Modeling of SiC single crystal growth in PVT reactor T. Wejrzanowski, J. Dagiel, M. Grybczuk, J. Niescior, K.J. Kurzydlowski Faculty of Materials Science and Engineering Warsaw University of Technology Woloska 141 str., 02-507 Warsaw, Poland e-mail: twejrzanowski@inmat.pw.edu.pl E. Tymicki Institute of Electronic Materials Technology Wolczynska 133 str., 01-919 Warszawa, Poland
Outline of the presentation 1. The purpose of the studies 2. The scope of the studies 3. The methods Model of the reactor geometry Finite Volume Method Implementation of the reactions Dislocation evolution model 4. Results and experimental verification 5. Summary
The purpose of the studies Optimization of SiC monocrystal growth process by computer modelling Silicon carbide polycrystal (left) and monocrystalline SiC wafers (right). Source: ITME
Thescopeof thestudies Optimization of the thermal conditions by modifications of the reactor geometry Different solutions related with geometry of insulation Optimization of the process conditions Temperature and temperature gradient Pressure
Virtual Reactor and reactor model Geometry Two-dimensional Axisymmetric Boundary conditions Temperatures Chemical activity Heat transfer Conductivity Convection radiation
Reactor model Seed crystal Source Graphite Argon Temp. measuring point Upper resistive heater
Image fromhttp://www.iue.tuwien.ac.at/phd/heinzl/node25.html Finite Volume Method Piecewise constant cell average for each control volume: Approximation of flux integral by a quadrature rule: Mesh density decreases with distance from the furnace axis. Less crucial parts, like outermost thermal inslulation, are less densly covered what simplifies calculations. (VR
Image from http://www.iue.tuwien.ac.at/phd/heinzl/ Heat Transfer Model Heat conduction in solids: Heat flux at the constant wall temperature boundary: Finite Volume Method has been utilized for heat transfer in the simulation Mesh density decreases with distance from the furnace axis. Less crucial parts, like outermost thermal inslulation, are less densly covered what simplifies calculations. (VR
Implementation of the reactions Gas phase consists of Si, Si 2 C, SiC 2 and Ar Reactions at crystal surface
Dislocation evolution model Threading dislocation traces, cut through crystal axis (above) Threading dislocation density mapping, 7mm from the seed sufrace (left) Output from VirtualReactor E seg = Kα ( ) L ( α) seg
Insulation geometry Narrow opening Wide opening 1 to 1 1 to 3 Low graphite plates High graphite plates
Insulation and heater power Comparison of simulated and experimentally obtained heater power in accordance to insulation geometry 25000 20000 power [W] 15000 10000 5000 0 all narrow opening all wide opening 1 to 1 1 to 3 with graphite plates higher insulation configuration with graphite plates lower upper heater (sim) lower heater (sim) upper heater (exp) lower heater (exp)
Insulation and seed temperatures 2320 Temperature distribution on the crystal surface in dependence on insulation geometry T [C] 2300 2280 2260 2240 2220 All wide opening All narrow opening Insulation 1 to 1 Insulation 1 to 3 2200 0 5 10 15 20 25 30 Distance from crystal axis [mm]
Growth rate The aim Investigation of crystal growth rate evolution in time Examination of pressure impact on growth rate Examination of temperature and temperature gradient impact on growth rate
Growth rate
The effect of pressure on crystal growth crystal thickne ess [mm] 12 10 8 6 4 2 0 Crystal thickness increase in time for various process pressures model 50 mbar model 75->20 mbar experiment 80->20 mbar 0 20 40 60 80 100 120 140 time [h]
The effect of pressure on growth rate Growth prędkość wzrostu rate [mm/h] Growth Prędkość rate wzrostuin time for various pressures 20 mbar model 50 mbar model 0.14 75 mbar model 80 mbar exp 0.12 20 mbar exp 0.1 0.08 0.06 0.04 0.02 0 0 10 20 30 40 50 60 70 Process czas trwania time procesu [h] prędkość Growth wzrostu rate [mm/h] [mm/h] 0.14 0.12 0.1 0.08 0.06 0.04 0.02 Growth rate comparison between experiment and simulation Prędkość wzrostu w zależności od ciśnienia model exp 80 mbar exp 20 mbar 0 0 20 40 60 80 100 120 Process pressure [h] ciśnienie [mbar]
Pressure and dislocations 40 mbar 20 mbar dislocation density [1/cm 2 ] 30000 25000 20000 15000 10000 5000 Comparison of dislocation densities as a function of distance from crystal axis. Cut 3 mm from crystal seed surface. 0 distance from crystal axis [mm] 40mbar 20mbar
Dislocations dislocat tion density [1/cm 2 ] 900000 800000 700000 600000 500000 400000 300000 200000 100000 0 Dislocation densities in real process 0 2 4 6 8 10 12 14 16 18 20 distance from crystal axis[mm] density increase seed dislocation density [1/cm 2 ] 160000 150000 140000 130000 120000 110000 100000 90000 80000 Discloation density distribution from simulation 1 2 3 4 5 6 7 8 9 10 11 seed distance from crystal axis [mm] cross-section
Effect of temperature on growth rate 0,6 Growth rate for various temperature settings (simulation) growth rate [mm/h] 0,5 0,4 0,3 0,2 0,1 0 2300 2350 temperature at lower measurement point [ C] temperature at upper measurement point 2250 C 2300 C
Effect of temperature gradient on projected crystal thickness thickness of the cry ystal [mm] 9 8 7 6 5 4 3 2 1 0 Crystal thickness dependence on temperature gradient (simulation) I II III IV V VI instance
Summary computer modelling is a viable tool for designing optimal conditions for SiC monocrystal growth modeling gives you opportunity to check the correctness of much more theories and ideas than the experiment alone saves time and resources