Modeling of the Sublimation Growth of Silicon Carbide ... - staff.csc.fi

Department of Engineering Physics and MathematicsHelsinki University of TechnologyFIN-02015 HUT, FinlandModeling of the Sublimation GrowthofSilicon Carbide CrystalsPeter RåbackDissertation for the degree of Doctor of Technologyto be presented with due permission for public examination and debatein Auditorium E at Helsinki University of Technology (Espoo, Finland)on the 30th of June 1999, at 12 o’clock noon.CSC Research Reports R01/99Center for Scientific Computing, Espoo 1999

Contents1 Introduction 12 General Information on SiC 32.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Crystalline Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 42.3 Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Defects in SiC Crystals . . . . . . . . . . . . . . . . . . . . . . . . . 62.5 Information Resources . . . . . . . . . . . . . . . . . . . . . . . . . 73 Growth Techniques for SiC Crystals 83.1 Growth from Melt . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83.2 Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . 93.3 Lely Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.4 Seeded Sublimation Growth . . . . . . . . . . . . . . . . . . . . . . 104 SiC Growth Modeling 144.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.2 This Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Physical Models 175.1 Equilibrium Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . 175.2 Mass Transport of Reactive Gases . . . . . . . . . . . . . . . . . . 205.3 Adsorption and Desorption . . . . . . . . . . . . . . . . . . . . . . 225.4 Temperature Distribution . . . . . . . . . . . . . . . . . . . . . . . 235.5 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Numerical Models 286.1 Equilibrium Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . 296.2 Temperature Distribution . . . . . . . . . . . . . . . . . . . . . . . 336.3 Diffusion of Reactive Gases . . . . . . . . . . . . . . . . . . . . . . 376.4 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426.5 Virtual Crystal Growth . . . . . . . . . . . . . . . . . . . . . . . . . 44v

6.6 Feedback Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 456.7 Coupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 Verification and Evaluation 507.1 Equilibrium Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . 517.2 Diffusion of Reactive Gases . . . . . . . . . . . . . . . . . . . . . . 537.3 Temperature Distribution . . . . . . . . . . . . . . . . . . . . . . . 547.4 Induction Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567.5 Feedback Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 587.6 Coupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588 Simulation Results 618.1 Equilibrium Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . 618.2 Diffusion of Reactive Gases . . . . . . . . . . . . . . . . . . . . . . 728.3 Temperature Distribution . . . . . . . . . . . . . . . . . . . . . . . 828.4 Coupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928.5 Virtual Crystal Growth . . . . . . . . . . . . . . . . . . . . . . . . . 959 Synthesis of Simulation and Practice 979.1 A Practical Model for the Growth Rate . . . . . . . . . . . . . . . . 979.2 Optimization of the Crystal Growth Process . . . . . . . . . . . . 10410 Conclusions 10710.1 About this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10710.2 About Sublimation Growth of SiC Crystals . . . . . . . . . . . . . 109A Transport Properties 111B Villars-Cruise-Smith Method 113C Weakly Coupled Induction Heating 114vi