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PAGE 1 1 STRESSED SOLIDPHASE EPITAXIAL GROWTH OF SILICON By NICHOLAS G. RUDAWSKI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 PAGE 2 2 2008 Nicholas G. Rudawski PAGE 3 3 To my loving family, Guy Rudawski, Rosanne Cottone, and Gregory Rudawski; and my wonderful fiance, Erica Kramer PAGE 4 4 ACKNOWLEDGMENTS Three years, three conference presentations three Se miconductor Research Corporation contract reviews, seven peerreviewed jour nal articles, and appr oximately fivehundred transmission electron microscopy samples later, I find myself on the eve of finishing graduate school at the University of Florid a. It would be an understatement to say that I worked hard to get to this point, but it would be an even grea ter understatement to say that I could have ever reached the end without the kind assistance of others. Foremost, I acknowledge my adviser, Dr. Kevin S. Jones, for accepting me as a graduate student, providing me with an in teresting research project, an d allowing me to see my work through to the fullest potential. His trust in my abilities has undoubtedly made me more scientifically selfconfident than I ever could have been alone, and for that I will be forever grateful. I am forever indebted to Dr. Russell Gwilliam from the Surrey Ion Beam Centre at the University of Surrey for graciously providing the ionimplantation services necessary for all the work contained herein. I sincer ely hope that he feels he rece ived a good return on his personal investment in me. I thank the Semiconductor Research Corporation for funding my work under Task 1372.003. I acknowledge Kerry Seibein, Dr. Kevin S. Jones, and Michelle Phen for teaching me the art of transmission electron microscopy. I acknowledge Sergey Maslov, J. Samuel Moore, and Dr. Gerald B ourne for teaching me use of the focused ion beam system. I am indebted to Diane Hickey for helping me th rough a rough point in my life when I first came to graduate school. Russell The Muscle Robiso n will always have a special place in my heart for being the best friend Ive ha d in a long time and making sure I always had a sense of humor. For having the perpetual ability to make me laugh, I acknowledge Sidan Jinny Jin (You like that, fatty?) and Leah Lee Edelman (And the boron exploded.). Dr. Lucia Romano (Youre a so cute!) is acknowledged for many thoughtful, interesting c onversations, graciously PAGE 5 5 assisting in the editing of my dissertation, making our trip to Monterey, California fun and exciting, cooking a nice Italian dinn er that (partially) fell within my somewhat stringent dietary constraints, and tolerating my incessant imitati on of her wonderful accent. Saurabh Morarka is acknowledged for many thoughtful discussions on solidphase epitaxial growth and making the ultimate comment regarding my drinking of straight olive oil (Is it drinkable?). I am eternally grateful to Dan Gostofish Gost ovic for making the nolessthan br illiant suggestion that I start dating the woman who would turn out to be my fiance. I thank Dr. Mark E. Law, Dr. David P. Norton, Dr. Brent P. Gila, and Dr. Scott E. Thompson for many thoughtful discussions and for kindly sitting on my s upervisory committee. It is impossible for me to fully appreciate the support and love of my parents, Guy Rudawski and Rosanne Cottone, for putting me through my undergraduate education at the University of Michigan, instilling in me a trem endous sense of work ethic, always encouraging me, and making valiant (albeit futile) attempts to read my journal articles. I also acknowledge my younger brother, Gregory Rudawski, for simply be ing a really cool little brother. Finally, I acknowledge the support and love of my wonde rful fiance, Erica Kramer, who has always reinforced my selfconfidence and abilities. PAGE 6 6 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........9 LIST OF FIGURES.......................................................................................................................10 ABSTRACT...................................................................................................................................13 CHAP TER 1 INTRODUCTION..................................................................................................................15 1.1 Motivation.........................................................................................................................15 1.2 The Technological Importance of SPEG.......................................................................... 16 1.3 Stresses in Device Processing........................................................................................... 17 1.4 Objectives and Statement of Thesis.................................................................................. 18 2 LITERATURE REVIEW.......................................................................................................26 2.1 Mechanical Behavior of Si...............................................................................................26 2.1.1 Generalized States of Elastic Stress and Strain...................................................... 26 2.1.2 Elastic Constants....................................................................................................28 2.1.3 Brittle Fracture........................................................................................................ 31 2.1.4 Plastic Deformation and Stress Relaxation ............................................................ 32 2.2 Transition State Theory....................................................................................................34 2.2.1 Basic Considerations.............................................................................................. 34 2.2.2 Influence of Stress.................................................................................................. 35 2.3 SolidPhase Epitaxial Growth........................................................................................... 36 2.3.1 Atomistics of Epitaxial Growth Processes............................................................. 36 2.3.2 Temperature Dependence.......................................................................................39 2.3.3 Substrate Orientation Dependence.........................................................................40 2.3.4 ElectricallyActive Impurity Dependence.............................................................. 41 2.3.5 ElectricallyInactive Impurity Dependence............................................................ 43 2.3.6 Defect Nucleation during SPEG............................................................................. 43 2.4 Stressed SolidPhase Epitaxial Growth............................................................................ 44 2.4.1 Pure Hydrostatic Compression............................................................................... 44 2.4.2 Inplane Uniaxial Stress......................................................................................... 45 2.4.3 Normal Uniaxial Com pressive Stress..................................................................... 47 3 EXPERIMENTAL TECHNIQUES........................................................................................62 3.1 Material Processing..........................................................................................................62 3.1.1 IonImplantation and Generation of Amorphous Layers.......................................62 3.1.2 Application of InPlane Uniaxial Stress.................................................................65 PAGE 7 7 3.1.3 Temperature Calibration and Annealing................................................................ 67 3.1.4 Transmission Electron Microscopy Sam ple Preparation.......................................67 3.2 Material Characterization.................................................................................................68 3.2.1 Transmission Electron Microscopy........................................................................ 68 3.2.2 Secondary Ion Mass Spectrometry......................................................................... 73 3.3 Data Analysis.............................................................................................................. ......74 3.3.1 Amorphous Layer Th ickness Measurem ents......................................................... 74 3.3.2 Velocity Calculations in Intrinsic Samples............................................................ 75 3.3.3 Generalized LeastSquares Regression Analysis................................................... 77 4 INTERFACIAL ROUGHENING A ND DE FECT NUCLEATION DURING STRESSED SOLIDPHASE EPITAXIA L GROWTH OF AsDOPED Si........................... 91 4.1 Introduction............................................................................................................... ........91 4.2 Experimental Procedures.................................................................................................. 91 4.3 SPEG of NonPreAnnealed Specimens........................................................................... 92 4.4 SPEG of Preannealed Specimens....................................................................................95 4.5 Summary...........................................................................................................................96 5 STRESSED SOLIDPHASE EPITAXIAL GR OWTH KINETICS OF INTRINSIC Si ..... 103 5.1 Introduction............................................................................................................... ......103 5.2 Experimental Procedures................................................................................................ 103 5.3 Intrinsic SPEG Kinetics.................................................................................................. 104 5.4 Model of StressedSPEG Kinetics.................................................................................. 105 5.5 Morphological Instability............................................................................................... 112 5.6 Summary.........................................................................................................................114 6 NUCLEATION AND MIGRATION PROC ESSE S DURING STRESSED SOLIDPHASE EPITAXIAL GROWTH OF INTRINSIC Si.......................................................... 123 6.1 Introduction............................................................................................................... ......123 6.2 Experimental............................................................................................................... ....123 6.3 TemperatureDependence of StressedSPEG Kinetics...................................................124 6.4 Discussion.......................................................................................................................124 6.5 A New Atomistic Picture of SPEG................................................................................. 125 6.6 Summary.........................................................................................................................127 7 DOPANTSTRESS SYNERGY DURING STRESSED SOLIDPHASE EPITAXIAL GROWTH OF BDOPED Si ................................................................................................ 132 7.1 Introduction............................................................................................................... ......132 7.2 Experimental Procedures................................................................................................ 135 7.3 BDoped SPEG Kinetics.................................................................................................135 7.4 Discussion.......................................................................................................................137 7.5 Summary.........................................................................................................................138 PAGE 8 8 8 EXTENSIONS OF THE SOLIDPHASE EPITAXIAL GROWTH M ODEL TO EXPLAIN PRIOR OBSERVATIONS................................................................................. 144 8.1 Prior SPEG Observations............................................................................................... 144 8.2 ElectricallyInactive Impurities...................................................................................... 144 8.2.1 OInfluenced SPEG..............................................................................................144 8.2.2 FInfluenced SPEG...............................................................................................146 8.3 Pure Hydrostatic Compressionand Norm al Uniaxial Compressionenhanced SPEG .. 147 8.3 Summary.........................................................................................................................149 9 SUMMARY AND FUTURE WORK.................................................................................. 154 9.1 Overview of Results.......................................................................................................154 9.2 Technological Significance and Future Work................................................................ 155 LIST OF REFERENCES.............................................................................................................158 BIOGRAPHICAL SKETCH.......................................................................................................166 PAGE 9 9 LIST OF TABLES Table page 61 Nucleation and migration parameters.............................................................................. 128 PAGE 10 10 LIST OF FIGURES Figure page 11 Stressinfluenced elec trical behavior of Si ........................................................................ 20 12 Doping of Si with el ectrically active impurities................................................................ 21 13 Active As concentration versus temperature at equilibrium and realized using SPEG..... 22 14 Crystallographic channels in Si.........................................................................................23 15 The influence of Si substrate crysta llinity on dopant profile control during ionim plantation................................................................................................................... ....24 16 Substrate stresses generated by the pr esence of a disconti nuous stressed film ................. 25 21 The mechanical behavior of a small cube of elastic m aterial subjected to external applied mechanical stress...................................................................................................48 22 The influence of stress on the energe tics of an arbitrary TST rate process .......................49 23 Atomistic schematics of VPEG and LPEG processes....................................................... 50 24 Macroscopic schematics of the (001)oriented SPEG process.......................................... 51 25 Atomistic schematics of the (001)oriented SPEG processes............................................ 52 26 Temperatureinfluenced intrinsic SPE G kinetics............................................................... 53 27 Substrate orientationinflue nced intrinsic SPEG kinetics .................................................. 54 28 Dopantinfluenced SPEG kinetics.....................................................................................55 29 Electricallyinactive impurity influenced SPEG kinetics .................................................. 56 210 Onaxis crosssectional transmission el ectron m icroscopy images of the maskedge defect nucleation process during tw odimensional, intrinsic SPEG..................................57 211 Hairpin dislocation nucleation during SPEG.....................................................................58 212 Prior observations of pure hydrostatic com pressive stressinfluenced SPEG kinetics...... 59 213 Prior observations of inplane uniax ial stressinfluenced SPEG kinetics ..........................60 214 Prior observations of normal compressive uniaxial stressinfluenced SPEG kinetics ......61 31 Schematic of a basic ionimplantation system................................................................... 79 PAGE 11 11 32 Schematic of a typical Cion versus xion distribution for an arbitrary ion species implanted into Si.............................................................................................................. ..80 33 Weakbeam darkfield cr osssectional transm ission el ectron microscopy image of a typical asimplanted specimen........................................................................................... 81 34 Application and measurement of inplane uniaxial stress ................................................. 82 35 Schematic of the tube furnace apparatu s used for annealing an d the method of temperature calibration......................................................................................................83 36 Schematic of a basic TEM column.................................................................................... 84 37 Possible interactions of the incide nt electron beam with the sam ple................................. 85 38 Schematic of Braggs law for constr uctive interference for an arbitra ry ( hkl ) plane........ 86 39 Onaxis XTEM diffraction and imaging............................................................................ 87 310 WBDFXTEM diffraction and imaging.............................................................................88 311 The SIMS analysis technique............................................................................................. 89 312 WBDFXTEM image of an annealed speci m en showing the process used to measure the thickness of the resulting Si layer and RRMS of the resulting growth interface......... 90 41 WBDFXTEM images of the stressinfluenced S PEG process in Asdoped specimens...........................................................................................................................98 42 Measured stressinfluenced grow th kinetics in A sdoped material................................... 99 43 Stressinfluenced defect nucleation and interfacial r oughening during SPEG of Asdoped sam ples.................................................................................................................. 100 44 The influence of stressfree preannea ling on subsequent stressedSPEG in Asdoped sam ples.............................................................................................................................101 45 Stressinfluenced crys tallite reorientation........................................................................ 102 51 WBDFXTEM images of the stressinfluen ced S PEG process in intrinsic material....... 116 52 Measured stressinfluenced SPE G kinetics in intrinsic m aterial..................................... 117 53 The influence of stress on measured growth velocity in intrinsic m aterial..................... 118 54 Stressinfluenced SPEG migration processes.................................................................. 119 55 Uncoordinated and coor dinated ledge m igration............................................................. 120 PAGE 12 12 56 Stressinfluenced gr owth interface stability..................................................................... 121 57 The temporal dependence of stressin fluenced growth interface roughening................. 122 61 Effect of annealing temperature on stressedSP EG kinetic s in intrinsic material........... 129 62 The influence of annealing temperature on the m easured stressedSPEG velocity in intrinsic material..............................................................................................................130 63 Temperatureinfluenced nucleation a nd m igration parameters during SPEG in intrinsic material..............................................................................................................131 71 Onaxis XTEM images of the stre ssedSPEG process in Bdoped m aterial...................140 72 Stressinfluenced SPEG ki netics in B doped material..................................................... 141 73 Measured growth velocities in stressedSPEG of Bdoped m aterial............................... 142 74 Possible band structures for the interface between Bdoped Si and Si for different stress states.................................................................................................................. .....143 81 Extension of the presented model to explain Oinfluenced SPE G kinetics.....................151 82 Extension of the presented model to explain Finfluenced SPEG kinetics .....................152 83 Extension of the presented model to e xplain prior observations of pure hydrostatic com pressive stressinfluenced SPEG kinetics.................................................................153 PAGE 13 13 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STRESSED SOLIDPHASE EPITAXIAL GROWTH OF SILICON By Nicholas G. Rudawski December 2008 Chair: Kevin S. Jones Major: Materials Science and Engineering The solidphase epitaxial growth (SPEG) process of the element silicon (Si) has long been important in integrated circuit fabricati on. However, due to the increasingly prevalent nature of stresses found during device processi ng, it has become of greater technological significance to study the stressed SPEG process. In this work, the stressedSPEG process of Si was studied in intrinsic material and material doped with electricallyactive impurities. Ionimplantation was used to created ~350 nmthick amorphous ( ) Si films on (001) Si wafers via Si+implantation at 50, 100, and 200 keV to doses of 115, 115, and 315 cm2, respectively (intrinsic samples). Some wafers were additionally As+implanted at 300 keV to a dose of 1.815 cm2 (Asdoped samples) or B+implanted at 60 keV to a dose of 3.515 cm2 (Bdoped samples). The wafers were cleaved into strips and annealed at temperatures of 500 575 C for times of 0.1 11.2 h while uniaxial stress was applied (during annealing) along the inplane [110] direction (11 ) to magnitude of 1.5.1 GPa. Both compressive (11 < 0) and tensile (11 > 0) stresses were studied. Crosssectional transmission electron microscopy wa s used to study the stressedSPEG process. The stressedSPEG process was first examined in Asdoped material. It was discovered that growth kinetics were retarded with 11 < 0, but unchanged with 11 > 0, relative to the PAGE 14 14 stressfree case. Significant roughening of the /crystalline (growth) in terface was observed with 11 < 0 which led to an elevated density of SPEGrelated dislocations. Interestingly, 11 > 0 also tended to elevate the density of SPEGrelated dislocations and this was attributed to slight stressinduced remnant crystal reorientation duri ng the initial stages of growth rather than interfacial roughening. Then, the stressedSPEG process was examined in intrinsic material. Similarly to the results from Asdoped samples, the gr owth kinetics were unchanged with 11 > 0, but retarded with 11 < 0. Interestingly, the growth interface velocity, v with 11 < 0 was found to be onehalf the value obtained with 11 0, thus making v a complicated function of 11 Also, this result was found to be independent of annealing te mperature. Using these results, in conjunction with considerations of the atomistic nature of the SPEG process, a model of stressedSPEG kinetics is advanced. The final portion of this work studied stressedSPEG in Bdoped material. Once again, similarly to the cases of Asdoped and in trinsic material, it was revealed that 11 > 0 did not alter the growth kinetics while 11 < 0 retarded the growth kinetics. However, careful examination of the dependence of v on B concentration with 11 << 0 suggested that v was retarded to approximately onesix th the stressfree value at high B concentrations. Thus, it is advanced that stress alters the electronic structur e of Si such that B and stress influences are synergistic in overall growth kinetics. Ultimately, this work provided understanding of the stressedSPEG process and provides a new atomistic picture of and greater insi ght into the SPEG process, in general. PAGE 15 15 CHAPTER 1 INTRODUCTION 1.1 Motivation Solidphase epitaxial growth (SPEG) of the element silicon (Si) is the process by which amorphous ( ) Si transforms into crystalline Si (hereafter, referred to simply as Si) at an elevated temperature and adds, epitaxially, to a singlecrystal Si substrate. The process is interchangeably referred to as solidphase epitaxy, solidphase epitaxial regrowth, solidphase epitaxial recrystallization, and soli dphase epitaxial crystallization. Since being reported in the 1960s, SPEG has become one of the most technologicall yimportant processes in the fabrication and production of Sibased integrated circuit (IC) devices [May68, Ols88] when it was realized that implementing SPEG in device fabrication could si gnificantly reduce electrical resistance and increase the computing power of IC devices. Use of SPEG in device fabrication was a major advance in IC processing. However, the integration of intentional stress into devices would provide another ma jor advancement in IC technology [Chi06]. Around the same time that SP EG was first reported, others reported that stress could be used to manipulate the elec tronic structure of Si [Bal66, Her66, Kan67, Van68, Wor64] [Figure 11] and ultimately reduce device resistance (known as the piezoresistive effect) [Col68, Sat69, Smi54]. As a result, the vast majority of IC devices produced today possess intentionallyadded stress as a means to increase performance. Since SPEG and piezoresistivity in Si have both been extensively studied and integrated into IC processing, it would appear that the study of stressed SPEG would also be of great technological importance to the IC processing community. However, surprisingly little attention has been given to the study of stressedSPEG. Hence, the motivation for this work stems from the importance of SPEG, the widespread use of stress in IC device technology, and the need to PAGE 16 16 understand the role of stress on the SPEG process. 1.2 The Technological Importance of SPEG The implementation of SPEG into IC fabri cation possesses two distinct advantages: 1) enhanced concentrations of charge carriers (e lectrons and holes) and 2) greater control of transistor dimensions in IC devices. Intrinsically, Si is very elect ricallyinsulating and possesses ch arge carrier concentrations on the order of ~110 cm3 at room temperature [Gre90]. In order to make Si more conductive, electricallyactive impurities (dopants) are added. At st andard temperature and pressure, Si possesses the diamond cubic crystal structure with each Si atom bonding to four other Si atoms and each bond being composed of two electrons. Ho wever, if an impurity atom with five (As or P) or three (B) valence electrons is added, subst itutionally, to Si in dilute concentrations, the impurities will behave like Si atoms and bond to four nearest neighbors. Thus, in the case of dopants with five valence electrons, one of the electrons will not participate in bonding and be free to facilitate electrical conducti on [Figure 12(a)]. Since the majority of charge carriers in this case are electrons (possessing negative charge), the material is referred to as ntype. In the case of dopants with three valenc e electrons, one of the four bonds between the impurity and the nearest neighbors will only have one electron instead of two [Figure 12(b)]. This absence of an electron is referred to as a hole and carries a positive charge. T hus, materials with holes as the majority charge carriers ar e referred to as ptype. At a given temperature, there is an equilib rium concentration of dopants which can be made electrically active (depe nding on the dopant) [Der91, Nob89, No b91]. In IC fabrication, this poses a significant challenge since there is an apparent li mit to the level of conductivity available in both nand ptype material. However, SPEG provides a means to achieve active dopant levels well in excess of equilibri um. As stated before, atoms in the Si phase add PAGE 17 17 epitaxially to a Si substrate during SPEG. Thus, dopants present in dilute concentrations (< ~1 atomic %), will all be substitutionally incorporat ed into the Si film and become electrically active. Experimentally, it has b een extensively shown that active impurity concentrations well in excess of equilibrium [Figure 13] can be realized using SPEG [Nis78a, Bou91, Von93]. SPEG also provides a distinct advantage re garding the control of transistor device dimensions. Currently, nearly all IC fabrication processes use ionimplantation as a means of introducing dopants into the Si substrate and form ing transistor junctions. However, controlling the distribution of dopants during implantation is challenging due to the phenomenon known as ion channeling [Mye79, Nis78b, Rob63]. Depending on the orientation of the incident ion beam relative to the Si substrate, crys tallographic directions in the s ubstrate (channels) will be present where incident ions can travel deep into the material and prod uce a dopant distribution deeper into the substrate than desired [Figure 14]. Ultimately, this can make controlling transistor device dimensions very difficult. However, it is possible to a void ion channeling by amorphizing the substrate prior to dopant implantation using a nondopant (Si+ or Ge+) species. By doing this, all crystallographic channels in the material are removed making it impossible for subsequently implanted dopant ions to channel deep into the substrate. Hence, greater control over the introduced dopant profile is achieved [Figure 15]. Subsequently, SPEG is then used to activate the implanted dopant [Ish83, Tsa83]. 1.3 Stresses in Device Processing The growth of thin films (SiO2 and/or Si3N4, typically) has long been an important step in IC fabrication. In the case of a thin, con tinuous film grown on a Si substrate, structural differences between the film and substrate as well as the nature of the growth process typically result in the film being in a state of intrinsic biaxial stress following growth [Sto09]. In such cases, the substrate is usually much thicker than the film and negligiblysmall stresses tend to be PAGE 18 18 generated in the substrate. The same is not true for the case of a disconti nuous film grown on a Si substrate. In this case, the film exerts a strong body force on the s ubstrate near the film edges which, in turn, generates significant substrate stresses (on the or der of ~1 GPa) near the film edge [Hu78, Hu79, Hu91]. Depending on the intrinsic film stress and geometry of the film, compressive, tensile, and shear stresses of different magnitudes are typically created in the substrate [Figure 16]. Thus, depending on the crystallogra phic direction used for current flow and the type of charge carrier (electrons or holes), th ese filmedge stresses can be used to enhance the electronic properties of the device [Col68, Sat69]. Additional considerations arise in filmedge st resses when the IC de vice is processed at high temperatures. At high temperatures, mismat ch between the thermal expansion coefficients of the film and Si substrate can also introduce significant stresses in to the Si substrate in addition to the stresses induced by the in trinsic film stress [Cla 85, Thu04]. This is typically not a concern for stressenhanced device performance as IC devi ces typically operate at room temperature, but this may be an issue regarding stressinfluenced SPEG, which is typically effected at temperatures in the vicinity of ~500 C. More recently, the use of SiGe alloys has been introduced into IC devices due to the inherently lower resistivity compared to Si and the volumetric mismatch between materials as a means to induce deviceenhancing stresses in certain parts of the substrate. Therefore, it is apparent that there are se veral different sources of stress which can be present during typical device fabric ation and thus there is a clear need to understand the role of stress on the SPEG process. 1.4 Objectives and Statement of Thesis Clearly, there is significan t technological motivation to understand the influence of PAGE 19 19 applied stress on the SPEG process and the work pr esented herein attempts address this issue in several ways. Specifically, the following considerations will be investigated: The relationship between applied stress and th e SPEG kinetics in bot h intrinsic and doped material. The relationship between applied stress and the morphological nature of the SPEG process. Specifically, roughening of the gr owth interface and the forma tion of dislocations during SPEG. Atomistic considerations of the SPEG process as means to advance a physical model of stressedSPEG kinetics and morphological (in)stability. Unification of all stressedSPEG results within a single selfconsistent model capable of successfully addressing the prior work of othe rs and providing a new atomistic picture of SPEG. PAGE 20 20 Figure 11. Stressinfluenced electr ical behavior of Si: plot of Si m inority carrier concentration enhancement versus applied [110] uniaxial stress [Wor64]. PAGE 21 21 Figure 12. Doping of Si with electricallyactive im purities: atomistic schematic representations of Si doped with a) As (n type) and b) B (ptype). PAGE 22 22 Figure 13. Active As concentration versus temperature at equilibrium and realized using SPEG. PAGE 23 23 Figure 14. Crystallographic channe ls in Si: crystallographic cha nnels for a) <110>aligned and b) <111>aligned Si crystals. PAGE 24 24 Figure 15. The influence of Si substrate crystallinity on dopa nt profile control during ionim plantation: schematic representations of dopant concentration versus depth for dopant implantation into a) Si and b) Si with a preexisting Si film. PAGE 25 25 Figure 16. Substrate stresses ge nerated by the p resence of a discontinuous stressed film: simulated plot of normal stress along the [ 110] inplane direction (logarithmic scale) resulting from a discontinuous Si3N4 film with an intrinsic stress of 1.0 GPa [Law98]. PAGE 26 26 CHAPTER 2 LITERATURE REVIEW 2.1 Mechanical Behavior of Si 2.1.1 Generalized States of Elastic Stress and Strain Consider a sm all cube of solid, elastic material with sides of area Aj, where j refers to the normal direction of the two j th faces (on opposite sides of the c ube) within the coordinate frame of reference. When a face of the cube is subjected an applied external force, Fi, and the opposite face of the cube is subjected to an equal an opposite external force, the material will suffer induced states of stress, ij, and strain, ij, where i and j refer to Cartesian axes within the coordinate frame of reference [Figure 21(a)]. Th ese induced states are referred to as elastic if the stress and strain achieved are instantly and full y relieved upon removal of Fi. Force is a vector quantity with individua l components specified using only a single Cartesian axis, i However, stress and strain are secondorder tens ors and thus individual components of each are described in reference to a surface normal, i as well as a Cartesian direction, j As the sides of the cube become infinitely small, the relationship between Fi and ij, is defined as j i ijA F (21) and thus ij can be thought of as the projection of the i th component of Fi onto Aj [Figure 21(b)]. In the case of i = j the stress element is defined as a normal stress while in the case of i j the stress element is defined as a shear stre ss. Normal stresses tend to cause volumetric deformation of the material while shear stresses tend to change the shape of the material. It is common to express ij in matrix form as 333231 232221 131211 ij, (22) PAGE 27 27 and thus i and j refer to rows and column in the matrix. By convention, a negative value of an element of ij is defined as compressive while a positive value of an element of ij is defined as tensile. As specified earlier, no net force exists on the piece since oppos ing sides are subjected to equal and opposite applied forces. However, in order for no net torque to exist on the piece, ij, must be symmetric as specified by jiij (23) When the net force and net torque on the piece ar e both zero, the piece is in a condition of static equilibrium. Thus, Equation (22) under c ondition of static equilibrium is given as 332313 232212 131211 ij. (24) For purposes of clarity, Equation (24) is ofte n reduced to a single co lumn matrix with six elements and is given by 6 5 4 3 2 1 i, (25) where the ij combinations of 11, 22, 33, 23 (32), 13 (31) and 12 (21) are replaced by the single i indices of 1, 2, 3, 4, 5 and 6, respectively. The application of Fi also creates a displacement vect or field within the material, iu defined as the linear displacement suffered by a specific point, P in the material after application of Fi [Figure 21]. Thus, ij is defined as PAGE 28 28 i j j i ijx u x u 2 1, (26) where xi and xj refer to the i th and j th coordinate axis. Similarly to ij, ij is described using a symmetric matrix as 332313 232212 131211 ij, (27) under conditions of static equilibrium with a negative value an element of ij is defined as compressive while a positive value an element of ij is defined as tensile. Again, this notation can be reduced to a 6 matrix of the form 6 5 4 3 2 1 i. (28) 2.1.2 Elastic Constants Elastic constants are used in or der to relate the response of ij to ij, or vice versa. Si possesses the diamond cubic crystal structure and thus the elastic constants of Si possess cubic symmetry. The stiffness tensor, Cijkl, is used to describe the elasti c response of stress to strain, where k and l are Cartesian axes in the coordinate fram e of reference, and has 81 elements in the most generalized form. Therefore, klijkl ijC (29) where summation over both k and l indices is implied. However, due to symmetry constraints of the cubic system, Cijkl can be reduced to a 6 PAGE 29 29 matrix, Cij, given by 44 44 44 111212 121112 12121100000 0 0000 00 000 000 000 000 C C C CCC CCC CCC Cij, (210) where i has replaced ij and j has replaced kl and with coordinate ax es aligned along <100>type crystal directions. In this notation, i and j may take values from 1 to 6, similarly for reduced notation for stress and strain. The nonzero terms, C11, C12, and C44, have values of 166, 64, and 80 GPa at room temperature, re spectively [Wor65]. Thus, if j of a specimen is known, i may be calculated by 6 5 4 3 2 1 44 44 44 111212 121112 121211 6 5 4 3 2 100000 0 0000 00 000 000 000 000 C C C CCC CCC CCC. (210) Similarly, it is also useful to define the compliance tensor, Sijkl, which describes the elastic response of strain to an applied stress. This can be similarly reduced as in Equation (210) to Sij and is given by 44 44 44 111212 121112 12121100000 0 0000 00000 000 000 000 S S S SSS SSS SSS Sij, (211) PAGE 30 30 with coordinate axes aligned along <100>type crystal directions. The nonzero terms, S11, S12, and S44, have values of 7.68, 2.14, and 12.6 TPa1 at room temperature [Wor65]. Hence, 6 5 4 3 2 1 44 44 44 111212 121112 121211 6 5 4 3 2 100000 00000 00000 000 000 000 S S S SSS SSS SSS. (212) Comparing Equations (210) a nd (211), it is apparent that Cij and Sij are inverses matrices of each other and thus C11, C12, and C44 describe all terms in both matrices. It is important to note that C11, C12, and C44 are not temperatureinde pendent and do decrease appreciably with increasing temp erature up to ~8 % from room temperature to 1050 C and this must be taken into account when measuring stress and strain during annealing [Nik71]. All of the stress states dealt with in these studies are uniaxial in natu re, and thus the stress analyses are somewhat simplified. In the case of a state of uniaxial stress for a generalized crystal orientation, 0 0 0 0 0 0 0 01 665646362616 565545352515 464544342414 363534332313 262524232212 161514131211 3 2 1 SSSSSS SSSSSS SSSSSS SSSSSS SSSSSS SSSSSS, (213) and thus 1111 S (214) which may be rearranged to produce 111 11 1 1 E S (215) PAGE 31 31 where E11 is the Youngs modulus along the 1 axis of the particular crystal orientation chosen. Equation (215) is often referred to as Hookes law. Thus, for a case of uniaxial stress only, E11 is defined as the reciprocal of S11 for the coordinate system of interest [Wor65]. 2.1.3 Brittle Fracture At room temperature, Si is mechanically characterized as being brittle in that it experiences only elastic deformation before failure [Bre91, Coo06]. This phenomenon is inherent to all diamond cubic crys tals, all of which e xperience strong covalent bonding. Due to the brittle nature of Si, the Gri ffith theory of fracture serves as a decent model for describing the brittle failure of Si. According to the Griffith theory of fracture, the strength of a specimen is limited by any flaws present in it, such as crack s or voids [Gri21]. Thus, a crack propagates when the strain energy in the specimen exceeds the energy require to form two fracture surfaces. Mathematically, this is expressed as aYKc IC, (216) where KIC is known as the plane strain fracture toughness, Y is a dimensionless parameter dependent on crack geometry, c is the applied uniaxial te nsile stress at fracture, and a is the semimajor axis of the largest present crack assuming it possesses elliptical geometry. In Si, KIC has been reported from 1 4 MPa m with slight crystallographic orientation dependence [And05, Ebr99, Li05, Tan03, Tan04]. Using Equation (216), it is straightforward to show that to attain a stress of ~1 GPa that the maximum present flaw si ze must be on the order of ~1 m in dimension. It is worth noti ng the relatively low value of KIC for Si. Structural metals such as Al and Fe (which exhibit metallic bond ing) typically have values of KIC well in excess of ~50 MPa m and are thus able to sustain la rger cracks before fracture. Thus, a specimen of this type possessing ~1 m flaws would be theoretically capable of sustaining stresses near ~50 GPa. PAGE 32 32 During brittle failure, cracks in a specimen propagate so quickly that the strain energy from loading cannot be accommodated by forming dislocations and moving them away from the crack vicinity fast enough. It is thus more energetically favorable to form two fracture surfaces. Thus, c is limited by KIC and the flaw size and the options to increase the fracture stress are to increase the plane strain fractur e toughness or decreas e the inherent flaw size. Regarding the former consideration, it has been shown that ionimplanting Si slightly increases KIC, provided that annealing is conducted after implantation [Hu82, Swa03]. This is explained by repairing of the lattice to a state with fewer defects than it possessed prior to implantation. However, the slight increase in KIC from ion implantation is not sufficien t to provide a drastic improvement in attainable stress and is somewhat thought to be due to experimental error rather than actual effect. The best option for increasing the applied stre ss is to decrease the inherent flaw size. Thus, specimens used in this work were limite d to possessing a polished finish as unpolished wafers contain many relatively large flaws on the order of 10 50 m. Next, cleaving of wafers is extremely important in limiting the formation of flaws. A clean cleave has minimal surface flaws and can thus sustain higher stresses. Experimentally, it was discovered that 50 m thick wafers produce better cleave surfaces than 750 m thick wafers. Scanning electron microscopy revealed cleaved surfaces of 50 m thick wafers which were esse ntially flawfree while cleaved surfaces of 750 m thick wafers possessed many flaws much greater than ~10 m in size. Presumably, this is due to the reduced surface ar ea available for the crea tion of flaws. Thus, polished wafers 50 mthick are employed for all the experiments presented. 2.1.4 Plastic Deformation and Stress Relaxation While it useful to consider the fracture of Si at room temperature, the mechanical integrity is more of concern dur ing annealing at temperatures in the vicinity of 500 C. At PAGE 33 33 temperatures greater than ~600 C Si experiences a brittle to duc tile transition (BDT) [Yas82]. Within this temperature regime, at sufficien tly high stress and sufficient annealing time specimens experience plastic deformation or yielding. A strain is considered plastic if it is not relieved following removal of the applied force. If this plastic deform ation is great enough, the applied stress can relax significantly. In the vicinity of the BDT and significantly higher, complete stress relaxation has been observed in Si after anneali ng for as little as 5 min [Fuk93, Gro89, Wal72]. However, appreciable stress relaxation is usually avoided by maintaining an anneal temperature at least 10 15 C below the BDT as the rate of relaxation is Arrhenius in nature. From a microscopic standpoint, during plasti c deformation, the temperature is high enough that dislocations not only have high m obility and can thus accommodate the strain energy, but can form more easily as both the velocity of dislocatio ns and the rate of dislocation formation are characterized as being thermally activated processes. While both of these mechanisms are important in plastic deformation, it has been a long standing debate as to which of these mechanisms is primarily responsible. In all likelihood, it probably pertains to the inherent microstructure prior to deformation. In a crystal initially co ntaining many dislocations, the dislocations must have high mobility in order to accommodate the strain energy produced by deformation [Geo96]. In contrast, a sample with few dislocations must first nucleate dislocations in order for plastic deformation to occur and then the dislocations may proceed to move via glide and cause macroscopic deformation [Kha97]. Similarly to the phenomenon seen in brittle fr acture, flaws reduce the yielding point of Si as flaws appear to provide places for the heteroge neous nucleation of dislocations due to the high stress fields present near the cracks [Hir91, Hsi94, Kha94]. PAGE 34 34 2.2 Transition State Theory 2.2.1 Basic Considerations A discussion of the transition state theory (TST) of rate processes is presented. Consider an arbitrary system where the Gibbs fr ee energy of the system at state 1, G1, has higher Gibbs free energy than if the system existed at state 2, G2 [Figure 22(a)]. In such a case, there is thermodynamic driving force for the system to transition from stat e 1 to state 2 since 1221GGG < 0, (217) where 21 G is the free energy difference be tween states 1 and 2 [Gib61]. However, as is typically the case with many different processes in nature, state 1 cannot instantaneously transform to state 2 because state 1 must transition to an intermediate transition state (denoted by asterisk) with free energy, G*, higher than G1 [Figure 22]. Thus, the system must overcome the activation barrier, G*, given by 1GGG (218) Thus, the rate, r, at which state 1 transforms into state 2 is dependent on two considerations: 1) the thermodynamic driving force for the transformation and 2) the activ ation barrier for the transformation. Therefore, kT G kT G rr21 0exp1 exp, (219) where r0 is a temperatureindependent prefactor [Gla48]. In many cases, the system is far from equilibrium (21 G= 0) such that 21 G << 0 and 21 GkT such that the bracketed term in Equation (219) is approximately unity and kT G rr exp0. (220) PAGE 35 35 Any transformation which exhibits r versus T behavior of the form presented in Equation (220) is referred to as an Arrheniustype process or a TST process. 2.2.2 Influence of Stress The influence of stress on r for a TST process is addressed with the case of pure hydrostatic pressure first consider ed. It was shown in the previous section that the activation barrier is the primary consideration controlling r and thus it is necessary to determine how stress will change the activation barrier. The term G* at normal atmospheric pressure, P0, and arbitrary temperature is mo re specifically given as STVPUG0 (221) where U is the change in internal energy, V is the change in volume, and S is the change in entropy between state 1 and the transition state. If the pressure is increased to P, G now becomes STVPUGP. (222) Combining Equations (221) and (222) produces GVPPGP 0. (223) Typically, P0 << P and thus r with P is given by kT GVP rr exp0. (224) Thus, V is more specifically given as P r kTV ln (225) PAGE 36 36 Hence, depending on the sign of V r will be enhanced or retarded with application of P [Figure 22(b)]. The application of P can also change 21 G, but the activation barrier typically still exerts the greatest influence on r provided 21 G < 0. In reality, the applied stress state, ij, can be more complicated than pure hydrostatic and the change in volume between state 1 and the transition state can be represented using the activation strain tensor, ijV, which is the volumetric deformation between the initial and transition states as represented in tensor form [Azi91]. Thus, in the most general case, Equation (224) is represented by kT GV rrijijexp0, (226) and the most general form of ijV is given by ij ijr kTV ln. (227) Hence, a positive (negative) ijijV product decreases (increases ) the activation barrier and r will be enhanced (retarded). Thus, it is this TST argument that provides the majority of the basis for explaining the influence of stress on SPEG kinetics. It is important to note that for the case of r being a scalar quantity, ijV is a secondorder tensor. However, many types of TST processe s are not scalar proper ties (diffusivity, for example) and thus the activation strain tensor may be higher order depending on the nature of r. 2.3 SolidPhase Epitaxial Growth 2.3.1 Atomistics of Epitaxial Growth Processes An epitaxial growth processe s is the growth of a singlecr ystal film on a single crystal substrate such that the grown film has the same cr ystal structure as the substrate. The film may PAGE 37 37 be the same material as the substrate (homoep itaxy) or a different mate rial (heteroepitaxy). Additionally, the film growth may occur from vapor, liquid, or solid phase sources. Atomistically, epitaxial growth processes ha ve been considered extensively since the early 1900s [Wil00, Gib61]. In particular, vapor phase epitaxial grow th (VPEG) and liquidphase epitaxial growth (LPEG) have been wells tudied (much more so than SPEG) and will be discussed first to provide a basis for comparison with growth from the solid phase. In the case of VPEG and LPEG, the vapor/solid and liquid/soli d interfaces are referred to as the growth interfaces since material is added to the film at these interfaces. In both cases, the atoms in the adjacent vapor and liquid phases are not directly bonded to the growth interface and thus the growth interface may be reasonably considered as a free surface in VPEG and LPEG. It was first recognized by Gibbs that inst antaneously forming a whole monolayer during epitaxial growth would be highly difficult [Gib61]. Thus, it wa s advanced (and has since been extensively confirmed using many experimental t echniques) that epitaxial growth from vapor and liquid phases occurs by the following steps: 1) diffusion and attachment of atoms from the vapor (or liquid) phase to the growth interface, 2) surface diffusi on of attached atoms (adatoms) on the growth interface, 3) meeting of adatoms to form atomic clusters and, subsequently, islands on the growth interface, and 4) a ddition of adatoms at islands ledges to complete the monolayer [Figure 23]. Hence the growth kinetics of VPEG and LP EG processes are essentially governed by the rate at which crystal islands form on the interface as well as the rate at which adatoms can attach to the island ledges. However, both of these processes are controll ed by the diffusion, or flux, of atoms to the growth interface. Thus, assuming th e temperature of the growth interface is such that the vaporsolid or liquidsolid phase tran sformation is energetica llyfavorable, it can be PAGE 38 38 readily shown that the macr oscopic growth velocity, v, of the vaporsolid or liquidsolid growth interfaces is given by C J v (228) where J is the flux of atoms incident on the growth interface and C is the concentration of atoms incorporated into the film [Wil00]. Keeping th ese considerations of VPEG and LPEG at hand, SPEG is now addressed. In the case of SPEG, a continuous Si film formed via ionim plantation or deposition is directly bonded to a single crysta l Si substrate. When the temper ature of the system is increased to a sufficiently high value, the crystall ine phase grows heterogeneously from the /crystalline (growth) interface consuming the Si and resulting in a single crys tal of Si [Figure 24] [May68, Cse75, Cse76, Rot77]. Thermodynamic driving force for growth exists as a result of the Si phase possessing a higher Gibbs free energy comp ared to the crystallin e phase [Don83, Don85]. Once again, as was postulated by Gibbs, the growth process likely proceeds in steps similarly to VPEG and LPEG. However, in the case of SPEG, the atoms used for growth (the Si film) are already bonded to the substrate. Thus, no flux of atoms to the growth in terface is necessary and SPEG occurs by the following atomistic step s: 1) small clusters of atoms in the Si phase in direct contact with the crystalline substrate rea rrange (via bond breaking and reforming) to form crystal islands on the growth interface and 2) atoms in the Si phase in contact with the island ledges rearrange and add to the islands to comple te the monolayer [Figure 25] [Spa78]. Thus, atomic flux to the interface and surfa ce diffusion are no long er relevant. Hence, the fact that no flux of atoms to the growth interface is necessary in SPEG profoundly changes modeling of the growth kinetics. In particular, it is necessary under some circumstances as will be shown, to account for the timescales associat ed with both nucleation PAGE 39 39 and migration processes in explai ning macroscopic growth kinetics. However, as is the case of point defects contributing to diffu sion in bulk Si, the energy barrier for point defect formation is typically much larger than that for migration su ch that the energy barrier for diffusion is almost entirely controlled by the nucleation barrier [Fah 89]. Interestingly, experimental evidence from Williams et al. suggested that this was also the case for SPEG [Wil85]. Thus, SPEG is typically simplified (absent any complicati ng factors) to being composed solely of a single timescale process. Keeping these considerations in mi nd, the important phenomena observed in SPEG of Si are discussed. 2.3.2 Temperature Dependence The temperature dependence of Si SPEG ki netics has been studied extensively by many different researchers since the 1970s. Early, preliminary work by Csepregi et al. [Cse77] studied the growth kinetics of (001)oriented intrinsi c Si using Rutherford backscattering (RBS) and determined the growth velocity of an advancing /crystalline interface, v, as a function of temperature, T, of the form kT G vvmacexp0, (229) where v0 is a temperaturei ndependent prefactor, k = 8.62 105 eV/K is Boltzmanns constant, and macG = 2.3 eV is the activation en ergy for macroscopic growth. Extensive, subsequent work by other resear chers also studied the temperature dependence of the (001)oriented growth ve locity using timeresolved refl ectivity (TRR) [Ols88, Rot90, Poa91] [Figure 26] and produced a v versus T relationship also of the form presented in Equation (229). However, macG = 2.7 eV was calculated, which is similar to, though slightly higher, than the value calculated by Csepregi et al. [Cse77]. Differences in analysis and PAGE 40 40 annealing techniques are often cited for the sma ll difference between observed activation barrier values and macG = 2.7 eV is usually cited as the accepted value. It is important to note that the studies of temperaturedependent growth kinetics c ould not address the at omistic nature of SPEG. Thus, the nature of macG as it pertained to the nucle ation and migration processes responsible for macroscopic growth was unclear at the time. Howe ver, as Equation (229) is of the same form as that for a generalized TST pr ocess, it appears the assumption of growth being mediated by a single atomistic process was r easonable to extend to explain temperatureinfluenced growth kinetics. 2.3.3 Substrate Orientation Dependence Early work by Csepregi et al. [Cse78] studied the effect of substrate orientation on Si SPEG kinetics using RBS. It was determined that v was a complicated function of substrate misorientation angle from [001] towards [110], [Figure 27]. Specifically, it was revealed that v was maximized for (001)oriented growth and mi nimized for (111)oriented growth. A simple bond breaking model based on the assumption that an atom in the Si could only add to the crystalline phase when bonded to two crystalline atoms was advanced to explain the results. Utilizing this approach proved capable of qualitative explaining the dramatic decrease in v as the substrate orientation changed from (001) toward s (111). However, the model also predicted (111)oriented SPEG to be incapab le of occurring and could not be extended to cover growth directions from [111] to [110]. In fact, the complicated v versus behavior can be readily explained by considering the nucleation and migration pr ocesses responsible for macroscopic growth. More specifically, it is foreseeable that the nucleation and migration kinetics will be str ongly influenced by the PAGE 41 41 crystallography of the Si/Si growth interface a nd this could easily be manifested in the macroscopic growth kinetics. 2.3.4 ElectricallyActive Impurity Dependence It has been readily observed by many researchers that the addition of dilute concentrations (less than ~1 at omic percent) of electricallyac tive (dopant) atoms (B, As, and P) drastically increases SPEG kinetics [Ade88, Cse 77, Joh07, McC99, Sun82, Wil83]. Due to the electricallyactive nature of these impurities, it is believed this effect is the result of electronic processes occurring at the growth interface. This is referred to as the generalized Fermi level shifting (GFLS) model of dopantenhanced SPEG [J oh07]. The central point of the GFLS model is the assumption that v is proportional to the planar density of growt hmediating defects on the growth interface or npiCCCv (230) where Ci, Cp, and Cn are the planar densities of uncharged, positivelycharged, and negativelycharged defects on the growth interface. In the ca se of intrinsic material, the number of charged nuclei is very small such that v is approximately given by iCv (231) However, if the material is, for example, ptype piCCv (232) since the contribution from negativel ycharged defects will be neg ligible. Next, it is advanced that Cp will be dependent on the Fermi level of the material. Thus, assuming a MaxwellBoltzmann approximation for dilute impurity levels [Dir29], kT EE g C CF p n i pexp, (233) PAGE 42 42 where p nE is the energy level at the growth interface of a positivelycharged defect, EF is the Fermi level of the material, and g is the degeneracy factor (unity for ptype material) [Figure 28(a)]. Typically, the band structure of the /crystalline interface is modeled with the Fermi level pinned at midgap in the amorphous phase with negligible band be nding in the crystalline phase, and all energy levels are measured relative to th e valence band. In the case of lightly Bdoped material, i B i FFn C kTEE ln, (234) where i FE is the Fermi level in intrinsic material, CB in the B concentration at the growth interface, and ni is the intrinsic carrier concentration at T. Combining Equations (232), (233), and (234), it can thus be shown that kT EE g n C vvp n i F i B iexp 1 (235) where vi is the intrinsic value of v at T [Joh07]. A similar expression can be derived for ntype doping. In either case, it is thus predicte d (and has been extensively confirmed) that v should increase linearly with dopant concentration [Figure 28(b)]. Within the context of the atomistic nature of growth, the growthmediating defects may actually be considered as crystal islands rather th an arbitrary, unidentifie d defects. Of course, growth kinetics are, more specifically, de pendent on the rate of island nucleation on the interface, rather than th e number of islands formed on the interface, which the GFLS model does not address. Thus, a more reasonable central assumption of the GFLS model would be that v is proportional to the sum of the rates of charged and uncharged island nucleation. Additionally, the GFLS model neglects any dopant influence on migration kinetics and only addresses PAGE 43 43 nucleation. 2.3.5 ElectricallyInactive Impurity Dependence In contrast to the case of electricallyac tive impurities, inactive impurities (H, C, O, and N) tend to dramatically retard growth kinetics [K en77, Rot90] [Figure 29]. In these cases, the Fermi level of the material is not affected and thus, presumably, the nucleation kinetics are not affected. Thus, the observed SPEG retardation with increasing inactive im purity concentration is likely the result of reta rded migration kinetics. As a mi grating island ledge moves along the growth interface, it is intuitive that the ledge wi ll be slowed as it encounters an impurity and must incorporate it into the cr ystalline phase. Thus, it takes longer for an island to reach sufficient size such that a second island may form on top of the initial island. Presumably, this migrationretarding eff ect also happens for electricallyactive impurities. However, as electricallyactive im purities are incorporated substitutionally while most electricallyinactive impurities are incor porated interstitially [Wal88, Ram98], the retardation in the later case is greater due to the greater amount of lattice deformation which must occur to incorporate an interstitial atom. 2.3.6 Defect Nucleation during SPEG If the SPEG process is somehow imperfect, de fects can form in the growing crystalline layer [Jon88]. In the case of a twodimensional Si region in a (001) wafer with <110>aligned features [Figure 210(a)], the /crystalline interface has variable orientation and, hence, a variable growth rate along the interface [Cse78]. With partial completio n of growth [Figure 210(b)], the {011}oriented grow th fronts bow inward and impinge on the (001)oriented front which generates a notch in the growth interface. When growth is complete, a defect (dislocation) forms in this notch as the growth fronts on both sides of the notch meet [Cer89, Cer93, Cer97] [Figure 210(c)]. These are referred to as maske dge defects and typically have a Burgers vector PAGE 44 44 of b = a<110>/2 where a = 0.543 nm is the Si lattice parame ter. Numerous studies have shown that controlling this interface geometry is critic al in forming the defects [Ols06, Ros04, Rud06, Rud07]. However, atomistically, it is unclear as to why these defects form as a result of the growth front impinging on itself. A possible explanation is that as the two portions of the front near, it is difficult for the atoms in the encompassed Si to correctly add to both sides of the front. Another means for defects to form during SPEG is due to a rough initial /crystalline interface resulting from the ionimplantation pr ocess. Depending on the ionimplantation conditions, small remnant crys tallites can exist in the Si near the initial /crystalline interface [Figure 211(a)]. Typically, ionbombardment has rotated the crysta llites slightly relative to the bulk crystal underneath. Thus, wh en SPEG occurs, the growth in terface meets these misoriented crystallites and a dislocation with b = a<110>/2 nucleates as a result of the slight misorientation [Glo76, San85]. As growth continues, the di slocations propagate upw ards through the grown layer and terminate at the surface [Figure 211(b)]. Due to the shape of the dislocations, they are often referred to as hairpin dislocations [Jon88]. 2.4 Stressed SolidPhase Epitaxial Growth 2.4.1 Pure Hydrostatic Compression The influence of pure hydrostatic stress () on SPEG kinetics of (001)oriented Si [Figure 212(a)] was first studied by Nygren et al. using RBS and, subsequently, others using TRR [Cha91, Cha94, Nyg85, Lu89, Lu91] and it was revealed that v was exponentiallyenhanced with compressive [Figure 212(b)]. Thus, v as a function of takes the form kT V vvhexp0, (236) PAGE 45 45 where hV = (0.28 0.03) is the activation volume under a st ate of pure hydrostatic stress and = 12.1 cm3/mol is the atomic volume of Si. Moreover, in conjunction with the strong Arrheniustype behavior of v(0) presented earlier, it thus appears that the simplificati on of SPEG being a single timescale process is reasonable for this case of stress. Also, the negative value of hV suggests a net volumetric contraction associated with th e transition state which may be due to the smaller density of Si compared to Si [Cus94]. 2.4.2 Inplane Uniaxial Stress A series of experiments by Aziz et al. studied the role of in plane uniaxial stress (11) on SPEG kinetics [Figure 213(a)] us ing RBS and a novel threepoin t bending technique [Azi91]. The overall trend in the v versus 11 data suggests that inplane tension tends to enhance the growth kinetics while inplane compression tends to retard the growth kinetics [Figure 213(b)]. However, the data produced as a whole is highly scattered and lacking clear order. In particular, there is a very large (and unexpected) variation in v in the vicinity of 11 = 0. None the less, Aziz et al. advanced v as a function of 11 of the form kT V vv1111exp0, (237) where 11V = (0.15 0.01) is the activation volume with inplane uniaxial stress, assuming a single timescale process. The positive value of 11V was rationalized by Aziz et al. as allowing easier atomic rearrangement in the growth interface by opening up the interface [Azi91]. In an effort to unify the results from pure hydrostatic pressure with those from inplane uniaxial stress experiments, ijV was extended to Si SPEG such that v as a function of arbitrary ij was of the form PAGE 46 46 kT V vvijijexp 0, (238) or more specifically, ij ijv kTV ln. (239) Again, due to the strong A rrheniustype nature of v(0), it was very reasonable to advance this model to nonhydrostatic stresses, even cons idering the highlyscattered data. The key assumption of Equations (238) and (239) is, again, that SPEG is a single timescale process, which implies m ij n ij ijVVV (240) where n ijV and m ijV are the nucleation and migration strain tensors associated with arriving at the transition state. In the case of the Si/(001) Si interface, due to symmetry constraints, 33 11 1100 0 0 00 V V V Vij. (241) In the case of pure hydrostatic stress, 11 = 22 = 33 = and thus 33 112VVVh, (242) which implies 33V = 0.58 since 11V = (0.15 0.01) [Azi91]. Hence, it is predicted by Equation (241) that normal uniaxial comp ressive stress should cause greater SPEG enhancement than pure h ydrostatic compression since 33VVh. Subsequent experiments of SPEG with inplane uniaxial compression [Bar95, Bar01, Bar04] confirmed the observations of re tarded growth kinetics from Aziz et al. [Azi91]. However, prior to the work contained herein, no other studies of SPEG with inplane tension PAGE 47 47 were conducted and thus the apparent growth enhancement observed by Aziz et al. with 11 > 0 remained uncorroborated. 2.4.3 Normal Uniaxial Compressive Stress A prediction of the Aziz et al. [Azi91] model is that the effect of normal uniaxial stress, 33, on SPEG kinetics [Figure 214(a )] would be characterized by kT V vv3333exp0. (243) Since the predicted magnitude of 33V is much larger than hV, though the sign is the same, it is predicted that normal uniaxial compression should cause gr eater enhancement to the SPEG rate than pure hydrostatic compression. BarvosaCa rter performed this experiment to test the prediction [Bar97a, Bar97b] [Figure 214(b)]. There is qualitative agreement between the observed and predicted behavior [Azi91] in that the growth ra te tends to show exponential enhancement with normal compression. However, 33V = ( 0.35 0.04) calculated by BarvosaCarters normal uniaxial compression experiments is nearly half the predicted value of 0.58 from Aziz et al. [Azi91]. It is very interesting that the measured value of 33V is very similar to hV= ( 0.28 0.03) measured by Lu et al. [Lu89, Lu91]. Thus, it appear s that there may be no major difference in the SPEG kinetics under hydrostatic pressure or normal uniaxial stress. However, this implies that 11V ~ 0 which contradicts the or iginal suggestio ns of Aziz et al. [Azi91]. Thus, there appears to be some inconsistencies in the Aziz et al. [Azi91] model in explaining all the prior collected stressedSPEG data. PAGE 48 48 Figure 21. The mechanical behavior of a small c ube of elastic m aterial subjected to external applied mechanical stress: schematic of a sma ll cube of elastic material a) with faces subjected to applied forces a nd b) under a generalized stat e of stress. Schematic of point, P, within a small cube of elastic material c) prior to deformation and d) after deformation. PAGE 49 49 Figure 22. The influence of stress on the ener getics of an arbitrary TST rate p rocess: a) schematic plot of the energetics of an arbi trary TST rate process and b) schematic plot of the energetics of arbitrary TST rate processes with different signs of V* under high hydrostatic pressure. PAGE 50 50 Figure 23. Atomistic schematics of VPEG and LPEG processes: a) flux of atom s to the growth interface with subsequent adsorption, b) su rface diffusion of adatoms, c) clustering of adatoms with subsequent island nucleation, and d) incorporation of adatoms into island ledges. PAGE 51 51 Figure 24. Macroscopic schematics of the (001) oriented SP EG proce ss: a) a continuous Si film in direct contact with a (001) Si substr ate, b) partial growth of an epitaxial layer on the substrate, and c) completed SPEG resulting in a single crystal Si film. PAGE 52 52 Figure 25. Atomistic schematics of the (001)oriented SPEG processes. PAGE 53 53 Figure 26. Temperatureinfluen ced intrinsic SPE G kinetics: plot of intrinsic (001)oriented v versus the reciprocal of kT as measured using TRR [Ols88]. PAGE 54 54 Figure 27. Substrate orientat ioninfluenced intrinsic SPEG kinetics: plot of intrinsic v versus at T = 550 C as measured using RBS [Cse78]. PAGE 55 55 Figure 28. Dopantinfluenced SPE G kinetics: a) schem atic of th e band structure of the interface between Bdoped Si and Si and b) plot of (001)oriented v versus P concentration at T = 475 C as measured using RBS [Cse77]. PAGE 56 56 Figure 29. Electricallyinactiv e im purity influenced SPEG kine tics: plot of (001)oriented v versus O concentration at T = 550 C as measured using RBS [Ken77]. PAGE 57 57 Figure 210. Onaxis crosssecti onal transm ission electron micros copy images of the maskedge defect nucleation process during twodimensional, intrinsic SPEG at T = 525 C: a) an asimplanted twodimensional Si region, b) partial completion of SPEG, and c) completion of SPEG resulting in maske dge defects (indicated by arrows). PAGE 58 58 Figure 211. Hairpin dislocation nu cleation during SPEG: weakbeam darkfield crosssectional transmission electron microscopy images of a) an asimplanted structure with remnant crystallites near the initial /crystalline interface and b) partial completion of SPEG resulting in hairpin dislocatio n nucleation (indicated by arrows). PAGE 59 59 Figure 212. Prior observations of pure hydrosta tic com pressive stressinfluenced SPEG: a) schematic of (001)oriented SPEG under pure hydrostatic compressive stress, and b) plot of intrinsic (001)oriented v versus at three different T as measured using TRR [Lu91]. PAGE 60 60 Figure 213. Prior observations of inplane un iax ial stressinfluen ced SPEG kinetics: a) schematic of (001)oriented SPEG under inplane uniaxial stress, 11 and b) plot of intrinsic (001)oriented v (normalized) versus 11 at T = 540 C as measured using RBS [Azi91]. PAGE 61 61 Figure 214. Prior observations of normal compre ssive uniaxial stressinfluenced SPEG kinetics: a) schem atic of (001)oriented SPEG under normal uniaxial compression, 33 and b) plot of intrinsic (001)oriented v versus 33 at T = 540 C as measured using TRR [Bar97]. PAGE 62 62 CHAPTER 3 EXPERIMENTAL TECHNIQUES 3.1 Material Processing 3.1.1 IonImplantation and Generation of Amorphous Layers The process of ionimplantation is the preferred method of introduc ing dopants or other atoms into Si wafers during device processing. It affords several advantag es in that it has high repeatability, extremely accurate control over amounts of dopant introduced, the ability to introduce dopants into hi ghly localized portions of a Si wafe r, and control of the profile of dopant introduced. In ionim plantation, atoms with mass, m, to be implanted are first ionized from a gas source using an ionizing co il to acquire a net electric charge, q, and accelerated through a potential difference, V. Subsequently, an analyzing ma gnet is used to isolate the desired ions for implantation from an y possible impurities (as specified by m/q) and the ions are then directed towards the Si target [Figure 31]. The relationship between m, q, V, and the velocity of the incoming ions, vion, is given by qVmvion22 1 (31) where qV = E0 is defined as the kinetic energy acquired by the ion. As the ions travel through the wafer, they experience nuclear and electroni c collisions with the Si atoms in the crystal lattice. During these collisions, the implanted io ns experience energy losses and eventually lose all acquired kinetic energy [Kin55] Nuclear losses result from ionsubstrate atom nucleus collisions while electronic losses result from ionsubstrate atom electron collisions. Furthermore, the implantation process is actually statistical in nature, since the nuclear and electronic collisions suffered will be different for each individual ion. For a given ion, the distance, R, the ion will travel into the substrate is given by PAGE 63 63 00/ 1EdE dxdE R, (32) where the quantity dE/dx is defined as the incremental en ergy loss with respect to distance traveled by the implanted ion. For the case of onedimensional ionimplantation, the mean value of R is defined as the ion projected range, Rp, and the standard deviation in R is defined as the longitudinal straggle, Rp. Typically, the concentration of implanted ions, Cion(xion), as a function of the distance into the substrate, xion, can be approximated as Gaussian in nature as given by 2 max2 1 expp pion ion ionionR Rx CxC, (33) where max ionC is the maximum ion con centration (occurring at xion = Rp) [Zie03] [Figure 32]. The value of max ionC is controlled by Rp and the number of ions implanted per unit area, Qion (referred to as the dose) as given by 2max p ion ionR Q C (34) The value of Qion is controlled by the implantation process and is given by implant ion iontJQ (35) where Jion is the incident ion flux and timplant is the implantation time (assuming Jion is invariant with time). It is important to note that th e Gaussian distribution is most reasonable for implantation into an amorphous solid (where no crystallographic channels are present) since channeling in crystalline solids [Mye78] can si gnificantly skew the implanted impurity profile. Nuclear collisions result in larger energy lo sses than electronic collisions and result in lattice disorder by displacing substrate atoms. In turn, the displaced Si atoms collide with other PAGE 64 64 Si atoms, creating what is known as a damage cascade [Gib60, Rob74]. A large number of vacancies and interstitials are crea ted (known as point defects). If the dose of ions is sufficiently high, the density of point defects can exceed a cr itical value and the Si undergoes a firstorder phase transformation to become Si [Dav67, Mor70]. This pro cess is highly sensitive to the type of ions being implanted. Larger, heavier ions such as As+, Ge+, or Si+ cause amorphization at lower doses (< 115 cm2) while lighter ions such as B+ amorphize a higher doses (> 116 cm2) since heavier ions tend to form denser damage cascades [Jon88b] In this work, the generation of continuous Si films on Si substrates was effected via Si+implantation at vacuum of ~88 Torr into singlecrystal 50 mthick polished impurityfree (001) Si substrates with room te mperature electrical resistivity > ~1 cm. Due to the high vacuum used for implantation, it is reasonabl y assumed that the amount s of any unintentional impurities implanted were negligible. All Si+implantation was conducte d at room temperature using a commercial ionimplantation system. A sequence of Si+ implants with energies of 50, 100, and 200 keV to doses of 115, 115, and 315 cm2, respectively, generated Si layers ~350 nmthick with high repeatabil ity [Figure 33]. Wafers receiving only Si+ implants are referred to as intrinsic samples since the in trinsic charge carrier c oncentration [Gre90] of bulk Si at T > 500 C (temperatures used for annealing) is much greater than the charge carrier concentration of the wafers at roomtemperature (Chapters 5 and 6). For some portions of this work, As+implantation at 300 keV to a dose of 1.615 cm2 (Asdoped samples) or B+implantation at 60 keV to a dose 3.515 cm2 (Bdoped samples) was also conducted (Chapters 4 and 7, respectively). A band of defective Si just beyond the initial /crystal inte rface, known as the endofrange (EOR) damage, was observed fo r all samples [Figure 33]. Upon annealing, this region evolves into extended defects (dislo cation loops and rodlike defects) which have PAGE 65 65 been thoroughly studied in the lit erature [Jon88]. Since the EOR de fects do not interact with the growth interface, it is believed that no influen ce from the EOR on SPEG kinetics exists [Ols88]. 3.1.2 Application of InPlane Uniaxial Stress The only stress state used in this work is uniaxial stress in the plane of the growth interface (11 0, all other elements of ij = 0) [Figure 213(a)]. T hus, as per Equation (215), determining 1 (using reduced notation) requires knowing E11 and 1. Since stress is being applied in the plane of the /crystalline growth interface and th e crystalline phase is growing while consuming the Si, E11 is assumed to be that of Si for the particular crystal direction in which 1 is being applied. Thus, determining E11 for a given crystal di rection is relatively straightforward considering the el astic constants of Si have b een extensively studied [Wor65]. The specific method of inducing 1 involves the use of a novel quartz selfsupported bending apparatus [Figure 34(a)]. In this method, an ionimplanted 50 mthick, impurityfree (001) Si wafer is cleaved into rectangular strips along <110> inplane directions with approximate dimensions of 0.2 1.8 cm2. By hand, the strips are bent along the elongated direction (by convention, taken to be 1 direction and the [110] crystal direction) into an arch shape and the ends inserted into th e slots in the quartz tray spaced ~1.5 cm apart. This places the strip in a state of pure uniaxi al bending and, hence, generate s uniaxial stress along the elongated direction of the strip [F il03]. Since the growth direction (a xis 3) is orthogonal to the elongated strip direction (axis 1 and direction of the applied stress), the stress generated is, indeed, in the plane of the growth interface. In such cases, the magnitude of 1(x) in the near vicinity of the top and bottom surfaces of the strip is a function of the horizon tal displacement from the strip apex, x, and can be readily shown to be inversely proportional to the ra dius of curvature al ong the bent strip, r(x), as given PAGE 66 66 by xr c Ex11 1, (36) where c is the wafer half thickness (25 m) of the strip [Figure 34(b)]. In the case of the top surface, 1(x) is positive (tensile stress) while in the case of the bottom surface, 1(x) is negative (compressive stress). In order to determine r(x), a Philtec laser displacement system is translated over the bent wafer and measur es the vertical deflection, y(x), of the strip as a function of x for a discrete set of points [Figure 34(b)]. Next, a continuous functi on was fit to the data. In all cases, a parabolic relationship between y(x) and x was a sufficient and very reasonable fit to the data. Once y(x) is known, r(x) is calculated [Ste07] via 2/3 2 21 1dx xdy dx xyd xr, (37) and thus, as per Equation (x), 1(x) can be calculated. Once annealing of the bent strips is comple ted and the strips are removed from the quartz tray, the strips will return to being flat. Thus, it must be determined what horizontal displacement for the bent wafer, x0, corresponds to the horizontal displacement for the unbent wafer x(x0). This is simply the arc length of the bent wafer measured from the apex (x = 0) to x = x0 as given by 00 2 01'xdx dx xdy xx. (38) Thus, 1(x) can be determined for sitespecific extraction of samples from the strip. PAGE 67 67 3.1.3 Temperature Calibration and Annealing Due to the exsitu nature of the experiments, T was not obtained during annealing. In this work, the quartz tray apparatus was inserted (starting at room temperatur e) into a tube furnace and allowed to come to thermal equilibrium with the furnace [Figure 35]. The position of the tray in the tube furnace was kept constant for all anneals. Then a thermocouple was placed on the middle of the tray to measure T and carefully manipulated so as not to touch any other part of the tray or the inside of the tube It was at this position on the tray that tensile, compressive, and stressfree specimens (three unique wafer strips) were annealed simultaneously for each time and temperature. The error in all T measurements was estimated at C 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) as well as for temperature measurements. For these studies, T = 500 575 C was used with anneal times of 0. 1 11.2 h. The quartz tray reached thermal equilibrium with the furnace very quickly (< 2 min). Thus, since the rampup time to reach equilibrium was much smaller than any of the anneal times it is reasonably assumed that the strips were given isothermal processing. As mentioned in Chapter 2, it is possible for applied stress to relax depending on the annealing temperature, time, and applied stress. Specifically, if a stressed strip experiences stress relaxation during annealing, the strip will exhibit a remnan t radius of curvature following removal from the quartz bending apparatus. Ho wever, all stressed strips annealed for all temperature, time, and applied stress configurati ons in this work did not exhibit any detectable remnant radii of curvature following removal fr om bending after annealin g indicating that any stress relaxation during anneali ng was essentially negligible. 3.1.4 Transmission Electron Microscopy Sample Preparation A focused ion beam (FIB) system was used to prepare sitespecifi c transmission electron PAGE 68 68 microscopy samples from the strips. In this method, a focused beam of Ga+ ions is accelerated to 30 keV and used to mill away small portions of the wafer [Yam85, Pel90]. Ultimately, a 100 200 nmthick 10 mlong, electrontransparent membrane (s pecimen) is produced which is then removed from the wafer surface exsitu and placed on a grid for imaging. Prior to FIB processing, the strips were placed on Al stubs with C adhesive and subsequently evaporationcoated with ~30 nm of C. Th e thin C film was used to make the surface conductive for imaging and for surface protection during the in itial stages of preparation. Subsequently, a layer of Pt ~1 mthick was FIBdeposited over the area of interest to protect the area from further beam damage during the main stages of sample prepar ation [Kat99]. Thus, negligible FIBinduced damage to the specimens was experienced. It is also important to address the issue of intraspecimen stress gradients. As mentioned previously, a continuous variation in 1(x) exists due to the variable curvature of the bent strips. Thus, a stress gradient exists over each FIBprepared specimen. However, due to the small ratio of FIB specimen length to strip length (~55) the stress gradient across a FIB specimen is exceedingly small such that the assumption of constant stress over the specimen is quite reasonable. Thus, considerations of possibl e intraspecimen stress gr adients are unnecessary. 3.2 Material Characterization 3.2.1 Transmission Electron Microscopy Transmission electron microscopy (TEM) is a valu able structural analys is technique. In TEM, a beam of electrons (usually generated from thermionic emission of a W filament under high vacuum) [Figure 36] is accelera ted across a potential difference, Ve = 200 keV, and directed at the specimen. As per the de Broglie hypothesis of particlew ave duality [deB27], an electron with acquired momentum, pe, can also be considered as a propagating wave with wavelength, Specifically, PAGE 69 69 h pe, (39) where h = 6.626 1034 Js is known as Plancks cons tant. The relationship between Ve and pe is given by e e eeV m p 22, (310) where me = 9.109 1031 kg is the mass of an electron and e = 1.602 1019 C is the electric charge of an electron. Combining Equations (39) and (310), it is easily shown that eeeVm h 2 (311) Thus, neglecting any relativisti c effects [Ein16] (which tend to become relevant at Ve >> 200 kV), an electron accelerated across Ve = 200 kV will have ~ 2.5 1012 m. The small value of is necessary to allow for resolution of nanometerscale features in TEM samples. Subsequently, the electron beam passes thr ough a condenser lens (some TEM systems use multiple condenser lenses) to collimate the beam before being incident on the specimen [Figure 36]. As the beam interacts with the sample, the in cident electrons can su ffer several different fates. A portion of the beam is backscattered and does not pass through the specimen [Figure 37]. These backscattered electrons do not contribute to TEM im aging and are not given further consideration. Regarding the portion of the beam which does pa ss through the specimen, these electrons can be transmitted (unscattered), elastic allyscattered, or inelasticallyscattered [Figure 37]. If the direction of trav el of the electrons is unchange d after passing through sample, the electrons are referred to as transmitted. Conversel y, electrons are referred to as scattered if the direction of travel is changed after passing through the specimen. If a scattered electron does not PAGE 70 70 lose any kinetic energy, it is referred to as elasticallyscattered, while if energy loss is experienced, the electron is said to be inelasticallyscattered. Following interaction with the specimen the beam is focused by the objective lens to form the first image of the specimen [Figure 36] Also of importance is the point along the TEM column where diffracted electrons travelin g in parallel directions converge after being focused by the objective lens. Th is is known as the back focal plane [Figure 36]. Finally, a projector lens (some TEM systems have multiple projector lenses and/or intermediate lenses) creates an image of the first image (created by the objective lens) on a phosfluorescent screen [Figure 36]. A portion of elasticallys cattered electrons suffer diffraction (reflection) by the different crystallographic planes of the sample. Sp ecifically, due to the waveparticle duality hypothesized by de Broglie [deB27], constructive interference of a diffracted electron incident on plane ( hkl ) will be experienced provided B hkldn sin2 (312) where n may take integer values greater than or equal to 1, dhkl is the planar spacing of the plane with Miller indices h k, and l and B is defined as the Bragg angle for constructive interference [Figure 38] [Bra13]. In the case of Si (cubic crystal structure), 222lkh a dhkl (313) However, constructive interference is not possible for all ( hkl ) planes in the diamondcubic structure of Si. In order to de termine which reflections are allo wed, calculation of the structure factor, Fhkl, of plane (hkl ) is necessary as given by, lwkvhuifFj Si hkl 2exp8 1, (314) PAGE 71 71 where fSi is the atomic scattering factor of Si, u v, and w are the Cartesian coordinates of the j th atom within the Si unit cell, and i (in this case only) refers to the imaginary number, 1. If Fhkl = 0, reflection from the ( hkl ) plane will not occur. For example, it can be readily shown that the (004) reflection is allowed while the (002) reflection is forbidden. In the case of a Si single crystal with a gi ven orientation relative to the incident beam, the electron beam is so finely collimated that only a few allowed reflections will be possible for a given specimen orientation and the rest of the in cident beam will be transmitted or inelasticallyscattered. It is in considerat ions of diffraction that the back focal plane is significant [Figure 36], because it is at this plane where the transmitted beam and allowed reflections will be manifested as a pattern of ordered points of high inte nsity. It is possible to form an image of this pattern, using the projector lens, and this is known as a selected area diffraction (SAD) pattern [Figure 39(a)]. Electrons which are inelastical lyscattered are also manifest ed as features in the SAD pattern. As electrons are incident on a specimen, small atomic th ermal vibrations cause a portion of the beam to be inelasticallys cattered and channe led by certain ( hkl ) crystallographic planes [Kik28]. These electrons appear as bands or lines (Ki kuchi bands) in the SAD pattern [Figure 39(b). The nature of the SAD pattern (both spots and Kikuchi bands) will be dependent on the crystallographic orientation of the sample relative to the inci dent electron beam direction, B (referred to as the zone axis). Thus, the or ientation of the specimen can be determined by observing the corresponding SAD patte rn. Once the desired zone axis has been obtained, the projector lens can then form an image of th e specimen. For all work presented herein, B = ]011[ (orthogonal to the wafer orientation) was used for TEM imaging. TEM imaging of this style is PAGE 72 72 known as crosssectional TEM (X TEM), since the wafer structur e is being observed from the side. In the case of Si, distinct crystalline planes do not exist and thus the portion of the beam incident on any Si region will be only minimally scat tered (compared to the crystalline counterpart). This gives rise to contrast between the two phases dur ing imaging. It is possible to increase this contrast between Si and Si phases by selectively al lowing certain electrons at the back focal plane to contribute to the generated image. This is done by inserting an aperture at the back focal plane to allow only the transmitted beam and the four nearest diffracted beams (all {111}type reflections) to generate the image [Figur es 39(a) and (b)]. This imaging condition is known as onaxis phasecontrast imaging. Weakbeam darkfield (WBDF) imaging is another type of imaging condition which is wellsuited to imaging dislocations in crystalline Si. In this style of imaging, the sample is tilted slightly away from the ]011 [ zone axis along the {220}type Kikuchi bands such that only the (220) set of planes suffers strong diffraction [Figure 310(a)]. Specifically, in the SAD pattern, the transmitted and diffracted spots will each di rectly overlap one of the two {220}type Kikuchi bands and each spot will be much brighter than any other beams. This is referred to as a twobeam condition. On the SAD pattern, the vector fr om the transmitted to the (220) diffracted spot is referred to as g220 [Figure 310(a)]. Once the twob eam condition has been obtained, the incident electron beam is tilted so th at the transmitted spot is translated g220 in the SAD pattern. Once this occurs, the diffraction spot 3g220 away from the transmitted spot will become bright [Figure 310(b)]. Subsequently, an aperture is placed in the back focal plane so only the diffracted spot where the transmitted beam wa s located before beam tilting (now weak in intensity) contributes to the image [Figure 310(b)]. PAGE 73 73 In a WBDF image, a portion of a dislocation will be visible provided 0 )(220 bg, (315) where refers to the line direction of the portion of the dislocation [Hir81]. The Burgers vector of a given dislocation is constant for the whole dislocation, but may be variable. In Si, b = a<111>/3 or a<110>/2 are the most common types of Burgers vectors and = <110> is typical since the PeierlsNabarro barrier for atomic di splacement is lowest al ong these crystallographic directions [Hir81]. Co nsidering the case of b = a<110>/2 (the Burgers vectors for hairpin dislocations addressed in Chapter 2), b tends to be oriented parallel to or 60 from for a given dislocation portion The former type of dislocation portion is known as a shear portion while the latter type of dislocation porti on is known as a mixed portion. It is important to note that TEM images are actually twodimensional projections of a threedimensional specimen. In the case of onaxis XTEM, the SPEG direction is orthogonal to the B = ]011 [ zone axis so that the true thickness of Si layer is measured while in the case of WBDFXTEM, the specimen is tilted slightly away from the B = ]011 [ zone axis and thus the imaged Si layer is actually thinne r than the true thickness. However, the amount of tilting away from the the B = ]011[ zone axis in WBDFXTEM is very small (typically < 1) such that the imaged Si layer thickness is still nominally the sa me as the true layer thickness measured using onaxis XTEM. Thus, it is reasonably a ssumed that the use of onaxis XTEM versus WBDFXTEM did not appreciabl y alter the measurement of Si layer thicknesses. 3.2.2 Secondary Ion Mass Spectrometry Secondary Ion Mass Spectrometry (SIMS) is a destructive chemical analysis technique which allows the atomic concentration of specific elements and/or isotopes of elements to be determined as a function of depth into the wafe r [Her49, Hon58, Lie63]. In this technique, a PAGE 74 74 beam of primary ions (usually Oor Cs+) is used to sputter away material from the wafer surface. During this process, atoms in the sputtered material become ionized and are thus referred to as secondary ions [Figure 311(a)]. An analyzing magnet is used to determine the mass to charge ratio of the secondary ions which allows the atomic species of the secondary ions to be determined. In conjunction with the sputtering rate used and the amount of ions collected as a function of time, the atomic concentration of di fferent species as a function of depth into the sample can be determined [Figure 311(b)]. 3.3 Data Analysis 3.3.1 Amorphous Layer Thickness Measurements In order to measure the growth kinetics, the amount of Si growth (or Si layer thickness, z) as a function of annealing time, t, must be determined. However, this work is exsitu in nature and thus the z versus t behavior must be discretized. For a given specimen condition (specific stress, annealing temperature, and annealing time), several XTEM micrographs of the specimen were collected (typically 5 7). Then, using ImageJ analysis software, the specimen surface and growth interface were finely discretized into sets of coordinates [Figure 312]. Using these two sets of data, the average Si thickness over a given image wa s calculated. Additionally, the rootmeansquared roughness, RRMS, of the growth interface was also determined for each image. Once z and RRMS were determined for each image, the standard deviation in z, z, and average RRMS, RMSR, were determined for the set of collected images for the specific specimen. Thus, a reported Si thickness measurement is the average value of z collected over all images for the specimen with the total reported error in the Si thickness measurement, ztotal, given as 2 2 RMS totalRzz (316) PAGE 75 75 In the cases where RMSR is reported, the error in RMSR, RRMS, is calculated as the standard deviation in RRMS measured over all images. 3.3.2 Velocity Calculations in Intrinsic Samples Once the Si layer thicknesses as a function of anneal time for given stress and temperature are known, v for the particular set of conditions can be calculated. In order to do this, it is first assumed that v is invariant with t. This is a reasonable assumption given that the wafers strips were given isothe rmal processing and prior work wh ere no significant variations in v were observed as a function of t for intrinsic samples [Ols88]. The special, isolated case of calculating v in material with nonuniform impurity conten t is treated in Chapter 7. Hence, for intrinsic material, z as function of t takes the form 0zvttz (317) where z0 is the initial Si layer thickness at t = 0. Leastsquares regr ession (LSR) analysis was used to fit Equation (3 17) to the measured z versus t behavior where v and z0 are fitting parameters. Specifically, i i izzvt v2 00 (318) and n i i izzvt z1 2 0 00, (319) need to be determined where there are n data points and zi and ti refer to the measured z and t for the ith data point. Thus, Equations (318) and (319) provide a system of two equations where v and z0 are unknown and can thus be determined. After extensive algebraic manipulation, it is easily shown that PAGE 76 76 2 1 2 1 1 2 0i n i i n i iii n i iitnt ztttz z (320) and 2 1 2 1i n i i ii n i iitnt tznzt v (321) where iz is the average value of zi and it is the average value of ti. The statistical error in v, vstat, is calculated as 2 1 2 2 1 1 2 1 22 1 n i ii n i iiii n i ii n i ii stattt ttzz tt zz n v. (322) Another source of error in the measurement of v is the roughness of the growth interface. In this work, the roughening error in v, vR,i, experienced over a given time interval, ti = ti+ 1 ti, is calculated as i iRMS iRt R v 1, ,, (323) where RRMS,i+ 1 is RRMS measured at the i+1th data point and thus the average value of vR,i, iRv,, is the contribution to the error in v from roughening. Taking into account vstat and iRv,, the overall error (the report ed error in all intrinsic v calculations) in v, v, is given as 2 2 iR statvvv (324) PAGE 77 77 3.3.3 Generalized LeastSquares Regression Analysis In the previous section, the use of LSR analysis was presented for the case of fitting v (a linear function) to a discrete set of z versus t data. However, LSR analysis can be readily applied to fit any arbitrary mathematical function to any set of discrete data. For example, consider vfit, a function of 11 and three generalized fitting parameters, 1, 2, and 3, for fitting measured v versus 11 data. In this case, the conditions for LSR analysis are n i ifitivv1 2 321,11 1,,, 0 (325) n i ifitivv1 2 321,11 2,,, 0 (326) and n i ifitivv1 2 321,11 3,,, 0 (327) where vi is the calculated value of v at the ith value of 11, 11 ,i. Hence, provided 3 < n, there are three unique values of 1, 2, and 3 which simultaneously satisfy Equations (325), (326) and (327). Determining the errors in 1, 2, and 3 is not straightforward as in the case of fitting a linear function to a set of data. In fact, there is no formal definition for calculating the statistical error for the fitting parameters of an arbitrary function. However, a measure of the degree of accuracy of vfit can be determined from th e normalized standard error, SER, given by n i i ifit Rv v SE1 2 321,11,,, 1. (328) Therefore, the error in 1, 2, and 3, for vfit can be estimated as SER multiplied by the fitted values of 1, 2, and 3, respectively. Hence, this treatment is used for calculating the error in the PAGE 78 78 fitting parameters of nonlinear mathematical equations as will be presented in Chapters 5, 6, and 7. PAGE 79 79 Figure 31. Schematic of a basic ionimplantation system. PAGE 80 80 Figure 32. Schematic of a typical Cion versus xion distribution for an arbitrary ion species implanted into Si. PAGE 81 81 Figure 33. Weakbeam darkfield crosssectional transm ission electron microscopy image of a typical asimplanted specimen. PAGE 82 82 Figure 34. Application and measurement of inp lane uniaxial stress: a) schem atic of the novel quartz bending apparatus used to induce and measure inplane uniaxial stress along [110] in (001) Si wafer stri ps and b) typi cal plot of y versus x as measured using a Philec laser displacement system. PAGE 83 83 Figure 35. Schematic of the tube furnace appa ratus used for annealing an d the method of temperature calibration. PAGE 84 84 Figure 36. Schematic of a basic TEM column. PAGE 85 85 Figure 37. Possible interactions of the incid ent electron beam with the sample. PAGE 86 86 Figure 38. Schematic of Braggs law for c onstructive interference for an arbitrary (hkl) plane. PAGE 87 87 Figure 39. Onaxis XTEM di ffraction and im aging: a) SAD pattern taken along the B = ]011 [ zone axis used for onaxis XTEM imaging conditions (Kikuchi bands represented as solid lines) and b) a corresponding TEM image. PAGE 88 88 Figure 310. WBDFXTEM diff raction and im aging: a) SAD pattern taken along the B ~ ]011 [ zone axis with a g220 twobeam condition and b) the same SAD pattern after tilting the incident electron beam to translate B by g220 to generate WBDF imaging conditions (weak (strong) diffraction spots de noted as unfilled (filled), Kikuchi bands represented as solid lines), a nd c) a corresponding TEM image. PAGE 89 89 Figure 311. The SIMS analysis t echnique: a) schem atic of the basi c SIMS process and b) plot of CB versus depth into the substrate for B+implantation at 60 keV to a dose of 3.515 cm2 as determined using SIMS. PAGE 90 90 Figure 312. WBDFXTEM image of an anneal ed specim en showing the process used to measure the thickness of the resulting Si layer and RRMS of the resulting growth interface. The surface and growth interface are discretely represented (+) with the arrows representing Si thickness variations within the image. PAGE 91 91 CHAPTER 4 INTERFACIAL ROUGHENING AND DEFE C T NUCLEATION DURING STRESSED SOLIDPHASE EPITAXIAL GR OWTH OF ASDOPED SI 4.1 Introduction As mentioned in the literature review section, the apparent effect of inplane stress on SPEG kinetics is far from conclusive [Azi91]. In part, this may have been due to the range of 11 used or other experimental details of the pr ior study but this is unclear. Thus, given the dispersed and somewhat scattered data of Aziz et al. and the new experiment al approaches taken in this work, it is important to determine to what degree, if any, the prior results are repeatable [Azi91]. Hence, the work in this chapter aims to address this concern while providing a starting point for the work of later chapters. 4.2 Experimental Procedures For this study, a polished 50 mthick impurityfree (001) Si wafer with room temperature resistivity > ~1 cm was used. The wafer was first Si+implanted at 50 and 200 keV with doses of 1.015 cm2 and subsequently As+implanted at 300 keV to a dose of 1.815 cm2. The wafer was cleaved along <110> directions into ~0.3.8 cm2 strips. The strips were then stressed to maximum 11 of 1.5 0.1 GPa along the in plane [110] direction. Stressfree, tensile, and compressive specimens were annealed simultaneously at 525 C in N2 ambient for 0.7 3.2 h (referred to as nonprean nealed samples). Additionally, another set of strips was first annealed without stress for 0.7 h and then subsequently annealed with stress for 1.3 h (referred to as preannealed samples). The stressed strips exhibited no detectable radii of curvature following unloading after annealing indicating no measurab le plastic strain or, thus, stress relaxation. The SPEG process was examined using WBDFXTEM with specimens prepared via FIB milling. PAGE 92 92 4.3 SPEG of NonPreAnnealed Specimens WBDFXTEM of an asimplanted specimen [Figure 41(a)] indicates an Si layer ~340 nm deep with an initial /crystalline interface with many small cr ystallites residing just inside the Si region. Following annealing for 1.3 h with 11 = 0 [Figure 41(e)], the specimens exhibit a smooth growth front with RMSR of 3 2 nm after 250 5 nm of growth with a few growthrelated defects (indicated by arrow). The defects (dislocations) tend to form near the original /crystalline interface and propagate upward and result from the growth interface meeting misoriented crystallites produced ionimplantation [Glo76, San85]. A small band of EOR defects is observed near the initial /crystalline interface [Jon88]. After annealing for 1.3 h with 11 = 0.5, 1.0, and 1.5 GPa [Figures 41(b) (d)], the specimens exhibit a resulting /crystalline interface with RMSR = 15 5 nm and a large number of SPEGrelated defects. In these cases, it appears the def ects nucleate from the initial /crystalline interface, as well as within the region of growth. The SPEG rate was retarded compared to the stressfree case, as ~200 nm of growth occurred a nd the growth interface roughened greatly which both agree with prior results [Azi91, Bar98]. However, due to the rough interface, the amount growth is approximate making quantification of the SPEG rate difficult. The generation of offaxis growth fronts during roughening which grow slower than th e [001] front may also be a factor in this observed retardation [Cse78]. Regarding the cases of 11 = 0.5, 1.0, and 1.5 GPa [Figures 41(f) (g)], the resulting /crystalline interfaces ar e smooth and strikingly similar to the stressfree case [Figure 41(e)] with RMSR = 3 2 nm. However, more growthrelated defects nucleate from the original /crystalline interface in tension compared to the stressfree case. The amounts of growth were very similar to the stressfree case with 250 5 nm of regrowth which disagrees with prior reports observing enhancement to SPEG [Azi91]. PAGE 93 93 To further examine the effect of tension on SPEG rate, specimens were annealed for 0.7 h with 11 0. In all cases, the resulting amount of growth was very similar with 100 5 nm of growth with RMSR = 3 2 nm (not presente d). The work from Aziz et al. [Azi91] measured an enhancement to v with 11 > 0 and proposed v as exponentiallyenhanced with 11 > 0 [Equation (237). The expression for v may be expanded to tdv /, where d is the growth interface displacement and t is the time for this displacement to occur. For the same amount of growth to occur without stress 0/0tdv where 0t is the time for the same amount of growth without stress. Thus Equation (237) may be rewritten as kT V tt11 11exp 0 11. (41) Using Equation (41), the predicted interface displacement versus time behavior for different 11 > 0 was estimated using the measured 11 = 0 growth data [Figure 42]. From these calculations, it appears the observed growth kinetics are significantly slower than predicted. One possible explanatio n for the differences between the observed effect of tension in the present and previous studi es is the presence of As, know n to enhance SPEG rates [Joh07, Wil83]. Hence, the As effect may have overwhe lmed the expected enhancement from tension. However, this explanation contradicts previous results suggesting inde pendent stress and dopant effects on SPEG rates [Bar04]. In addition, it is unlikely the presence of As is influencing volume changes between Si and Si as previously proposed due to the similarity in size between As and Si atoms and the As concentrati ons used. Experiments eliminating the As+implantation step will be presented in Chapters 5 and 6. Annealing for 3.2 h completed growth in all cases as observed using WBDFXTEM (not presented). Following SPEG, th e average defect density (ND) as a function of 11 was estimated PAGE 94 94 by assuming a sample thickness of ~200 nm (as fi xed by FIB sample preparation) and measuring the number of defects intersecting the midpoint of the grown layer. The error in all ND measurements is given as the standard deviation of ND measured over all XTEM micrographs of a specific specimen. It is interes ting consider the relationship between ND after completion of SPEG and RRMS after annealing for 1.3 h [Figur e 43]. It is evident that ND and RMSR with 11 < 0 are significantly higher than 11 0 and likely correlated. However, it is interesting that RRMS is very small both in stre ssfree and tension cases but ND appears higher in te nsion relative to the stressfree case. Thus, it appears that roughening of the /crystalline interface during SPEG is not a primary mechanism responsible for grow threlated defect formation in tension. Furthermore, the observation that most of the defects nucleated near the initial /crystalline interface with 11 > 0 indicates the very early stages of SPEG are critically important for defect formation. In terms of roughnessinduced defect formati on, it appears defects tend to nucleate at deep cusps (or troughs) in the grow th interface [Figure 41]. To explain this observation, it is necessary to first consider that perfect atomic registry exists throughout the crystalline phase in the vicinity of a cusp. This perf ect registry is maintained as th e growth front on both sides of the cusp evolves. However, as the growth front be gins to advance on itself from both sides of the cusp, atoms in the encompassed Si region must add to both portions of the growth front simultaneously. Presumably, it is more difficult to maintain perfect crystal registry in such a situation as it is necessary for the atoms to coordinate incorporation between two (rather than one) portions of the front. Thus, as the Si region is consumed, a defect is nucleated at the cusp and the local portion of the growth front once ag ain becomes planar. This process is analogous PAGE 95 95 to the formation of maskedge defects discussed in Chapter 2 where two growth fronts advance on each other [Figure 210]. In contrast, no defects nucleate on a growth interface without cusps. In this case, the growth front is never advancing on itself and thus the issue of an incorporating atom maintaining perfect registry between two porti ons of the front does not exist. 4.4 SPEG of Preannealed Specimens As was revealed in the previous section, it appears the very early stages of growth are instrumental in the formation of greater numbers of growthrelated defects with 11 > 0. To further examine this, some specimens were part ially grown by annealing for 0.7 h without stress [Figure 44(a)] and then annealed for an additional 1.3 h with st ress. The goal of performing the stressfree anneal was to partia lly grow the layer to planarize the growth front and remove the influence of the misoriented crystallites near the original /crystalline interface on subsequent stressedSPEG. With 11 = 1.5 GPa during the stressed porti on of annealing [Figure 44(b)] the growth interface exhibits significant interfacial roughening with nucleation of several growthrelated defects within th e portion of the layer grown with stress. In contrast, the specimen subjected to annealing for 1.3 h with 11 = 1.5 GPa after stressfree annealing for 0.7 h [Figure 44(c)] exhibits a smooth resulting /crystalline interf ace with no growth related defects nucleating at the new interface. Since misoriented crystallites [Glo76, San85] near the initial /crystalline interface and roughening of the growth interface cause growthrelated defect formation, it is plausible that stress acts to cause greater misorientation of these crystallites which accounts for the observed higher defect density in tension compared to the stressfree case [Figure 45]. This misorientation may, in part, be driven by mi nimization of strain energy, since the Youngs PAGE 96 96 modulus of Si is greatest along < 111> directions [Wor65]. Furthe rmore, very slight crystallite reorientation in Si is highly plausible given the reported viscoelastic nature of Si [Wit93]. Presumably, this effect occurs equally for co mpression and tension and thus the values of ND with 11 < 0 are indicative of both stre ssinduced crystallite misorientation as well as interfacial roughening. It is interesting to note the in sensitivity of SPEG kinetics with 11 > 0 [Figure 42] though ND tends to increase with tension [Figure 43]. Thus, since the SPEG rates were very similar in all cases of 11 0, the observed influence of stress on ND was not due to differences in SPEG rates. This is important to consider since annealing the vicinity of ~450 C is known to reduce the amount of misoriented crys tallites though it is unclear if th is effect is due to crystallite dissolution or SPEG proceeding very slowly to allo w misoriented crystallites time to reorient prior to meeting the growth interface [Jon88]. In any case, the observati ons of tensile stress on defect density presented in this study indicate the effect is not related to SPEG kinetics. 4.5 Summary In summary, the effect of inplane uniaxial stress to magnitude of 1.5 0.1 GPa on solid phase epitaxial growth and growthrelated def ect formation of amorphized, Asdoped (001) Si created via ionimplantation was examined. No apparent effect on SPEG kinetics was observed for inplane tension though compre ssion did cause significant retardat ion. It is interesting that the prior accepted model of stressedSPEG advanced by Aziz et al. [Azi91] predicts growth behavior with inplane tension va stly different from that observed herein. It is unclear from the work of this Chapter why this is the case as th e presence of As may be a confounding variable. Thus, a similar study in intrinsic material is necessary to reso lve this issue. The results indicated that compressive stre sses caused the greatest density of defects PAGE 97 97 primarily due to roughening of the growing amorphous /crystalline interface. Interestingly, the application of tensile stresses cau sed greater defect formation compared to stressfree cases even though no significant interfacial r oughening or changes in growth kinetics were observed in tension. This was possibly the result of stressinduced reorientation of crystallites near the original amorphous/crystalline interface during the very early stages of growth. PAGE 98 98 Figure 41. WBDFXTEM images of the stressinfluenced S PEG process in Asdoped specimens: a) WBDFXTEM image of an as implanted Asdoped specimen. WBDFXTEM images of Asdoped specimens annealed at T = 525 C for 1.3 h with 11 = b) 0.5, c) 1.0, d) 1.5, e) 0, f) 0.5, g) 1.0, and h) 1.5 GPa. PAGE 99 99 Figure 42. Measured stressinfl uenced growth kinetics in A s doped material: plot of the measured Si thickness versus anneal time at T = 525 C in Asdoped samples for 0 11 1.5 GPa compared with the predicted Si thickness versus anneal time behavior from Aziz et al. [Azi91]. PAGE 100 100 Figure 43. Stressinfluenced de fect nucleation and interfacial roughening during SPEG of Asdoped sam ples: plots of ND (after annealing for 3.2 h) and RMSR (after annealing for 1.3 h) versus 11 in at T = 525 C in Asdoped samples. PAGE 101 101 Figure 44. The influence of st ressfree preannealing on subse quent stressedSPEG in Asdoped sam ples: WBDFXTEM micrographs of Asdoped specimens a) preannealed (stressfree) for 0.7 h and subsequently annealed for 1.3 h at T = 525 C with 11 = b) 1.5 and c) 1.5 GPa. PAGE 102 102 Figure 45. Stressinfluenced cr ys tallite reorientation: schematics of remnant crystallite orientation near the initial /crystalline interface a) stre ssfree and b) with tension. PAGE 103 103 CHAPTER 5 STRESSED SOLIDPHASE EPITAXIAL GR OWTH KINE TICS OF INTRINSIC SI 5.1 Introduction As was shown in Chapter 4, it appears th at the currently accepted model of stressedSPEG was not able explain the observed growth ki netics. However, the presence of As is a confounding issue with the work of Chapter 4 and thus the study of intrinsic SPEG is necessary to rule out the possibility that the observed effects were impurityrelated. Furthermore, there are inconsistencies between understanding of the atomistic nature of SPEG and the current model of stressdependent SPEG. Current atomistic theory suggests growth occurs via nucleation of twodimensional crystal islands with subsequent migration of island ledges in the growth in terface [Spa, Wil85]. However, the current stressdependent growth model does not account for the individual nucleation and migration kinetics and assumes growth occurs via a single, unspecified atomistic process [Azi91]. Thus, this Chapter attempts resolve the confounding issue of the prior Chapter while reevaluating the prior model and advancing a new theory of stressedSPEG which accounts for the atomistic nature of growth. 5.2 Experimental Procedures In this study, a polished 50 mthick impurityfree (001) Si wafer with room temperature resistivity > ~1 cm was Si+implanted at 50, 100, and 200 keV to doses of 115, 115, and 315 cm2. Subsequently, samples were cleaved along <110> directions into ~0.2.8 cm2 strips and uniaxiallystr essed up to magnitude of 11 1.3 0.1 GPa along the inplane [110] direction. Stressfree, tensilelystressed, a nd compressivelystressed strips were annealed simultaneously at 525 C in N2 ambient for 1.0 4.0 h. Th e stressed strips exhibited no detectable radii of curvature following unloa ding after annealing i ndicating no measurable PAGE 104 104 plastic strain or, thus, stress relaxation. The SPEG process was examined using WBDFXTEM with specimens prepared via FIB milling. 5.3 Intrinsic SPEG Kinetics WBDFXTEM of the asimplanted structure indicates an initial Si layer 350 5 nm thick continuous to the surface as confirmed using selected area diffraction [Figure 51(a)]. Following annealing for 4.0 h with 11 = 0 [Figure 51(e)], 138 5 nm of growth occurred. EOR defects were observed near the initial /crystalline interface for all specimens [Jon88]. As reported by others, these defects do not interact with the growth interface and do not influence SPEG kinetics [Jon88, Ols88]. In the cases of 11 = 0.5, 1.0, and 1.3 GPa [Figures 51(b) (d)], 77 9, 72 8, and 68 9 nm of gr owth occurred which is less than the 11 = 0 case. Growth interface roughening was observed with 11 < 0, consistent with prior reports [Bar98, Bar01, Bar04]. For cases of 11 = 0.5, 1.0, and 1.3 GPa [Figures 51(f) (g)], 138 6 nm of growth occurred, similarly to the 11 = 0 case. The surfaceEOR distance showed no detectable variation between asimplanted and annealed specimens indicating no detectable flow of Si [Wit93]. Annealing of specimens for 1.0, 2.0, and 3.0 h was performed for all values of 11 and the resulting amounts of growth measur ed [Figure 52]. From this data, v versus 11 was calculated [Figure 53]. No detectable difference was observed in v for 0 11 1.3 GPa with v = 34 2 nm/h. In compression, v was retarded to a limiting rate of 17 2 nm/h for 1.3 11 0.5, while 11 = 0.25 GPa retarded v to 22 2 nm/h. The behavior of v versus 11 predicted by Aziz et al. [Equation (237), with v(0) = 34 nm/h] is provided for reference [Azi91]. No predicted increases in v were observed for 11 > 0 while retardation for 11 < 0 was PAGE 105 105 consistent with prior work [Azi91]. However, in compression, the retardation appears to reach a limit and the reductions are greater than predicted. 5.4 Model of StressedSPEG Kinetics It appears that the pres ented results cannot be reas onably explained by the Aziz et al. model of stressed SPEG and thus it becomes nece ssary to consider a new model to explain the data [Azi91]. In particular, as was first suggested by Williams et al. for Si SPEG, the sequential nature of nucleation and migration processes must be addressed [Wil85]. It must first be recognized that a growth interface has an equilibrium planar density of nuclei, nucN, which is a function of T [Kai34, Vol31]. Of course, time is re quired to reach this equilibrium planar concentration. Hence, the differentia l equation governing the planar density,nucN, as a function of time, t, is given as n nuc nuc nucNN dt dN (51) where n is a characteristic tim escale required to reach nucN for a give T The solution of Equation (51) is thus n nuc nuct NNexp 1, (52) assuming nucN = 0 at t = 0 as the initial conditions. The quantity of interest in evaluating growth kinetics is dtdNnuc/, or J, which is the rate of nuclei formation per unit area. As per Equation (51), J is approximated as n nucN J~, (53) since nucN is reached quickly for tn PAGE 106 106 The rate of ledge migration for a generalized /crystalline interface, 1 ijm, is a second order tensor property analogous to diffusivity or mobility given in expanded form by 1 22, 1 21, 1 12, 1 11, 1 m m m m ijm (54) In the case of the Si/(001) Si interface without any stress, Equation (54) reduces to 1 11, 1 11, 1 ,0 0m m ijm (55) as the result of symmetry constraints. Thus, the velocity of ledge migration, imv,, in expanded form is given by 2 1 1 11, 1 11, 2, 1,0 0x x v vm m m m (56) where jx is the ledge migration vector de pendent on the crys tallography of the /crystalline interface and the coordinate frame of reference. In this case, 1x = 2x = 0.38 nm. Both 1, mv and 2, mv contribute to the overall growth veloci ty and are presumably independent of one another. In other words, even if the migration velocity along one direction becomes infinitely slow, macroscopic growth will still continue from migration along the other direction since nuclei possess nonzero size upon formation. The nucleation of crystal islands with monolayer thickness x (0.14 nm) causes contribution to the overall growth rate as xJA where A is the surface area of one nuclei. Thus, accounting for the sequential, ratelimiting nature of nucleation and migration and the independence of migration directions, v is given by The rate of ledge migration does not refer to the inverse of another matrix. PAGE 107 107 2, 1,11 1 11 1m mvxJAvxJA v (57) which further reduces to 2 1 11, 1 1 11,11 1 11 1x xAJ x xJA vm m (58) Using the relationship of Equation (53), Equation (58) becomes 2 1 11, 1 1 1 11, 11 1 1 1 1 1x xNAx xNA vm nnuc m nnuc (59) Mathematically manipulating Equation (59) results in 2 11, 1 11,x x AN x x x AN x vm nuc n m nuc n (510) Next, it is assumed that nucAN ~ 1, since approximately 1 island will be found in area A on a surface with planar density nucN. Hence, Equation (510) in final form is given as 2 11, 1 11,x x x x x x vmn mn (511) Therefore, v is independent of nucN and is only dependent on 1n, and 11, m Presumably, both 1n and 1 ,ijm are Arrheniustype processes and thus each can be theoretically modified by the application of ij as given by TST [Gla48]. However, since 1 ,ijm is a secondorder tensor prope rty, a fourthorder tensor, ijm klV,must be used to describe the change in each component of 1 ,ijm with respect to kl as given by PAGE 108 108 kl ijm ijm klkTV 1 ,ln. (512) Hence, kT Vkl ijm kl ijm ijm 1 1 ,exp0, (513) where 1 ,0ijmis the stressfree migration rate tensor. Similar models describe point defect motion in bulk Si [Azi97]. Since 1 12,0m1 = 1 21,0m= 0 and the only term in ij is 11 11, 11 mV and 22, 11 mV are the only relevant terms in ijm klV,. During ledge motion, the greatest inplane volume change presumably occurs parallel to rather than orthogonal to a given migration direction which implies 22, 11 mV << 11, 11 mV Furthermore, due to symmetry, 22, 22 11, 11 m mVV 11, 22 22, 11 m mVV and 22, 33 11, 33 m mVV Thus, only migration along 1 is significantly altered by 11 Regarding 1n, a second order tensor, n ijV is used to describe the response of 1nwith respect to ij which is given by ij n n ijkTV 1ln. (514) For the Si/(001) Si interface, Equation (514) has the expanded form n n n n ijV V V V33 11 1100 0 0 00 (515) The nucleation of a crystal island causes volume cha nge primarily in the gr owth direction rather than the inplane directions, similar to the forma tion of a Si selfinterstitial or vacancy near a PAGE 109 109 surface [Azi91]. Thus, nV11 ~ 0 and only nV33 is relevant reduci ng Equation (515) to approximately n n ijV V3300 000 000, (516) and thus implying 1n~ 10n, where 10n is the stressfree nuclea tion rate. Thus, Equation (511) may be represented with the application of 11 as 2 11, 1 11 11, 11 11,00 exp00x x x x x kT V x vm n m m n (517) For the Si/(001) Si interface, 1/xx = 2/xx = 23/2 and Equation (517) reduces further to 020 exp02011, 2/3 11 11, 11 11, 2/3 m n m m nx kT V x v (518) Equation (518) was fit to the v versus 11 data [Figure 53] and 0n 011, m and 11, 11 mV were calculated to be 29 1 s, 1.00 0.01 s, and (12 1) ,. The value of 0n is nearly two orders of magnitude greater than 011, m which is consistent with prior observations suggesting that the nucleation rate is much slower than migrati on [Wil85]. The positive value of 11, 11 mV suggests inplane expansion associated w ith ledge migration. In the case of 11 >> 0, Equation (518) reduces to the tensile saturation velocity, 0 2n tx v (519) and the growth process is limited by the nuc leation rate. However, in the case of 11 << 0, Equation (518) reduces to th e compressive limit velocity, PAGE 110 110 0n cx v (520) and growth is still lim ited by nucleation with 2 c tv v, (521) with Equation (521) predicted to be independent of growth temperature. It is important to note the interfacial roughening with 11 < 0 which generates offaxis growth interfaces which grow up to ~25 times slower than [001] SPEG [Cse78] However, this cannot primarily account for the retardation with 11 < 0 since ctvv / ~ 2. The Si/(001) Si interface model advanced by Sp aepen [Spa78] is used as a basis for an atomistic picture of stressedSPEG in c onjunction with the work of Williams et al suggesting growth is a twostep process [Wil85] For island ledge migration with 11 = 0 [Figure 54(a)], a crystal island nucleates and the crystal ledges mi grate (indicated by arrows) rapidly and evenly in both inplane directions since 1 ,0 ijm is isotropic. In the case of 11 < 0 [Figure 54(b)], a crystal island nucleates and ledge migration along 1 is enhanced re lative to 2. Thus, nucleation is the limiting step for 11 0 since migration is rapid in bot h directions thus explaining why v does not change for 11 0 contradictory to the predicted behavior of Aziz et al [Azi91]. With 11 < 0 [Figure 54(c)], migration along 1 is reta rded but unchanged along 2. Thus, the growth rate is effectively halved since only migration along 2 effectively c ontributes to the growth rate. This explains why v cannot be retarded indefinitely by 11 < 0 contrary to the predictions of Aziz et al [Azi91]. Interestingly, the actual data from Aziz et al [Azi91] does show that v increases (retards) with 11 > 0 (11 < 0) in some (though not all) specimens. However, though Equation PAGE 111 111 (237) seems to describe the data from Aziz et al [Azi91], there are many significant deviations in the data from this trend and the results as a whole are somewhat weaklyordered. It is mentioned in the prior work that intrasample thermal fluctuations may have influenced the results and the analysis technique s used were less sitespecific relative those used in this study giving rise to the possible influence of intraspecimen stress gradients. Also, 11 0.6 GPa was applied in the prior work which is smaller than the range used in this study. However, while these issues may explain why the scatter in the presented work is less than prior work, it is important to note Aziz et al. [Azi91] were the first to observe and model stressinfluenced SPEG kinetics. Furthermore, the prior model [Azi91] of growth occurring via a single, unspecified process is a reasonable theory to explain the some what scattered results observed in prior work. However, Equation (518) provide s an equally reasonable explanat ion for the prior data and the model of Aziz et al [Azi91] cannot reasonably e xplain the results presented in this study. Thus, consideration of the nucl eation and migration processes during gr owth is necessary to explain the new results. Importantly, the results provide suggestions as to the atomistic nature of migration during SPEG. In particular, the large value of 11, 11mV suggests that inplane ledge motion is coordinated and involves the late ral advancement of multiple atoms along a growing island ledge [Figure 55(b)] rather than indi vidual atomic motion as originally suggested [Figure 55(a)]. Analogous coordination is observed in the deformati on of metals which is typically characterized by activation volumes on the orde r of ~100 times the atomic volume of the material [Asa05, Yan06]. Thus, 11, 11mV = (12 1) is reasonable considering migration may be coordinated and not due to independent atomic motion. PAGE 112 112 5.5 Morphological Instability An interesting result of SPEG with 11 < 0 is morphological instability of the growth interface. In fact, Equation (518) readily predicts this behavi or as well as interface roughening observed in prior studies of stressedSPEG of other materials systems. Specifically, such behavior is observed in SPEG of compressive, biaxiallystressed SiGe [Cor96, Ell96, Lee93, Hon92, Pai90]. A growth interface with perturbations under inplane macroscopic compression [Figure 56(a)] has localized concentrated inplane compressive stress (local11) in the troughs of the interface and localized tens ile stress in the peaks of the interface, since Si has a Youngs modulus nearly half that of th e crystalline counterpart [Wit93]. Thus, as per Equation (518), the peaks grow faster than the troughs and the in terface roughens. However, the application of macroscopic tension [Figure 56(b)] causes a reve rsal of the localized stress states which dampens of any perturbations in the growth interface due to kine tic limitations. Hence, this model explains observed morphological instabilities during stressedSPEG. As per Equation (518), it appe ars morphological instability with 11 < 0 is kineticallydriven and occurs due to stressinfluenced ledge migration. However, it is worth considering other possible explanations for this observation. During VPEG the phenomenon of a critical radius ( Rc) necessary for nucleation is wellestablishe d [Ter94]. The theory states that a twodimensional crystal island growing in the plane of the vapor/solid interface must achieve a radius beyond Rc to start nucleating a second cr ystal island on top of itself. Furthermore, this theory is very successful at explaining morphological instab ilities associated with the vapor phase epitaxy growth of many semiconductor systems [Rea07, Li 06, The96, Kar97]. However, the case of SPEG is inherently different from vapor phase epitaxy since the atoms used for growth in the PAGE 113 113 former case are presumably not required to diffuse any significant dist ance along the growth front. Furthermore, the Rc theory predicts complicated temperaturesensitive interface instability via a complex interplay of nucleation and surface diffusion processes which are stressindependent. In contrast, SPEG of Si is always planar (in the absence of any applied stress) for all growth temperatures [O ls88] and thus it appears Rc may not be relevant in considerations of morphological instability. Another perspective for consid ering roughening during SPEG with 11 < 0 may be that of a growth mode transition which is associated with heteroepitaxy. De pending on the strain and interface energy between the substrate and epitaxi al film, the film may grow by layerbylayer (Frankvan der Merwe), island growth (VolmerWeb er), and layerbylayer plus islands growth (StranskiKrastanow) modes [Fra49, Vol26, Str39]. Typically, the interface energy is very small for semiconductor heteroepitaxy and strain ener gy controls the film morphology during growth. Hence, it may be reasonable to consider that the application of 11 < 0 changes the growth mode from Frankvan der Merwe to VolmerWeber or StranskiKrastanow growth modes thus suggesting morphological instability during stressed SPEG of Si is straindriven as reported by others studying vapor phase heteroepitaxy [Eag90 Che96]. However, fu ndamental differences between vapor phase heteroepitaxy and solid pha se homoepitaxy suggest otherwise. During the initial stages of vapor phase he teroepitaxy, the strain is concen trated in the film while for stressedSPEG of Si the strain is uniform th roughout the substrate and film. Thus, there is effectively no strain energy cons ideration between the film and s ubstrate for stressed SPEG of Si and morphological instabilitie s in such cases cannot be strain driven. Therefore, it appears interfacial roughening during stressed SPEG is entirely kineticallydriven. PAGE 114 114 Finally, the temporal dependence of RMSR [Figure 57] is addressed. It is evident that RMSR decreases from 5.0 1.0 nm in the asimpla nted state to 3.0 1.0 nm after 4.0 h of annealing at T = 525 C with 0.0 11 1.3 GPa and there appears to be only very slight variation in RMSR with time after 1.0 h of annealing for th e case of tension. This behavior is expected since the interface is st able against perturbations with macroscopic inplane tension [Figure 56(a)]. In the cases of 1.3 11 0.25 GPa, RMSR appears to continually increase with annealing time approaching 8.0 1.0 nm after 4.0 h with RMSR apparently insensitive to the level of compression. This behavior is al so somewhat predicted [Figure 56(b)] since v at the peaks of the interface should always be faster than v in the troughs with macroscopic inplane compression as per Equation (518). However, trough annihilation likely also occurs as the interface perturbations increase and portions of the growth front impinge upon itself. Presumably, this would immediately reduce the interfaci al roughness, and RMSR would increase again after sufficient annealing time until trough annihilation again occurs and thus it may be that the evolution of RMSR with annealing time under inplane compression is somewhat cyclical in nature. Interestingly, RMSR does appear cyclical with a nnealing time in the cases of 11 = 0.25 and 0.5 GPa but not in the cases of 11 = 1.0 and 1.3 GPa [Figure 57]. Hence, greater examination of temporallydepe ndent morphological stability is needed. 5.6 Summary In summary, this study of stressedSPEG of intrinsic Si strongly suggests the currently accepted model of stressed SPEG cannot reasonably explain the stressdependent growth kinetics observed in this Chapter. To explain these results, an atomistic model of stressed SPEG kinetics PAGE 115 115 is advanced which considers growth to be medi ated by crystal island nucleation with subsequent island ledge migration with applied stress alteri ng each process differently. The results also suggest that inplane migration may involve c oordinated motion of atoms along a growing island ledge. This approach of isol ating nucleation and migration pr ocesses not only explains the observed growth kinetics, but also morphological in stabilities observed in this and prior studies of stressedSPEG. PAGE 116 116 Figure 51. WBDFXTEM images of the stressinflu enced S PEG process in intrinsic material: a) WBDFXTEM image of an asimplanted in trinsic specimen. WBDFXTEM images of intrinsic specimens annealed at T = 525 C for 4.0 h with 11 = b) 0.5, c) 1.0, d) 1.3, e) 0, f) 0.5, g) 1.0, and h) 1.3 GPa. PAGE 117 117 Figure 52. Measured stressinfluenced SPEG kinetic s in intrinsic material: plot of Si thickness versus annealing time of intrinsic samples at T = 525 C for different values of 11 as measured using WBDFXTEM. PAGE 118 118 Figure 53. The influence of stre ss o n measured growth velocity in intrinsic material: plot of v versus 11 of intrinsic samples at T = 525 C as measured using WBDFXTEM. PAGE 119 119 Figure 54. Stressinfluenced SPE G m igration processes: atomistic schematics of the inplane SPEG migration process with a) 11 = 0, b) 0 < 11 and c) 11 < 0. PAGE 120 120 Figure 55. Uncoordinated and coordinated ledge m igration: atomistic schematics of a) uncoordinated and b) coordinated le dge motion along the 1 direction. PAGE 121 121 Figure 56. Stressinfluenced growth interf ace stability: s chematics of growth interface morphological (in)stability with inplane m acroscopic a) compressi on and b) tension. PAGE 122 122 Figure 57. The temporal dependence of stressi n fluenced growth interface roughening: plot of RMSR versus anneal time for different 11 in intrinsic samples annealed at T = 525 C as measured using WBDFXTEM. PAGE 123 123 CHAPTER 6 NUCLEATION AND MIGRATION PROCESSE S DURI NG STRESSED SOLIDPHASE EPITAXIAL GROWTH OF INTRINSIC SI 6.1 Introduction From the previous Chapter, the expression derived for v as a function of 11 [Equation (518)] accounted for the atomistic nucleation and migration processes responsible for SPEG. Of course, the extracted parameters, 0n = 29 1 s, 011,m = 1.00 0.01 s, and 11, 11mV = (12 1) were calculated for growth at T = 525 C. Presumably, 11, 11mV is temperatureindependent as the atomic volumes of Si and Si are effectively invariant w ith temperature (both are solids). Of course, the same cannot be said for 10n and 1 11,0m which are Arrheniustype processes. Thus, by studying stressedSPEG kinetics at di fferent annealing temperatures, it becomes possible to determine the activation energies for nucleation, nG and migration, 11,mG, since it was assumed in the previous chapter that kT Gn n n* 1 0 1exp 0, (61) and kT Gm m m* 11, 1 110, 1 11,exp 0, (62) where 1 0 n and 1 110, m are temperatureand stressindependent prefactors. Ultimately, this provides a greater understanding of the atomistic nature of SPEG which has been extensively studied on a macroscopic scale, bu t is still somewhat poorly understood on an atomistic scale. 6.2 Experimental A polished 50 mthick impurityfree (001) Si wafer w ith room temperature resistivity > ~1 cm was Si+implanted at 50, 100, and 200 keV to doses of 115, 115, and 315 cm PAGE 124 124 2. Subsequently, samples were cleaved along <110> directions into ~0.2.8 cm2 strips and uniaxiallystressed up to magnitude of 11 1.0 0.1 GPa along the inp lane [110] direction. Stressfree, tensilelystressed, and compressivelystressed strips were annealed simultaneously at T = 500, 550, or 575 C in N2 ambient for 0.1 7.5 h. No de tectable stress relaxation occurred during annealing. The stressed strips exhibite d no detectable radii of curvature following unloading after annealing indicating no measurable plastic strain or, thus, stress relaxation. The SPEG process was examined using WBDFXTEM with specimens prepared via FIB milling. 6.3 TemperatureDependence of StressedSPEG Kinetics No significant variation in the Si thickness versus annealing time behavior was observed with 11 0 for T = 500, 550, or 575 C [Figure 61]. However, growth kinetics were retarded with 11 < 0. These observations are very sim ilar to the growth kinetics observed at 525 C as presented in the previous chapter [Figure 52]. Furthermore, the calculated v versus 11 behavior was qualitatively similar for all T in that 11 0 did not measurably change v (vt) while 11 < 0 tended to retard v to half the stressfree growth velocity (vc) [Figure 62]. Thus, vt and vc are apparently independent of T as predicted in Chapter 5. 6.4 Discussion Equation (518) was fit to the measured v versus 11 behavior for each T [Figure 62] and the values of 10n, 1 11,0m, and 11, 11mV determined as a function of T [Table 61]. For each T, the nucleation timescale is n early two orders of magnitude greater than the migration timescale which is consistent with prior suggestions from Williams et al. [Wil85]. Additionally, all timescales decrease with increasing temperature while 11, 11mV = (12 1) independently of T. It is worth noting that vt/vc is slightly less than 2 for T = 550 and 575 C. However, the fit of PAGE 125 125 Equation (518) in these cases is still within the reported errors for all v calculations and is thus quite reasonable. As proposed by Equations (61) and (62), the logarithm of 10n and 1 11,0m plotted versus the reciprocal of kT appears linear in both cases [Figure 63]. Thus, it is reasonable to fit Equations (61) and (62) to the measured 10n and 1 11,0m versus reciprocal kT data [Figure 63] producing nG = 2.5 0.1 eV,11,mG = 2.7 0.1 eV, n 0 = (4.8 0.1)016 s, and m, 110 = (2.5 0.1)18 s. 6.5 A New Atomistic Picture of SPEG The striking similarity between nG and 11,mG is interesting, since it is typically the case that the activation barrier for point defect fo rmation is larger than the barrier for migration [Fah89]. The SiSi bond energy is ~2.5 eV, for reference [Cot72]. Phys ically, it is somewhat intuitive to rationalize that nG and 11,mG should be similar for both processes and similar to the SiSi bond energy since on the most basic level, SPEG is th e rearrangement, breaking, and reforming of SiSi bonds. Thus, at the most ba sic atomistic level, nucleation and migration processes may be the same process of SiSi bond rearrangement. This rationalization also explains the observation of macG being equivalent for all s ubstrate orientations since bondrearrangement energetics are presumably orientationindependent [Cse78]. Therefore, it appears n 0 and m, 110 are almost entirely res ponsible for the differences between migration and nucleation timescales. The difference between the two prefactors may be related to the relative scales or geometry of the two processe s. In the case of nucleation, presumably only small groups of atoms must rearrange to form a crystal island to start growth The activation energy for migration is not a tensor property. PAGE 126 126 while in the case of migration large numbers of atoms along the island ledges are involved in continuing growth (coordinated motion). It is interesting to compare thes e results with the study of Williams et al. [Wil85] which showed macG for SPEG enacted via ionirradiation to be nearly an order of magnitude smaller than macG for SPEG enacted via furnace annealing si nce it was speculated that the activation barrier for nucleation was reduced during ionirradiation. However, if the activation barrier for migration was unaffected, migration would then be the limiting step during SPEG and the value of macG should still be close to ~2.7 eV. The fact that this was not the case indicates that ionbombardment influenced both nucleation and migrat ion processes to the same degree and this is a reasonable conclusion to draw since nucleati on and migration processe s both involve the same basic rearrangement of SiSi bonds. Thus, the nucleation term dominates Equation (511) due to the magnitude of n 0 and in the absence of any stress and can be reduced to kT G x vn nexp 20, (63) since mac nGG ~. Thus, 0 0/2nxv is the preexponential factor in Equation (229) with v0 = (5.8 0.5) 7 cm/s within the range of values for v0 calculated in prior work [Poa91, Ols88, Cse78]. The slightly lower value of nG compared to macG= 2.7 eV may be related to the larger relative portion of rampup time to total a nneal time in higher temperature samples as well as the larger error in SPEG rates observed with inplane compression at higher temperatures. Therefore, the observed macG for SPEG is indicative of the ratelimiting step of crystal island nucleation. PAGE 127 127 The results provide a greater understanding of the role of individua l atomistic processes on the value of macG for the epitaxial Si/Si phase transformation. Important is the observation that the activation barriers for migration and nucleation processes are nearly equivalent and similar to the Si Si bond energy. Specifically, it ha s now been revealed that the nucleation timescale was longer than migration timescale but it was not understood that the difference in the timescales was not due to ener getic considerations but only due to the relative geometric scales of nucleation compared to migration. However, it can now be advanced that the observed macG = 2.7 eV is reflective of the activation energy for crysta l island nucleation and the geometric scale of nucleation. 6.6 Summary Studying stressed SPEG at different T provided a window into examining the energetics of the nucleation and migration processes associated with growth. Interestingly, it was revealed that the activation energy was nearly equivalent for both nucleation and migration processes. This observation is somewhat intuitive since bo th processes are mediated by the breaking and reforming of SiSi bonds. Thus, it appears that the preexponen tial factors asso ciated with nucleation and migration timescal es are entirely res ponsible for the observation that the nucleation timescale is nearly two orders of magnitude greater th an the migration timescale. Furthermore, it was determined that the activat ion energy for macroscopic growth kinetics was representative of the atomistic pr ocess of crystal island nucleation as well as the geometric scale of the nucleation process. PAGE 128 128 Table 61. Nucleation and migration parameters. T n(0) m, 11(0) 11, 11mV (C) (s) (s) ( ) 500 4.1.4 1.44.10 12 525 1.0.10 0.36.03 12 550 0.28.03 0.10.01 12 575 0.11.01 0.04.01 12 PAGE 129 129 Figure 61. Effect of annealing tem perature on stressedSPEG kinetics in intrinsic material: plot of Si thickness versus annealing time of intrinsic samples at T = a) 500, b) 550, and c) 575 C for different values of 11 as measured using WBDFXTEM. PAGE 130 130 Figure 62. The influence of annealing temperat ure on the m easured stressedSPEG velocity in intrinsic material: plot of v versus 11 of intrinsic samples at T = 500 575 C as measured using WBDFXTEM. The dashed line near each data se t is Equation (518) fit to the data. PAGE 131 131 Figure 63. Temperatureinfluenced nucleati on and m igration parameters during SPEG in intrinsic material: plot of 10n and 1 11,0m of intrinsic samples versus the reciprocal of kT The dashed line near each data set is Equation (61) or Equation (62) fit to the corre sponding data set. PAGE 132 132 CHAPTER 7 DOPANTSTRESS SYNERGY DURING ST RESSED SOLIDPHASE EPITAXIAL GROWT H OF BDOPED SI 7.1 Introduction StressedSPEG of intrinsic (001) Si was studied in detail in Chapters 5 and 6. From that work, compelling evidence was produced sugges ting the growth velocity was a complicated function of inplane uniaxial stress with 11 0 causing no appreciable change in macroscopic growth kinetics and application of 11 << 0 retarding v to approximately half the value observed with 11 0. Recalling the work of Chapter 4, where stressedSPEG was studied in Asdoped Si, it was difficult to rule out the presence of As as an influence in the results, but in conjunction with the work of Chapters 5 a nd 6 it is now clear that application of 11 0 does not alter growth kinetics in d oped or intrinsic material. However, the case of 11 < 0 is not as clear and the issu e with variable As concentration in Chapter 4 was a confounding variable. In the case of stressfree SPEG of Bdoped Si, it was shown that v as a function of BCwas of the form kT EE g n C vvp n i F i B iexp1 (71) wherei FE = 0.55 eV is the intrinsic Fermi level and p nE = 0.23 0.02 eV is the acceptor energy level for B at the /crystalline inte rface in nondegenerate Si [Lu91]. From the GFLS model of dopantenhanced SPEG, individual crystal nuclei may possess charge states and thus the equilibrium planar density of nuclei will be Fermilevel dependent. Of course, this only addresses equilib rium considerations and not kine tic considerations. From an atomistic standpoint, it was shown in Chapter 5 that PAGE 133 133 xAJ v 2~0. (72) Thus, it appears that, more specifically, J is Fermilevel dependent rather than simply the equilibrium planar density of crys tal nuclei. For Bdoped material, Jis given by piJJJ, (73) where iJ and pJ are the nucleation rates per unit area of uncharged and positivelycharged nuclei, respectively. As per Equation (53), p n nuc i n nucNN J 00* *, (74) where innucN0/* and p nnucN0/*are the contributions to J from intrinsic (Ji) and positivelycharged (Jp) nuclei absent any applied st ress. Next, it is assumed pJ is given by kT EE N g NF p n i n nuc p n nucexp 0 0* (75) for dilute B concentrations, analogously to th e concentrations of uncharged and positivelycharged growthmediating defects [Equation (2 33)]. Using Equation (75), Equation (74) may be rewritten as kT EE n gC N Np n i F i B i n nuc p n nucexp 0 0* *. (76) Substituting Equation (76) into Equation (73) yields kT EE g n C N Jp n i F i B i n nucexp 1 0*, (77) and thus as per Equation (72) kT EE n gC N xAvp n i F i B i n nucexp1 0 2*. (78) PAGE 134 134 Since *nucNA ~ 1, Equation (78) is rewritten as kT EE g n Cx vp n i F i B i nexp1 0 2, (79) where 0i n is the intrinsic stressfree nucleation time. Thus, the total nucleation time, 0n is given as kT EE g n Cp n i F i B i n nexp1001 1. (710) Hence, the contributions to 0n from uncharged and positivelycharged nuclei are additive as given by 1 1 1000 p n i n n (711) where the nucleation time for positivelycharged nuclei, 0p n, is given as kT EE n gCp n i F i B i n p n1 100, (712) as per Equation (75). It was already shown th at the application of 11 does not alter 0i n as per the nature of n ijV However, the same cannot necessarily be said of 0p n. As was stated in Chapter 1, the application of stress profoundly changes the electr onic structure of Si [Bal66, Her66, Kan67, Van68, Wor64]. Thus, since dopantenhanced SPEG is accepted to be the result of electronic processes occurring at the growth interface, it is conceivable th at application of stress could alter the Si band structure such that dopants and stress are synergistic in macroscopic growth kinetics. Furthermore, it would be important to reveal an y dopantstress synergy sin ce prior work with the combined presence of dopant and stress simply assumed the dopant and stress influences on PAGE 135 135 SPEG were independent and sepa rable [Bar01, Bar04, Rud08]. Hence, assuming the GFLS model remains valid with 11 it is thus of importance to determine what, if any, effect of 11 on 1 110p n exists. Hence, this Chapter aims to study, in finer detail using careful measurements, the combined effects of dopant s and stress on SPEG kinetics using Bdoped material. 7.2 Experimental Procedures For the work of this Chapter, a polished 50 mthick impurityfree (001) Si wafer with room temperature resistivity > ~1 cm was Si+implanted at 50, 100, and 200 keV to doses of 115, 1015, and 315 cm2 and subsequently B+implanted at 60 keV to a dose of 3.515 cm2. The wafer was subsequently cleaved along <110> directions into ~0.2.8 cm2 strips and uniaxiallystressed up to magnitude of 11 = 1.0 GPa along [110]. The error in all nonzero stress measurements is estimated to be .1 GPa. Stressfree, tensilelystressed, and compressivelystressed strips were annealed simultaneously at 500 1 C in N2 ambient up to 11.2 h. No detectable stress relaxation occurred during annealing. Growth was examined using onaxis XTEM. Approximately 70 XTEM specimens ~10 m long were prepared via sitespecific FIB milling within a distance of mm from the strip centers to minimize the presence of any thermal gradient. Due to the very small specimen length to strip length ratio, it is reasonably assumed no intraspecim en stress gradients existed. 7.3 BDoped SPEG Kinetics Onaxis XTEM revealed an initial Si layer 365 5 nm thick [F igures 71(a) and (e)]. Annealing for 7.0 h with 11 = 0 resulted in 328 3 nm of growth with a planar /crystalline interface [Figure 71(f)]. EOR defects from ionimplantation were present in all samples [Jon88]. In the case of annealing for 7.0 h with 11 = 0.25, 0.5, and 1.0 GPa, 83 25, 64 PAGE 136 136 14, and 57 10 nm of growth occurred which is less than the 11 = 0 case [Figures 71(b) (d)]. The growth interface was observe d to roughen significantly with 11 < 0, presumably due to kineticallydriven instabilities as reported in Chapter 5. In contrast, annealing with 11 = 0.5 and 1.0 GPa [Figures 71(g) and (h)], produced nom inally the same amount of growth as the 11 = 0 case. These observations are qualitatively cons istent with the work of Asdoped intrinsic stressed SPEG in Chapters 4 6. The Si thickness as a function of anneal time was measured for different 11 [Figure 72]. The implanted BC profile as measured using SIMS is superimposed indicating a peak BC of ~3.020 cm3 ~200 nm deep. The diffusivity of B in both Si and Si at 500 C is sufficiently low such that negligible B redi stribution during annea ling is reasonably assu med [Fah89, Jac06]. In cases of 0 11 1.0 GPa, the Si thickness versus time behavior was nominally the same for all 11 in this range and thus only the 11 = 0 set of data is reported for clarity. The growth kinetics for 11 < 0 were greatly retarded compared to the 11 0 cases. For all 11 the growth kinetics appear to vary with anneal time and increase with BC as reported by others [Joh07]. The v versus BC behavior for different 11 [Figure 73] was estimated from the data of Figure 72 using the following met hod: 1) the average growth rate between two subsequent anneal times was calculated as the change in Si thickness between the anneal times divided by the time interval (this is the reported v) and 2) the median value of BC over the Si thickness interval was obtained (t his is the reported BC). For all BC, v was unchanged with 11 > 0 and retarded for 1.0 11 0.25 GPa. Recall from Chapters 5 and 6 that v (in intrinsic material) as a function of 11 had finite PAGE 137 137 limits. In the case of 11 0, v approaches the tensile saturation velocity 102~i n txv [Equation (519)] while in the case of 11 << 0, v approaches the compressive velocity limit 10~i n cxv [Equation (520)] and thus ctvv / ~ 2 [Equation (521)]. It is also evident clear tv and approximate cv limits at a given BC are observed [Figure 73]. However, the estimated ctvv / for lower BC is near 2 (as in the intrinsic case) but ctvv / ~ 6 as BC increases past ~1.520 cm3 [Figure 73]. 7.4 Discussion Since v versus BC is constant for 11 0 it is reasonable to extend Equation (79) to tvv Equation (79) was fit to the tv data in Figure 73 using LSR analysis (assuming stressindependent in ~ 1017 cm3 [Gre90]) producing 0i n = (9.0 0.5) 103 h, g = 1.0 0.1, and E = 0.34 0.02 eV where E =i FEp nE, (713) The values of g and E are in agreement with those from the GFLS model [Joh07]. Thus, it appears 11 > 0 does not appreciably alter i FEp nE. The results also support the assumption of in being stressindependent [Figure 74(a) ]. However, considering the vast body of prior work regarding stressinduced band st ructure changes [Bal66, Her66, Kan67, Van68, Wor64], it may also be the case that application of 11 > 0 induces compensa ting alterations to i FE and p nEsuch that i FEp nE remains constant. Therefore, in the case of Bdoped Si, 102~p n txv, (714) as nucleation kinetics do not appear to be influenced by 11 > 0. Thus, as per the observed PAGE 138 138 ctvv / values, 1 110 ~ p n cxv, (715) in Bdoped Si where 1 1 110~0 3 p n p n (716) In intrinsic SPEG, 11 does not alter nuclea tion kinetics as per n ijV advanced in Chapter 5. Presumably, n ijV for charged nuclei is of the same form. Thus, an explanation for the retarded nucleation kinetics with 11 << 0 is due to stressinduced changes in the Si band structure. Specifically, assuming the GFLS model is valid for inplane compression, it therefore appears that 11 < 0 increases in and/or increases i FEp nE [Figure 74(b)]. The results of this study suggest dopan t and stress influences in SPEG may be synergistic. This is an importa nt result as prior work of comb ined dopantand stressinfluenced SPEG assumed the two influences were independent [Bar01, Bar04, Rud08]. In particular, such synergy would be important to consid er in any SPEG simulations [Mor08]. Of course, there are several challenges in this work. Accurately characterizing v as a function of BC with a variable dopant profile is difficult, especially due to the exsitu nature of the experiments. Another issue is growth interface roughening with 11 < 0 which is partly stressdriven, but is also dopa nt gradientdriven as reporte d by BarvosaCarter and Aziz [Bar01]. Furthermore, the work of intrinsic SPEG with 11 << 0 in Chapters 5 and 6 observed roughening nearly an order of magnitude less than that observed herein. A possi ble way to avoid these issues in future work would be to use Si wafers with epitaxial layers with constant BC. 7.5 Summary In summary, the influence of combined dopantand stressinfluenced SPEG of PAGE 139 139 amorphized (001) Si was investigated using Bdo ped (001) Si subjected to inplane uniaxial stress. As per the GFLS model of dopantenh anced SPEG, it appears stress may alter the Si electronic structure such that dopa nt and stress influences are syne rgistic in growth kinetics. Specifically, this synergy becomes apparent in cases of inplane uniaxial compression. PAGE 140 140 Figure 71. Onaxis XTEM images of the stresse dSPEG process in Bdoped m aterial: a) and e) onaxis XTEM images of an asimplanted Bdoped specimen. Onaxis XTEM images of Bdoped specimens annealed at T = 500 C for 7.0 h with 11 = b) 0.25, c) 0.5, d) 1.0, f) 0, g) 0.5, and h) 1.0 GPa. PAGE 141 141 Figure 72. Stressinfluenced SPE G kinetics in B doped material: Si thickness versus anneal time behavior of Bdoped material at T = 500 C for different11 as measured using onaxis XTEM superimposed on the SIMSdetermined BC profile. PAGE 142 142 Figure 73. Measured growth velocities in stressedSPEG of Bdope d m aterial: plot of v versus BC at T = 500 C for Bdoped material for different 11 [estimated from Figure 72 data]. PAGE 143 143 Figure 74. Possible band structures for the interface between Bdoped Si and Si for different stress states: with a) 0 11 (tension) and b) 11 > 0 (compression). PAGE 144 144 CHAPTER 8 EXTENSIONS OF THE SOLIDPHASE EPIT AXIAL GROWTH M ODEL TO EXPLAIN PRIOR OBSERVATIONS 8.1 Prior SPEG Observations It was first mentioned in Chapter 2 that island nucleation and ledge migration are both responsible for controlling macr oscopic growth kinetics. This was extended to explain the growth kinetics of intrinsic and doped (001) Si under application of inp lane uniaxial stress as presented in Chapters 5 7. However, while th e developed mathematical model is successful at explaining these specific stressedSPEG results, it is important to determine if said mathematical construct can be extended to explain other welle stablished SPEG phenomena. Specifically, the influence of electricallyinactive impurities as well as pure hydrostatic and normal uniaxial compressive stress on growth kinetics must be addressed. 8.2 ElectricallyInactive Impurities 8.2.1 OInfluenced SPEG It was revealed in Chapter 2 that the introduction of electrica llyinactive impurities during the SPEG process can dramatically retard gr owth kinetics [Ken77, Rot90]. Specifically, this effect appears to be due to changes in ledge mobility rather than changes in nucleation kinetics as electricallyinactive impurities do not appreciably alter the Fermi level, in contrast with active impurities [Joh07]. Thus, 1 10~0 i n n in cases of inactive impurities. However, the same cannot be said for the migration timescale. Using O as an example, it is advanced that 00 1 011, 11, 1 11,O m i m m (81) where 011,O m is the contribution to the migration timescale from O. Physically, 011,O m can be thought of as the time between ledgeimpurity intera ctions along the 1 direc tion. It is reasonable PAGE 145 145 to predict that 1,mv, will be slowed by the presence of im purities on the growth interface since it presumably takes additional time to incor porate and accommodate an impurity atom into a moving island ledge. The planar density of O at the /crystalline in terface is ~3/2OC where OC is the bulk O concentration at the growth front and each O at om has an influential radius (diameter) of OR (02 R). Thus, it is expected 3/2 1, 11,2 1 0OOm O mCRv, (82) or 3/2 11,1 0O O mC (83) The proportionality of Equation (83) may be scaled with 011,i m as given by 3/2 0 11, 11,00 O O i m O mC C, (84) and thus 1 3/2 0 1 11, 1 11,10 0 O O i m mC C (85) as per Equation (81) where 0OC is the O proportionality c onstant for a given growth temperature. Presumably, each impurity has an associated proportionality constant where a larger proportionality constant implies a weaker sensitivity of ledge migration to content of the specific impurity. Combining Equations (511) and (85), v as a function of OC is given by PAGE 146 146 3/2 0 11, 2/31020 2O O i m i nC C x v (86) Fitting Equation (86) to the v versus OC data from Kennedy et al. [Ken77] at the annealing temperature of 550 C produces 0i n = 1.9 0.1 s, 011, i m = (8.9 0.9)2 s, and 0 OC = (4.2 0.1)17 cm3 with good agreement between the mode l and the results [Figure 81]. Importantly, 0i n/011, i m ~ 30 similar to the case of intrinsic SPEG presented in Chapters 5 and 6. 8.2.2 FInfluenced SPEG Olsen and Roth [Ols88] studied the influen ce of F on SPEG kinetics and an annealing temperature of 625 C and determined, similar to the Oinfluenced SPE G results from Kennedy et al. [Ken77], that F dramatically retards SPEG kineti cs [Figure 82]. In the case of F, Equation (86) can be rewritten as 3/2 0 11, 2/31020 2F F i m i nC C x v (87) where FC is the F concentration and 0 FC is the F proportionality constant. Fitting Equation (87) to the Finfluenced SPEG data from Olsen and Roth [Ols88] produces 0i n = 0.11 0.01 s, 011, i m = (3.7 0.4)3 s, and 0 FC = (4.0 0.3)15 cm3 [Figure 82]. The fit of Equation (87) to the reported data is very strong and the observation that 0i n/011, i m ~ 30 is, once again, consistent with the prior work of intr insic SPEG from Chapters 5 and 6. The smaller value of 0 FC compared to 0 OC indicates that SPEG kinetics are more sensitive to F than O. However, direct comparison of the two proportionality constants is difficult si nce both sets of O PAGE 147 147 and Finfluenced SPEG data were collected at different anne aling temperatures and using different methods. However, and more importantly, it appears the mathematical construct used to explain stressinfluence SPEG results can also be reason ably extended to explain the retarded SPEG kinetics observed with elect ricallyinactive impurities. 8.3 Pure Hydrostatic Compressionand Normal Uniaxial Compressionenhanced SPEG Explaining the compelling evidence that SPE G kinetics are exponentiallyenhanced with application of pure hydrostatic compression [Lu9 1] and normal uniaxial compression [Bar98] to the same degree within the mathematical construct presented in Chapter 5 first requires a comparison of n ijV and ijm klV,. In the former case, only nV33 is nonzero while the inplane term, nV11, is negligible. Thus, it is predicted that application of pure hydrostatic compression and normal uniaxial compression s hould alter the nucleation time s cale equivalently. However, in the case of ijm klV,, it is possible that the migration time scale may be altered differently for each type of stress state. For a general case of ij, v for (001)oriented SPEG is given by kT V V V kT V x kT V V V kT V x vm m m m n n m m m m n n 33 11, 33 22 11, 11 11 11, 22 11, 3333 33 11, 33 22 11, 22 11 11, 11 11, 3333exp0 exp0 exp0 exp0 (88) Reasonably neglecting the tr ansverse coefficient of ijm klV, further reduces Equation (88) to PAGE 148 148 kT V V kT V x kT V V kT V x vm m m n n m m m n n 33 11, 33 22 11, 11 11, 3333 33 11, 33 11 11, 11 11, 3333exp0 exp0 exp0 exp0 (89) In the case of pure hydrostatic stress, Equa tion (89) may be further simplified to kT VV kT V x vm m m n n 11, 33 11, 11 11, 33exp0 exp0 2, (810) while in the case of normal uniaxial stress, Equation (89) simplifies to kT V kT V x vm m n n 33 11, 33 11, 3333exp0 exp0 2 (811) For both pure hydrostatic compression and normal uniaxial compression, it was shown that a single timescale process with an activation volume of (0.28 0.03) reasonably described the response of v to both stress states [Equations (2 36) and (243)]. Here, it is advanced that this activation volume is actually equivalent to nV33 since, as was shown in Chapters 5 and 6, the nucleation timescale is inhe rently limiting in SPEG kinetics. However, as per Equations (810) and (811), this implies that both stress states are enhancing migration kinetics such that the migration timescale e ssentially becomes negligible in determining macroscopic growth kinetics. It was revealed in Chapters 5 and 6 that 11, 11 mV = (12 1) implying inplane expansion associated with ledge migration. However, it is necessary to also consider the out of plane activation volume, 11, 33 mV. Equation (810) was fit to Equation (236) [Lu91] for different PAGE 149 149 values of 11, 11 mV+11, 33 mV using T = 525 C, v(0) = 34 nm/h, n(0) = 29 s and m, 11(0) = 0.36 s as calculated in Chapter 5 [Figure 83]. In the case of 0 < 11, 33 11, 11m mVV, both Equations (236) and (810) match well for lower values of pure hydrostatic compression, but Equati on (810) predicts lowe r SPEG rates at higher stresses than predicted by Equa tion (236). In contrast, when 11, 33 11, 11m mVV 0, the two models match quite well for all values of pure hydrostatic compression. T hus, there may be a net volumetric contraction associated wi th the migration transition state. This is consistent with the observation that Si is less dense than the crysta lline counterpart [Cus94]. Thus, 11, 33 mV must be on the order of 12 which is very large, similarly to the inplane term, but this value may once again be reasonable considering the like lihood of coordinated migration proposed in Chapter 5. Hence, if 11, 33 mV < 0 and is of sufficient magnitude Equations (810) and (811) both reduce to kT V x vn n 3333exp 0 2 (812) for both pure hydrostatic compression and normal uniaxial compression, thus explaining the observations from Chapter 2 that both stress states enhance v in nominally the same qualitative and quantitative manor. Hence, though the mathematical construct presented in Chapter 5 was developed to explain the results of SPEG with inplane uniaxia l stress, the same model can be easily extended to explain the results of other stress states and is therefore selfconsistent. 8.3 Summary In summary, the prior model used to explai n the stressinfluenced SPEG results presented PAGE 150 150 in Chapters5 7 was extended to explain prior results regarding impurityretarded SPEG and pure hydrostatic/normal uniaxial comp ressive stressenhanced SPEG. It appears that the model is able to be reasonably extende d to address these prior results while remaining selfconsistent. PAGE 151 151 Figure 81. Extension of the presented model to explain Oinfluenced SPE G kinetics: plot of (001)oriented v versus CO at T = 550 C as measured using RBS [Ken77] with the predicted behavior of Equation (86). PAGE 152 152 Figure 82. Extension of the presented model to explain Finfluenced SPEG kinetics: plot of (001)o riented v versus CF at T = 625 C as measured us ing TRR [Ols88] with the predicted behavior of Equation (87). PAGE 153 153 Figure 83. Extension of the presented model to explain prior observati ons of pure hydrostatic com pressive stressinfluenced SPEG kineti cs: plot of predicted (001)oriented v versus behavior at T = 525 C using Equation (236) [Lu91] and using Equation (810) with different values of 11, 33 11, 11m mVV. PAGE 154 154 CHAPTER 9 SUMMARY AND FUTURE WORK 9.1 Overview of Results In this work, the influence of inplane [ 110] uniaxial stress on the solidphase epitaxial growth of (001) Si was studied in intrinsic and doped material. Initial experiments in Asdoped material showed that the density of growthrela ted defects was influen ced by the level of inplane applied during growth. Inte restingly, it was also revealed that stressinfluenced growth kinetics could not be explained by a prior model of stressed epitaxial growth. Specifically, it was shown that inplane tension did not alter the growth kinetics while inplane compression retarded the kinetics. In intrinsic material, it was revealed that th e qualitative behavior of the growth kinetics was very similar to that in Asdoped material. Once again, inplane tension did not change growth kinetics and inplane co mpression retarded growth kinetics. Furthermore, it was shown that the growth interface velocity was a complicated function of inplane uniaxial stress, where the velocity has finite limits in tension and co mpression. This behavior was explained using a atomistic model of growth kinetics with the a ssumption of growth being a twostep process (island nucleation and subsequent ledge migration) and applie d stress altering each process differently. It was also shown that coordinated motion may play a role in ledge migration. Interfacial roughening with inplane compression was also show n to be readily predicted by the atomistic model of stressedgrowth kinetics. Importantly, the application of stress dur ing growth allowed for isolation of the timescales associated with nucleation and mi gration processes. Thus, by studying stressed growth at many temperatures, the activati on energy of each process was determined. Interestingly, the activation energy (~2.7 eV) wa s nearly identical for each process and very PAGE 155 155 close to the observed activation en ergy for macroscopic stressfree growth (2.7 eV). From these results, a new atomistic picture of solidphase epitaxial growth was advanced which is based on the central premise that nucleation and migratio n are both the same inhe rent process of SiSi bond rearrangement and differ only by the activation volume for each process. Further work attempted to address the eff ect of stress on dopante nhanced growth in Bdoped Si. Once again, it was shown that inplane tension did not alter the growth kinetics while compression retarded growth kinetics, similarly to Asdoped and intrinsic Si However, the ratio of the growth velocity in tension to that in compression for a given B concentration tended to increase with increasing B concen tration. Thus, as per prior work suggesting stress influences the electronic properties of Si, it was advanced that inplane stress was altering the acceptor state of B at the growth interface. Ultimately, this implies dopant and stress in fluences are synergistic in terms of macrosc opic growth kinetics. It was also shown that the atomistic model could also be reasonably extended to explain retarded SPEG kinetics resulting from the presen ce of electricallyinactive impurities as well as the enhanced SPEG kinetics observed with pur e hydrostatic and normal uniaxial compressive stress. Thus, the presented work provides insight into not only the stressed solidphase epitaxial growth process, but the gene ral atomistic nature of solidphase epitaxial growth 9.2 Technological Significance and Future Work The technological importance of stressedSPEG is evident as SPEG and the incorporation of stress into device fabrication continue to remain commonplace. Moreover, the lack of study of stressedSPEG appears to be a large oversight on the part of the IC fabrication community. Furthermore, this work has shown that stress can have complicated and farreaching effects on the nature of the SPEG process which clearly needs to be accounted for in processing. However, PAGE 156 156 though this work has provided significant f undamental advancement and understanding of stressedSPEG, there are many paths for worthwhile future work which need to be explored. Notably, there is growing interest in the simulation of the SPEG growth process [Pha01, Mor08] and it would thus be interesting to e xplore simulation of the stressedSPEG process to see if the results observed herein could be reproduced. In prior work by Phan et al. [Pha01], the (001)oriented stressedSPEG process was simula ted using levelset methods, but under the assumption that the activation strain tensor model of stressinfluenced SPEG from Aziz et al [Azi91] was correctly describing the macroscopic nature of stressed growth kinetics. As has been shown in this work, the Aziz et al. model fails to account for the presented observations and thus new simulations of the stressedSPEG process are needed. It is also important to note that (001)orie nted SPEG was studied in this work. However, that is not to say that (001) Si the only technologicallyrelevant wafer orientation. In particular, there is growing interest in the use of (011)ori ented Si due to greater possible enhancements to device performance (both intrinsically and exploi ted by stress) [Col68, Sa t69]. Some initial work into the nature of the (011)oriented SPEG process has been conducted [Sae05, Sae06, Yan05], but the nature of stressed (011)oriented SPEG remains unknown. In fact, it is entirely foreseeable that the nature of the activation vo lumes associated with nucleation and migration processes could be different for (011) Si which could potentially give rise to vastly different stressdependent growth kinetics (compared to (001) Si). Thus the study of stressed (011) SPEG would certainly be worthwhile in future work. In Chapter 5, it was suggested that the e volution of roughening of the growth interface with inplane macroscopic compression may be cyclical in nature. However, due to the exsitu nature of this work, detection of any cyclical behavior in mo rphological instability is very PAGE 157 157 challenging. Thus, insitu analysis techniques would be necess ary to conduct a detailed study of the temporal dependence of interf ace instability. However, the sens itivity and sitespecificity of most insitu analysis techniques which c ould be used for such work are meager compared to the FIB/XTEM method used herein. Thus, characteriza tion of timedepending interface instability is worth future investigation, but it is unclear as to what analysis technique will prove best for studying this phenomenon. It was suggested in Chapter 7 that dopants and stress may be synergistically influencing growth kinetics via stressinduced changes to the Si band structure. Specifically, it appears that stress may be influencing the dopant acceptor leve l at the growth interface. Of course, it is somewhat challenging to accurately measure th e growth velocity as a function of dopant concentration when the dopant conc entration profile is variable w ithin the wafer. Thus, it would certainly be worth repeating the study of the co mbined influence of stress and dopants on growth kinetics using wafers with epita xial layers with c onstant dopant concentr ation (using VPEG). Doing this would eliminate much of the c onfounding problems associated with measuring growth kinetics in material with variable dopant concentration. Hence, it may be possible to determine the exact nature of the stressi nduced change to the acceptor energy level. Thus, there are many possible future dire ctions for the study of stressedSPEG, both theoretical and experimental and as the combined use of SPEG and stress in device processing continues, it will certainly be necessary and wo rthwhile to continue studying the stressedSPEG process. PAGE 158 158 LIST OF REFERENCES [Ade88] W. O. 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Goldman studying the growth and characterization of GaAsbased thin film semiconductors which sparked his continued interest in crystal growth processe s. After graduating from the University of Michigan, Summa Cum Laude, in Ma y 2005, he had to decide between enrolling in the applied physics Ph. D. program at Harvard University in Boston, Massachusetts or the materials science and engineering Ph. D. program at the University of Florida in Gainesville, Florida. He initially favored Harvard, but decided to enroll at the Univ ersity of Florida after meeting with potential adviser Dr. Kevin S. Jones. Upon completing his Ph. D. degree, he plans to pursue a postdoctoral research opportun ity and eventually become a facult y member at a Tier I materials science and engineering progr am in the United States. 