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2-D Modeling of Solid Phase Epitaxial Regrowth Using Level Set Methods

Permanent Link: http://ufdc.ufl.edu/UFE0041076/00001

Material Information

Title: 2-D Modeling of Solid Phase Epitaxial Regrowth Using Level Set Methods
Physical Description: 1 online resource (129 p.)
Language: english
Creator: Morarka, Saurabh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: dopants, epitaxy, floops, level, regrowth, semiconductor, silicon, sper
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Solid Phase Epitxial Regrowth (SPER) has a huge technological relevance in the formation of source/drain regions of MOS devices. Source/drain regions are patterned amorphous regions that need to be modeled in 2D/3D. The macroscopic velocity, v, of an interface between amorphous (?) and crystalline (c) phases (also referred to as the SPER or regrowth front/interface) is known to be a thermally-activated process with an activation energy of ~2.7 eV. Additionally, SPER is affected by the crystal orientation of ?-Si/c-Si interface, impurities, and applied mechanical stress. In this work, level set model was set up to model SPER. The ?-c Si interface propagation velocity was computed using a substrate orientation dependent velocity term along with a local interface curvature term. This velocity was fed to the advection equation of level set formulation for simulating SPER. Simulations were checked against observed TEM images of SPER of ~120 nm deep, patterned amorphous trench at T = 500 C and at t = 1 h, 2 h and a good matching was observed for all times. More experiments were done to confirm the presence of interface curvature term on SPER using structures containing both convex and concave interfaces. During SPER at T = 500 C, the concave interface sharpened while the convex interface flattened out. The simulations were successfully able to predict the shapes of ?-c Si interface during SPER at all times. The experiment when repeated at a higher temperature of 575 C resulted in similar regrowth shapes implying a negligible effect of temperature on the curvature factor. Effect of n and p dopants on patterned SPER was studied in an experiment with very low resistivity (~0.003 ohm-cm) wafers. The results showed the isotropic nature of dopant enhancement (both p and n type) on SPER, something that extends the generalized Fermi level shifting theory (for dopant enhancement of SPER) for all substrate orientations. The results also helped de-link the curvature effect from the electronic effect of dopants on SPER. Models for dopant diffusion in amorphous Si were linked to the SPER model to get accurate dopant profile after regrowth. Finally, the effect of uniaxial stress on patterned SPER was studied in an experiment where stresses (both tensile and compressive) upto ~1.3 GPa were applied. The experiments showed the strong effect of in-plane uniaxial compression on regrowth shapes that resulted in the formation of mask-edge defects. The results for the tensile case were found to be exactly the same as no-stress case, something that was observed previously for planar regrowth of (001) Si. The curvature factor was able to encapsulate the effect of external in-plane uniaxial stress and simulations matched up to the observed results. A more physical understanding of the curvature factor was explored using simulations with rough ?-c Si interfaces. Ultimately, a complete 2-D model for patterned SPER was developed using level set methods for interface propagation.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Saurabh Morarka.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Law, Mark E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041076:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041076/00001

Material Information

Title: 2-D Modeling of Solid Phase Epitaxial Regrowth Using Level Set Methods
Physical Description: 1 online resource (129 p.)
Language: english
Creator: Morarka, Saurabh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: dopants, epitaxy, floops, level, regrowth, semiconductor, silicon, sper
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Solid Phase Epitxial Regrowth (SPER) has a huge technological relevance in the formation of source/drain regions of MOS devices. Source/drain regions are patterned amorphous regions that need to be modeled in 2D/3D. The macroscopic velocity, v, of an interface between amorphous (?) and crystalline (c) phases (also referred to as the SPER or regrowth front/interface) is known to be a thermally-activated process with an activation energy of ~2.7 eV. Additionally, SPER is affected by the crystal orientation of ?-Si/c-Si interface, impurities, and applied mechanical stress. In this work, level set model was set up to model SPER. The ?-c Si interface propagation velocity was computed using a substrate orientation dependent velocity term along with a local interface curvature term. This velocity was fed to the advection equation of level set formulation for simulating SPER. Simulations were checked against observed TEM images of SPER of ~120 nm deep, patterned amorphous trench at T = 500 C and at t = 1 h, 2 h and a good matching was observed for all times. More experiments were done to confirm the presence of interface curvature term on SPER using structures containing both convex and concave interfaces. During SPER at T = 500 C, the concave interface sharpened while the convex interface flattened out. The simulations were successfully able to predict the shapes of ?-c Si interface during SPER at all times. The experiment when repeated at a higher temperature of 575 C resulted in similar regrowth shapes implying a negligible effect of temperature on the curvature factor. Effect of n and p dopants on patterned SPER was studied in an experiment with very low resistivity (~0.003 ohm-cm) wafers. The results showed the isotropic nature of dopant enhancement (both p and n type) on SPER, something that extends the generalized Fermi level shifting theory (for dopant enhancement of SPER) for all substrate orientations. The results also helped de-link the curvature effect from the electronic effect of dopants on SPER. Models for dopant diffusion in amorphous Si were linked to the SPER model to get accurate dopant profile after regrowth. Finally, the effect of uniaxial stress on patterned SPER was studied in an experiment where stresses (both tensile and compressive) upto ~1.3 GPa were applied. The experiments showed the strong effect of in-plane uniaxial compression on regrowth shapes that resulted in the formation of mask-edge defects. The results for the tensile case were found to be exactly the same as no-stress case, something that was observed previously for planar regrowth of (001) Si. The curvature factor was able to encapsulate the effect of external in-plane uniaxial stress and simulations matched up to the observed results. A more physical understanding of the curvature factor was explored using simulations with rough ?-c Si interfaces. Ultimately, a complete 2-D model for patterned SPER was developed using level set methods for interface propagation.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Saurabh Morarka.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Law, Mark E.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041076:00001


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1 2 D M ODELING OF SOLID PHASE EPITAXIAL REGROWTH USING LEVEL SET METHODS By SAURABH MORARKA A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGRE E OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2010

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2 2010 Saurabh Morarka

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3 To my loving family

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4 ACKNOWLEDGMENTS I would like to acknowledge my advisor Dr. Mark E. Law for his support and encouragement. I was amazed to see the extent to which he was willing to help his students despite having a packed schedule. I feel fortunate to have learnt the intricacies of device and process simulation from him. I also want to thank my committee members Dr. Kevin S. Jones, Dr. Scott E. Thompson and Dr. David P. Arnold for their valuable suggestions in my thesis. This work would not have been possible without the help of Nicholas Rudawski and Sidan Jin who helped me out with transmission electron microscopy (TEM) imag es. Last but not the least, Id like to thank all the past and present SWAMP group members for all their support.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF FIGURES .............................................................................................................................. 7 ABSTRACT ........................................................................................................................................ 10 CH A P T E R 1 INTRODUCTION ....................................................................................................................... 12 1.1 Metal Oxide Semiconductor (MOS) Transistor ................................................................. 12 1.2 Technological Relevance of Solid Phase Epitaxial Regrowth ........................................... 14 1.3 Motivation ............................................................................................................................. 15 2 LITERATURE REVIEW ........................................................................................................... 20 2.1 Planar Solid Phase Epitaxial Regrowth ............................................................................... 20 2.1.1 Introduction................................................................................................................. 20 2.1.2 Substrate Orientation Depende nce ............................................................................ 20 2.1.3 Doping Effect on SPER ............................................................................................. 22 2.1.4 Stress Effect on SPER ................................................................................................ 24 2.2 Patterned SPER ..................................................................................................................... 26 2.2.1 Substrate Orientation Effect and Mask Edge Defects ............................................. 26 2.2.2 InPlane Uniaxial Stress Effect on Patterned SPER ................................................ 28 2.3 SPER Modeling..................................................................................................................... 29 2.3.1 2D Analytical Model .................................................................................................. 29 2.3.2 Atomistic Modeling of SPER .................................................................................... 32 3 EXPERIMENTAL AND SIMU LATION TECHNIQUES ...................................................... 42 3.1 Material Processing ............................................................................................................... 42 3.1.1 Pattern Creation Using Electron Beam Lithography and Reactive Ion Etching (RIE) ................................................................................................................................. 42 3.1.2 Ion-Implantation ......................................................................................................... 44 3.1.3 Application of InPlane U niaxial Stress ................................................................... 46 3.1.4 Temperature Calibration and Annealing ................................................................... 47 3.1.5 Cross -section Transmission Electron Microscopy Sample Preparation ................. 48 3.2 Material Characterization ..................................................................................................... 48 3.2.1 Transmission Elec tron Microscopy ........................................................................... 48 3.3 Simulation Techniques ......................................................................................................... 49 3.3.1 Level Set Methods ...................................................................................................... 49

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6 4 IMPLEMENTATION OF LEVEL SET METHODS FOR SOLID PHASE EPITAXIAL REGROWTH AND INITIAL RESULTS ................................................................................. 62 4.1 Introduction ........................................................................................................................... 62 4.2 Level Set Implementation ..................................................................................................... 62 4.3 Experiments and Initial Simulations .................................................................................... 65 4.4 Summary................................................................................................................................ 66 5 ROLE OF CURVATURE PARAMETER IN SOLID PHAS E EPITAXIAL REGROWTH OF INTRINSIC SILICON ................................................................................. 72 5.1 Introduction ........................................................................................................................... 72 5.2 Model for SPER Including Curvature ................................................................................. 72 5.3 Curvature Confirming Experiment and Simulation ............................................................ 7 4 5.4 Interpretation of the Curvature Factor in SPER .................................................................. 77 5.5 Predicting 2D Regrowth Shapes .......................................................................................... 79 5.6 Summary................................................................................................................................ 81 6 DOPANT EFFECT ON SOLID PHASE EPITAXIAL REGROWTH OF SILICON ........... 88 6.1 Introduction ........................................................................................................................... 88 6.2 Experiment for Dopant Effect on SPER .............................................................................. 89 6.3 Discussion .............................................................................................................................. 92 6.3 Linking Diffusion and SPER ................................................................................................ 93 6.4 1D SPER and Diffusi on ........................................................................................................ 94 6.5 2D SPER and Diffusion ........................................................................................................ 95 6.6 Summary................................................................................................................................ 96 7 STRESS EFFECT ON SOLID PHASE EPITAXIAL REGROWTH OF SILICON ........... 103 7.1 Introduction ......................................................................................................................... 103 7.2 Interfacial Roughening During SPER ............................................................................... 104 7.3 InPlane Uniaxial Stress Experiments ............................................................................... 106 7.4 Simulation and Curvature Effect ........................................................................................ 108 7.4 Physical Expl anation of Curvature Effect ......................................................................... 110 7.5 Summary.............................................................................................................................. 112 8 SUMMARY AND FUTURE WORK ..................................................................................... 117 8.1 Overview of Results ............................................................................................................ 117 8.2 Future Work ........................................................................................................................ 119 LIST OF REFERENCES ................................................................................................................. 124 BIOGRAPHICAL SKETCH ........................................................................................................... 129

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7 LIST OF FIGURES Fi gure page 1 1 Schematic of a basic n -MOSFET transistor. ............................................................................. 18 1 2 Cartoon of a MOS transistor with mask -edge defects. ............................................................. 18 1 3 (a) Mask edge defects shown in plan view TEM image, (b) cross -section TEM image of the initial -c interface that creates defects after SPER. ..................................................... 19 1 4 Boron diffusion in amorphous Si licon (Si) is shown by the yel low line. Significant diffusion at 600 0C for 1 min. implies a high diffusivity30. ................................................. 19 2 1 Solid Ph ase Epitaxial Regrowth process ................................................................................... 34 2 2 Two -dimensional atom istic model for regrowth13 .................................................................... 35 2 3 Band -diagram of amorphous Si and p type doped crystalline Si ............................................. 36 2 4 Cartoon of a patterned a s implanted amorphous trench region. The interface consists of varying substrate orientations that result in nonisotropic regrowth18. ............................... 37 2 6 TEM images showi ng patterned amorphous regrowth ............................................................. 3 8 2 7 TEM images representing patterned SPER for two Si substrates ............................................ 39 2 8 Cartoon (based on TEM images 15) showing SPER of a sinusoidal shaped as implanted amorphous interface ............................................................................................................... 40 2 9 TEM images of SPER of patterned trench -c Si interface under stress ................................ 41 3 1 Scattering effects during e -beam lithography. Figure shows the forward scattered electrons (FSE) and the back scattered electrons (BSE) 65. ................................................. 53 3 2 E -beam lithography for patterned regions ................................................................................. 54 3 3 A diagram of a common Reactive Ion Etch (RIE) setup. An RIE consists of two electrodes (1 and 4) that create an electric field (3) meant to accelerate ions (2) toward the surface of the samples (5).66 ............................................................................... 55 3 5 Schematic of a basic ion implantation system.53 ...................................................................... 57 3 6 Cross -sectional Transmission Electron Microscopy image of an as implanted Si sample. ... 57 3 7 Schematic of the apparatus used to induce and measure in -plane uniaxial stress in Si wafers 37,53 ............................................................................................................................... 58

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8 3 8 Schematic of the tube furnace apparatus used for annealing and the method of temperature calibration 53 ...................................................................................................... 58 3 9 Figure shows the initialization of the Level Set higher order function as a signed distance to the interface58. ...................................................................................................... 59 3 10 Pictorial view o f level set function (x, y, t) on the right. Left figure shows the interface at x,y at time t=t1 where (x, y, t1) = 0. The position of the interface is embedded in the function 58. ............................................................................................... 59 3 11 Time evolution of the level s et function and extracted interface at different times. The interface is circular and expanding with a fixed isotropic velocity58. ................................. 60 3 12 Ability of Level Set method to merge two disjoint regions :(a) level sets at t=0. ( b) level sets at t=1 58. .................................................................................................................. 61 4 1 Asimplanted amorphous -crystalline interface showing various substrate orientations and the surface angle ( ) for orientation dependent factor f(). .......................................... 68 4 2 Simulation of regrowth using Level Set Methods with isotropic velocity 14. Contours represent the position of -c interface at different times of regrowth. ............................... 69 4 3 The normalized SPER veloci ty, f ( ) 14, as a function of the substrate orientation angle from [001] towards [110], as measured by Csepregi et al .13 ........................................... 69 4 4 Simulation of regrowth with orientation dependence included (velocity from Equation 4 3). Contou rs represent the -c interface at different times of regrowth. Region outside the contour is crystalline and inside is amorphous. ................................................ 70 4 5 -c interfacial pinni ng at the surface at T = 500 C. .................................................................................................. 71 5 1 The observed and curvature c interfacial pinning at the surface at T = 500 C ................................................................. 82 5 2 -c interfacial pinning ................................. 83 5 3 The observed and curvature included simulated 2D SPER pr ocess in a structure without c interfacial pinning at the surface at T = 500 C ............................................................. 84 5 4 -c interfacial pinning at the surface. .......................................................................................... 85 5 5 c interfacial pinning. ................................................................................................................. 85 5 6 -c interface curvature near the corner region on the level set simulations using both regrowth orientation and interfacial curvature dependence .......... 86

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9 5 7 The effe -c interface width to -depth (W/D) ratio on the regrowth shapes for 2D SPER using level set simulations .................................................................................... 87 6 1 Asimplanted -c interface of Si for semi -insulating, n -type and p-type samples. Si3N4 mask patterned to get a patterned -c interface. .................................................................. 98 6 2 The observed 2D SPER process at T=500 0C with dopants ..................................................... 99 6 3 Figure shows the effect of dopants on Csepregis 13 SPER data. Experimental results suggest shifting up of the data due to the isotropic SPER dopant enhanced velocity. .... 100 6 4 Level set simulations showing the effect of the curvature param eter A on the shape of regrowth for t=5 h. and T=500 0 C. ..................................................................................... 100 6 5 1D diffusion of Boron during SPER. The figure shows the SIMS profile of Boron as implanted and after annealing at T=550 0 C for t=30mins. 30,82 ........................................ 101 6 6 Figure shows the effect of 2D SPER on dopant profile .......................................................... 102 7 1 XTEM images of SPER und er in -plane u niaxial compression .............................................. 113 7 2 Level set simulations of SPER with varying curvature factor A. (a), (b), (c), (d) represent SPER after 1h. at 525 0C with values of A = 0, 1.5e 7, 2e 7, 4e 7cm res pectively. .......................................................................................................................... 113 7 3 Weak beam dark field (WBDF) -XTEM images of the stress influenced SPER process in As -doped specimens53 ..................................................................................................... 114 7 4 XTEM images of patterned SPER under no external stress ................................................... 115 7 5 XTEM images of patterned SPER under in-plane uniaxial stresses ...................................... 115 7 6 Level set simulations of SPER for matching the observations shown in Figure 7 5 by varying curvature factor A ................................................................................................... 116 8 1 XTEM images of SPER at 525 0C for 4h. under uniaxial in -plane compression into the page of the figure (or parallel to lines 22 300MPa) ...................................................... 122 8 2 XTEM images of SPER under uniaxial in-plane stresses into the page of the figure (or parallel to lines 22 300MPa) ......................................................................................... 123

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10 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2 D M ODELING OF SOL ID PHASE EPITAXIAL REGROWTH USING LEVEL SET METHODS By Saurabh Morarka M ay 2010 Chair: Mark E. Law Major: Electrical and Computer Engineering Solid Phase Epitxial Regrowth (SPER) has a huge technological relevance in the formation of source/drain regions of MOS devices. Source/drain regions are patterned amorphous regions that need to be modeled in 2D/3D. The macroscopic velocity, v of an interface between front/interface) is known to be a thermallyactivated process with an activation energy of ~2.7 eV. Additionally, SPER is affected by the crystal o -Si/c -Si interface impurities, and applied mechanical stress. In this work, level set model was set up to model SPER. The -c Si interface propagation velocity was computed using a substrate orientation dependent velocity term along with a local interface curvature term. This velocity was fed to the advection equation of level set formulation for simulating SPER. Simulations were checked against observed TEM images of SPER of ~120 nm deep, patterned amorphous trench at T = 500 0 C and at t = 1 h, 2 h and a good matching was observed for all times. More experiments were done to confirm the presence of interface curvature term on SPER using structures containing both convex and concave interfaces. During SPER at T = 500 0 C, the concave interfa ce sharpened while the convex interface flattened out. The simulations were

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11 successfully able to predict the shapes of -c Si interface during SPER at all times. The experiment when repeated at a higher temperature of 575 0 C resulted in similar regrowth s hapes implying a negligible effect of temperature on the curvature factor. Effect of n and p dopants on patterned SPER was studied in an experiment with very low resistivity (~0.003 ohm -cm) wafers. The results showed the isotropic nature of dopant enhance ment (both p and n type) on SPER, something that extends the generalized Fermi level shifting theory (for dopant enhancement of SPER) for all substrate orientations. The results also helped de link the curvature effect from the electronic effect of dopants on SPER. Models for dopant diffusion in amorphous Si were linked to the SPER model to get accurate dopant profile after regrowth. Finally, the effect of uniaxial stress on patterned SPER was studied in an experiment where stresses (both tensile and compr essive) upto ~1.3 GPa were applied. The experiments showed the strong effect of in -plane uniaxial compression on regrowth shapes that resulted in the formation of mask edge defects. The results for the tensile case were found to be exactly the same as no s tress case, something that was observed previously for planar regrowth of (001) Si. The curvature factor was able to encapsulate the effect of external in -plane uniaxial stress and simulations matched up to the observed results. A more physical understandi ng of the curvature factor was explored using simulations with rough -c Si interfaces. Ultimately, a complete 2 D model for patterned SPER was developed using level set methods for interface propagation.

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12 CHAPTER 1 INTRODUCTION 1.1 Metal -Oxide Semiconductor (MOS) Transistor MOS transistor has revolutionized the electroni cs circuits for low power and faster speeds. The scaling of the transistor size using MOS has led to circuits becoming faster and denser. The scaling of MOS transistor has been driving the semiconductor industry for four decades. As expressed in an observa tion from Gordon Moore 1, the transistors per square inch has been doubling every two years ever si nce the integrated circuits were invented. The MOS transistor is a field effect transistor (hence called MOSFET) where the current through the transistor depends upon the field in the channel region. It is unipolar meaning only one carrier is responsible f or conduction. n-MOSFET has electrons as carriers for conduction while p MOSFET has holes. A basic structure of n -MOSFET transistor is shown in Figure 1 1. As Figure 1 1 shows, the transistor has four terminals: gate, source, drain and body. A positive g ate terminals voltage with respect to the source above a certain threshold voltage creates a conducting channel below the gate oxide. The conducting channel is composed of electrons for a p -body, hence it is called inversion of the channel. When a posit ive bias is applied on the drain side, it sweeps the carriers in the channel and there is conduction of current. It is observed that with decreasing channel length, the field in channel increases and the on-current increases. This is known as scaling. Con stant Electric field scaling and constant voltage scaling are the two ways scaling of transistor can be done. In constant field scaling, the applied voltages are scaled along with the device dimensions (most importantly L, the channel length) so that the field in the channel stays constant. This assures that that reliability of the scaled devices does not degrade with scaling. It increases the circuit speed and reduces the power dissipation. However, the fact that

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13 the shape of the field pattern in the cha nnel can only be preserved if the voltage is kept constant (because the built in potential of the source junction is independent of scaling), hence called constant voltage scaling. Constant voltage scaling increases the power dissipation though, that is a major challenge. Hence, in practice a combination of the two has been used. Silicon has been the choice of semiconductor for the MOSFETs especially because of the presence of a stable oxide (SiO2) that had very good physical and electrical properties for MOSFET operation. SiO2 is used as the gate oxide for its superior interface with Si that has very less traps and recombination sites. Reducing SiO2 thickness is one of the requirements of scaling (SiO2 acts as a capacitor for charge build up in the channel ). However, gate leakage through the SiO2 has given rise to high -K dielectrics like HfO2 that have a higher dielectric constant and therefore results in more capacitance for same physical thickness. Scaling of the MOSFET has also required the source and drain highly doped regions to become shallower and have higher dopant activation. Shallower source/drain regions are required to reduce the leakage current (during off condition). Higher dopant activation is important since, only a part of the implanted dop ant becomes active and takes part in the conduction process. This has led to a search for more innovative thermal processing steps like rapid thermal annealing, flash annealing or laser annealing. These annealing processes use high temperatures (up to 1300 0 C) for very short times (~1 millisecond) that serve to create high dopant activation and ultra -shallow junctions 2. Apart from scaling, applying stress to the MOSFET channel has been found to increase carrier mobility () and thus boost the current drive of the transistor 3. Liners of Si3N4 and related compounds (e.g. Oxynitrides) have been found to possess high stress depending on the way the thermal processing grows these liners. n -MOSFETs require tensile stress liners for

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14 improving their cu rrent drive while p -MOSFETs require compressive stress liners 4. p MOSFETs have also utilized the addition of Ge to form SixGe1x source/drain regions to provide additional compressive stress in the channel 5. 1.2 Technological Relev ance of Solid Phase Epitaxial Regrowth Solid Phase Epitaxial Regrowth (SPER) for the element Si is the process of converting amorphous Si into crystalline Si by thermal processing. The epitaxially regrown Si has the same substrate orientation as that of it s seed. The process is interchangeably known as solid phase epitaxy, solid phase growth and solid phase epitaxial recrystallization. SPER finds its technological relevance in the formation of source/drain regions of MOSFET. For SPER to happen, the crystall ine source/drain Si regions are intentionally bombarded with high -energy ions to cause lattice damage to an extent that the Si become amorphous. This is followed by ion implantation of dopant atoms like B, As or P. When the dopants are implanted in a cryst alline Si, they have a tendency to channel through the lattice and form a tailing profile that is deeper than anticipated. This process is called channeling6,7. Thus, implanting dopants in amorphous Si reduces channeling since the lattice structure ceases to exist in amorphous Si. This is followed by a thermal processing step to regrow the broken lattice and hence, helps in shallower junctions for the dopants. The high dose of dopants required in source/drain regions causes some heavier dopants like As to amorphize the Si without the need for pre amorphizing implant. Thus, SPER in such cases becomes unavoidable. SPER is also known to increase the active dopant concentration that is essential for scaled MOS transistors. The possible reason for increase in active dopant concentration is that SPER involves rearrangement of Si lattice and the dopants get incorporated during this rearrangement. The dopa nt incorporation is more than the solid -solubility of those dopants at the temperature SPER occurs810.

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15 As mentioned in section 1.1, stress is helpful in increasing carrier mobility that results in higher on -state current. SPER has been believed to be a reason for a phenomenon called Stress Memorization. Stress memorization occurs when a preamorphized polysilicon gate recrystallizes under external stress from liner 11,12. Th e stress transferred from the liner through the polysilicon into the channel is retained even after the removal of the liner material. It is helpful for current enhancement in n MOSFET devices since an out of plane stress is created that affects n -MOSFETs much stronger than p -MOSFETs. 1.3 Motivation SPER has been studied in great detail as a bulk process where the growth front advances only in one substrate orientation. However, since SPER is a used for the formation of source and drain regions in scaled M OS devices, it has to be viewed as a multidimensional process (patterned amorphous regrowth). During the regrowth of a patterned amorphous region, the advancing regrowth front velocity is temporally dependent on the immediate regrowth shape. Since, the reg rowth is non isotropic for different substrate orientations13,14, it is a non -trivial problem to solve analytically; hence simulations are necessary to get the right regrowth shapes. Previous attempts15 to model and simulate the orientation dependence of SPER in the c interfaces with any shape other than rectilinear. This somewhat limits the capability of prior models in -c interfaces and makes it difficult to gain further insight into the nature of regrowth. In particular, predicting and modeling the evolution of 2D SPER in patterned amorphized regions is very important since mask edge defects are known to occur during this process1626. It is believed that mask edge defects are caused by the regrowth dependence on substrate orientation16 26. Specifically, since the [001] and [110] directions are much faster than the [111]

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16 -Si near the [111] fronts can become encompassed and pinched off -Si layer via the regrowth interface collapsing upon itself. Saenger et. al.15 showed that the defects were created along <111> type directions in both (001) and (011) wafers which suggests that impingement of the [111] front is primarily responsible for mask edge d efect formation. These defects are deleterious to the device performance as they increase the leakage current. Figure 12 shows the presence of mask edge defects in a transistor structure. Figure 1 3(a) shows the plan -view of mask -edge defects for an as im -c interface shown in Figure 1 3(b). Apart from substrate orientation dependence, the SPER velocity is affected by the presence of dopants27. The experiments to observe the effect of dopants on regrowth have been mostly planar (001) samples28,29. The dopant related enhancement of regrowth rate has been known to be an electronic process because both p and n -type dopants increase the rate when present separately and there is no enhancement when both are present together27. The generalized Fermi level shifting method gives the dopant enhancement of SPER velocity28,29. However, the validity of the model has not been experimentally tested in orientations other than (001) for Si. Boron has an extremely high diffusivity in amorphous Si when compared to crystalline Si30,31 (Figure 1 4). This results in the diffusion of Boron competing with simultaneously occurring SPER. The final profile of Boron is a result of the time Boron spends in the amorphous Si. FLOOPS (Florida Object Oriented Proces s Simulator)32 has the capability of simulating ion implantation and dopant diffusion. Thus, an im plementation of SPER in FLOOPS can leverage these simulation capabilites to simulate accurate Boron profile after SPER. Effect of uniaxial stress on planar SPER has been studied in great detail 21,33 40. Prior exper iments have shown that hydrostatic compression and uniaxial compression (out of plane)

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17 41,42 lead to an enhancement in SPER velocity for planar (001) Si -c interface. Biaxial (in -plane) and uniaxial (in -plane) compression lead to a re duction in SPER velocity37,41. Experiments done for studying the effect of stress on patterned amorphous regions have revealed that i n -plane tension can result in l esser mask -edge defects 19,22. It has been attributed to the difference in enhancements of the side (011) and bottom (001) fronts velocity due to tension. These experiments use stres se s upto ~250 MP a22. However, stresses in actual MOS transistors go as high as ~1 GP a. Thus, it would be interesting to see the effect of higher stresses on SPER. A new SPER model can use the stress simulation capability of FLOOPS to get accurate shapes during regrowth. Prior models included a n activation volume tensor to compute stress effect on SPER velocity that was based on a scattered data set. The new theory that includes nucleation and migration mechanism for SPER has invalidated the previous results that resulted in t hat activation volu me tensor38,41. Hence, a new model for SPER with correct stress effect is required.

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18 Figure 1 1. Schematic of a basic n -MOSFET transistor. Figure 1 2. Cartoon of a MOS transistor with mask-edge defects.

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19 Figure 1 3. (a) Mask -edge defects shown in plan-view TEM image, (b) cross -section TEM image of the initial -c interface that creates defects after SPER. Figure 1 4. Boron diffusion in amorphous Si licon (Si) is shown by the yellow line. S ignificant diffusion at 600 0C for 1 min. implies a high diffusivity30.

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20 CHAPTER 2 LITERATURE REVIEW 2.1 Planar Solid Phase Epitaxial Regrowth 2.1.1 Introduction Solid Phase Epitaxial Regrowth (SPER) for Si re fers to the conversion of amorphous Si into crystalline Si when thermally activated. The regrown amorphous Si has the same substrate orientation as that of the seeding crystalline Si (Figure 2 1). The activation barrier for SPER for intrinsic Si is known t o be ~2.7 eV 27. It is very interesting to note that th e Si -Si bond energy is ~2.5 eV 43. Thus the regrowth mechanism has been suggested to be a mere remaking of new Si Si bonds. The free energy of crystalline silicon is less than amorphous silicon, which is the driving force for the SPER. There have been a lot of theories about the atomistic defect that is responsible for the regrowth of the amorphous material into crystalline. Lu et al.42 have shown that dangling bonds or kink sites (special case of dangling bonds) at the amorphous -crystalline ( -c) interface are the two plausible mechanisms (defects) that govern regrowth. The other defects that include interstitials, vacancies etc. have been studied for regrowth governing mechanisms. However, their rate of creation and tr ansport to the ( -c) interface does not match up with the measured activation energy of SPER. Hence, they have been rejected as the possible mechanisms governing SPER. SPER is known to be a process of bond rearrangement at the -c interface. Thus, any depe ndence of SPER on doping, stress or substrate orientation needs to be known only at the -c interface during regrowth. 2.1.2 Substrate Orientation Dependence Substrate orientation dependence has a strong influence on SPER. Figure 2 -2(a) shows an atomistic view of SPER process on a (001) Si substrate (cross -sectional view is shown in the figure with <110> direction into the plane of the shown image). Csepregi et al .13 suggested that

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21 every atom in the amorphous phase requires two bonds in the crystalline region to be considered as regrown. Figure 2 2(a) clearly shows how atom A would be the first to regrow. Regrowth of atom B is dependent on A being regrown. Thus A s regrows first followed by B then C and finally D It is interesting to note that the 2 -dimensional image shows the position of D and B to be in equal proximity to A However, because of the face -centered cubic (FCC) structure of Si, D takes longer than B to regrow. This forms the basis for the orientation dependence of SPER in Si. Csepregis data13 shows that regrowth velocity in <001> direction is almost thrice that of <110> direction and ~25 times bigger than in <111>, as shown in Figure 2 2(b). The data was collected by regrowing planar substrates with orientations ranging from (001) up to (110) (a full 900 tilt). Csepregis model13 encapsulates the orientation dependence in a sinusoidal function with the a ngle calculated from the (111) front. The model predicts the substrate orientation effect on SPER from (001) to (111) range correctly. However, it predicts a zero velocity (that implies no regrowth possible) for (111) substrate that is not correct. Moreove r, it fails to explain the increasing regrowth rate for the substrate orientations from (111) to (110). A more complicated model to understand the orientation dependence on regrowth was given by Narayanan et al.44. In the model, Narayana n shows a 3D image of the crystal structure for the three main substrate orientations (001), (110) and (111). The model suggests the completion of a hexaring in the (111) plane as the basis for the conversion of amorphous into crystalline silicon. The form ation of hexaring is shown to be much easier in (001) when compared to (110) and (111) substrates. Every atom on these substrates faces a number of combinations in which it can either join or not join a crystalline site44. These available combinations are much more for (001) substrates followed by (110) and then (111). Hence, the

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22 effect of substrate orientation on SPER was explained for all the orientations ranging from (001) to (110). 2.1.3 Doping Effect on SPER Dopants (both electrically active and inactive) have been known to have a significant impact on the SPER rate 27 29,4547. Olson et al.27 showed the effects of various dopants on regrowth rate for bulk (001) substrates using Rutherford Backscattering Mechanism (RBS). Dopants of the III and V group of periodic table like B, P and As increase the regrowth rate significantly27. These electrically active dopants are mostly used for the formation of highly doped p and n types source/drain regions for CMOS devices. It has also been shown that if equal concentrations of p-type and n-type dopants are present in Si, the regrowth rate returns to its intrinsic value27. Thus, the effect of electrically active dopants on SPER is believed to be an electronic process. The regrowth rate enhancement from Boron can reach up to ~30 times the intrinsic rate, while for Phosphorus can reach up to ~8 times for T=6250 C 27. Since the electrically active dopants have been known to a ffect the Fermi level of Si, a generalized Fermi level shifting (GFLS) model of dopant enhanced SPER was proposed 28,29,47. The theory suggests the presence of kink-like growth sites that possess electronic energ y levels within the band gap. The Fermi level in amorphous silicon is assumed to be pinned at the mid band. For aligning of the Fermi levels, the bands on the crystalline side bend, as shown in Figure 2 3. The regrowth velocity is assumed to be proportiona l to the concentration of the kink like growth sites29. For intrinsic Si, the regrowth rate is proportional uncharged kink sites C0 (independent of doping) concentration, since the charged kink sites (Ci) are negligible. However, for doped semiconductor, regrowth rate is proportional to the sum of uncharged kink sites C0 (in dependent of doping) and the charged kink sites (Cp). The ratio of charged sites to

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23 uncharged sites at the growth interface is given by the Fermi Dirac statistics that becomes Maxwell -Boltzmann approximation for dilute dopant concentration29. CpC0 g exp En p EFkT (2 1) where En p is the energy level at the growth interface of a posi tively charged defect, EF is the Fermi level of the material, and g is the degeneracy factor. In case of lightly B -doped material, EF EF i kT ln CBni (2 2) where EF i is the Fermi level in intrinsic material, CB is the B concentration at the growth interface and ni i s the intrinsic carrier concentrat ion at T. Combining equations (2 1) and (2 2) and under the approximation that charged kink sites in intrinsic Si are much less than uncharged kink sites, v vi1 CBni g exp EF i En pkT (2 3 ) where vi is the intrinsic value of v at T 29. A similar expression can be derived for n type doping. The key point of the above equation is that v should increase linearly with the concentration of the dopant (till the dopant is active). This has been confirmed by experiments 45. Electrically inactive impurities like H, O, C and N tend to redu ce the regrowth velocity 46. The notion is that these impurities do not affect the Fermi level of the semiconductor and do not affect the nucleation kinetics. However, they slow down the migration kinetics much more than the electrically active impuritie s do because of their slowness to accommodate on the Si lattice sites However, there is no comprehensive theory regarding the effect of electricallyinactive dopants on SPER. F is another impurity that decreases the regrowth velocity and it is important f rom device perspective since it is added along with B in the form of BF2 for the

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24 formation of highly doped source/drain regions of PMOS transistors31. B enhances the regrowth rate and F reduces it. The overall effect is that the regrowth rate does not change much from the intrinsic value 27. Ho et al .48 studied the effect of B and P enhancement of SPER velocity in (001), (110) and (111) substrate orientations using RBS The enhancement from P was found to be isotropic, while B was observed to have a higher enhancement on (001) substrate compared to (110) and (111). However, the data on B for (110) substrate had data scattering (upto ~17%) and (111) substrates were plagu ed by the formation of twin defects that can offset measurement of velocity48. 2.1.4 Stress Effect on SPER Stress effect on SPER has been extensively studied for planar (001) Si substrates21,33,34,36 38,41,42,4951. The f irst attempts to study stress during SPER was done by Nygren et al.36. The influence of pure hydrostatic stress on SPER kinetics was studied using Rutherford Backscattering Mechanism (RBS). It was found that the regrowth velocity, v was exponentially enhanced by compressive stress. Thus, v as a functi on of takes the form, v v (0 ) exp Vh *kT (2 4) where v (0) is the unstressed velocity, Vh = ( 0.28 0.03) is the activation volume for pure hydrostatic stress and = 12.1 cm3/mol is the atomic volume of Si. Negative activation volume suggests the reduction in the net volume associated with the transition state which may be due to the lower density of -Si as compared to c -Si 52. Following the hydrostatic stress effect on SPER, Aziz et al.41 conducted a series of experiments to study the role of in-plane uniaxial stress ( 11) on SPER. It emerged from a

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25 scattered data set that tension was increasing the v while compression was reducing it. In line with Equation (2 4), Aziz 41 advanced v as a function of 11 as, v v (0 ) exp V11 *11kT (2 5) where V11 = (0.15 0.01) The expression was then generalized to take into account arbitrary stress ij as41, v v (0 ) exp Vij *ijkT (2 6) where Vij is the ac tivation volume tensor such that Vij = 0 for i = j due to symmetry constraints. The effect of shear stresses on SPER is thus assumed to be negligible. Also, SPER is assumed to be a single timescale process implying Vij is a sum of nucleation and migration processes in SPER. Furthermore, the activation volume for normal uniaxial stress ( V33 ) was calculated based on the hydrostatic and in plane stress measurements. It was predicted that V33 = 0.58 41 implying an enhancement in v under normal compression (and more than the hydrostatic compression). However, the experimental values for V33 were found to be ( 0.15 0.01) much lower than the pr edicted value. Recently Rudawski et al.21,39 attempted to reproduce the results of in -plane stress effects on SPER by applying high stresses using a novel wafer bending technique (as explained in section 3.1.3). C ross-sectional Transmission Electron Microscope images were used to accurately determine the position of the interface for the purpose of calculating SPER velocity. It was observed that in-plane tension in <110> directions did not affect the SPER velocity even for stresses upto ~1.5 GPa. It was also observed that inplane compression (in <110> directions)

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26 reduced the SPER velocity till it reached a factor of half at ~0.5 GPa, at which the rate reduction saturated. Thus, an S -shaped curve was observed21,39. This contradicted the prior theory of a single timescale process from Aziz et al.41. The results were explained by Rudawski et al. 21,22,38,39,50 by the nucleation and migration kinetics model for SPER process. The model matches the experimental data very well and the results of the model are shown in Figure 2 5. SPER is assumed to be a two -step process that includes island nucleation and subsequent le dge migration. Under no-stress conditions, nucleation process is assumed to be rate limiting. Stress is assumed to affect only the migration process. In -plane tension increases the migration velocity thereby not affecting the SPER velocity since nucleation is rate limiting. However, compression is believed to reduce migration velocity 39. For a (0 01) Si substrate the compression reduces migration of ledges in the direction of applied stress and slowing down the SPER process. Its effect saturates once it has reduced the migration velocity of ledges in the direction of applied stress (one out of the two orthogonal <110> directions) to zero 39. In addition to rate reduction due to in -plane co mpression, interface roughness was also observed during regrowth 53. This led to the formation of defects on the cusps of roughened interface. For a rough starting interface, the roughness was found to increase due to compression and reduce in tension53. The reasons for it are still not wholly understood. 2.2 Patterned SPER 2.2.1 Substrate Orientation Effect and Mask -Edge Defects As mentioned in section 2.1.2 the substrate orientation strongly affects the regrowth velocity. A patterned amorphous region is replete of various substrate orientations especially around the corner of the pattern as shown in Figure 2 5. The effect of these orientations manifests itself in the form of a non isotropic regrowth velocity for the -c interface. The first

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27 expe riments on patterned regrowth were done by Cerva et al. 17,18 with a high -energy As+ implant causing amorphization. Figure 2 6(a) shows the as implanted -c interface for (001) Si with <110> inplane directions18. Figure 2 6(b) shows the interface after partial regrowth. It can be readily observed that the bottom interface (001) regr ew the fastest, followed by the side front (110). The notch at the corner formed by (111) and neighboring fronts is noticeable suggesting a very slow regrowth in that direction18. These observations match completely with the orientation effect data from Csepregi et al.13 mentioned in section 2.1.2. Figure 2 6(c) shows the fully regrown Si along with the presence of a defect created along the notch direction (<111> direction). The defect is believed to be formed when the edges of the notch approach each other during further annealing, resulting in the generation of corner defects due to the mismatch between the merging interfaces 24 26. These defects are called mask -edge defects because they normally occur below the edge of the mask. The theory about mask -edge defects formation dur to mismatch of merging interfaces is supported by prior experiments54 which showed the formation of clamshell defects when two interfaces of a buried amorphous layer merge on the completion of SPER. Some later experiments from Shin et al.24 26 with a similar structure as Cerva et al.18 suggested the formation of vacancyrelated half loop defects in the corners without the formation of a notch. These were attributed to the presence of As+ in the samples. Thus, to confirm the effect of orientation on the formation of notch in the corner followed by the mask-edge defect formation, Saenger et al.15 created the patterned amorphous regions by Ge+ implantation. Upon regrowth, the pinching of the corners was observed followed by formation of mask -edge defects. Experiment was done on (001) and (011) substrates (Figure 2 7 (a), (b) respectively). For (001) substrates, the defects were angled at ~540 from the bottom (001) front while they were ~350

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28 from the bottom (011) front for (011) substrates. Thus, the defects on the two substrate s were clearly angled in the <111> directions (Figure 27 (c)) 15. Another noticeable factor in all the ex periments15,18,26,55,56 done for patterned regrowth is that the regrowth interface contacting the SiO2 layer just under the masking constri cts SPER at that point The reason was attributed to the fact that the bonds between amorphous Si and O are stable and do not allow Si to recrystallize at the contacting interface55. Hence, these samples are usually referred to as having the regrowth interfac e subjected to surface pinning. The effect of surface pinning is that the regrowth interface on the side front bows inwards in the regrowth direction. The possibility of surface pinning affecting the formation of mask-edge defects is not clearly understood 2.2.2 In -Plane Uniaxial Stress Effect on Patterned SPER Stress effect on planar SPER has been studied in great detail as shown in section 2.1.4. Stress effect on patterned SPER was first observed by Barvosa Carter et al.34 with (001) Si -c interface patterned like a sinusoidal wave of small amplitude ~25 nm and ~400 nm wavelength (Figure 2 8(a)). It was observed that in -plane uniaxial compression increased the amplitude of the sinusoidal interface during regrowth while corresponding tension decreased the amplitude (Figures 2 8(b), (c)). The results were explained by the difference in stress experienced by the peaks and the valleys of the interface It was suggested that for compression, the valleys find themselves under stress concentration while the peaks have stress relaxation34. Thus, if in -plane compression reduces the interface mobility41, the perturbations would amplify. The reverse is true for in -plane tension. The results of stress -effect on sinusoidal wave shaped -c interface suggested that different interfac e shape would play a big role in how it evolved under stress. This was further confirmed

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29 when Shin et al.2426 conducted experiments with SPER for rectilinear -c interfaces with and without stress from a SiO2 layer on (001) Si with <110> in-plane directions. High tensile stressed plasma enhanced chemical vapor deposited (PE CVD) SiO2 layer led to the formation of mask edge defects while no defects were observed in low stress case. The formation of defects was attrib uted to the creation of notch in the corners. The presence of high shear stress near the trench corners was believed to create the notch. Following Shins work, Ross et al.19 studied the Si3N4 mask induced stress effect on SPER. Tensile stress ed Si3N4 created tension in the amorphous trench. This led to reduction in the formation of mask edge defects compared to no -stress case. Furthermore, Rudawski et al.22 conducted wafer bending experiments with in plane compressive and tensile stress (~250 MPa) in an effort to control the reg rowth velocity of interfaces in two -dimensional -Si. The results from the experiment are shown in Figure 29(a i). The evolving interface angle between the <110> and <100> regrowth fronts was observed to increase with increasing tensile stress. Thus, in p lane tension was found to reduce the formation of pinching corners and thereby reducing the possibility of mask -edge defects. Compression, however led to stronger pinching of the corners and thus more possibility of formation of maskedge defects22. 2.3 SPER Modeling 2.3.1 2D Analytical Mode l The first comprehensive modeling for regrowth was done by Phan et al.57. Transition stat e theory (TST) was used to describe the phase transformation at the Si -c interface. The assumption of the model is that a single, unimolecular, defect mediated mechanism controls the silicon crystal to amorphous transition rate. The growth rate normal to the interface for a (001) Si substrate at any point of the interface can be given by 57

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30 v v0() expV* E*kBT sinh Gac2 kBT (2 7) where, v0() is the orientation dependent regrowt h as shown in Figure 22(b) where is angle between the normal to the -c interface and the <100> direction. The first exponential factor in equation (2 9) represents the thermal dependence of the interface mobility. E* =2.68 eV is the activation energy known from literature, V* is the activation strain tensor, is the stress at the interface evaluated at the crystal side, T is the temperature, and kB is the Boltzmann constant. The stress is b elieved to affect the activation barrier. The assumption is that the stress state on the amorphous side does not influence the growth rate. The sinh term is the free energy driving force with Gac being the difference between amorphous and crystalline silic on. The free energy term is composed of three terms, Gac( T ,,) Gac 0( T ) G G (2 8) where Gac 0( T ) is the temperature -dependent free energy per unit volume from amorphous to crystalline silicon. The second term represents G represents the change in free energy due to interface curvature. The third term G includes the changes in the total energy of the crystal when a volume of materials is crystallized. Under stress, the free energy change will be affected because the system must do work against these forces. The term also includes change in the internal strain energy when a volume of material crystallizes. Further explanation of the free energy terms can be found elsewhere57. Advanced numerical methods were used to solve a system of equations. Level Set Methods58 were used to propagate the initial -c interface with the velocity given by equation (2 7). For the stress simulation, the crystalline side is considered to be elastic and for the amorphous side three cases are used: stress free amorphous, viscous amorphous, elastic amorphous57. After

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31 every time -step for regrowth using level set equations, the stress simulation was done using a fairly complicated set of equations from Symmetric Galerkin boundary integral analysis. The results of the simulations show that the viscous amorphous case fits the best to the data. However, the large scatter in the data puts some of the predictions in question. The model is able to correctly predict that for an initial sinusoidal wave like -c interface would grow in amplitude for a uniaxial stress in -plane compression and would dampen in tension case and the no-stress case 34,51. However, as shown in section 2.1.4, Rudawski et al. 21,37,53 have shown the inability of the activation strain tensor to predict the in -plane uniaxial stress effects. In Phans model57 effect of stress on the mobility of atoms in the interface is strongly affected by the term V* in equation 2 9. The model predicts exponential increase of the SPER velocity for in-plan e uniaxial tensile stress while the experiments have shown no increase in velocity for tensile stresses up to ~1.5 GPa (Figure 2 4)21. This has put a question mark on the validity of the model. Moreover, the curvature effect as a free energy term is suggested to have a negligible effect on SPER57. However, the fact that the model was never applied to highly curved interfaces, it is difficult to confirm the negligible effe ct of curvature effect on SPER. Phans model is however the first and one of the only attempts to analytically model 2D SPER. Ex periments from Drosd et al.59 have shown that curvatur e effect on SPER is significant for radius of curvature smaller than 20 m. The curvature effect was observed to be more important on (001) Si substrates and in <011> direction of regrowth because of the formation of <111> fronts. <111> fronts require the nucleation and migration of ledges for regrowth. An imp lication of the results from 59 would be that concave interface that has some built in ledges

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32 (more than a planar interface) wi ll have a higher SPER velocity than its planar counterpart. However, this effect has not been captured in the simulations yet. 2.3.2 Atomistic Modeling of SPER Marques et al.60,61 did an atomistic study to ex plain t he defect mechanism that control s the recrystallization process Their results suggested the agglomeration of defects called I -V pair s (interstitial -vacancy pair) as the cause of amorphization This defect is essentially a bond defect that creates five -mem ber and seven -member ring s in Si62 instead of the six -member rings ( a misnomer since there are no interstitial s and vacancies for an amorphous region). Incomplete recombination of a migrating interstitial and vacancy results in the formation of this I -V pair62. Marques argued that the presence of these I -V pairs above a threshold concentration results in amorphization. The process of recrystallization is then given by the thermal energy disentangling these I -V pairs. The activation barrier for the dissolution of a single I -V pair is 0.4 3 eV 61,63. However, the presence of neighboring I -V pairs increases this barrier. Thus, the activation barrier of these I -V pairs ranges between 0.43 eV for an isolated I -V pair to 5 eV 60 for a fully coordinated I -V pair. The dependence of the activation barrier for recrystallization on the coordination number of I -V pairs is given by, E ( n ) 0.6 0.2 n 0..0012 n3 (in eV) for n>0 (2 9 ) and E (0 ) = 0.43 eV for n=0. The maximum value of n=12 (coordination limit). For a planar -c interface n=7 and the activation barrier is 2.44 eV 60 that is fairly close to the generally accepted value of 2.7 eV For patterned amorphous trench regions as discussed in section 2.2.1 t he corner of amorphous region is encompassed by crystalline region. Thi s results in a lower coordination number of I -V pair and thus should have a faster regrowth. It also corroborates the curvature effect observed by Drosd et

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33 al. 59. Marquess60 atomistic model is not appropriate for continuum simulators because of the high simulation time it takes. The time -steps during simulation fluctu ate quite a bit resulting in significant simulation time.

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34 Figure 2 1. Solid Phase Epitaxial Regrowth process. (a) shows the as -implanted -c interface, (b) shows partial regrowth, (c) shows complete regrowth where the -Si is converte d in to c -Si with the same orientation as the seed.

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35 Figure 2 2. Two -dimensional atomistic model for regrowth13. (a) Re printed with permission from Csepregi et al. Journal of Applied Physics 49(7), 3906 (1978). Copyright 1978, American Institute of Physics. (b) Csepregis data13 on substrate orientation dependence of SPER.

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36 Figure 2 3 Band -diagram of amorphous Si and p -type doped crystalline Si. The Fermi level is pinned at the mid -level for amorphous Si and band bending occurs in the crystalline region29. En p is the energy level of acceptor defect level at t he -c interface.

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37 Figure 2 4 Cartoon of a patterned as -implanted amorphous trench region. The interface consists of varying substrate orientations that result in nonisotropic regrowth18. Figure 2 5 Effect of externally applied in -plane uniaxial stress on SPER velocity 21.

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38 Figure 2 6 TEM images showing patterned amorphous regrowth. (a) as implanted -c interface, (b) notch formation at corner due to non isotropic regrowth, (c) m ask edge defect after SPER18. Reprint ed with permission from Cerva et al. Journal of Applied Physics 66(10), 4723 (1989). Copyright 1989, American Institute of Physics.

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39 Figure 2 7 TEM images representing patterned SPER for two Si substrates. (a) SPER splits at various times for (001) Si with in -plane <110> directions, (b) SPER splits corresponding to (a) for (011) Si with in -plane <100> directions. (c) After completion of SPER, mask -edge defects left behind for the two substrates.15 Reprint ed with permission from Saenger et al. Journal of Applied Physics 101(10), 104908 (2007). Copyright 2007, American Institute of Physics.

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40 Figure 2 8. Cartoon (based on TEM images 15) showing SPER of a sinusoidal shaped as implanted amorphous interface: (a) As implanted -c interface, (b) partial SPER under in-plane uniaxial compression shows increase in interface perturbation, (c) partial SPER under in plane uniaxial tension shows decrease in interface perturbation 34.

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41 Figure 2 9. TEM images of SPER of patterned trench -c Si interface under stress, (a), (d), (f) are identical as implanted c Si interfaces; (b), (c) show SPER for increasing times with n o external stress applied; (e), (f) show SPER for increasing times under inplane compressive stress of ~250 MPa; (g), (i) show SPER for increasing times under in -plane tension stress of ~250 MPa. Stress affects the regrowth shapes and tension case shows n o formation of mask -edge defects 22. Reprint ed with permission from Rudawski et al. Applied Physics Letters, 89(8), 082107 (2006). Copyright 2006, American Institute of Physics.

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42 CHAPTER 3 EXPERIMENTAL AND SIM ULATION TECHNIQUES 3.1 Material Processing 3.1.1 Pattern Creation U sing Electro n Beam Lithography and Reactive Ion Etching (RIE) When focused beam of electrons are used to form patterns with high resolution, it is referred to as Electron Beam Lithography (EBL)64. As opposed to optical lithography that uses light for creating patterns, the EBL uses focused beam of electrons accelerated to ~10 50 keV potential. The high energy allows electrons to have a shorter wavelength, thus creating patterns with resolution as small as 10 nm. While diffrac tion is the limiting factor for optical lithography, resist scattering the limiting factor for EBL. The collision of electrons with the material causes them to penetrate the material but lose energy at the same time. These collisions can cause the striking electrons to 'scatter' The electrons can be backscattered in this process, but more often they proceed forward through small angles with respect to the original path (Figure 3 1)65. As the electron beam interacts with the resist and substrate atoms, it scatters. This scattering has two main effects: 1) the incident electron beam broadens while penetrating, 2) the back -scattered electrons from the substrate add to the ones in the resisit and hence the total dose of electrons in resist increases. This results in wider and blurrier images than what would be ideally expected from EBL. Moreover, if the mask lines are closely spaced, the effect of exposed areas on adjacent lines can add up under the unexposed areas to create a phenomenon known as 'proximity effect.' For the presented study, the spacing of the adjacent lines used were ~0 .5 m and were not strongly affected by proximity effect65. Electron lithogra phy uses positive and negative resists that are sensitive to electron beams. The resist used for the presented work was PMMA A4 ( polymethylmethacrylate anisole 4)

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43 which is a positive resist implying that it softens on interaction with electron beam. A thi n layer (~200 nm.) of PMMA was spin-coated on the Si wafer and baked on a hot plate at 175 0 C for 15 mins. Subsequently, e beam lithography was done on the 100 100 m2 squares that were distributed on a 2 2 cm2 sample (Figure 3 2). Since, the electron bea m lithography is very slow compared to optical lithography, only a small area out of the total sample area was exposed. The electron beam was accelerated at 10 keV from a working distance of 7 mm (above the sample surface) and an aperture of 30 m. For a P MMA thickness of ~200 nm exposure dose of 75 2 was used. PMMA was developed using MIBK (methyl isobutyl ketone) 1:3 solvent. After the patterning of PMMA, the Si was etched using Reactive ion etching (RIE)66, an etching technology commonly used in microfabrication. It is a dry etch technology used for creating anisotropic etches. It uses chemically reactive plasma to remove material deposited on wafers. The plasma is generated under low pressure by an electromagnetic field. High-energy ions from plasma attack the wafer surface and react with it (Fi gure 3 3)66. A typical (p arallel plate) RIE system consists of a cylindrical vacuum chamber, with a wafer platter situated in the bottom portion of the chamber. The wafer platter is electrically isolated from the rest of the chamber, which is usually grounded. Gas enters through s mall inlets in the top of the chamber, and exits to the vacuum pump system through the bottom. The types and amount of gas used vary depending upon the etch process; for instance, SF6 is commonly used for etching silicon. Gas pressure is typically maintain ed in a range between a few millitorr and a few hundred millitorr by adjusting gas flow rates and/or adjusting an exhaust orifice. The structures shown in Chapter 7 used Deep Reactive Ion Etching (DRIE) 67 which is a subclass of RIE and used to etch deep structures (~20 m for DRAM capacitors) with highly vertical sidewalls. Bosch process is the most commonl y used DRIE process that includes SF6 for

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44 etching (Si) and C4F8 for creating a passivation layer to protect the mask. These two processes of etching and deposition alternate to create very high aspect ratio etches. However, for the study in Chapter 7, the etch required was only 150 nm. Thus, a very slow continuous recipe was used with the parameters as: C4F8 = 90 sccm, SF6 = 40 sccm, RF = 700 W, bias = 32 W, time = 25 sec. Other types of RIE systems exist, including inductively coupled plasma (ICP) RIE. I n this type of system, the plasma is generated with an RF powered magnetic field. Very high plasma densities can be achieved. A combination of parallel plate and inductively coupled plasma RIE is possible. In this system, the ICP is employed as a high dens ity source of ions which increases the etch rate, whereas a separate RF bias is applied to the substrate (silicon wafer) to create directional electric fields near the substrate to achieve more anisotropic etch profiles. For etching Si3N4 ~150 nm (for stru cture shown in Chapter 6, Figure 6 1), ICP/RIE etch was used with the parameters as: CHF3 = 40 sccm, Pressure = 10 torr, ICP1=50 W, ICP2=300 W, time =1min 40sec. Figure 3 4 shows the complete process of e -beam lithography, RIE etch and resist stripping to get the required structure. 3.1.2 Ion -Implantation Ion -implantation process is the preferred method of introducing dopants into Si wafers during device processing. It offers several advantages that include dopant profile control, high repeatability and the ability to introduce dopants into highly localized portions of a Si wafer (e.g. halo implants for MOS devices). In ion implantation, atoms with mass, m to be implanted are first ionized from a gas source using an ionizing coil to acquire a net electric c harge, q and accelerated through a potential difference, V Then, an analyzing magnet is used to isolate the desired ions for implantation from any possible impurities and the ions are then directed towards

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45 the Si target (Figure 3 5). The relationship bet ween m q V and the velocity of the incoming ions, vion, is given by 1 2 mvion 2 qV (3 1) where qV = E0 is defined as the kinetic energy acquired by the ion. As ions travel through the crystal, their collisions with th e lattice can be nuclear or electronic. Nuclear collisions make the implanted ions lose their kinetic energy and t hey finally come to rest 68. The implantation process is known to be statistical in nature (and thus simulated by probability events using Monte Carlo simulations) and the collisions suffered by each ion would be different. For a given ion, the distance, R, the ion will tr avel into the substrate is given by R 1 dE / dx dEE00 (3 2) where the quantity dE/dx is defined as the incremental energy loss with respect to distance traveled by the implanted ion. For the case of one -dimensional ionimplantation, Rp is defined as the mean variance of R and is referred to as the ion projected range. The standard deviation of R gives the straggle, Rp. Typically, the concentration of implanted ions, N(x) as a function of the distance into the substrate, x can be approximated as Gaussian function given by N ( x ) Q Rp2 exp ( x Rp)22 Rp 2 (3 3) where Q is the implant dose. This is valid for an ideal case of uniform and amorphous target, with the collision frequency and energy transfer per collision being random. For cr ystalline target, the distribution is somewhat different. Certain directions in the crystal structure allow for channeling of ions i.e. fewer collisions and there is deeper pene tration of incoming ions69.

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46 The nuclear collisions between the in coming ions and the Si lattice leads to displacement of Si atoms from their lattice. These displaced atoms acquire enough energy to dis place more lattice atoms and this leads to, what is known as a damage cascade70. A large number of vacancies and interstitials are created (known as point defects) as the lattice atoms are displaced. If the dose of ions is sufficiently high, the damage can displace a percentage of the lattice atoms (over 10% 71, creating amorphous region ( -Si). This process is highly sensitive to the type of ions being implanted. Lar ge, heavier ions such as Xe+, Ge+, or Si+ cause amorphization at lower doses (< 11015 cm2) while lighter ions such as B+ amorphize at higher doses (> 11016 cm2) since heavier ions tend to form denser damage cas cades72. In the presented work, the generation of Si films on Si substrates was effected via Si+implantation at vacuum of ~8108 torr into single -crystal (001) Si substrates. All implants in this study were done on patterned Si3N4 or patterned Si. A sequence of Si+ implants with energies of 20, 60 and 160 keV to doses of 1015, 1 015, 31015 cm2, respectively, generated an undulating Si layer ~270 nm thick. A band of defective Si just beyond the initial -of range (EOR) damage, was observed for all sa mples (Figure 3 6). Upon annealing, this region evolves into extended defects (dislocation loops and rod -like 311 defects) which have been thoroughly studied in the literature 54. However, the temperatures used in this work were low (500 575 0 C) and no evolution of EOR or their interaction with the regrowth process was observed. 3.1.3 Application of In -Plane Uniaxial Str ess As shown in Chapter 2, stress plays a major role in SPER process. It affects the planar regrowth growth velocity and in addition it affects the regrowth shape of the corners in patterned amorphous regions. To delineate the effects of various component s of stress on regrowth,

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47 uniaxial stress was applied in the plane of the regrowth interface (only 11 0). It is well known that stress is a product of Youngs modulus (E) and strain ( ) under the elastic limit (Hookes law). 11=E11. 1 (3 4) where E11 for this study is in the <011> crystal orientations (since they are the inplane directions for (001) Si substrate). The method for applying the uniaxial in -plane stress involves the use of a quartz se lf supported bending apparatus ( Figure 3 7) This was first implemented by Ruda wski et al.21,37,38. The experiments in this study using that apparatus have been completely based on his study. For more information on the apparatus refer to Rudawsk is thesis53. The amorphous interface in for prior experiments using the bending apparaturs were planar 53. Presented study, however involves stress on patterned amorphous regions. For applying uniaxial in plane stress, the patterned lines were placed perpendicular to the stress direction in most cases as shown in Chapter 7. In some cases the lines were parallel to the stress direction (see Chapter 7). It must be noted that in both cases the stress application was in the <011> directions that wer e the in -plane directions. 3.1.4 Temperature Calibration and Annealing SPER process is a thermally activated process and the temperature needs to be accurately measured. Even a variation of temperature from 525 to 530 0 C results in a regrowth velocity i ncrease of ~28% 27. To ensure temperature correctness, the quartz tray (shown in Figure 3 8) was inserted in the tube furnace and the temperature on the tray was measured using a thermocouple after temperature stabilization. The tray with the samples was inserted at the same spot. The tensile, compressive and non -stressed samples were annealed simultaneously and kept

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48 close to each other to avoid any temperature variation amongst them. The error in all T measurements was estimated to be 2 0C as per the accuracy of the thermocouple device. N2 gas was flowed at ~ 1 l/min through the tube furnace for all annealing to prevent thermal oxidation. For the present study, T = 500 575 0C was used with anneal times of 2 10 h. As mentioned in Chapter 2, it is possible for the applied stress to relax depending on the anneal ing temperature, time and applied stress. The experiments done in this study assume that there is no stress relaxation in the samples. To confirm that no stress relaxation happened during annealing, the radius of curvature was measured for the annealed str ips. No measureable difference was seen in the radius when compared to before annealing case. Thus, it can be safely assumed that the strips retained the applied stress during annealing. 3.1.5 Cross -section Transmission Electron Microscopy Sample Prepar ation A focused ion beam (FIB) system was used to prepare site -specific transmission electron microscopy samples from the strips. The patterns created by e beam lithography were located at a specific distance from the strip end and had 100 m side lengths. In this method, a focused beam of Ga+ ions from the FIB system is accelerated to 30 keV and used to mill away small portions of the wafer 73,74. A 100 200 nm -long, electron -transparent specimen is pro duced which is lifted out externally and placed on a grid for imaging. Since, the Ga+ ions charge the surface of the sample, a thin C film ~30 nm was evaporation-coated on the sample before FIB processing. Subsequently, a layer of Pt ~1 m thick was FIB -de posited over the area of interest to protect the sample from beam damage during sample preparation. 3.2 Material Characterization 3.2.1 Transmission Electron Microscopy Transmission electron microscopy (TEM) is widely used for microstructural characteriza tion. In TEM, a beam of electrons is accelerated using a thermionic emission source

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49 across a potential difference of ~200 keV and directed at the specimen. Electrons at such high energies show wave -like behavior and according to de Broglies hypothesis an accelerating voltage ~200 keV creates a wavelength ~ 2.5 1012 m. Small allows for resolution of nanometer -scale features in TEM samples. -Si, since no distinct crystalline planes exist, the scattering of the incident beam would be different as compared to c -Si. This gives rise to contrast between the two phases during imaging. It is possible to increase this contrast between -Si and c -Si phases by selectively allowing certain electrons to contribute to the generated image (using selected area diffraction). More analysis of the TEM instrument and imaging conditions can be found in53. For all work presented in this stud y B = [ 1 1 0 ] (orthogonal to the wafer orientation) was used for TEM imaging. This TEM imaging style is known as cross -sectional TEM (XTEM), since the wafer structure is being observed from the side. A sample XTEM image from the study is shown in Figure 3 6. 3.3 Simulation Techniques 3.3.1 Level Set Methods Level Set Methods are computational techniques that were proposed by Sethian and Osher to track the evolution of a moving interface in 2D/3D 58. These methods work on embedding the solution of the equation, i.e. the position of the interface, in a higher order function. This higher order function is solved using a partial differential equation (convection equation) given, the initial position of the interface and the velocity of interface propagat ion (normal to the interface). The reason this technique became popular was the failure of traditional interface tracking techniques like the marker/string methods in cases of sharp corners. The marker/string methods use the standard Lagrangian form of the equations of motion. In this approach, the parameterization is discretized into a set of marker particles whose positions

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50 at any time are used to reconstruct the front. The problem with the marker method is that it has a positive feedback on error. The w ay the error grows is quoted by Sethian 58 as: (1) A small error in approximate marker positions produces, (2) local variations in the computed derivatives leading to (3) variation in computed particle velocities causing (4) uneven advancement of the markers, which yields (5) larger errors in approximate marker positions. Hence, within a few time steps the small oscillations grow and solution becomes unbounded. The other problem with marker methods comes in computing derivatives of curves that have singularities. Th e derivative of singularities leads to the growth of oscillations and cannot be controlled. Level Set Methods on the other hand do not compute the interface position. They compute a higher -dimensional function that embeds the interface position in it. For our case, the function is the signed distance. The initialization is done by allotting all the points on the level set grid as the signed distances to the original interface as shown in Equation (35) (Figure 3 9) ( x y z t 0) d (3 5) where is the higher -dimensional function. Equation (3 5 ) implies that the value of is zero at the interface. Rest of the grid points get a value of equal to their distance from the interface (positive on one side and nega tive on the other side of interface). The function then evolves using a convection Equation (3 6) that contains a velocity that controls the interface propagation. t F 0 (3 6 ) where F is the velocity of interface, t is the time deri vative of and is the spatial derivative of The derivation of the above equation can be found elsewhere 18. Since, the

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51 above equation needs to be discretized for solving on the level set grid, it is necessary to know if the operators (spatial and tem poral) need to be backward, forward or centered. The time derivative is definitely a forward difference operator as we are trying to find the value of at the next time instant For the spatial derivative, the operator needs to have the upwinding schem e for getting the correct results 58. For F >0, the backward operator needs to be used and for F<0, the forward operator needs to be used. This scheme is called upwinding because it uses values upwind of the direction of information. This is done so that the numerical solution matches up with the analytical solution. More analysis on the use of upwinding scheme can be found in 18. The final update of is given by i n 1i n t [max(Fi, 0) min( Fi, 0) ] (3 7) where [max( Di x, 0 )2 min( Di x, 0 )2]1 / 2 and [max( Di x, 0 )2 min( Di x, 0 )2]1 / 2 Here Di x Di xi n Figure 3 10 gives an example as to how is one dimension more tha n its solution. Figure 3 11 shows the propagation of the interface with time given the velocity of the interface is constant and positive. It can be seen how the interface is embedded in the function Level Set Methods have been extensively used in simulating etching, deposition, surface diffusion etc. They have several key advantages that include: 1) Sharp corners are handled effectively and do not create unstability, 2) Ability to merge two disjoint surfaces as shown in Figure 3 12 58, analogous to two oil drops merging to become one bigger drop, 3) Accuracy and ease in computation of normals and curvatures at the interface using the function

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52 1) and 3) are very important for SPER of patterned region because formation of the pinching corner is the key feature of regrowth as shown in Chapter 2. 2) is helpful for the regrowth of buri ed amorphous layers in which two regrowing fronts move towards each other and finally merge It is also important for lateral solid phase epitaxy in which the two disjoint regrowing fronts from the sides eventually merge to complete regrowth. The computation of normal and curvature, is given as follows: Normal nij *x,y(x 2y 2)1 / 2 (3 8) where x is the spatial derivative of with respect to x, y is the spatial derivative of with respect to y. First, the one -sided difference approximations to the unit normal in each possible direction are formed. All four limiting normals are then averaged to give the approximate normal at the corner. Normalizing nij *, gives the normal nij Curvature xxy 2 2xyxyyyx 2(x 2y 2)3 / 2 (3 9) Similar expressions for normal and curvature can be made for three dimensions as well 58.

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53 Figure 3 1. Scattering effects during e -beam lithography. Figure shows the forward scattered electrons (FSE) and the back scattered electrons (BSE) 65.

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54 Figure 3 2 E -beam lithography for patterned regions : (a) shows the patter ned square on the (001) Si wafer with <110> inplane orientations. (b) shows the 2 2 cm2 piece that contained patterned squares. (c) shows the 100 100 m2 squares that had the pattern of lines created by e-beam lithography.

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55 Figure 3 3 A diagram of a co mmon R eactive Ion E tch (RIE) setup. An RIE consists of two electrodes (1 and 4) that create an electric field (3) meant to accelerate ions (2) toward the surface of the samples (5).66

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56 Figure 3 4 Complete process of pattern formation using E -beam lithography and RIE etc hing.

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57 Figure 3 5. Schematic of a basic ion -implantation system .53 Figure 3 6. Cross -sectional Transmission Electron Microscopy image of an as implanted Si sample. The Bright field image also shows the end of range (EOR) defects, a ban d of 56.

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58 Figure 3 7. Schematic of the apparatus used to induce and measure in -plane uniaxial stress in Si wafers 37, 53. Reprint ed with permission from Rudawski, PhD. Thesis, University of Florida. Copyright 2008, Nicholas G. Rudawski. Figure 3 8. Schematic of the tube furnace apparatus used for annealing and the method of temperature calibration 53. Reprint ed with permission from Rudawski, PhD. Thesis, University of Florida. Copyright 2008, Nicholas G. Rudawski.

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59 Figure 3 9. Figure shows the initialization of t he Level Set higher order function as a signed distance to the interface58. Figure 3 10. Pictorial view of level set function (x, y, t) on the right. Left figure shows the interface at x,y at time t=t1 where (x, y, t1) = 0. The position of the interface is embedded in the function 58.

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60 Figure 3 11. T ime evolution of the level set function and extracted interf a ce at different times The interface is circular and expanding with a fixed isotropic velocity58.

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61 Figure 3 12. Ability of Level Set method to merge two disjoint regions : (a) level sets at t=0. (b ) level sets at t=1 58.

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62 CHAPTER 4 IMPLEMENTATION OF LE VEL SET METHODS FOR SOLID PHASE EPITAXIAL REGROWTH AND INITIAL RESULTS 4.1 Introduction As mentioned in the Literature review section, the Level Set Methods provide a very stable numerical technique for the implementation of interface evolution. For their implementation, the interface velocity is required. For solid phase epitaxial regrowth (SPER) the velocity could be dependent on an isotropic velocity function (normal to the interface) 27 and curvature of interface 14,56. SPER is also known to be dependent on a lot of other factors th at include temperature 27, orientation of the amorphous -crystalline ( -c) interface 13, stress (or pressure) 19,34,53,57, dopant concentra tion 28,29,47 etc. This chapter focuses on implementing Level Set Methods for regrowth of patterned amorphous intrinsic Silicon (Si). It also includes the results of experiments done on regrowing patterned amorphous intrinsic Si regions. The initial simulation results from Level Set Methods are matched to the experimental results. The chapter provides a starting point for the work shown in future chapters. 4.2 Level Set Implementation Implementation of Level Set mo del for regrowth involved setting up the grid first. Rectangular grid was found to be the best one for Level Set discretization. Level sets are computed by solving an advection equation as given by (same as Equation 3 6) (4 1) where F is the velocity normal to the interface and is the level set function that is being solved for. As mentioned in chapter 3, represents the higher order function that contains the interface location (x, y, z) using Equation 3 5. in our case was defined as the signed distance from the t F 0

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63 c interface. Planar regrowth velocity for intrinsic Si has been known to have a thermal activation barrier of ~2.7 eV 27 and is given by v[ 001] v0exp( Ea/ kT ) (4 2) where v [001] is the value of v along [001] direction, v0 is the prefactor from [ ], v0= 3.1 108 cm s1. However, a patterned amorphous region contains fronts that have varying orientations to the wafer normal (001 for our case) as shown in Figure 4 1. Csepregis data 13 showed that for Si, orientations affect the regrowth velocity of -c interface. Figure 4 2 shows the simulation of regrowth of patterned amorphous region with an isotropic planar velocity and no orientation d ependence. The outermost contour represents the initial -c interface. The other contours represent the position of interface at different times of regrowth (the innermost contour being the longest time) It is clear from the TEM images of regrowth from pr ior e xperiments (shown in Figures 2 6 and 27 ) that these regrowth simulations do not match up in shape with them Hence, it was important to add the orientation dependence on the regrowth velocity. The normalized regrowth velocity, as a function of the substrate orientation angle et al 13 as sh own in Fig. 4 3 with the given by v () v[ 001 ]f () (4 3) where v[001] is the value of v along [001] and is temperat ure independent and accurately fit using a least -s quares fifth order polynomial 14. The [001] regrowth velocit y is ~25 times faster than the slowest regrowth direction of [111] and almost ~3 times faster than the [110] direction.

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64 This orientation dependence was also observed in studies using patterned amorphized wafers15,18,22. The polynomial for orientation dependence factor is given by : f() A15 A24 A33 A42 A5 A6 (4 4) where A1= 5.3e 10 A2= 2.0e 7 A3= 2.4e 5 A4= 8.9e 4 A5= 1.4e 2, A6= 1.02 and is the angle in degrees 14. f( ) is valid for sweeping from 0 to 900 which was sufficient for covering the entire as implanted -c interface in our case (for (001) wafer and <110> in plane directions). Since f( ) is unitless, the units of A1-A6 are accordingly (e.g. A5 has unit degrees1). f( ) being temperatureindependent implies that the intermediate regrow th shapes are not a function of temperature. Temperature independence of the orientation effect was shown by Csepregis experiments 13 for temperature between 500600 0 C. Thus, the regrowth times would scale with temperature (for intrinsic Si) isotropically. As a proof of concept, a simulation of regrowth (Figure 4 4) for a patterned amorphous trench region (0.2 m deep and 0 .2 m wide). The velocity expression given in Equation 4 3 was substituted as F in Equation 4 1 for solving the level set equation. Rectangular grid was used with a constant spacing of 0.002 m 0.002 m and bounding box area of 0.3 m 0.3 m. The boundary conditions for the simulation were: 1) The left and right grid boundaries were reflecting. For the computation of normal and curvature of the boundary nodes, both backward and forward spatial derivatives were required for averaging as shown in chapter 3 Hence, reflecting boundary condition was required so that the boundary node s would not regrow differently from their neighboring node s, otherwise, oscillations could start at the boundary. 2) The top surface was not allowed to regrow. The top laye r of grid represents the surface of the silicon that usually has native oxide or nitride mask above it. The presence of any material other

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65 than c Si on the top stops the regrowth of the top surface 23,55. This bound ary condition had the tendency to create grid dependence for the regrowing side -front near the top surface. But the formation of (111) fronts near the top surface made the regrowth rate became very small (orientation dependence 13) and thus there was no noticeable grid dependence. 3) The bottom surface was free to regrow depending on the value of function (though for our case the bottom surface was already c-Si and did not affect the regrowing interface). Figure 4 4 shows the regrowth patterned amorphous regrowth at various times. The outermost contour is the as implanted interface of -c Si. It also shows the pinching of co rners in the <111> directions and a hump in <001> bottom front. They seem to qualitatively show the same regrowth shapes that were observed in previous studies 15,18. 4.3 Experiments and Initial Simulations For thi s study, a polished 750 m thick impurity -free (001) Si wafer with room temperature resistivity of ~200 -cm was used. Masked regions consisted of lines ~0.5 m wide aligned along <110> inplane directions with 150 nm of Si3N4 (~1 GPa intrinsic tensile str ess) on ~10 nm of SiO2 separated by ~0.5 m wide unmasked area between adjacent lines. Samples were Si+-implanted at 20 and 60 keV with doses of 1 1015 cm2. This produced an Si layer -c interface under the mask edge as shown in the cross -sectional transmission electron microscopy (XTEM) image presented in Figure 4 5a. ). From the work of Burbure et al 55, it is expected that t he regrowth interface contacting the SiO2 layer just under the masking will constrict SPER at that point. Hence, these samples are referred to as having the regrowth interface subjected to surface pinning. The samples were annealed at a temperature of T = 500 0 C in N2 ambient for times of 0.5 4.0 h. Anneal times were chosen to see different points during the regrowth process when the

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66 regrowth evolution showed important changes. Bright -field (BF) cross -sectional transmission electron microscopy (XTEM) imaging using a g022 two -beam condition was used to image the regrowth of the Si layers and the formation of mask -edge defects. Specimens were prepared via focused ion beam milling (see Chapter 3 for details). Figures 4 5 (a) (c) present XTEM images of the 2D SPER process at T = 500 C. After -c interface has taken on a rectangular shape with the initially round corner area becoming v ery sharp as shown in Figure 4 5 (b). After annealing for 2 h, the regrowth interface near the corner regions has further sharpened as shown in Figure 45 (c). The level set SPER simulations after 1 and 2 h of annealing based on the orientation dependent regrowth velocity from Equation 4 3 (using v[001] = 27 nm/h from Equation 42) are shown in Figures 4 5 (e) and (f), respectively, with v = 0 specified for the point at which the interface contacts the SiO2 layer It is evident from Figure 4 5 that the p ortions of the regrowth fronts near the corner regions do not match the XTEM images. Specifically, it appears regrowth along [111] is slower in the simulations than actually observed. Furthermore, enhancing the relative regrowth velocity of the [111] dir ection from ~25 times slower than [001] to ~15 times slower (as per results from Csepregi et al 13 who indicated two differ ent velocities for [111] SPER) did not appreciably change the simulated SPER process (not presented). Thus, it appears that differences in the relative regrowth rates of different crystallographic fronts cannot entirely account for the observed SPER evolution. 4.4 Summary In summary, level set model was i mplemented for simulating solid phase amorphous regrowth for Si. Simulations done using an isotropic regrowth velocity did not show any qualitative agreement with prior studies15,18,26, thus highlighting the need for adding the effect of

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67 substrate orientation on regrowth. Simulations done including the orientation dependent velocity (by encapsulating the orientation dependence data in a curve fitted factor, f( )) did show good qualitative matching with the XTEMs from prior studies15,18,26. An experiment to accurately match the simulations to the XTEMs was done. The simulations showed some differences with the TEM images near th e <111> corners, where the actual regrowth was slower than the simulations showed. Thus, some critical parameter is missing in the simulations that can take into account the mismatch around the corners during regrowth.

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68 Figure 4 1. A s implanted amorphous -crystalline interface showing various substrate orientations and the surface angle ( ) for orientation dependent factor f().

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69 Figure 4 2 Simulation of regrowth using Level Set Methods with isotropic velocity 14. Contours represent the position of -c interface at different times of regrowth. Figure 4 3 The normalized SPER velocit y, f ( ) 14, as a function of the substrate orientation angle from [001] towards [110], as measured by Csepregi e t al.13. Inset shows an XTEM micrograph of a typical 2D structure where the SPER process occurs.

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70 Figure 4 4 Simulation of regrowth with orientation dependence included (velocity from Equation 4 3). Contours represent the -c interface at different times of regrowth. Region outside the contour is crystalline and inside is amorphous.

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71 Figure 4 5 The observed and simulated -c interfacial pinning at the surface at T = 500 C: XTEM images of the structure a) as implanted, b) after 1 h of annealing and c) after 2 h of annealing. Level set simulations of the structure evolution using only re growth orientation dependence [Equation (4 3 )] d) as implanted, e) after 1 h of annealing, and f) after 2 h of annealing 14.

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72 CHAPTER 5 ROLE OF CURVATURE PARAMET ER IN SOLID PH ASE EPITAXIAL REGROW TH OF INTRINSIC SI LICON 5.1 Introduction As was demonstrated in chapter 4, orientation dependence is an important parameter in the simulations for getting the correct sha pes of regrowth time -splits. However, it alone is not sufficient for accurately matching the observed results. There seems to be a missing parameter in the velocity function shown in Equation 4 3. Some of the prior studies 57,59 have mentioned the role of local interfacial curvature in the regrowth process for Si. This chapter attempts to implement the curvature parameter in the level set simulations and match them up with the observed results of chapter 4. It also c ritically examines the prior models 57 that have suggested the role of curvature as a driv ing force in the regrowth process. Furthermore, the structure in experiment from chapter 4 includes the -c interface surface pinning that could affect regrowth shapes. This chapter includes results of an experiment with no interface surface pinning to re solve that issue. The model for 2D SPER of semi -insulating -c interfaces. 5.2 Model for SPER Including Curvature Chapter 4 highlighted the mismatch of experiments and simulations (with only orientation dependent velocity taken into account) especially around the corner regions. These corner regions are composed {111} and neighboring fronts. Furthermore, these regions are curved implying that they contain some built in ledges that may move faster than a planar front for the same substrate orientation. This idea was shown in prior work from Drosd et al. 59 where it was observed that local interfacia l curvature, affected the regrowth rate of {111} planes. It was

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73 attributed to the fact that {111} interface is smooth and should grow by nucleation and migration of atomic ledges. Hence, if a portion of c -Si (negative or convex cu Si is encompassed by c -Si (positive or concave curvature) as shown in Figure 5 1, SPER should be enhanced. Furthermore, it was shown that when the radius of curvature, r = 1/ e increase in regrowth rate occurred. In the presented cases (and in Chapter 4) the growth interface has portions where r The curvature parameter was implemented as a small component of the driving force in the SPER velocity functions as shown i n Equations 2 7 and 2 8 by Phan et al. 57. The model was however never tested in cases of high interface curvature (i.e. very small radius of curvature). In most of those relatively planar structures, the effect of curvature factor was overwhelmed by the orientation dependence or the external stress factors. When Equation 2 7 was tested against experimental results of Chapter 4, it could not reproduce the corners (the same way as Equation 4 3 could not). The curvature parameter in Equation 27 was too small to have any effect on the regrowth shapes. Thus, a new model for curvature was needed. A simplistic linear function for modeling curvature was tested using level set simulations. The Equation 4 3 was thus modified to include curvature as following v, v[ 001]f ( 1 A) (5 1) where A is a constant with units of length. For the pre sented work A = 2.0107 cm was used. Equation (5 1) was used for level set simulation of the 2D SPER process at T = 500 C in samples with surface regrowth interface pinning as shown in Figure 5 1. After annealing for 1 h, the XTEM image and level set simulation of SPER shown in Figures 5 1(b) and 5 1(f ) are in good agreement. This is also the case after annealing for 2 h as shown in Figures 5 1(c) and 51(g ) as well as after anneali ng for 4 h as shown in Figures 5 1(d) and 5 1(h ). The pinching of the

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74 cor ners leading to the formation of mask -edge defects is also noticeable in Figure 5 1(h) something that has been seen in previous works a s well 15,18,19,22. The annealing was done with and without the Si3N4 mask to al ienate the effect of stress from the Si3N4 mask on SPER. The regrowth shapes (not presented) did not show any difference in the two cases. Since, stress is known to affect regrowth rates 22,37,41 as well as regrowth shapes 22 in patterned wafers, the r esult presented above suggests that the stress transferred from the Si3N4 mask to the regrowing Si was small. 5.3 Curvature Confirming Experiment and Simulation The implication of Equation (5 1 ) is that portions of the regrowth interface with > 0 ( < 0) should have enhanced (reduced) velocity. It is evident from Figure 5 1 (surface interfacial pinning) that Equation (5 1 ) appears to be valid for the case of front is of this type. However, the converse is no t necessarily evident. For confirming the validity of the model in case of < 0 another experiment was done. Cartoon in Figure 5 2(a) shows the patterned and amorphized wafer from experiment described in section 4.3 that was used as the starting wafer for further processing. The samples were Si+implanted at 160 keV with a dose of 31015 cm2 -Si layer ~100 nm thick under the masking and ~300 nm thick in the open areas as shown in Figure 52(c). In this case, the regrowth inte rface is not in contact with any portion of the surface and is therefore not subjected to any surface pin ning. Thus, these sample s are referred to as being without regrowth interface pinning. To test the influence of < 0 on the 2D SPER process, structur e lacking interfacial pinning, shown in Figure 5 3, was annealed at T = 500 C in a N2 ambient up to 10 h. It can be readily seen that both concave and convex portions of the regrowth interface exist in this structure and both are oriented in the same dir ection (close to <111> direction) After annealin g

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75 for 2.5 h, shown in Figure 5 3 (b), the concave portion of the interface becomes sharp while the convex part begins to flatten. After annealing f or 5.0 h, as presented in Figure 5 3 (c), mask edge defects started to form as the corner region of the interface has impinged upon itself. Following annea ling for 10.0 h, shown in Figure 5 3 Si regions remain ed under the mask edge. It is noticeable i n all the XTEM images that mask edge defect s show up only when the corner becomes very sharp and the angle between the two merging fronts becomes equal to or less than 90o. This experiment also proves that the regrowth sh ape and the defect formation are not related to the -c interface being pinned at the Si -SiO2 interface (because that constraint was removed in this experiment and the defects still formed). Level set simulation of the 2D SPER process at T = 500 C in structures without interfacial pinning was done assuming Equation 5 1 to be vali d. In all cases of annealing, the simulated SPER process, sho wn in Figures 5 3 (f) (h), matches very well with the correspondi ng XTEM images, shown in Figures 5 3 (b) (d). The simulations did not take into account the regrowth rate reduction (if any) du e to the formation of mask edge defects. However, the parameters used in the simulations were enough to predict the shapes of regrowth before and after the formation of mask -edge defects. This suggests that mask edge defects do not lead to the creation of pinching corners but it is vice -versa. It also suggests that mask -edge defects do not significantly affect the regrowth rate. The TEM images also showed a suppression of the SPER velocity below the Si3N4 pad near the Si interface. This is consistent with some prior work 40 which attributed the slowing down to two probable effects: 1) The rigidity of the Si3N4 could reduce the mobility of the Si atoms at the underlying a -Si/Si interface, slowing the rate at which they arrive at the lattice sites appropriate for recrystallization. 2) The SPER might be slowed down by a higher concentration

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76 of Si H bonds under the Si3N4 feautres, since Si3N4 can act as a source of H that is lost during the densification proc ess of Si3N4. The suppression of SPER velocity due to the presence of H has been well documented 75,76. However, the regrowth rate showed (not presented) the same slowing down even with the Si3N4 pads stripped off before annealing. Thus, some other effect was responsible for the slowing down. As mentioned in section 2.1.3, nitrogen (N) is known to suppress SPER rate 46. Thus, the presence of N recoils during the last amorphizing implant (Si+ 160 keV energy, 31015 cm2 dose) could be responsible for the effect. CTRIM (crystal trim of formerly called software ISE FLOOPS) simulations were done to figure out the concentration and depth of the N profile created during amorphization. The simulations showed N profile tails off within 60 nm of the Si surface. Literature values 46 were used to incorporate slowing down of the regrowth in the presence of N atoms as shown in Figures 5 3 (f) -(h) and they had a perfect matching with the TEM images as shown in Figures 5 3 (b) (d). It is also notable that since N profile is far from the areas of high curvatures (both concave and convex), the slowing down of regrowth near the surface did not in any way affect the evolution of regrowth in high curvature areas. Thus, the effec t of N on curvature (if any) did not have to be taken into account. The effect of dopants on curvature parameter has been further discussed in Chapter 6. The 2D SPER process in samples without interface pinning was also examined at T = 575 C using XTEM to see the effect of temperature on regrowth shapes and hence on the curvature parameter. The results are shown in Figure 5 4. In this case the SPER evolution was faster (as expected due to the thermally activated 27 nature of SPE R) but the shape of the regrowth interface was nearly identical to the case of T = 500 C. The presence of mask -edge defects at the same depth is another indication that the pinching of the corners happened at the same depth.

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77 The implication is that the apparent influence of interfacial curvature on SPER is nearly temperatureindependent. Beyond this temperature, the regrowth would be very fast and it would not be possible to take various time -splits during regrowth. 5.4 Interpretation of the Curvature Factor in SPER Even though curvature factor was implemented as a fitting parameter, some prior atomistic modeling work on regrowth by Marques et al.60,61 supports the idea of curvature. As shown in Chapter 2, the model suggests the presence of bond-defects as the reason for amorphization. The bonddefect is also known as I -V pair or Interstitial -Vacancy pair because of the inability of an interstitial and a vacancy (migrating towards each other) to recombine in a crystalline semiconductor. The activation energy for the recombination of an isolated I -V pair is 0.43 eV 60,61, which would imply a very fast recombination of the interstitial and a vacancy. The activation energy, however, becomes larger as more I -V pairs surround the I -V pair. The accumulation of t hese I -V pairs leads to the formation of amorphous region. The activation energy dependence on the neighboring I -V pairs is given in Equation 2 9. It is evident from the model that a planar interface would regrow faster than a convex interface (a portion o f c -Si is -Si) because the planar interface would have less neighboring I -V pairs than Si is encompassed by c -Si). Comparison between the I -V pair model and the one presented in Equation 5 1 is difficult. The linear interpolation of I -V pairs to the curvature would give different results in the two cases, since the I -V pair model would then include the curvature term in the activation energy. This would mean different effect of the curvature at different temperatures (with respect to planar). However, experiments done at different temperatures (Figure 5 4) suggest no difference in the regrowth shapes and the mask -edge defect depth. Hence, only qualitative agree ment is sought from the I -V pair model for the curvature parameter.

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78 Another supportive argument for the curvature implementation comes from the ledge based regrowth theory (recently confirmed by Rudawski et al. 21, 3739). The theory states that regrowth is mediated by crystal island nucleation with subsequent island ledge migration. It also states that in plane migration involves the coordinated motion of atoms along a growing island ledge. Figure 5 5 shows the for mation and migration of ledges. The fact that the bottom front propagates by nucleation and migration of ledges leads to a sharpening of the corner at the concave curvature. However, on the upper front near the convex curvature, the ledge migration does no t help the regrowth of the corner. Instead, it makes the convex front more planar and leads to the formation of (111) fronts that are slow regrowing. The above process can be simulated on a macroscopic scale using the curvature factor along with orientatio n dependence as shown in Equation 5 1. Prior simulation work by Phan et al 57 advanced t hat the curvature of a regrowth interface does not influence the activation barrier for SPER. Additionally, Phan et al 57 addressed the influence of curvature on the driving force for recrystallization and determined it produced a negligible impact on the regrowth kinetics. However, though thermodynamic considerations may be negligible, it d oes appear from the work presented herein that interfacial curvature is altering SPER kinetics. Perhaps no curvature effect was observed because of the relatively planar nature of the structures used in the prior work. In terms of explaining the apparent linear dependence of the SPER velocity with -c interface having an inherent amount of internal tension as has been suggested by others 77,78. Thus, it is foreseeable that portions of an interface with non -zero curvature would experience localized stresses much different from the case of an interface with zero curvature. Furthermore, it has

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79 been well establi shed that stress on the regrowth interface can significantly alter the kinetics of SPER due to changes in volume associated with the process 19,34,40,41,51,53,79. Hence, it is possible that interfacial curvature is influencing the localiz ed stress states on the interface and altering regrowth. 5.5 Predicting 2D Regrowth Shapes The 2D SPER model from section 5.2 has successfully simulated regrowth shapes for different as implanted c interfaces for various temperatures. Thus, the capabilit y was tested to predict the regrowth shapes of some other -c interfaces that would be helpful in device engineering. Figure 5 6 shows the simulated 2D SPER process in samples with surface interface pinning at different initial values of r under the mask -Si thickness of ~150 nm. As r increases, it is more difficult for the regrowth interface to collapse upon itself (and thus form mask edge defects). In fact, this prediction is verified by a prior study in which a sine wave -ty pe regrowth interface with very low amplitude completely flattened after sufficient annealing and exhibited no defects 34,51. Thus, the model can be used to successfully predict the formation of mask edge defects de pend -c interface shape. The result is very important from the semiconductor industry perspective, for reducing the mask -edge defects that have known increase leakage current80. Angled implants are very common during CMOS device fabrication for the fo rmation of source -drain extension implants or halo implants. Thus, creation of initial amorphous shapes as shown in Figure 5 6 for alleviating mask -edge defects can be easily integrated in the device fabrication process The model described in section 5.2 gives some insight into the regrowth when the amorphous trench depth or width is varied. It is intuitive to see that increasing or decreasing the

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80 width (W) or depth (D) of the amorphous region while keeping the width to -depth (W/D) ratio constant will not affect the regrowth shapes. However, varying the W/D ratio leads to very different regrowth shapes. Figure 57 shows different starting -c interfaces with varying W/D ratios (W varying, D stays constant). The contours represent the various stages of regr owth starting with a perfectly rectilinear amorphous shape. The first noticeable feature of regrowth in all four cases is that the pinching of the corners takes place at same depths. The pinching of the corners happens due to the merging of the side and th e bottom fronts and the inability of the encompassed regrowing -Si corner to add to both the fronts while maintaining a perfect atomic registry However, that is totally dependent on the starting -c interface shape and the amorphous depth as was shown in Figure 5 6. Nevertheless, the regrowth beyond the pinching of the corners is highly dependent on W/D ratio. Figure 5 6 (a) shows the case with W/D = 2.5 and represents all the cases where W/D > 2 (all will have similar regrowth shapes). The figure shows the flat bottom (001) front reaching the surface as a flat (001) front. The side fronts composed of (110) planes can be seen encroaching from the sides and the pinching of the (111) corners can also be seen. The flat bottom reaching the top surface leaves behind two triangular amorphous regions composed of (111) fronts that finally regrow very slowly and with defects. This has been observed in prior experiments 15,22. Figures 5 6 (b) and (c) show regrowth with W/D = 2 and W/D = 1.5 respectively. The bottom regrowing front in the two cases is not able to reach the surface a flat front. Instead, it converts into two slow regrowing (111) fronts that slow down the regrowth at the center of the pattern.

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81 Figure 5 6 (d) sh ows regrowth for W/D = 1 and is representative of the regrowth shapes for cases with W/D < 1. In this case, the regrowth was controlled by the side fronts which collapsed into each other to create an inverted V -shape of amorphous region at the center that is composed of slow growing (111) fronts. Since, the propagation of the -c interface can influence the dopant profile by dopant segregation81, diffusion30,31,82 etc. it is essential to know the -c interface shapes during regrowth. 5.6 Summary In summary, a model for 2D SPER for semi insulating Si was proposed. The model from Chapter 4 considered only orientat ion dependence of regrowth, but that approach failed to accurately predict the evolution of regrowth process in structures where the regrowth interface was pinned at the surface. However, modifying the orientation dependent regrowth model to also be linear ly dependent on local interaface curvature did accurately account for regrowth evolution. This same curvature dependence was also successful in predicting the regrowth evolution in structures where regrowth interface pinning was not present. Interestingly, the apparent linear dependence of regrowth kinetics on interface curvature was temperature insensitive. The regrowth model was also used to predict the regrowth for different starting -c interfaces. This included varying the i nitial curvature of the -c interfaces and varying the width to -depth (W/D) ratio of the amorphous region. The simulations gave an insight about the evolution of regrowth shapes and how different starting -c interfaces could be used for the betterment of device fabrication and performance.

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82 Figure 5 1 The observed and curvature included simulated 2D SPER process in a structure with c interfacial pinning at the surface at T = 500 C: XTEM images of the structure a) as implanted, b) after annealing for 1 h, c) after annealing for 2 h, and d) after annea ling for 4 h. Level set simulations of the structure evolution using both regrowth orientation and interfacial curvature dependence [Equation 5 1 ] for e) as implanted f) after annealing for 1 h, g) after annealing for 2 h and h) after annealing for 4 h.56

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83 Figure 5 2 Shows cartoons for creating a structure with out -c interfacial pinning : a) The starting wafer with patterned amorphous region with -c interfacial pinning b) Ion Implantation of the wafer by Si+ with 160 keV energy and 31015 cm2 dose (with the mask still present), c) The as -implanted structure with out -c interfacial pinning with -Si layer ~100 nm thick under the masking and ~300 nm thick in the open areas.

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84 Figure 5 3 The observed and curvature included simulated 2D SPER process in a structure -c interfacial pinning at the surface at T = 500 C: XTEM images of the structure a) as implanted, b) after annealing for 2.5 h, c) after annealing for 5.0 h, and d) after annealing for 10.0 h. Level set simulations of the structure evolution using both regrowth orientation an d interfacial curvature dependence [Equation 5 -1 ] e) as implanted, f) after annealing for 2.5 h, g) after annealing for 5.0 h, and h) after annealing for 10.0 h 56.

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85 Figure 5 4 2D SPER shapes showing no dependenc e on temperature -c interfacial pinning at the surface : XTEM images of the structure for T = 500 C a) after annealing for t = 2.5 h, b) after annealing for t = 10 h, for T = 575 C c) after annealing for t = 10 mins., d) after anne aling for t = 20 mins. Figure 5 5 Cartoon depicting the ledge theory argument for the 2D SPER of a structure without c interfacial pinning

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86 Figure 5 6 -c interface curvature near the corner region on the level set simul ations using both regrowth orientation and interfacial curvature dependence [Equation 5 -c interfacial pinning at the surface: r = a) 40 b) 80 and c) 120 nm 56.

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87 Figure 5 7 The effect of -c interface width -to -depth (W/D) ratio on the regrowth shapes for 2D SPER using level set simulations [Equation 5 1], a) W/D = 2.5, b) W/D = 2, c) W/D =1.5, d) W/D = 1.

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88 CHAPTER 6 D OPANT EFFECT ON SOLI D PHAS E EPITAXIAL REGROWTH OF SILICON 6.1 Introduction Chapters 4 and 5 provide the velocity expression for SPER of semi -insulating Si. However, the source and drain regions where SPER is typically known to happen in a CMOS device are heavily doped. It was also mentioned in the Chapter 2 that dopants of both n and p -type strongly enhance the SPER velocity in Si. The dopant related enhancement of SPER velocity has been known to be an electronic process because both p and n -type dopants increase the rate when prese nt separately and no enhancement is observed when both are present together. The GFLS (generalized Fermi level shifting) model 28,29,47,75,76 attributes the enhancement of SPER velocity to the increase in the densit y of charged defects. However, most of the experimental work in studying the dopant effect on SPER has been on planar interfaces28,29,47,75,76. Only a few prior studies have studied the effect of dopants on patterne d regrowth20. These studies suffer from the non uniformity of dopant profiles in the depth direction because of ion implantation of dopants. Subsequently, the various regrowth fronts in the patterned -c interface are affected by different dopant concentration. In addition to that the dopants suffer from diffusion during regrowth in case of non uniform doping. Also, in light of the curva ture factor suggested in Chapters 4 and 5, it is extremely important to have a constant doping in the structure to make any useful conclusions about the effect of doping on patterned SPER. This Chapter shows the effect of Arsenic (n type) and Boron (p type ) on the velocities of various substrate orientations. In addition to that, the effect of dopants on the curvature effect is also studied. Apart from the dopants affecting the SPER, the SPER also affects the dopant profile by diffusion and segregation30,31,81,82. Some dopants like Boron (B) have known to diffuse

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89 significantly more in the amorphous Si as compared to crystalline Si (diffusivity difference ~five order of magnitude)30,31,82. Thus, SPER was simulated simultaneously with dopant diffusion in FLOOPS and some interesting results were seen. 6.2 Experiment for Dopant Effect on SPER For this work the experimental design was similar to the one shown in section 5.3. Howeve r, semi insulating wafer ( ~ 250 -cm) was used as a control for the p type ( ~ 0.0030.004 cm) and n -type ( ~ 0.0030.004 -cm) wafers. The n and p type wafers were chosen with very low resistivity to see the maximum effect of dopants on regrowth sh apes. These 500 m thick (001) Si wafers were patterned using masked regions that consisted of lines ~0.5 m wide. The lines were aligned along <110> inplane directions with 150 nm of Si3N4 separated by ~0.5 m wide unmasked area between adjacent lines (d ue to some under etch, the unmasked areas had ~ 20 nm nitride left as shown in Fig. 6 1. We will still refer to it as unmasked region for clarity). All the samples were Si+-implanted at 20, 60, and 160 keV with doses of 11015, 11015, and 31015 cm2 to g enera Si layer ~7 0 nm thick under the masking and ~230 nm thick in the unmasked areas as shown in Fig. 6 1. As with the prior experiment 56, this as -implanted regrowth interface includes both convex an d concave curvatures. T he regrowth interface is not in contact with any portion of the surface and is therefore not subjected to any surface pinning effect which would constrict the regrowth of interface contacting the Si3N4 55. All the samples were annealed at 500 0 C in N2 ambient. The semi insulating samples were annealed for times 0.5 10.0 h. Anneal times were chosen to see different points during the regrowth process when the regrowth evolution showed important changes. Since, the n and ptype dopants are known to increase planar regrowth rates27, appropriate anneal times were chosen depending on the doping concentration to catch regrowth at similar points as the semi -

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90 insulating case. XT EM imaging was used to image the 2D SPER process with XTEM specimens prepared via focused ion beam milling. Fig. 6 1 shows the as-implanted XTEM image for the experiment that includes both n and p type low resistivity wafers in addition to the semiinsulat ing (same as -implanted for all three cases). Figures 6 2 (a) (c) show the regrowth of semi insulating sample at T = 500 0 C and t = 2.5 h, 5.0 h and 10.0 h respectively (very similar to experiment in section 5.3). The sharpening of the concave corners and flattening of the convex corners is visible at 2.5 h. The pinching of the [111] corner leading to the formation of mask -edge defects can be observed at 5.0 h and 10.0 h. The regrowth however slows down as the interface approaches the surface at 10.0 h when compared to Figure 5 3 (d) where the bottom (001) front had reached the Si surface leaving behind two triangular Si regions The presence of the thin Si3N4 in the unmasked region (something that was absent in Figure 5 3 (d)) is responsible for this slow ing down. Saenger et al.40 explained the slowing down of regrowth below a Si3N4 layer to the body effect (arising from the rigidity of Si3N4 layer) or a localized increase in -Si hydrogen concentration. The presence of nitrogen recoils from the ion -implantation of Si is possibly responsible for the slowing down as well (since N is known to cause slow regrowth rate46). However, the slowing down takes place closer to the surface that is far from the pinching concave corner (the region of interest) so it does not affect the validity of our results. Figures 6 2 (d) (f) show th e regrowth of n type sample at T = 500 0 C and t = 1 h 40 min, 3 h 20 min and 6 h respectively. The n type dopant was Arsenic and the doping concentration was found to be ~71019 cm3 (from resistivity values). This resulted in a planar regrowth velocity e nhancement of ~2 times 28. Hence, the regrowth times were chosen to be almost half of the semi insulating case. The XTEM images showed no difference from the corresponding semi -

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91 insulating case. The same amount of pinching was observed in the concave corners and the defects formed at the same depths. Figures 6 2 (g) (i) show the regrowth of ptype sample (B) at T = 500 0 C and t = 40 min, 1 h 20 min and 2 h 40 min respectively. The p type dopant was Boron and the doping concentration was found to be ~41019 cm3. This resulted in a planar regrowth velocity enhancement of ~4 times. The XTEM images, like n type case, showed no change in shape of regrowth. The defects still formed at the same depth. The last regrowth split at 2h 40min. seems a little different from its counterparts because once the mask -edge defects are formed, the regrowth of the defective corner can have some variations. However, it is clear that the regrowth shapes that lead to the pinching of the corner are the same for all cases. The charged defects that lead to the enhancement of regrowth rate enhancement are believed to come from the dopants. However, at higher processing temperatures the intrinsic carrier concentration ( ni) ri ses exponentially with temperature 3 and the Fermi level (EF) approaches the intrinsic Fermi level (Ei). Thus, it is important to confirm that the intrinsic carrier concentration and the Fermi level fall within reasonable assumptions of the GFLS model show n in Chapter 2. The computed ni at T = 500 0 C (used in presented work) was 1.11018 cm3 which is almost an order of magnitude lower than the dopant concentration of the n and p-type wafers used in the presented work. Thus, the enhancement in regrowth rat e is dominated by the charged defects due to dopants. The band gap of Silicon ( EG) at T = 500 0 C was found to be ~0.96 eV that is less than 1.12 eV at room temperature (25 0 C). According to Johnson 3, degenerate semiconductor statistics are required at the dopant concentrations used in the presented work and the Fermi level ( EF) was found to be ~0.16 eV below the conduction band for Arsenic (As) with ~71019 cm3 doping

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92 concentration at T = 460 0 C. Interpolating from the graph shown in 3, the degeneracy factor (g) for As in the presented work is 0.5 and En p the defect energy level responsible for regrowth rate enhancement is ~0.15 eV below the conduction band edge. This makes sense since for a regrowth rate enhancement of ~2 from As, the EF En p needs to be ~0.015 eV. The case is similar for Boron. 6.3 Discussion The implication of the SPER shapes being the same for all three cases (semi insulating, ntype and p type) is twofold: 1) Dopants increase the planar regrowth rate isotropically (Figure 6 3). 2) T he electronic effect that is known to control the enhancement of regrowth rate due to dopants has to be independent of the curvature effect (Figure 6 4). The first conclusion being that the enhancement is isotropic implies that the Csepregis 13 regrowth data curve shifts upwards in the presence of dopants. It also suggests that the defects that are responsible for the rate en hancement are the same for all orientations. This conclusion is understandable because the enhancement is known to be a Fermi -level effect 28,29,47. Since Fermi level is known to be a function of the material and no t the orientation, the results are in conformity with literature. The second conclusion is that the curvature effect and the dopant electronic effect are independent of each other. Figures 6 4 (a) (c) show the simulations of regrowth with varying curvat ure parameter A = 4e 7 cm, 6e 7 cm and 8e 7 cm respectively (keeping all other parameters constant). As the curvature parameter increases, the pinching of the corner reduces. No pinching implies no mask edge defects. Experimentally, this was shown to happe n in the presence of external in plane unaxial tensile stress 22,26,79 (higher stresses in corners because the

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93 stress -curvature relationship implies stronger effect in the corners). However, no such effect was seen in the presence of dopants only. Hence, Equation 5 1 has been modified to include the effect of dopants as: v,, dopant v[ 001]f F ( dopant ).(1 A) (6 1) where, F (dopant) is the Fermi level dependent regrowth rate enhancement given in Equation 2 v[001] is the value of v along [001] is the orientation dependent factor, is the localized curvature of the -c interface and A is the curvature parameter. The dopant concentration for every node on the Level set grid is acquired at every time step to be fed into the F (dopant) factor Thus, any changes in the dopant concentration due to diffusion or segregation are refreshed into the velocity expression to get an accurate dopant effect on rate enhancement. The simulations showed that changing the parameter A from 2.0107 cm to 4 .0107 cm did not make much difference in regrowth shape. However, increasing A beyond 4.0107 cm changed the regrowth shape significantly as shown in Figure 6 4. When A reaches 8 .0107 cm (Figure 6 4 (c)), there is no pinching of the corner. Since the planar regrowth rate enhancement from Boron was ~4 times and no change in regrowth shape was seen, curvature effect can be said to be independent of the electronic effect within a reasonable error window. It would be nice to have a much higher dopant effect to m ake this error window smaller. However, with increased doping (for p type dopants like Boron), stress effects from the dopants83 can start affecting the regrowth as well and that will make it difficult to isolate the different effects. 6.3 Linking Diffusion and SPER SPER for Si for temperatures in the range of 500 650 0 C is much faster than dopant diffusion in crystalline Si27. However, dopants like Boron have shown a significantly higher diffusivity in amorphous Si. The high diffusivity of Boron in amorphous Si makes diffusion a

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94 competing process with the SPER and the combination of the two processes determines the fi nal Boron profile after the SPER has completed. Boron segregation and clustering are also known to affect the final Boron profile, however concentration dependent diffusion has been known to be the most important factor in determining the final profile of the dopant 30,31,82. The capability of FLOOPS was used to simulate different diffusion on either side of the -c interface, with negligible diffusion on crystalline side and concentration dependent diffusion on the amorphous side. The interface of the amorphous -crystalline Si moved simultaneously as time progressed (usi ng Level set m ethod). Simultaneous implementation of Level set method and diffusion required the coupling of the time steps of the two processes. The level set time step was kept constant and limited by the stability condition (CFL stability criterion 58). The criterion states that for stability the time step cannot be big enough for the level set to move more than one grid spacing. The diffusion was manually initialized from a small time step that doubled in value if the initial guess was good and halved otherwise. The time steps of the two processes were looped so that the smaller time step controlled the simulation time. Furthermore, Level set was implemented on rectangular mesh as opposed to diffusion that used a triangular mesh from FLOOPS. Hence, after every time step, the level set values that represented the -c interface were interpolated onto the FLOOPS grid for different diffusion in amorphous and crystal line Si. Also, the dopant profile from the FLOOPS grid was interpolated onto the Level set mesh to take into account dopant effect on regrowth velocity. 6.4 1D SPER and Diffusion 1D SPER represents regrowth of a planar -c interface Simulations were don e to confirm the results of one of the prior experiments done by Jacques et al. 30,31,82. The experiment was done on (001) bulk Si wafer to compute the diffusivity of Boron in amorphous Si. The implant

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95 conditions we re Si+ at 70 keV energy and 1 1015 cm2 dose that formed an amorphous layer of 150 nm. Then, B+ was implanted at 500 eV, 1 1015 cm2 to get a very shallow boron profile (completely contained within the amorphous layer) as shown in Figure 6 5. A low tempera ture of 550 0C for 30 mins was subsequently done to completely recrystallize the amorphous layer. The solid -solubility of Boron at this annealing temperature was found to be 2.3 1020 atoms/cm3 (any Boron concentration above this, did not diffuse). Boron di ffusivity was found to be concentration dependent with DB = 3 1017 + 3 1037 CB cm2/s in amorphous Si. Boron diffusion in crystalline Si was found to be negligible. The above given parameters were used to simulate diffusion along with SPER with a rate of 325 nm/h (determined by the temperature of regrowth, using equation 42). Simulated profile is shown along with the measured SIMS profile of Boron after annealing in Figure 6 5 and they seem to match up well. However, it was observed that the interplay between diffusion and SPER was not a lot because the Boron had mostly diffused by the time the -c interface reached the Boron. Once, the interface reached the Boron profile, it regrew very quickly and no significant diffusion was observed during that time. 6.5 2D SPER and Diffusion SPER, in the most general sense is a three-dimensional (3D) proces s but in case of one of the dimensions of the structure being very long, it effectively can be treated as a 2D process. The long dimension in our study corresponds to the dimension into the page in all of the figures (similar to Chapters 4 and 5). Simulati ons were done for the as implanted profile of Boron from section 6.4 and a patterned amorphous region with amorphous depth of 150 nm (same as section 6.4) and width of 300 nm as shown in Figure 6 6 (b). It was observed that the regrowth for the same amorph ous depth as planar case did not complete in 30 mins. This is attributed to the formation of fronts other than (001) which have slower regrowth velocites (as mentioned in

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96 Chapter 4). The simulated regrowth fronts upto t = 30 mins. are shown in Figure 6 6 (b). The time for complete regrowth was found to be 1 h. from simulations. Figure 6 6 (a) shows the as implanted profile and annealed profile of Boron after 30 mins. for planar regrowth from Figure 6 5. In addition to those profiles, simulated profiles for Boron after annealing for 1 h. (that was required for complete recrystallization of patterned amorphous region) are shown. The two simulated profiles have been taken from different cutlines in the patterned region (green and red colored cutlines from the center and edge of the pattern respectively have their corresponding colored profile in 6 6 (a)). The simulated dopant profile at the center of the pattern (t = 1 h) matches well with the annealed SIMS profile (t = 30 mins). The reason being that the cent er of the pattern regrew almost fully after 30 mins. as shown in Figure 6 6 (b) and there was no Boron diffusion after that (since Boron diffusion in c -Si is comparatively negligible). On the other hand, the regrowth at the corners was incomplete at t = 30 mins. as shown in Figure 6 6 (b). Hence, the Boron was in the amorphous Si for more time and diffused further after t = 30 mins. as is evident in simulated profile in Figure 66 (a). Thus, the final Boron profile was found to be nonuniform in the pattern ed region. From device perspective, this result has a lot of significance as the nonuniform doping profile could lead to more leakage between source/drain regions. 6.6 Summary In summary, a novel experiment was done to see the effect of p type and n type dopants on regrowth. It was concluded that dopants enhance the regrowth rate of Si isotropically. Furthermore, they were not found to affect the regrowth shapes and hence the mask edge defects. The Level set model was expanded to incorporate the dopant de pendent velocity enhancement factor. Furthermore, diffusion and SPER processes were linked in the FLOOPS simulator. This

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97 allowed for the simultaneous simulation of the two processes that helped in simulating accurate dopant profiles.

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98 Figure 6 1 As-i mplanted -c interface of Si for semi insulating, ntype and p type samples. Si3N4 mask patterned to get a patterned -c interface.

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99 Figure 6 2 The observed 2D SPER process at T=500 0C with dopants : XTEM images of Semi insulating (a -c), a) after annealing for 2h 30 min, b ) after annealing for 5 h, and c) after annealing for 10 h ; N -type As samples (d -f), d) after annealing for 1h 40min, e ) after annealing for 3h 20min, and f) after annealing for 6 h ; P -type B samples (g i), g) after annealing for 40 min, h) after annealing for 1h 20min, and i) after annealing for 2 h 40min.

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100 Figure 6 3 Figure shows the effect of dopants on Csepregis 13 SPER data. Experimental results suggest shifting up of the data due to the isotropic SPER dopant enhanced velocity. Figure 6 4 Level set simulations showing the effect of the curvature parameter A on the shape of regrowth for t=5 h. and T=500 0 C. a) A = 4 .0107 cm (same as A= 2 .0107 cm ), b) A = 6 .0107 cm shows less pinching of the concave [111] corner, c) A= 8.0107 cm shows no pinching implying no mask edge defect formation.

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101 Figure 6 5. 1D diffusion of Boron during SPER. The figure shows the SIMS profile of Boron as implanted and after annealing at T=550 0 C for t=30mins. 30,82. Simulation of the diffusion and SPER in FLOOPS is shown to match the SIM S profile.

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102 Figure 6 6. Figure shows the effect of 2D SPER on dopant profile. (a) shows the SIMS profile of Boron as -implanted and after annealing at T = 550 0 C for t=30mins. 30,82 (same as figure 6 5). The simulation profiles show the profile of Boron after complete recrystallization of 2D amorphous trench shown in (b). The cutlines are taken at center and side of the trench. (b) shows the simulated SPER process (T = 550 0 C) for a rectilinear amorphous region. The contours represent -c interface at different times during regrowth.

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103 CHAPTER 7 STRESS EFFECT ON SOL ID PHASE EPITAXIAL REGR OWTH OF SI LICON 7.1 Introduction Stress has known to play a major role in the SPER process33,34,37,41,49,53. As explained in Chapter 2, externally applied out of plane compression and hydrostatic compression increase the planar SPER rate exponentially36,41. This was attributed to the negativ e activation volume associated with conversion of Si into c Si41. The converse was found to be true for tension. However, Rudawski et al.21,37,38,53 showed that the theory could not be extende d to external in plane stress. No increase in planar SPER rate was observed for uniaxial in plane tension and the decrease in the planar SPER saturated at ~0.5 GPa. The results were explained by the nucleation and migration phenomena that control SPER53. Nucleation was suggested to be the rate limiting step. In -plane stress on the other hand affects the migration phenomena thus not affecting the SPER rate strongly. However, no model exists for patterned SPER in presence of in-plane stress. This Chapter explores the effect of uniaxial in plane stress on patterned SPER. Experiments were done with inplane uniaxial stresses upto ~1.5GPa and their effect on SPER were studied. Interface roughening ( -c Si) is another aspect of SPER that results from the ap plication of in -plane compression during SPER34,49,51,57. In -plane compression increases the interfacial roughening while no-stress or tensile stress reduces the roughness (details in Chapter 2). However, no models have been proposed to explain this phenomenon. Using level set methods approach and the curvature factor; this chapter aims to give possible explanations for interfacial roughening. This chapter also analyzes the physical reasons for the presence of curvat ure factor. Its relation to nucleation and migration processes is explained. The effect of stress on the curvature factor and encapsulation of stress in the curvature factor for patterned SPER is shown.

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104 7.2 Interfacial Roughening During SPER Section 2.2. 2 showed the effect of uniaxial in-plane stress on the SPER of small amplitude sinusoidal shaped -c Si interface. External compression tends to increase the amplitude of the shape while no -stress or tension tends to flatten it out. An experiment was done to confirm the experiments done by Barvosa -Carter et al .34,49 and also to see the effect of higher stresses on the regrowth of sinusoidal shaped -c Si interface. Figure 7 1 shows the SPER under compression uniaxial in plane stress applied using the novel bending apparatus as mentioned in section 3.1.3. Figure 7 1(a) shows the cartoon of as implanted interface created by implanting Si+ at 20, 60, and 160 keV with doses of 11015, 11015, and 31015 cm2 to generate a n undulating Si layer ~270 nm deep and in the shape of a sinewave with amplitude ~15 nm and wavelength ~500 nm. Figure 7 1(b) shows the SPER after 4h. at 525 0C under 250 MPa compression and Figure 7 1(c) shows SPER after 4h. at 525 0C under 500 MPa compression. Fig ure 7 1(b) expectedly shows increase the interface shape amplitude under compression similar to prior work34,51. However, Figure 7 1(c) shows interface roughening as well. Prior work did not show roughening at 500MP a though51. It is possible that the different techniques of applying and measuring the stress in the two experiments led to the error. Still, its clear that stresses beyond a certain value (close to 500MPa) would start causing interfacial roughening. Stress simulations were done using FLOOPS for calculating the stress on the sinewave interface between amorphous and crystalline Si. The amorphous Si was assumed to have a youngs modulus half that of crystalline S i84. Both materials were considered elastic for the simulations. The initial displacement of the wafer strip computed from the experiments was fed to the stress simula tions. The stress simulation results showed the stress contours along the sinewave interface, implying no apparent difference in stress between peaks and valleys. Thus,

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105 prior explanations34,49 of the sinewave amplit ude getting affected due to unequal stresses in peaks and valleys cannot be substantiated. Moreover, the fact that even under no external stress, the amplitude of the interface decreases implies that curvature factor is responsible for this effect. It is i ntuitive that curvature effect would help flatten out the sinewave and the absence of it would lead to the amplitude increasing (due to orientation dependent velocity). Crystalline Si is known to be denser than amorphous Si by ~3% 52. Thus, as the -Si is consumed by c -Si during SPER, there should be a stress build up. However, since the top surface of Si is free, it leads to a relaxation of most of the out of plane stress. The effect of any stress that might be present in plane of the -c Si interface is taken into account in the orientation dependent velocity. The planar regrowth experiment of different substrate orientation by Csepregi13 by default includes all the internal stresses while computation of orientation dependent velocity. SPER with the orientation dependent velocity is capable of creating the interface roughening in the absence of curvature effect. This was shown by Level Set simulations of sinewave with different curvature fa ctors (Figure 7 2). Figure 7 2(a) shows SPER at 525 0C after 1h with the curvature factor A (defined in Chapter 5) equal to zero. It is noticeable that in absence of curvature effect, the interface roughens up. The roughening can be attributed to the non -s mooth as -implanted -c Si interface. The rougher the starting interface, higher the interface roughening during SPER. It also implies that a rougher interface requires lower in-plane compression stress to start causing the roughening. Figure 7 2(b), (c), (d) show SPER at 525 0C after 1h with A = 1.5e 7, 2e 7, 4e 7 cm respectively. The regrowth in all these cases is more than the case with A =0 because of lack of roughening. Roughening creates many slow regrowing {111} fronts, thus leading to a reduction

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106 in overall SPER rate. Stronger curvature (higher A ) shows faster flattening of the sinewave and is thus closer to tension case. The above simulations are a clear indication that external in plane stress modulates the curvature factor and is thus responsible f or interfacial roughening or smoothing of the -c Si interface during SPER. The role of starting interface on the regrowing shape was demonstrated by Rudawski et al.53. SPER under in-plane uniaxial stress for a planar -c Si interface showed much mo re roughening for a rough starting interface. Figure 7 3(b), (c), (d) show SPER under 0.5GPa, 1GPa and1.5GPa compression respectively at 525 0C for 1.3h (with starting interface at 7 3(a)). Figure 7 3(e) shows pre annealing under no-stress for 0.7h to planarize the interface (for the same starting interface at 7 3(a)). Figure 7 3(f) shows the following SPER under 1.5GPa compression at 525 0C for 1.3h. All the samples had As implant to increase the planar SPER rate. It shows very less roughening that is also demonstrated by less defect density (since these defects form due to the roughening of the interface53). Moreover, it is almost impossible to get a perfectly smooth interface and thus there will always be some interfacial roughening after SPER under compression. The Level Set simulations are capable of capturing these results with rougher starting interfaces becoming even rougher in absence of the smoothing curvature effect. 7.3 In -Plane Uniaxial Stress Experiments After exploring the effect of stres s on relatively planar interfaces, it needs to be seen how the stress affect SPER of patterned trench regions -Si that are known to create mask edge defects. For consistency with experiments in Chapters 5 and 6, the as implanted interface was created under similar experimental conditions. Some differences exist however. Instead of the 500m thick Si wafers, ultra thin (001) Si wafers (50m thick) with double side polishing and high resistivity (~250 cm) were used. This helped very clean cleaves of the wa fer strips for

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107 bending. Consequently, the wafer bending produced stresses upto 1.5GPa (as explained in Chapter 3). Si3N4 that was used for masking in experiments from Chapters 4,5 and 6 was not used because the stress from the deposited Si3N4 would have af fected the total stress applied on the samples. Thus, PMMA was used as the mask that consisted of lines ~0.5 m wide for etching Si ~150nm deep. The lines were aligned along <110> in-plane directions. DRIE was used to etch Si anisotropically. However, some variations were noticed between the samples and the etch depth varied between 110 140 nm. Also, due to significant undercutting during DRIE, the masked lines were reduced to ~0.2 0.3 m (Figure 7 4 (a) surface). It did not have any effect on the outcome o f the experiment since similar results were observed for some test cases with wider lines (~1m). Subsequently, all the samples were Si+-implanted at 20, 60, and 150keV with doses of 11015, 11015, and 31015 cm2 -Si layer of ~ 110 nm amplitude and ~270nm depth from the surface. The as -implanted image is shown in Figure 7 4(a). Some samples were allowed to regrow under no external stress conditions. They were annealed at 525 0C in N2 ambient for 2h and 4h (Figures 7 4(b), (c) re spectively). The SPER happens without the formation of mask -edge defect. This confirms the results from Chapter 5 where it was shown that the formation of defects was controlled not only the amplitude of Si undulation but also by the curvature of the as implanted -c interface (Figure 5 6). In the presented case, the corner is not as sharply curved when compared to experiments in Chapter 5 (Figure 5 3). Thus, SPER under no external stress does not result in formation of mask -edge defects. The SPER rate was found to be ~100 nm/h that is in conformity with previous works27. In -plane uniaxial stress was applied to the rest of the samples. Figure 7 5 (a), (b), (c) and (d) show partial SPER at 525 0C in N2 ambient for 4h. under compression of 250 MPa, 500 MPa,

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108 1.0 GPa and 1.5 GPa respectively. The planar part of the structure grew slower than the no -stress case. This was observed previously21,37,38 where the planar regrowth velocity reduces upto half under in-plane compressi on. Most noticeable is the formation of mask -edge defects in all the four compression cases. This can be attributed to a lower curvature effect, i.e. lower enhancement of the concave corner velocity and hence more pinching of the corner. For cases with hig her compression (1GPa and 1.5GPa), interface roughening of the planar part was observed. The interface roughening also leads to formation of more defects as was observed by Rudawski et al.53 in the planar regrowth studies. In -plane uniaxial tension c ases are shown in Figures 7 5 (e), (f), (g), (h). The anneals for tension cases were done for 2 h. at 525 0C so as to catch the regrowth at a similar position as the compression case anneals (tension SPER is twice as fast as compression). All the cases of tension look exactly the same and are no different from the no -stress case shown in Figure 7 4(b). This is similar to planar SPER where tension made no difference to the SPER rate53. As shown in Chapter 2, tension has been known to help get rid of mas k -edge defects19,22. However, if no mask -edge defects exist in the no -stress case, then tension does not affect the SPER. This fact has been noticed in sinewave experiments of section 7.2 as well. The tension and c ompression cases shown in Figure 7 5 have some difference in the Si surface used for creating undulation of -Si The compression case seems to have a narrower line width (by ~100 nm) and a deeper etch (by ~40nm). However, the results dont get too strongl y affected by it. This is further confirmed in the simulations as shown in section 7.4. 7.4 Simulation and Curvature Effect Level set simulations were done with varying the curvature factor A to simulate experiments shown in section 7.4. Prior simulations in Chapters 4, 5 and 6 had initialized the simulations using geometrical functions to match the as -implanted c interface. However, to get

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109 a more accurate initial interface, actual cross -section transmission electron microscopy (XTEM) images were fed to MATLAB and discrete x,y coordinates of the as -implanted interface were extracted. These were used for initiali zing the level set simulations. One of the benefits of using the actual XTEM image for initialization is the slight roughness present on the initial interface, something that actually exists in the structure. The previous geometrical arguments used for sim ulations considered the planar interface to be very smooth and hence interface roughening after SPER was not visible. Figures 7 6(a), (b) and (c) show the simulations of SPER for the compression case. The simulations include orientation dependent velocity varying curvature parameter ( A ) and SPER velocity computed at 525 0C (and t= 4h) for planar compression case (i.e. half the no -stress velocity). Figure 7 6(a) represents the case with A =1.5e 7 cm. The planar regions of the as implanted -c interface (on either side of the triangular region) do not regrow smoothly. They include interface roughening after SPER. Apart from that the notch and the triangular front as observed in experiments with compression are clearly noticeable in the simulation. Thus, it re sembles cases of higher compression (1GPa and 1.5GPa). Figure 76(b) represents the case with A =2e 7 cm which resembles the lower compression cases (250MPa and 500MPa). The planar regions regrow do smooth out. The triangular region is visible with the notc h on either side predicting the formation of defects. Figure 7 6(c) represents the case with A =4e 7 cm and clearly is not matching with any of the compression cases. Figures 7 6(d), (e), (f) show simulations of SPER for the tension case (and also the nos tress case since it is same as tension) with SPER velocity computed at 525 0C (and t= 2h) for planar tension case (same as no -stress velocity). It is very evident that Figure 7 6(d) that

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110 represents A =2e 7 cm does not match up with the observed results. Fig ures 7 6(e) and (f) that represent A =4e 7 cm and 6e 7 cm are much closer to the XTEMs shown in Figures 7 5(e h). The above mentioned curvature factor of A =4e 7 cm and 6e 7 cm fitting the observed results seems to be different than Chapters 5 and 6 where A =2e 7 cm was used. However, simulations done with A =4e 7 cm and 6e 7 cm seem to fit the results in Chapters 5 and 6 as well (not presented). Thus, there seems to be an error window for the curvature factor. The factor can be between 4e7 cm and 6e7 cm. Fo r cases where defects form (in no external stress case), even A =2e 7 cm would work. However, since that does not fit the cases where no defects form, implies A is between 4e 7 cm and 6e7 cm. For compression cases though this value goes down to A =2e 7 cm f or lower stress and A =1.5e 7 cm for higher stresses. For structures where no stress case does not lead to defect formation, tension does not affect regrowth shapes and increasing A beyond 6e 7 cm does not alter simulation results. Though for cases where de fects do form for no -stress case, increasing A beyond 6e 7 cm correctly predicts no defect formation as was observed in prior experiments19,22. 7.4 Physical Explanation of Curvature Effect Since the curvature effe ct plays a vital role in the SPER process, it is important to understand what physical mechanism is governing it. The information about the curvature factor that has been gathered from experiments and simulations in the presented work are the following: 1 Cu rvature factor plays a big role in determining the shape of patterned SPER. Curvature effect is also necessary for planarization of rough as implanted interface (for no -external stress case). 2 Curvature effect is independent of the temperature dependence (s imilar to orientation effect).

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111 3 Electronic processes that govern the enhancement of SPER due to dopants, do not affect curvature parameter. 4 Stress increases the curvature parameter for in -plane external tension and decreases the curvature parameter for in -p lane external compression. Apart from the above information, prior results confirm the two results as follows, 1 I-V pair (or bond defect) is believed to be responsible for amorphization and recrystallization60 from Molecular Dynamics simulations. The theory of I -V pair recombination suggests a higher activation for recombination of I -V pairs (and thus for recrystallization) when one pair is su rrounded by more of its kind. This is a clear proof of a curvature like effect playing an important role in SPER. 2 SPER has been analytically modeled as the combination of nucleation and migration time constants37,38,53. For planar SPER, nucleation time constant is believed to be the rate -limiting step. Migration time -constant is affected by in plane stress. In -plane tension reduces the time for migration but does not affect the process since nucleation is the rate l imiter. However, in -plane compression increases the migration time -constant and reduces the overall SPER rate. Curvature factor (as shown in section 7.3) is affected by stress as well. In light of all the above observations, curvature factor should be a pa rt of nucleation mechanism. Simulations suggest that the impact of curvature is higher for planes like {111} and {011} as compared to {001} since the latter has a higher SPER rate. This is also confirmed by the prior theory85 whe re the nucleation mechanism is most important for the fronts other than {001}. This was attributed to the fact that the formation of the six -member ring requires nucleation of three atoms for {111} plane and two atoms for {011} plane (and no nucleation of

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112 {001} plane since it requires just one atom). The presence of concave curvature would help in the nucleation of these atoms. This supports the use of curvature factor in no external stress simulations (in Chapters 5,6 and 7). Since, curvature is temperatu re independent, it should be a part of prefactor of the nucleation term just like the orientation dependent velocity factor is13. The curvature term should also play a role in the migration of the ledges since a concave curvature would provide with built in ledges and migration would be faster. However, an analytical expression for the curvature factor in nucleation and migrati on processes has not been worked out. 7.5 Summary In summary, the strong effect of curvature on smoothing out the interfacial roughening during SPER was shown. For in -plane compression, the reduction of curvature factor was shown to cause more roughening. Experiments were done with trench amorphous regions (~110 150nm perturbed) to explore the effect of large in -plane uniaxial stress on SPER. No defects were observed after SPER of no-stress case. This confirmed the simulation predictions from Chapter 5 w here it was mentioned that initial curvature of the interface was as much responsible for creation of mask -edge defects as the trench depth. In -plane uniaxial tension upto 1.5GPa did not affect the SPER in any way (similar to planar case). However, in -plan e uniaxial compression led to the formation of mask edge defects. Higher compression (above 1GPa) caused the roughening of the planar regions of the -c interface. Level set simulations predicted the observed results accurately by modulating the curvature factor ( A ) for different stresses. Tension was found to increase the curvature factor and compression reduced it. Thus, encapsulation of the stress effect in the curvature effect was shown. Physical interpretation of the curvature effect as part of nucleat ion and migration processes was proposed.

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113 Figure 7 1 XTEM images of SPER under in-plane uniaxial compression : (a) shows cartoon of as implanted -c interface with perturbation of ~15nm. (b) shows SPER at 525 0C for 4h. under compression with 11= 250M Pa. (c) shows SPER at 525 0C for 4h. under compression with 11= 500MPa. Figure 7 2 Level set simulations of SPER with varying curvature factor A (a), (b), (c), (d) represent SPER after 1h. at 525 0C with values of A = 0 1.5e 7, 2e 7, 4e 7cm respe ctively.

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114 Figure 7 3 Weak beam dark field (WBDF) -XTEM images of the stress -influenced SPER process in Asdoped specimens53: a) WBDF -XTEM image of an as implanted As doped specimen. WBDF -XTEM images of As -doped specimens annealed at T = 525 0C for 1 .3 h with 11= b) 0.5, c) 1.0, d) 1.5GPa respectively. (e) WBDF -XTEM image after pre annealing under no stress for t=0.7h at T = 525 0C. (f) WBDF -XTEM image after annealing at T = 525 0C for 1.3 h with 11= 1.5GPa (done after pre annealing)53. Rep rinted with permission from Rudawski, PhD. Thesis, University of Florida. Copyright 2008, Nicholas G. Rudawski.

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115 Figure 7 4 XTEM images of patterned SPER under no external stress : (a) shows the as implanted -c in terface with perturbation of ~110 nm. (b), (c) show SPER at 525 0C for 2 h. 4h. respectively. Figure 7 5 XTEM images of patterned SPER under in -plane uniaxial stresses : (a) (b), (c), (d) show SPER at T = 525 0C for 4h. under compression with 11= 0.25, 0.5, -1.0, 1.5 GPa respectively. (e ) (f), (g), (h) show SPER at T = 525 0C for 2h. under tension with 11= 0.25, 0.5, 1.0, 1.5 GPa respectively. End of range (EOR) shows the position of as implanted interface. Surface (Surf.) of the patterned Si is shown as well.

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116 Figure 7 6 Level set simulations of SPER for matching the observations shown in Figure 7 5 by varying curvature factor A (a), (b), (c) represent SPER after 4h. at 525 0C with values of A = 1.5e 7, 2e 7, 4e 7cm respectively. (d), (e), (f) represent SPER after 2h. at 525 0C with values of A = 2e 7, 4e 7, 6e 7cm respectively.

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117 CHAPTER 8 SUMMARY AND FUTURE W ORK 8.1 Overview of Results The presented work has given a better understanding of the Solid Phase Epitaxial Regrowth (SPER) process for patterned amorphous regions in more detail than has been ever done before. Different aspects of SPER for patterned regions were studied that included the shape of initial -c interface, dopant effect, in -plane stress. Simulations based on a complex mathematical technique called Level set methods were done to confirm and predict experimental results. Level set model was initially implemented using regrowth velocity that included thermal activation27 and substrate orientation dependent velocity (by encapsulating the orientation dependence data in a curve fitted factor, f( ) ). However, it fail ed to accurately match the simulations to the observed cross sectional transmission electron microscopy (XTEM) images. The simulations showed some differences with the TEM images near the <111> corners and a variation in the velocity near the corners was i nsufficient to match up with observed results. Thus, a curvature factor was introduced that increased the velocity of concave corners and decreased for the convex. Modifying the orientation dependent regrowth model to be linearly dependent on local interaf ace curvature did accurately account for regrowth evolution56. The same curvature dependence was successful in predicting the regrowth evolution in structures with or without surface pinning of the interface. The a pparent linear dependence of regrowth kinetics on interface curvature was experimentally found to be temperature insensitive. The regrowth model was then used to predict the regrowth for different starting -c interfaces. This i ncluded varying the initial curvature of the -c interfaces and varying the width to depth (W/D) ratio of the amorphous region. The

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118 simulations gave an insight about the evolution of regrowth shapes and how different starting c interfaces could be used for the betterment of device fabrication and performance. Simulations predicted lesser mask -edge defect formation if the initial curvature of the -c interface was low (larg er radius of curvature). This was experimentally confirmed in Chapter 7 when even a ~110nm perturbed -c interface did not create mask -edge defects (in absence of external stress) after SPER. Regarding dopant effect on SPER, a novel experiment was done to see the effect of ptype and n type dopants on patterned regrowth. Using low resistivity wafers (both p and ntype), SPER of patterned amorphous region showed that dopants enhance the regrowth rate of Si isotropically. Further more, they were not found to affect the regrowth shapes and hence the mask -edge defects. The Level set model was expanded to incorporate the dopant dependent velocity enhancement factor. Since, dopant related enhancement of SPER is known to be an electroni c process, the experiment proved (within an error window) the dissociation of curvature factor from the electronic effect. Also, the diffusion capabilities of FLOOPS (Florida Object Oriented Process Simulator) simulator were used in conjunction with level set simulations to predict 2D dopant profiles during and after SPER. Planar SPER has been known to create interface roughness in the presence of external in plane compressive stress. Also, SPER of a small amplitude sinewave shaped -c interface is known to increase in amplitude in presence of in -plane compression. This work attempted to see both interface roughness and amplitude increase in presence of inplane compression on SPER of a sinewave shaped interface. Level set simulations and stress simulations were done together to draw inferences on the observed results. Prior theory related the increase amplitude due to inplane compression to different stresses on peaks and valleys34,49. However, stress simulations

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119 don e in this work showed no difference in stresses on peaks and valleys. Level set simulations emphasized the need for curvature factor to smooth out interface perturbation. Lack of curvature factor caused the orientation dependent velocity to cause amplitude increase and also interface roughening. For the first time, experiments were done with patterned amorphous regions (110150nm perturbation) to explore the effect of large ( 11 = 1.5 GPa ) in plane uniaxial stresses on SPER. No defects were observed after SPER of no -stress case. In plane uniaxial tension upto 1.5GPa did not affect the SPER in any way (similar to planar case). However, in -plane uniaxial compression led to the formation of mask -edge defects. Higher compression ( | 11| 1 GPa ) caused the roughe ning of the planar regions of the c interface. Level set simulations predicted the observed results accurately by modulating the curvature factor ( A ) for different stresses. Tension was found to increase the curvature factor and compression reduced it. T hus, encapsulation of the stress effect in the curvature effect was shown. Physical interpretation of the curvature effect as part of nucleation and migration processes was proposed. 8.2 Future Work The role of stress on SPER is complex. The effects of o ut -of -plane stress and in -plane stress have been known to be vastly different 21,41. However, the role of both the in-plane stress directions is believed to be same on SPER. This has been shown to be true of planar SPER with both the in plane directions being <011>. Some recent experiments (unpublished) have studied the effect of in -plane stress in direction parallel to the patterned lines, i.e. into the page of all the figures (as opposed to perpendicular to the lines shown in Chapter 7). Figure 8 1 shows SPER at 525 0C for 4h. under uniaxial in -plane compression parallel to lines (22 300MPa). The end of range (EOR) in the figures show the as implanted -c

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120 interface. The line structure for patterning was repetitive and Figures 8 1(a), (b), (c) and (d) show different line structures as observed in cross -section transmission electron microscopy (XTEM). Different lines showing different SPER implies that over the width of the lines (into the page of the figure), the defects randomly form and they show up in some lines (since XTEM takes a sample slice of ~100nm in the width direction). It would be more conclusive to do plan view transmission electron microscopy (PTEM) to further confirm the presence of random defects over the width of the lines in the future. Figure 8 1(a) shows no mask -edge defects that were observed due to in-plane compression in Figure 7 5(a) (with 11 = 250MPa). Rudawski et al .21,53 showed that in plane com pression reduced the migration of the ledges in the direction of stress. This suggests that migration of ledges is affected in the width direction for the case presented in Figure 8 1. This would lead to roughening of the interface in that direction. From curvature factor perspective, the curvature in the width direction would control the defects in that direction. In the plane of the page, the curvature factor would not be influenced since the stress is in the perpendicular direction. However, more work ne eds to be done to confirm this theory by implementing 3 D Level set simulations. SPER in Figure 8 1(a) was faster than what was observed in Figure 7 5(a) (for the same time -temperature anneal). Thus, to confirm that the compressive stress applied was not negligible, the same bend was applied perpendicular to the lines and the annealing was done for 4h. at 525 0C (as shown in Figure 8 2(a)). The formation of mask -edge defects and higher SPER of the planar regions showed that the stress was applied correctl y; it was probably a temperature variation between the samples that led to faster regrowth in Figures 8 1 and 82. Bending of the samples for this experiment was done using a different quartz tray than the one used for

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121 experiments in Chapter 7. Thus, there was a definite possibility of a variation in positioning of the samples for the two different trays. Figure 8 2(b) shows SPER for 2h. at 525 0C under uniaxial in plane tension (22 300MPa) parallel to the lines (into the page of figures). Tension did no t affect the regrowth when compared to no -stress case or when compared to tension in the direction perpendicular to the lines (not presented). Regarding the mask edge defects, it is still not clear as to what their effect is on relieving the stress on the -c interface. The regrowth of the pinched corners after the formation of defects also needs to be explored more. Some experimental results23 show that the regrowth at the corners after the d efect formation becomes faster due to formation of planes with orientations other than <111>. This observation led to Saenger et al.23 proposing a nano -facet model for SPER. However, the nano-facet model is very simplistic and more work is required to quantitatively describe the SPER of corners after defect formation. Chapter 6 dealt with issues of B diffusion during SPER and integrated the diffusion model with regrowth model to get a more acc urate B profile after SPER. However, some dopants like As exhibit segregation at the -c interface27. The final profile of As after SPER is strongly affected by the segregation effect. Thus, segregation model needs to be added to the regrowth model to more accurately predict dopant profiles after SPER.

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122 Figure 8 1. XTEM images of SPER at 525 0C for 4h. under uniaxial in -plane compression into the page of the figure (or parallel to lines 22 300MPa). (a), (b), (c), (d) show variation of regrowth for different lines.

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123 Figure 8 2. XTEM images of SPE R under uniaxial in-plane stresses into the page of the figure (or parallel to lines 22 300MPa). (a) shows SPER under compression for 4h. at 525 0C, (b) shows SPER under tension for 2h. at 525 0C

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129 BIOGRAPHICAL SKETCH Saurabh Morarka was born in Jaipur, India. He attended the Bhartiya Vidya Bhavans School in Jaipur from 1989 until 2001. He completed his Bachelor of Technology from Insti tute of Technology, Banaras Hindu University in electronics engineering in 2005. During the first year studies, he received award for academic excellence for four consecutive years. He then joined the University of Florida to study device and process simul ations of Metal oxide semiconductor (MOS) devices. The graduate research involved amorphous regrowth, boron diffusion in silicon and effect of stress on regrowth.