Multi length Scale Modeling of CVD of Diamond Films M Grujicic and S G Lai Departments of Mechanical Engineering Clemson University Abstract Chemical Vapor Deposition CVD of singlecrystalline and polycrystalline diamond films in a rotating disk hot filament reactor is analyzed by combining a reactor scale fluid flow heat transfer reactive gas continuum model with an atomic scale kinetic Monte Carlo model and in turn with a grainscale model Such a multi length scale modeling scheme is found to be very instrumental in predicting the effect of processing conditions on the film deposition rate surface morphology crystal defects formation grain structure and crystallographic and morphological texture Multi length Scale Approach Grain Scale Atomic Scale Reactor Scale Bond Scale Laboratory Scale Processing Reactor scale Modeling of CVD Deposition of Diamond Films Rotating disk Hot filament CVD Reactor Governing Differential Equations Boundary Conditions Chemical Reactions In Gas At the Substrate Film Surface Typical Results Rotating disk Hot filament CVD Reactor Inlet Gas Heater Substrate Governing Differential Equations Mixture Continuity Mass Conservation Dependent Variables u z V z v z r W z w z r T z Yk z k 1 Kg 1 Zl l 1 Ks 1 am m 1 Kb 1 Radial Momentum Conservation Circumferential Momentum Conservation Thermal Energy Balance Species Continuity Boundary Conditions At the Heating Element Boundary Conditions cont d At the Substrate Additional Relations in Gas Phase Additional Relations in Gas Phase cont d Additional Relations at the Substrate Additional Reactions at the Substrate cont d Additional Reactions at the Substrate cont d Gas phase Chemical Reactions M the effect of third body collisions Surface Chemical Reactions G gas species S surface species R1 R2 R3radicals D diamond Chemical Reactions cont d Possible Reaction Paths at the Substrate Fi l Surface More Likely a c d e Reactions Involved b c c f Less Likely 111 Chemical Reactions cont d Possible Reaction Paths for the Trough Insertion Mechanisms at the Substrate Film Surface a b Reactions Involved c c d d More Likely Less Likely 100 Typical Results Processing Conditions Theat 2000 K Tsubs 1000 K p 20 Torr CH4 0 4 H2 92 5 L 1 3 cm 111 100 100 111 H C2H2 100 CH4 111 CH3 100 111 Typical Results cont d Atomic scale Atomic scale Reactor scale Reactor scale Chu et al 20 100 100 111 111 Atomic scale Modeling of CVD Deposition of Diamond Films Deposition Mechanisms Surface Reconstruction Point Line and Planar Crystal Defects Rigid lattice Substrate Kinetic Monte Carlo Method Deposition Mechanisms Island Formation 111 Deposition Mechanisms cont d Edges Kinks 111 Deposition Mechanisms cont d Dimer Insertion 100 Deposition Mechanisms cont d Trough Insertion 100 Deposition Mechanisms cont d BCN 100 100 Surface Reconstruction 100 2x1 H 100 1x1 100 2x1 111 Surface Reconstruction 1D 111 2x1 H 1D 111 1x1 H 1D 111 2x1 111 Surface Reconstruction 3D 111 2x1 H 3D 111 1x1 H 3D 111 2x1 111 Surface Reconstruction 3D 111 V3 x V3 R30 3D 111 1x1 3D 111 V3 x V3 R30 STM of 100 Facets of Polycrystalline Diamond 10 nm 3 nm TS 1273K 1 2 100 2x1 H TS 1093K 1 5 Busmann and Hertel Carbon 36 1998 391 100 2x1 STM of 111 Facets of Polycrystalline Diamond 1 nm 1D 111 1x1 H TS 1273K 1 2 2D Fourier Transform Busmann and Hertel Carbon 36 1998 391 1 nm 1D 111 2x1 H STM of 111 Facets of Polycrystalline Diamond 4 nm 3D 111 2x1 H TS 1273K 1 2 2D Fourier Transform Busmann and Hertel Carbon 36 1998 391 2 nm 3D 111 V3 x V3 R30 Point type Crystalline Defects 111 Vacancy Entrapped H 100 Line and Plane type Crystalline Defects Dislocation Isomer 111 Twin Rigid lattice Substrate 100 111 Kinetic Monte Carlo Method Event Selection Scheme I C A G E H D B F 0 1 Variable Time Increment Site Reaction Event Transitional Probability 1 0 1 Typical Results 0 87s 1 85s 2 01s 2 85s 111 Typical Results cont d N D T 0 87s T twin D dislocation N nucleus I island G gap 2 01s I I G T 1 85s T 2 85s 111 Short Movie Patch Atoms 111 Typical Results cont d 0 1s 0 18s 0 32s 2 08s 100 Typical Results cont d D B T 0 1s 0 18s T B D D dimer ins T trough ins B BCN 0 32s 2 08s 100 Short Movie The Atoms Family 100 Typical Results cont d 100 111 31 2v 100 v 111 Typical Results cont d 111 100 Entrapped Hydrogen Long Time Short Time Vacancies 111 Grain scale Modeling of CVD Deposition of Diamond Films SEM of Diamond Single Crystals 100 111 based Idiomorphs SEM based Determination of Growth Rate Parameter SEM of Polycrystalline Diamond Films 3D and 2D Nuclei and Vertex Velocities Van der Drift 2D Model Grain Microstructure Evolution Evolution of Grain Size and Grain size Distribution Growth Rate of Polycrystalline Diamond Films Evolution of Surface Roughness Texture Evolution 100 vs 111 facet Grown Film Sectors Evolution of Defect Density and Content SEM of Diamond Single Crystals TS 1273K 1 2 1 m TS 1073K 2 3 TS 1093K 1 5 3 m TS 993K 2 9 1 m Busmann and Hertel Carbon 36 1998 391 1 m 100 111 based Idiomorphs 111 1 0 1 5 110 100 a 1 5 1 0 1 5 3 0 3 0 SEM based Determination of Growth Rate Parameter 1 0 1 5 a1 100 a2 3a1 2a1 a2 1 5 3 0 b1 111 b2 1 5b2 2b1 b2 1 5 Effect of Substrate Temperature on Growth Rate parameter NEEDS UPDATE Busmann and Hertel Carbon 36 1998 391 SEM Micrographs of Polycrystalline Diamond Films TS 1273K 1 2 TS 1093K 1 5 1 m TS 1073K 2 3 1 m TS 993K 2 9 Busmann and Hertel Carbon 36 1998 391 SEM Micrographs of a Polycrystalline Diamond Film thickness 4 m thickness 22 m 2 9 Effect of Film Thickness Y von Kaenel et al Phys Stat Sol 154 1996 219 Types of 3D Nuclei 3D2 3D1 3D4 3D3 3D and 2D Nuclei and Vertex Velocities Van der Drift 2D Model Determination of Vertex Velocity Components 111 111 100 100 Nucleus 2D3b Substrate Evolution of Grain Microstructure 1 0 1 05 767 111 1 Evolution of Grain Microstructure cont d 110 1 5 Evolution of Grain Microstructure cont d 100 3 0 5901 2 95 Evolution of Grain Size Evolution of Grain Size cont d Grain Size Distribution 1 5 Film Growth Rate Evolution of Surface Roughness Initial Evolution of Texture 1 05 2 95 1 0 1 5 3 0 Evolution of Texture cont d 100 vs 111 facet Grown Film Sectors Evolution of Defect Density and Content Conclusions By proper coupling of the models the chemical vapor deposition rates for single crystalline diamond films predicted by the reactor and atomic scale models can be made mutually consistent The atomic scale models are very instrumental in elucidating the rate controlling surface reactions and deposition mechanisms and in