

tensile stress. The size mismatch of the dopant compared to silicon also plays a large role

in the solubility enhancement. The maximum solubility enhancement occurs when the

charge and size mismatch with silicon favor the same type of strain.

Stress from Dislocation Loops

Dislocations are a break in the regular lattice spacing, and when too much stress is

applied, the silicon substrate will yield by generating dislocations to relax the stress in the

material. The presence of many dislocations forms loops, and the growth rate of these

loops is dependent on point defect concentration. When combined with ion implantation

or oxidation, dislocation loops will nucleate below the substrate's yielding point [Avc02].

The regions of highest stress typically exist on non-planar topologies and at film edges.

During several process steps in the fabrication process, a nitride layer is used to mask the

oxidation of silicon in active regions. A high shear stress develops at the nitride edge and

if the stress becomes too significant, dislocation loops are generated and can glide

[Avc02]. To alleviate some of the stress around the nitride edge, a pad oxide can be

inserted between the nitride edge and the substrate. Dislocation loops are also generated

from STI formation. Fahey et al. [Fah92] demonstrated that minimizing the stress from

the STI process such by changing the nitride thickness or using different fill materials









with less intrinsic stress, will help reduce the dislocation density in the substrate. A more

in depth explanation of stress from dislocation loops can be found in Chapter I.

3.5 Dopant Diffusion in Silicon and Silicon Germanium (SiGe)

As we move towards the next technology node in the ITRS Roadmap, shallow

source/drain junctions requiring high concentrations of active dopants are packed into

smaller regions of the substrate. Achieving shallow junctions with active dopants is

becoming increasingly difficult due to excessive dopant diffusion. Phosphorus, boron and

indium are considered "fast" diffusers, where arsenic and antimony are "slow" diffusers.

Arsenic has been the dopant of choice to fabricate NMOS transistors, however PMOS

transistors encounter more problems because boron is the only dopant with a high enough

solid solubility for the processing temperatures required. Effects such as transient

enhanced diffusion (TED) cause the dopant profile to move significantly during

annealing, resulting in deeper junction regions.

Ion implantation is used to introduce dopants into the substrate but it creates

significant crystal damage. Annealing is used to remove the damage from the implant,

return the silicon lattice to a crystalline configuration, and place dopants on substitutional

sites to become electrically active. During the early stages of the annealing process,

excess interstitials react with dopants resulting in TED; boron is a dopant that strongly

exhibits this behavior. Boron interacts with excess interstitials to form BI pairs and they

diffuse by breaking atomic bonds and moving the BI pair throughout the lattice. At lower

temperatures the damage is not repaired and enhances the dopant diffusion, while at

higher temperatures the damage annihilates faster and a transient diffusion is not as

significant [Plu00].









Fick's Laws describe dopant diffusion, and the first law relates dopant diffusion to

the concentration gradient by [Plu00]:


F = -D (2-8)


QC)
ac
where F is the flux, D is the diffusivity, and ax is the concentration gradient. Fick's

second law of diffusion states that the rate of change of concentration is proportional to

the second derivative of the concentration:


S=D- = V*F = V(DVC) (2-9)
ot ax2

In a zero stress-state, dopants diffusivity is characterized by:

-E
D = D exp( ) (2-10)
kT

where D is the diffusivity, Do is the exponential prefactor, EA is the activation energy, k is

Boltzman's constant, and T is the temperature. When compressive and tensile strain is

introduced, dopants diffusivities change. Boron for example has an enhanced diffusivity

under tensile stress, and a decreased diffusivity under compressive stress. Thus,

compressive stress is applied to retard boron diffusion when forming shallow junctions.

Boron is a known interstitial diffuser, and the diffusion coefficient is composed of two

parts: the neutral and positive charged state of the interstitial [Zan03]:


DB =DBRI +DBI+ (P) (2-11)
n,

where ni is the intrinsic carrier concentration and p is the hole concentration. In

equilibrium, ni=p. The DBI terms can be expressed in Arrhenius form as:

DB1 = D,1 exp(-QI /kT) (2-12)









where DOBI is the prefactor and QBI is the enthalpy.

Diffusion in alloys such as Sil-xGex is different that in pure silicon due to a lattice

mismatch between the two materials. There is a 4.2% difference in the lattice constants

of Si and Ge; Si has a lattice constant of- 5.43A while Ge has a lattice constant of-

5.65A. When a layer of Sil-xGex is grown on top of Si, it has a bulk relaxed lattice

constant which is larger than Si. Layers grown below the critical thickness become

strained, but once the critical thickness is exceeded, misfit dislocations are released to

relieve the strain of the layer.

Impurity diffusion in SiGe is a debated topic, and many researchers have observed

the diffusivity of boron in SiGe. Aziz et al [Raj 03] looked at diffusion under biaxial strain

with a strain-induced activation enthalpy term. Kuo et al found that increasing Ge

content from 0-60% decreased B diffusion and that strain was not a significant factor. He

attributed the decrease in B diffusion to the binding between B and Ge atoms which

immobilized the B [Kou95]. Rajendran et al found results similar to Kuo and modeled

the diffusion of B in Sil-xGex as a result of GeB- clusters. This behavior can be

attributed to the fact that B creates a local tensile strain around a B atom, and Ge provides

a local compressive strain around a Ge atom. The positive and negative strains are

attracted to each other and form a complex to release the stress energy. The total strain

from Ge incorporation is [Raj03]:

SGe =(aS,Ge aS, )a (2-13)

aS,-Ge = s, + (aGe as ) x (2-14)

where a is the lattice constant and x is the atomic fractions of Ge, and substitution the in

the lattice constants for Ge and Si gives the strain S = 0.0425x.









The boron diffusivity is modeled as (2-10) in silicon. However, in SiGe the incorporation

of Ge atoms changes the overall B diffusivity to [Raj 03]:

DBe = DBO exp(-E/ kT)exp(-QS/kT) (2-15)

where S is the local strain from Ge, and Q is the rate of change of activation energy per

unit strain.

3.6 Summary

This chapter discussed the multiple stress and strain sources that arise during the

fabrication process Oxidation-induced stress was described and issues such as the

oxidation of non-planar surfaces were addressed. To go into more depth, stress from

LOCOS formation such as intrinsic stresses, bending stresses, non-planar oxidation

stresses, and thermal expansion stresses between the Si and SiO2 were discussed. In the

next section, thin film stresses were described. Thin films exhibit residual stresses and

are composed of two components: thermal mismatch strains as a result of materials

having different thermal expansion coefficients, and intrinsic stresses as a result of

varying conditions during the deposition process. The next section introduced stress

from STI structures. The formation of an STI was described and the stress as a result of

non-planar oxidation, thermal mismatch strain, and intrinsic stresses were explained.

When accounting for stress from an STI, all of the sources are necessary and none can be

ignored in computations. Methods to alleviate STI stress such as strain compensation and

corner rounding were also touched on. The next section discussed dopant induced stress

due to lattice mismatch between different dopants and stress from dislocation loops.

Finally, boron diffusion in silicon and silicon germanium under was explored. Chapter IV






49


focuses on the software implementation in the process simulator FLOOPS, and their

applications for boron doping and nitride deposition.














CHAPTER 4
SOFTWARE ENHANCEMENTS TO FLOOPS

Mechanical stresses from process steps such as trench isolation, doping, and

epitaxial regrowth play a large role in the scaling of semiconductor devices.

Understanding how these stresses affect phenomenon such as dopant diffusion and defect

evolution is critical for understanding the limitations of each process technology.

Continuum mechanics, which is a branch of mechanics that deals with continuous matter,

is used to study these behaviors. More specifically, solid mechanics is the study of the

physics of continuous solids. Differential equations are used to solve problems in

continuum mechanics, and the equations are specific to the materials under investigation.

For example linear elasticity in silicon is described using the constitutive equation known

as Hooke's Law that was described in Chapter II. Most of the materials used in silicon

processing are modeled as simple elastic materials which make process modeling

simpler.

This chapter focuses on the software implementation in the process simulator,

FLOOPS (Florida Object Oriented Process Simulator). The "elastic", "bodyforce",

"stress" and "strain" operators were developed in FLOOPS to calculate the displacement

and stress in the silicon substrate due to boron doping and nitride deposition. The Finite

Element Method was implemented using the 2-D plane strain approximation to discretize

the region and solve the equations. Simulations were performed to verify the software

functionality. The model that FLOOPS currently utilizes to compute stress is a

viscoelastic model that was developed for LOCOS; an outdated process. This model









utilizes nonlinear and stress dependent viscosities to describe the behavior of the

material, which is no longer an accurate assumption. First, the viscous flow of the oxide

is computed in response to the growth forces and then changing forces are calculated as a

result of the growth rate [Sim04].

For current fabrication processes, however, the material model that most accurately

describes the behavior of materials is the linear elastic model. Unlike the current

viscoelastic model that is used, the linear elastic model will couple the mechanical

equations with the diffusion solution. In addition, the operators listed above were

integrated with the property database and process commands [Law02].

As discussed in Chapter III, the introduction of different dopants into the silicon

substrate causes change in the mechanical state of the lattice. Dopants come in a variety

of sizes and cause a local tensile or compressive strain in the lattice due to the size

mismatch between the dopants and silicon. Boron is a substitutional dopant that is

smaller than silicon, and it introduces a local tensile strain in the lattice. Chu et al.,

Rueda et al., and Yang et al. demonstrated that bending occurs in boron doped cantilever

beams, and the amount and direction of bending are dependent on the beam length,

width, and doping profile into the depth of the beam [Chu93, Rue98, Yan95]. The strain

from boron doping was used to calculate the deflection of the cantilever beam, and results

were compared with those of Rueda. Other structures such as a strip of nitride on silicon,

and silicon doped with boron source/drain regions were simulated and the stresses were

observed. The results will be discussed in Section Chapter V.

4.1 FLOOPS Background

FLOOPS is a C+ based simulation program which uses physical models to

describe various process steps such as ion implantation, oxidation and diffusion.









Furthermore, FLOOPS uses the Alagator scripting language to define partial differential

equations to solve these models by reading in material properties from the parameter

database. To arrive at a solution, the program solves a series of differential equations and

utilizes matrix mathematics to generate a solution. An internal Newtonian solver is used

to converge to a solution. Newton's Method is defined as [Adl04]:

f(xn)
+1 = Xn (4-1)
f'(x )
Equation 4-1 states that the next solution is equal to the previous solution minus the value

of the function at the previous solution divided by the value of the function's derivative at

the previous solution.

Operators such as gradients and time derivatives are needed when solving partial

differential equations. FLOOPS currently has five operators "ddt", "grad", "sgrad",

"diff', and "trans". The "elastic," "bodyforce," "stress," and "strain" are the new

operators created in this work. The "ddt" operator computes time derivatives and the

"grad" and "sgrad" operators take spatial derivatives. These operators are necessary

when performing a diffusion simulation. The "diff' and "trans" operators can be used to

compute the parallel and perpendicular electric field components needed to evaluate

device mobility [Law02]. The "elastic", "bodyforce", "stress" and "strain" operators

calculate the stiffness, displacement, stress and strain in the silicon substrate respectively,

and will be used to couple the mechanical stress equations with the diffusion process

step.

4.2 The Finite Element Method

The Finite Element Method (FEM) is a numerical technique used for solving

differential equations that describes a variety of problems, such as the solution to









displacement in an elastic continuum The principle of this method allows a complicated

region to be sub-divided into elements in a process called discretization. By solving the

differential equations of each region, the behavior of the complete domain is determined.

First, the geometry of the solid was identified as a three-noded triangle and a 2-D finite

element mesh was generated. Each node in the mesh was assigned a number and a set of

coordinates (x, y) which specified the position of the node, and as forces were applied,

nodes of the solid moves accordingly.

Lets revisit the mechanical equation to be solved isf=kx, wherefis the force

applied, k is the material stiffness, and x is the unknown, displacement. For this notation,

the "f" term (and any force discussed from here on) is referred to as the "right hand side,"

and the "k" term, or stiffness, is referred to as the "left hand side."

The first step in solving the mechanical problem is finding the element stiffness

matrix (left hand side), which describes the how each element will respond to forces.

The element stiffness matrix for each element is then assembled into a global stiffness

matrix that describes the behavior of the entire material region. Next, the "right hand

side" needs to be constructed, which consists of the force, specifically the force from

boron doping. Reflecting boundary conditions were applied and the unknown was solved

for, in this case, displacement. From the calculated displacements, other parameters of

interest such as stress were computed. Silicon was modeled as an isotropic elastic

material and the two-dimensional plane strain approximation was used to implement the

operators into FLOOPS.










4.2.1 Constructing FEM Elements for the Elastic, Bodyforce, Stress, and Strain
Operators

Consider a three-noded triangle e, defined by nodes i, j, and k numbered in the

counter-clockwise direction with an area A and displacements in the x and y directions.



Node k







Element e with
area A


Node j
(x y,)
Node i
(x,, y,)
Figure 4-1: Triangular element in coordinate system

There are two degrees of freedom (x, y) for each node and three nodes per triangle,

creating six degrees of freedom per element. The stiffness of a finite element describes

how the element responds to external forces. The stiffer a material, the less deformation

it will experience, whereas a flexible material will deform more. Under mechanical

equilibrium, all of the nodal forces are equal to zero, qe = 0. Integrating over the

triangular element gives the stiffness matrix:


k = IB D B d(vol) (4-2)


or in discretized form [Zie89]:

k" = B' D. B A (4-3)









where k is the element stiffness, A is the element area in two dimensions, and the element

volume in three dimensions. The B matrix is a constant matrix dependent on nodal

coordinates and [Zie89]:

S Y j-k 0 yk -y, 0 y yj 0
B = 0 xk x X, -k 0 x -X, (4-4)
Xk- X Yj-Yk X, -k Yk Y, x -x, y, -y

where 2 A is twice the area of the triangle and is equal to:

2 A = [(x, yk ) xyY) + (x, x jy,)] (4-5)

The B matrix is used to relate the strain to the displacements, which will be

discussed more in Section 4.2.2. The D matrix contains the material properties E and v.

For plane strain, the D matrix is equal to:


1 0
l-v
E (1 v) v
D = E 1 0 (4-6)
(1+v).(1-2v) 1-v
0 0 (1- 2v)
2. (1- v)
To find the displacements due to external forces, a matrix mathematics solver

called UMF is used to solve the equation Ax=b, where A represents the stiffness, b

represents the external forces, and x represents the nodal displacements. Below is a

portion of the code developed to build the stiffness matrix for a single element.

The B matrix routine takes the six coordinates of a triangle as arguments (three

nodes two displacements x, y per node) and returns the [3x6] matrix that was illustrated

in (4-4). From the B matrix, the transpose of the B matrix is easily obtained. The D

matrix contains the material properties such as Young's Modulus and Poisson's Ratio and

returns a [3x3] matrix. As illustrated in (4-4), the stiffness routine multiplies the B










matrix, transpose of the B matrix, and the D matrix together and returns the [6x6]

stiffness matrix for a single element.

B Matrix( Bmatrix, x[0], y[O], x[l], y[l], x[2], y[2] );

BT Matrix(Bmatrix, BTmatrix);

D Matrix(Dmatrix, E, nu);

Stiffness(BTmatrix, Dmatrix, Bmatrix, C, stiffness);

The sum of all element stiffness matrices is known as the global stiffness matrix,

which determines the stiffness of the each material region in the mesh. The flowchart

below in figure 4-2 demonstrates the step-by-step procedure to create the stiffness matrix

for an element.



Create B matrix Create B transpose Create D matrix [Stiffness= BT*D*B
----[3x6] ,matrix [3x3] [6x3]*[3x3]*[3x6]=6x6]
[3x6][6x3]





Are there more mesh
S Yes points to create
\ elements?




Create Global
Stiffness Matrix and
solve for nodal
displacements, stress,
and strain

Figure 4-2: Flowchart to create element stiffness matrix

4.2.1.1 Plane Strain Assumption


The plane strain approximation assumes that x = y = Z = ; however stress in

the z-direction is not equal to zero. This assumption can be used to solve problems with

infinitely long dimensions in the z-direction; therefore the strain in the z-direction will

approach zero [Rue97]. A problem with the plane strain assumption arises with dopant










and thermal mismatch strain because both dopant and thermal mismatch strains have

stress components in the z-direction. To compensate for the 3-D behavior in a 2-D

domain, the 2-D strain must be multiplied by a factor of (l+v):



E= E, =(1+ ) E (4-7)

Szz 0
4.2.1.2 Boundary Conditions

Reflecting boundaries require that the normal component of the velocity and

displacement field is set to zero across the interface, which corresponds to a mirror-

reflected symmetry across the boundary [Rue97]. To verify the boundary conditions was

working, simple simulations were performed that fixed one side of the mesh to zero with

the boundary condition, and displaced the other side to a specified distance. The proper

displacements were observed across the mesh, verifying the boundary functioned

correctly.

Lflxed dlsp+.3e-4 Rflxed dlsp+.3e-4











4 -04-

Figure 4 Verification of boundary conditions -displacements due to external forces
Figure 4-3: Verification of boundary conditions -displacements due to external forces









4.2.2 Forces from Boron Doping

The equivalent nodal force q," at node i due to element e must have the same

number of components as the nodal displacements, six values two for each node. This

force is described by:

qe = IB -.cd(vol) f," (4-8)
Ve
where BT is the transpose of the vector relating strain to nodal displacements, fb is the

distributed body forces of the element, and a is the stress tensor. The "bodyforce"

operator was created to model the force from boron and is modeled by [Zie89]

fe =IBT .D.Be d(vol) (4-9)
Ve
Integrating over the volume of the element gives the body force in discretized form:

feb = BT D eB.A (4-10)

The general stress-strain relationship of linear elastic materials is given by:

a= D(E ,)+ a, (4-11)

where D is the elasticity matrix, and Go and So and are the initial stress and strain tensors.

The elemental strain is related to the elemental displacements by:

,e = Bae (4-12)

where a is the displacements and B is the constant matrix given in (4-4). By substituting

equation (4-11) into (4-8), the expression for nodal forces becomes:

qe = JB'D. -D e d(vol) -B' -D.-e .d(vol)+JB' D.-c" d(vol) fb, (4-13)
Ve Ve Ve
The "bodyforce" operator was developed to model the elemental strain (Es) from

boron doping, and is modeled by [Cha96, Rue97]:


e = C oron (100) (4-14)
As, Cs,










Where 8, is the lattice contraction parameter for boron in silicon, CB,,or is the


boron concentration, (C, =5x1022cm-3) is the atomic density of silicon, and


(As, =5.4295A) is the lattice constant of silicon. Horn et al found that the silicon lattice

contracts 0.0141A per atomic percentage of boron concentration [Hor55]. Since the

boron concentration is a nodal quantity, the elemental boron concentration must be

calculated from the nodal concentrations. To obtain the elemental values of boron strain

from the nodal values, the boron concentration is first divided by the atomic density of


silicon ( CBoro ). The lattice displacement is equal to ( CBoro ) times the lattice
C, CS


contraction parameter ( ,). Then the strain is computed by dividing the lattice

displacement by the lattice constant of silicon (As,) [Rue98]. The average elemental

strain is then computed as the average of the strain value at each of the nodes. Below is

part of the code to calculate the nodal displacements and a flowchart for the procedure:

double sl = a.Val(0).get(k); //evaluate the strain at each node
double s2 = a.Val(2).get(k);
double s3 = a.Val(4).get(k);

//compute the average elemental strain by taking the average of all
nodal values.

Strain[O] = sqrt(2.0) (sl+s2+s3) / 6.0;
strain[l] = sqrt(2.0) (sl+s2+s3) / 6.0;

//assume no shear component for dopant-induced stress
strain[2] = 0.0;

B Matrix( Bmatrix, x[0], y[0], x[l], y[l], x[2], y[2] );
BT Matrix(Bmatrix, Btmatrix); //create B transpose from B matrix
D Matrix(Dmatrix, E, nu); //create D matrix
BTMultD(Btmatrix, Dmatrix, C); //multiply B transpose[6x3]
*D[3x3]=C [6x3]
MultBtDBF(C, strain, fx); //multiply C [6x3] elemental strain
[3x1]= nodal displacements [6x1]











Create B transpose Create D Obtain Elemental Multiply all matrices to
matrix Create D matrix Strain Values solve for forces from
matrix Strain Values a d
S[3x3] -r31 boron doping
[6x] [3x/l [6x3]*[3x3]*[3x1]=[6x1]


Figure 4-4: Flowchart to solve for forces from boron doping

4.2.3 Strain and Stress Computation

The strains and stresses were calculated from the displacements described in

section 4.2.2. The strain is related to the nodal displacements by (4-12) and is equal to

the B matrix times the nodal displacements that were calculated in 4.2.2. The strain is a

[3x1] column vector containing the normal xx, yy and the shear xy values:



s.= (4-15)




The stress is related to the strain by the D matrix as defined in (4-11), and by

multiplying the strain values above by the D matrix, another [3x1] column vector of the

stresses is obtained:



c= D-= cyy (4-16)



Once the displacements in the silicon were solved for, the function on the

command line to solve for stress or strain is: select z= "Stress/Strain(xx/yy/xy,

displacement) ", which calls the stress or strain operators and calculates their values based

on the displacements. The xx, yy, or xy stress or strain values can be obtained with this

function. As noted in (4-15) and (4-16), the column array of stress and strain represent










the xx, yy, and xy directions respectively; all of the strain or stress components are

initially solved for, and additional code will determine which direction of stress is

desired. Contours of the stress fields were plotted, and will be illustrated in chapter V.

Below is part of the code and the flowchart to calculate the strains and stresses from the

nodal displacements:

B Matrix( Bmatrix, x[0], y[O], x[l], y[l], x[2], y[2] );

//multiply [3x6]B*[6xl]displacement=elestrain[3x1] strain[xx, yy, xy]
MultiplyStrain(Bmatrix, elestrain, displacement);

// find tt to determine if want xx, yy, or xy direction
if (tt==Dir XX) val = elestrain[0];

else if (tt==Dir YY) val = elestrain[l];
else val = elestrain[2];

//now calculate the stresses from the strains
MultiplyStress(Dmatrix, elestrain, stress); //elestrain
[3x1]*Dmatrix[3x3]=stress[3x1]



Multiply B matrix [3x6] Multiply strain [3x1] by
by displacements Dmatrix
[6x1]=strain[3xl] [3x3]=stress[3x1]



Figure 4-5: Flowchart to calculate strain and stress

4.3 Summary

This chapter began by introducing continuum mechanics and the finite element

method. Large areas were sub-divided into smaller regions in a process called

discretization to create elements. The stiffness of a region describes how it responds to

external forces, and the procedure to create the stiffness matrix for a single element was

described. Next, the bodyforce operator defined as representing the forces due to boron

doping. The mechanical equationf=kx was solved for, and from the calculated

displacements, the stresses in the silicon substrate were calculated. In the next chapter,






62


applications such as beam bending, nitride deposition, and channel stress from boron

doping will be explored.














CHAPTER 5
APPLICATIONS AND COMPARISONS OF TWO-DIMENSIONAL SIMULATIONS

As device channel lengths are scaled into the deep submicron realm, stress

components that once could be ignored are now significant. A few examples of how

stress is introduced during different process steps is by creating STI structures, doping the

source and drain regions, and depositing thin films. At channel lengths as short as 0.1

um, these stress sources can create enough undesirable stress in the channel to alter the

carrier mobility and decrease overall device performance. Methods to either suppress the

undesirable stress, or enhance the advantageous stress are under research. The software

operators, discussed in Chapter IV, were used to calculate stress from various process

steps, and the results were compared with experiments from literature and simulations

from the commercial version of ISE FLOOPS for software validation.

This chapter presents finite element based models that calculate the residual

stresses in various structures. To illustrate the effect of strain from boron doping, a

silicon cantilever beam was simulated and the beam length, width, and concentration

gradient were varied to observe the bending behavior from a particular boron diffusion

process. Next, the stress caused by depositing a strip of nitride on silicon was simulated,

and the stress around the corner of the nitride/silicon interface was compared with the

values simulated from the ISE version of FLOOPS. Lastly, the stress from doping the

source drain regions with boron was observed, and the effects of scaling the channel

length, source/drain length, and boron concentration were quantified.









5.1 Boron-Doped Beam Bending

Cantilever beams are used in silicon fabrication technology to create sensors and

other MEMS devices. Beam structures are fabricated by thermally diffusing or

implanting boron on one side of the silicon wafer, and etching through a mask on the

other side of the wafer. sing etchants such as KOH, silicon layers with boron

concentrations greater than 7x1019 cm-3 (p+ Si) show significant slower etching rates than

compared to undoped silicon [Yan95]. Since boron is a substitutional atom in silicon, the

silicon lattice will contract in the boron diffused layer, and layers with different

concentrations of boron will be subjected to different tensile stresses. The wafers bend

up or downwards after the cantilever beams are released due to the stress gradient

through the depth of the beam [Jae02, Nin96, Rue98,Yan95]. Yang and Chu et al.

demonstrated that as-implanted cantilever beams with tensile residual stresses bend

upwards to maintain equilibrium. However, subsequent processing steps such as

oxidation or annealing can change the residual stress state from tensile to compressive

[Yan95]. The results of these experiments however are not comparable because of the

difference in experimental conditions.

For a cantilever beam made of linear elastic material such as silicon, the beam

deflection is [Nin96]

Mi2
Vd 2E (5-1)
Ar 2El

where M is the bending moment, I is the moment of inertia of the beam, and E is

Young's Modulus. For cantilever beams of different lengths, but identical M, E, and I,

the deflection curves are the same.










Beams with a uniform dopant profile, or a profile that is symmetric to the center of the

beam, do not exhibit bending due to equal distribution of forces from boron through the

thickness of the beam.

CB






x=O x=O
x=0



Figure 5-1: A uniform or symmetric doping profile about the center of the cantilever
beam thickness results in no bending

However, under a concentration gradient, the beam will bend towards the more

heavily doped boron side with respect to the center of the beam thickness to relieve the

tension. This is a similar concept to applying a nitride strip on top of silicon, and it will

be explored in the next section. For example, a doping profile located near the surface of

the beam will bend upwards, while a profile located towards the bottom of the beam will

bend downwards.


CB CB





x=0 x=0

x=0 x=0



Figure 5-2: The strain from boron causes bending towards the more heavily doped boron
side of the beam (a) downwards bending (b) upwards bending









5.1.1 Beam Bending Simulation Results

Simulations in FLOOPS were performed to observe how varying the length, width,

and concentration gradient affected the deflection of the cantilever beam. The

experimental conditions of Rueda et al. [Rue98] were replicated to obtain accurate

results. A boron profile with a peak concentration of 8x1019 cm-3 was implanted into

silicon. The initial beam dimensions were 50um long by 0.6um thick. The grid spacing

was 0.05 um in the x-direction to resolve the boron profile, and 0.5um in the y-direction.

The material properties used for silicon were: Young's Modulus =1.22xl012 dyn/cm2 and

Poisson's Ratio=0.3 [Rue98]. The boundary condition requirement for cantilever beams

is the displacement and the first derivative of the displacement (velocity) is equal to zero.

To achieve this, the left side of the boundary was fixed.

5.1.2 Effect of Varying Beam Length

Figure 5-3 demonstrates the beam deflection versus beam lengths for a 0.6 um

thick beam. As stated in equation (5-1), a beam with identical material properties will

follow the same deflection curve. As the beam length was increased from 25 um to 50

um, the deflection increased accordingly and fit a parabolic curve. These results agree

with those of Rueda et al. and Chu et al.











Deflection vs distance for various beam lengths,
width=0.6um


0.12

0.1
-E 50 um
0.08
-0.08 -0--45 um

0.06 40 um
30 um
0.04
--25 um
0.02

0
0 10 20 30 40 50 60
beam length

Figure 5-3: Beam deflection vs. beam length

5.1.3 Effect of Varying Beam Width

The next figure illustrates the effect of varying the beam width on the beam

deflection. Notice the cantilever beams deflect in the negative-x direction, equating to an

upwards bending as in Figure 5-2 (b). The beam width is varied from 0.6 um to 1.15 um

and the deflection is observed. As anticipated, narrower beams deflect more than thicker

beams. The deflections observed were in agreement with those of Rueda et al.


Deflection vs distance for various beam widths

0 .
-0.01

E -0.02 0.6 um
-0.03 ---0.8 um
-0.04 1.0 um
| -0.05 1.15 um
-0.06
-0.07
beam length (um)


Figure 5-4: Beam deflection vs. beam length for varying beam widths










5.1.4 Effect of Varying Dopant Profile

The diffusion of boron in silicon is concentration dependent and is modeled by

[Jae02]:

X
N(x, t) = N exp- ( )2 (5-2)
2 Dt
where Np is the peak concentration in cm-3, x is the distance in cm into the bulk of the

wafer, D is the diffusivity of boron in silicon in cm2/sec, and t is the time in seconds. The

effect of varying the concentration gradient on beam deflection is shown below in Figure

5-5. For simulation purposes, the Dt factor was varied and the deflection of the beam

was observed for a beam length of 50 um and width of 0.6 um. The beam with a larger

boron distribution resulted in greater beam deflection.


Defleciton for various doping profiles, length=50 um,
thickness=0.6 um

0.1
0;
E-0.1 10 c --- N(x)=8e19exp(-x^2/.01)
a-0.2
C- ---N(x)=8e 9exp(-xA2/.001)
o -0.2
N(x)=8e19exp(-x^2/.0001)
-0.3 N(x)=8el9exp(-xA2/.1)
-0.4
-0.5
beam length (um)


Figure 5-5: Beam deflection vs. beam length for varying doping profiles


5.2 Multiple Material Layer Bending Simulations

Due to its excellent mechanical properties, silicon nitride can be used for a variety

of applications such as: a structural material to fabricate MEMS devices, isolation layers

between transistors, masks for diffusion and etching, and recently, to induce uniaxial










tensile strain in the channel of NMOS transistors. Nitride is deposited by chemical vapor

deposition typically around 7000C, and has a higher thermal expansion coefficient than

silicon. If the resulting stress is below a certain threshold, the structure relaxes by

distorting, and above the threshold it will generate dislocations. In equilibrium, the

forces and moments between the silicon and silicon nitride must balance, creating a

bending in the materials. The tensile residual stress in the nitride causes it to curl up at

the edges, creating a pocket of tension near the edges of the silicon nitride/silicon

interface, and compressive stress underneath the nitride. The bending behavior is

illustrated in Figure 5-6 below:

X FLOOPS.AB Plot Window *I]IA
File Axis Style Markers Help

Plot File Name: lacelhomelfacel randeliffloopsisrciElastic Simulationsinitrideonsi/nitridecuriupatedges

Nitride curling up at edges from intrinsic stress
Nitride Grid Silicon Grid






-005 -




0I l l 1 -,I lI IIIII i1 1
I I "~' ,,I,


6 10


Figure 5-6: Nitride curling up at edges due to tensile residual stress

A functionality test was performed to ensure the multiple material layer structure behaved

as expected. In FLOOPS, a region of silicon nitride was defined on top of a silicon

region. The material properties used for each material were [Jae02]:









Table 1: Material parameters used for nitride on silicon simulations
Young's Modulus Poisson's Ratio

Silicon Nitride 3x1012 dyn/cm2 .25

Silicon 1.22x1012 .3


In the first set of simulations, the nitride thickness was varied while the silicon

thickness was kept constant at 10 um. Fixed boundary conditions were set at the bottom

of the wafer, so a relatively thick substrate was selected to ensure that a small structure

would not interfere with the bottom boundary. An intrinsic stress, approximately

1.6x1010 dyn/cm2, was defined in they (channel direction) direction of the nitride. The

bodyforce operator, discussed in Chapter IV, was used to provide the intrinsic stress in

the nitride. By varying the elemental strain in the silicon nitride layer, an approximate

value of the intrinsic stress can be computed. These stress values were compared with

results from the ISE version of FLOOPS for the same simulation. When the stresses

were equal, the elemental strain in the nitride was approximately equal to the intrinsic

stress of 1.6x1010 dyn/cm2. This is an unpractical way to provide intrinsic stress in a

material layer and is discussed in the future work section of Chapter VI. The effect of

varying the nitride thickness, while maintaining a constant silicon thickness, on wafer

bending is illustrated in Figure 5-7. As the nitride thickness is increased, the structure

curls up more appreciably due to a greater constant force distributed through the nitride

layer.






























Figure 5-7: Deflection vs. distance for varying nitride thicknesses

Next, the effect of varying the silicon substrate thickness on wafer bending was

observed. The nitride thickness was kept constant at 0.1 um, while the silicon thickness

was varied. As the silicon thickness was decreased from 15 to 5 um, an increase in wafer

curvature was observed as expected.


Deflection for varying silicon thickness, nitride
thickness= 0.1 um

0.006
0.005
0.004 ---Silicon=15 um
S0.003 -
c 0- --Silicon=10 um
o 0.002 -
o 0.Silicon=8 um
,- Silicon=5 um

-0.0011- 25 3
-0.002
distance (um)



Figure 5-8: Deflection vs. distance for varying silicon thicknesses


Deflection vs distance for varying nitride
thickness, silicon thickness=10um

0.012
0.01
E 0.008 -
3 ---Nitride=0.1 um
, 0.006 -X*^
o 0 -u-Nitride=0.2 um
0.004
8 Nitride=0.25 um
5 0.002 -
-a0

-0.002 1 ? 1 6
distance (um)











The stress fields from the structure in Figure 5-6 are illustrated in Figures 5-9, 5-10,


and 5-11. The lateral edges are not constrained and bottom boundary condition is used.


The substrate is 20 um thick and the nitride is 0.1 um thick. The deposited nitride is


assumed to be in tension. If the nitride extends over the entire substrate, minimal stress


in the substrate would result since the substrate several orders of magnitude larger than


the nitride. However the nitride is patterned and large stresses are generated in regions


close to the edge, which is known as the "lift-off' effect, causing the edges to go into


tension [Sen01]. The region below the nitride is pushed down in compression. The


stress in the yy (channel) direction is larger than the xx (bulk) direction because the


intrinsic stress in the nitride is defined in the yy direction. These results are in accordance


with a similar simulation performed by Chaudhry [Cha96].

X FLOOPS.9B Plot Window 10[Ix
File Axis Style Markers Help

Pot File Name: lace/homelfacellrandell/floops/srclElastic Simulationsinitrideonsilstress.yy from nitride

Stress.yy from nitride on silicon
Nitrde Silicon Val3e+09 Vail e+10 Val-5e+09 al-3e+09 --Va5e+09 Val-8e+09


-0 1


0-


01-


02-


0.3

4 6 8 10


Figure 5-9: Stress.yy from silicon nitride on silicon








73


X FLOOPS.98 Plot Window IGAR
File Axis Style Markers Help

Plot File Name: lacelhomelfacelirandellifloopsisrclElastic Simulationsinitrideonsilstress.xx from nitride

Stress.xx from a nitride layer
Nitride Silicon -- \lle+09 --Va-le+09 -- a5e+09 -Va 2e+09 -Val-2e+09



05



ot I ,
I^ I I I
05I



















File Axis Slyle Marters

Plot File Name:

Stress.xy RB
Nitride Vae+09 i5e+09 /-3e+09
Silicon e+09 5e+09 3e+09
Figure 5-10: Stress.xx from silicon nitride on silicon

X FLOOPS.9B Plol Window |-[-][r-
File Arxls Slyle Markers Helpi

Plot File Name:

Stress.xy RB
SNitride Valle+09 Va15e+09 -- Val-3e+09
SSilicon Va-e+09 VAl-5e+09 V 13e+09


4;

/d
i' 7


5 10




Figure 5-11: Stress.xy from silicon nitride on silicon









The shear components of stress have implications on bulk processing (dislocation

loop glide and substrate yielding), thus it is of use to explore these stresses. The slip

pattern in silicon for the <111> plane is the [110] direction, which corresponds to shear

stresses. The contours of the xy simulations indicate that the shear stress lobes peak at

approximately 450 and represent the area for dislocation loop glide. The contour is a

double lobe because the shear stress is related to the polar coordinates as [Cha96]:

a, = (c, ca) sin 20 + a,, cos 20 a, sin 20 (5-3)

In the experiments performed by Ross, dislocation loops from a nitride strip on silicon

formed in the same region indicated by the stress contours. In simulation, Chaudhry also

found lobes of the same shape to form on nitride strips in silicon.



Effect of Boundary Conditions on Stress Fields

Two different reflecting boundary conditions were simulated for the nitride on

silicon structure to observe the overall shape of the stress contours. The reflecting

bottom boundary condition and reflecting left and reflecting right boundary conditions

were applied and the stress in the xx, yy, and xy directions are illustrated:


wI fl. h. 'PI i. harw.











Figure 5-12: Stress xx for reflecting bottom (left) and reflecting left and right (right)
boundary conditions
boundary conditions














lurt m taur m.I

sIrt .yy RB









S---


rrss.yy RL and R


Figure 5-13: Stress yy for reflecting bottom (left) and reflecting left and right (right)
boundary conditions


F0 m 'YW F "


ires5.xyRB











.Ji


5 FLIXPIw Pi0i vn A.C* ij


Aflt FH i-:


Figure 5-14: Stress xy for reflecting bottom (left) and reflecting left and right (right)
boundary conditions


For the xx and yy stress simulations, stresses build up near the edges for the


reflecting left and right boundary conditions. This would be expected because the left


and right hand sides are fixed and there is no free surface for the stresses to relax. For the


reflecting bottom xx andyy simulations, the compressive region underneath the nitride


extends slightly lower than for the reflecting left and right boundary conditions. Overall,


although the stress distribution for each simulation varies somewhat throughout the


complete structure, the local stresses around the nitride/silicon interface are well-


represented.


SFLO S.r Ploaltm i G* .Z

M FU mN-

--Wre








1

,..^__


K1


"-J


.~


ressxy RL and RR
---w~lca --yt-3Blt --wuSr^









5.3 Channel Stress from Boron Source/Drain Doping

As discussed in Chapter IV and demonstrated in Section 5.1, boron doping

introduces a local tensile strain in the substrate due to its size mismatch with silicon. The

strain from the boron doping causes the silicon to warp and the deformations are used to

calculate the resulting stresses in the substrate. While this phenomenon is beneficial for

fabricating MEMS devices such as sensors and membranes, it can be deleterious to

device operation as channel lengths are decreased below 100 nm.

Stress in the channel from doping the source and drain regions was a relatively

insignificant factor until CMOS transistor channel lengths entered the nanometer realm.

Consider a PMOS transistor doped with boron source drains. Boron is the p-type dopant

of choice due to its high solubility limit in silicon; at 11000C, boron has a solubility limit

in silicon of 3.3x1020/cm-3 [Jae02]. Negatively charged dopants, such as boron, become

more soluble under compressive stress, but the tensile stress induced from boron doping

can counteract the desired compressive channel stress applied to increase hole mobility

[Sad02]. For PMOS devices, tensile stress from boron incorporation as low as 100 MPa

can compensate the intentional compressive stress engineered into the channel, resulting

in a net close to zero stress. This example could be applicable for the compressive stress

introduced from STI structures.

The bending behavior of a boron-doped silicon beam was properly calculated and

compared with experimental data in Section 5.1. This technique is taken one step further

and applied to a PMOS-like device; a silicon substrate and source/drain regions doped

with boron. To observe the channel stress under varying process parameters, the stress at

the center of the channel from boron doping in the source/drain region was observed.

The channel length, source drain length, and boron concentration were varied to observe









scaling trends for different technology nodes. The finite element structure showing the

parameters to be varied is illustrated in Figure 5-15.

S/D Length

Boron Boron

Channel Length



Silicon

Figure 5-15: Silicon doped with boron source drain regions general structure

5.3.1 Effects of Channel Length Scaling

The channel is used for carrier conduction and is defined as the region between the

source and the drain; approximately 100 A below the surface. The first structure

simulated had a peak boron concentration of 2x1020/cm3 in the source/drain regions,

source/drain lengths of 1 um, and a junction depth of 0.12um. As the channel lengths

were varied from 1 um to 45 nm, the stress at the center of the channel was observed.

The results illustrate that as channel lengths decreased, the increased stress in the center

of the channel approached exponentially. At a 45 nm channel length, approximately 80

MPa of stress exists from source drain doping alone. Due to the free surface at the top of

the structure, the structure relaxes and deformed more than if a realistic PMOS device

with a gate and spacers were present.











Stress vs Channel Length

9.00E+07
8.00E+07
7.00E+07 -
W 6.00E+07
5.00E+07
C 4.00E+07
C 3.00E+07
2.00E+07
1.00E+07 -
0.00E+00
0 0.2 0.4 0.6 0.8 1 1.2
Channel Length (um)


Figure 5-16: The effect of scaling channel length on stress from boron doping

5.3.2 Effect of Source/Drain Length Scaling

The length of the source and drain is determined by design rules specific to each

technology, and is equal to 6 lambda, where lambda is half of the minimum feature size.

The simulated structure had a peak boron concentration of 2x1020/cm3 in the source/drain

regions and a junction depth of 0.12um. As the source/drain lengths were varied from 0.3

um to 1 um, the stress at the center of the channel was observed. This was performed for

both 45 nm and 100 nm channel lengths. For longer source/drain lengths, larger amounts

of boron are available to pull on the channel, thus increasing the stress. This trend is

shown in Figure 5-17.











Stress vs Source/Drain Length

9.00E+07
8.00E+07 -
7.00E+07
F 6.00E+07
-5.00E+07 100 nm channel
w 4.00E+07 45 nm channel
3 3.00E+07
2.00E+07
1.00E+07
0.00E+00
0 0.5 1 1.5
Source/Drain Length (um)



Figure 5-17: The effect of scaling the source/drain length on channel stress for 100 nm
and 45 nm channel lengths

5.3.3 Effect of Boron Concentration Scaling

The effect of varying the boron concentration in the source/drain regions on

channel stress was explored. Of all the factors affecting the stress in the channel, the

boron concentration appears to have the largest influence on the channel stress. The

simulated structure had a source/drain length of 1 um and a junction depth at 0.12 um.

The boron concentration was varied from 6x1019 to 5x1020/cm3, and the stress at the

center of the channel was observed. Although boron is soluble in silicon up to

approximately -3.3x1020/cm3, it is soluble at larger concentrations in silicon germanium.

For 45 nm and 100 nm devices, the stress in the channel approaches 100 MPa at

concentrations above 2.5x1020/cm3 and 3x 1020/cm3 respectively.










Stress vs Boron Concentration

2.50E+08

2.00E+08

-. 1.50E+08 -*-100 nm channel

| 1.00E+08 -U-45nm channel

5.00E+07

0.OOE+00
O.OOE 1.00E 2.00E 3.00E 4.00E 5.00E 6.00E
+00 +20 +20 +20 +20 +20 +20
Boron Concentration /cm^3

Figure 5-18: The effect of scaling the source/drain length on channel stress for 100 nm
and 45 nm channel lengths

5.4 Summary

As the semiconductor industry enters the nanometer realm, stress from sources that

were given little recognition in the past are becoming significant such as: stresses from

STI structures, film deposition, and dopants. This chapter provided results regarding the

stress from boron doping and the stress from nitride deposition. Boron is the main dopant

for PMOS transistors due to it high solid solubility limit in silicon, however at large

concentrations and small device dimensions, the presence of boron can alter intentional

stress placed in the channel for carrier mobility enhancement, as well as introducing

unintentional stress in the wafer.

Boron-doped cantilever beams were simulated to demonstrate the effect of boron

doping on beam deflection that resulted from a non-uniform doping profile. The

simulation setup was identical to that of Rueda et al., and the bending behavior results

were in accordance. The beam length and width dictated the amount of beam deflection.

Shorter, thicker beams deflected less than longer, thinner beams with identical boron









diffusion profiles. Beams with larger boron concentrations or wider diffusion profiles

deflected more than beams with lower concentrations, or steeper diffusion profiles.

Next, the stress from depositing a strip of nitride on silicon was observed. The

intrinsic stress of approximately 1.6x1010 dyn/cm2 in the longitudinal direction is the

main source of stress in nitride. As the edge regions of the nitride curl up, the silicon to

curls up as well. This known behavior creates significant stress in the [110] direction.

Tensile lobes are observed at the silicon nitride/silicon interface, and large compressive

stresses are observed underneath the nitride film. Different boundary conditions were

also simulated to investigate how the stress distributions differ throughout the structure.

Although the stress distribution throughout the entire structure varied slightly, the local

stresses around the nitride on silicon structure were approximately equal. Stresses built

up more along the sides of the structure with fixed left and right hand side boundary

conditions, as expected.

Table 2: Results summarizing the effect of boron doping on channel stress
Parameters varied Effect on Stress

Channel Length As channel length decreased, stress

in the center of the channel increased

Source/Drain Length As source/drain length decreased,

stress in the center of the channel decreased

Boron Concentration As the boron concentration increased,

the stress in the center of the channel

increased






82


Lastly, the effect of stress in the channel from boron doping was examined. The

channel length, source/drain length, and boron concentration were varied and the stress at

the center of the channel was quantified. Above is a table summarizing the results:

Increasing the boron concentration appeared to have the most significant effect on

increasing the stress in the channel. For concentrations greater than 2.5x1020/cm3 for 45

nm channel lengths and 3x1020/cm3 for 100 nm channel lengths, the stress in the channel

was greater than 100 MPa. In chapter IV, a summary of each chapter will be presented,

and future work will be discussed.














CHAPTER 6
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE WORK

6.1 Summary and Conclusions

In this thesis, many important sources of stress in silicon technology have been

investigated. Finite element code was implemented in FLOOPS to develop a two-

dimensional model for dopant induced stress in the silicon substrate. The model was

verified with experimental data when possible, and was compared to simulation data

otherwise.

In Chapter I, a survey of existing literature on stress applications in silicon

technology and driving motivations for studying stress was discussed. Stress-induced

defect formation from patterned structures was quantified by experimentation and

through simulation. Next, strained silicon was introduced because this work will have

many future implications in this area of research. Applications of how the advantageous

stress enhances device performance and how the unintentional stress hinders device

performance were exemplified.

Chapter II introduced the concepts of stress, strain, and linear elasticity. Examples

of normal and shear stresses were presented. Stress from patterned films are commonly

encountered in IC fabrication, and understanding the stresses generated as a result of

deposition are important. Examples are provided to describe the plane stress that results

due to a thin film on a thick substrate.

Chapter III discusses various unintentional stress sources that arise during

semiconductor fabrication processes such as STI formation, film deposition, and dopant









induced stresses. Non-planar oxidation, thermal mismatch, and intrinsic stresses all

accumulate in and around the STI structure to contribute to the total stresses. In addition

to STI formation, variations in the deposition process of thin films can affect the

magnitude and amount of residual stress in the film and substrate.

Next, stress from dopants and dislocation loops, and stress assisted diffusion was

discussed. Since boron is smaller than silicon, it contracts the silicon lattice and creates a

local tensile region. Germanium, on the other hand, is larger than silicon and creates a

lattice expansion. Due to dopant incorporation, the silicon will distort to relax the stress.

This was demonstrated in Chapter V in the beam bending simulations. If the stress in the

substrate is too high, it will yield by generating dislocations. Dislocation loops form as a

result of high shear stresses in the { 111 plane and can glide in the [110] plane if the

critical glide stress is exceeded. Lastly, stress assisted diffusion of boron in silicon and

silicon germanium was discussed. A possible explanation to boron diffusion retardation

in silicon germanium is attributed to the boron-germanium binding.

Chapter IV focuses on the software enhancements in FLOOPS to calculate the

displacements and stresses in the silicon substrate due to boron doping. The finite

element method was implemented using the 2-D plane strain equation to create the

"elastic", "bodyforce", "strain", and "stress" operators. The equation to be solved is

essentially f=kx, where f is the force from the dopants, k is the stiffness, and x is the

resulting displacements. The "elastic" operator was developed to find the stiffness (k) of

the silicon mesh, and the "bodyforce" operator equated the strain from boron doping into

an elemental force (f). The matrix equation was solved, and the resulting displacements

were transformed into strains and stresses through the "strain" and "stress" operators.









The linear elastic model was also integrated with the property database and process

commands.

Chapter V provided applications and results to the beam bending, nitride

deposition, and PMOS-like structure simulations. A beam bending experiment was

performed to observe the effect of strain from boron doping. The beam length, thickness,

and doping profile were adjusted independently and the bending behavior was observed.

Due to the non-uniform boron doping profile in the beam, the beam will bend upwards

towards the tensile region to relieve the stress. Larger deflections resulted from longer

beam lengths, thinner beams, and wider diffusion profiles. The simulation values agreed

with those of Rueda.

Next the stress from a nitride deposition was simulated by applying a constant force

to the nitride layer and equating the force to an intrinsic stress. Stress contours were

compared with ISE FLOOPS, and when the substrate stresses were equivalent, the proper

intrinsic stress of 1.6x1010 dyne/cm2 was defined in the nitride. These results were

comparable to the simulation of Chaudhry as well. Two different boundary conditions

reflecting bottom, and reflecting left and right were simulated to observe the xx, yy, and

xy stress in the silicon substrate from nitride deposition. Although the stress contours

varied slightly throughout the structure, the local stresses around the nitride/silicon

interface were approximately equal for both boundary conditions. It was concluded that

the different boundary conditions did not have significant effect on the stress simulation

results.

Finally, the stress in the center of the channel due to boron doping in the source

drain was investigated. Since the boron atom is smaller than the silicon atom, it exerts a