L. Kadinski

On the sublimation growth of SiC bulk crystals: development of a numerical process model

Abstract The development of a numerical process model to simulate the sublimation growth of SiC bulk crystals is discussed. Radiation, conduction and convection are considered as heat transfer mechanisms. Mass transport by diffusion and convection is taken into account. First results on the simulation of heat and mass transfer in a 2 inch SiC growth set-up show a negligible effect of convection on process conditions. Chemical reactions in the SiC-graphite system have also been implemented into our model. Preliminary analysis on the dependence of concentration fields and growth velocity on possible chemical reaction mechanisms, e.g. graphitization, reveal that the incorporation of chemical processes into modelling is very important for an accurate description of SiC sublimation growth.

Global numerical simulation of heat and mass transfer for SiC bulk crystal growth by PVT

Abstract A modeling approach for the numerical simulation of heat and mass transfer during SiC sublimation growth in inductively heated physical vapor transport (PVT) reactors is introduced. The physical model is based on the two-dimensional solution of the coupled differential equations describing mass conservation, momentum conservation, conjugate heat transfer including surface to surface radiation, multicomponent chemical species mass transfer and advective flow. The model also includes the Joule volume heat sources induced by the electromagnetic field. The evolution of the temperature profiles inside the crucible and of the crystallization front is studied. The radial temperature gradient at the crystal/gas interface causes strong radial non-uniformity of the growth rate and, in turn, influences the shape of the growing crystal. Results of calculations are compared to experimental observations to analyse the validity of the modeling approach. Both the computed growth rates, their temporal evolution and the shape of the growing crystal agree with experimental data.

Heat transfer and mass transport in a multiwafer MOVPE reactor: modelling and experimental studies

Abstract An improved detailed model for the calculation of the temperature distribution in a multiwafer Planetary Reactor™ has been developed. The temperature field of the reactor has been calculated in dependence of the reactor parameters for (Al,Ga)As growth as well as on the kind and the thickness of the wall and susceptor deposits. The amount of parasitic wall deposits can be minimized by a proper tuning of the reactor temperature distribution. Calculated GaAs growth rate profiles on 3 inch wafers show a strong dependence on the temperature field in the reactor and the amount of parasitic deposits. These predicted relationships have been used to optimize the reactor temperature distribution in order to minimize parasitic wall depositions. By this procedure a growth rate uniformity of

Global modeling of the SiC sublimation growth process: prediction of thermoelastic stress and control of growth conditions

Abstract The current status of the mathematical model for heat and mass transfer during SiC bulk crystal growth from the vapor phase in inductively heated reactors is reviewed. Results on the simulation of thermoelastic stresses during the growth process are presented. Stresses have been analyzed to exceed considerably the critical resolved shear stress σ CRS =1 MPa which is generally assumed to be the indicator for the onset of dislocation formation in SiC. It is shown that the conditions for stress formation at fixed positions in the crystal vary considerably during growth and that geometric modifications can contribute significantly to a reduction of the stress level. The possible impact of semitransparency of SiC on additional stress generation is discussed. As effective tool for process control and optimization an inverse modeling procedure is introduced.

Modeling and experimental verification of deposition behavior during AlGaAs growth: a comparison for the carrier gases N2 and H2

Abstract A modeling and experimental study is carried out to understand why low-pressure metalorganic vapor-phase epitaxy (LP-MOVPE) of AlGaAs in nitrogen atmosphere differs from that in hydrogen in a horizontal tube type of reactor. To this end flow, heat transfer as well as the key chemical species’ mass transport are considered. The increased uniformity in N 2 atmosphere is related to the higher molecular weight and, therefore to the higher gas density of the carrier resulting in a flow structure that is more favorable for improved growth rate uniformity of AlGaAs on the substrate. Due to the so called “cold finger” [L. Stock, W. Richter, J. Crystal Growth 77 (1986) 144; D.F. Fotiadis, M. Boekholt, K.F. Jensen, W. Richter, J. Crystal Growth 100 (1990) 577.] effect as well as the enhanced inertia of the carrier gas and lower diffusion coefficients of the growth rate limiting chemical species in N 2 , lower total flow rates are found to be optimal for material quality and layer thickness uniformity when using N 2 as carrier gas. The dependence of growth rate uniformity on the carrier gas and total flow rate can only be understood by the detailed numerical modeling of three-dimensional flow, heat and species’ mass transfer with resulting layer deposition on the susceptor. The results of experiments are in good agreement with the modeling computations.

In situ visualization and analysis of silicon carbide physical vapor transport growth using digital X-ray imaging

Using digital X-ray imaging we have investigated the on-going processes during physical vapor transport growth of SiC. A high-resolution and high-speed X-ray detector based on image plates and digital recording has been used to monitor SiC bulk crystal growth as well as SiC source material degradation on-line during growth. We have analyzed the shape of the growth interface and the evolution of the SiC source morphology. The crystal growth process will be discussed in terms of growth rate and limitations of the physical vapor transport of SiC gas species from the source to the growth interface.

Process optimisation of MOVPE growth by numerical modelling of transport phenomena including thermal radiation

Abstract A global transport model for the MOVPE of III–V growth based on the finite volume solution of coupled flow, heat and mass transfer, including detailed radiative transfer, multicomponent diffusion and homogeneous and heterogeneous chemical reactions, is presented. For radiative transfer modelling, a combined approach is used of grey-diffuse view-factor based heat flux exchange between the semi-transparent reactor walls through the transparent reactor interior, and a spherical harmonics approximation for the radiative-conductive heat transfer problem in participating massive quartz elements with complex shapes. The described modelling approach is applied to the horizontal multiwafer radial flow Planetary Reactor™, validated experimentally and used for process improvements. The mutual interaction of changing radiation properties at internal solid boundaries due to semiconductor coatings and thermal behaviour in that particular MOVPE reactor is discussed.

Modeling and experimental verification of transport and deposition behavior during MOVPE of Ga1-xInxP in the Planetary Reactor

Abstract Modeling and experimental studies of Ga 1− x In x P growth in the Planetary Reactor ® are presented and the mechanisms governing growth rate and compositional uniformity are identified. Reaction rate constants for the kinetically limited formation of wall deposits in this specific reactor are determined and included in the computational model. Several types of the Planetary Reactor are compared to each other. The reasons for the non-unity group III solid–vapor distribution coefficient of Ga 1− x In x P are analyzed.

A multigrid solver for fluid flow and mass transfer coupled with grey-body surface radiation for the numerical simulation of chemical vapor deposition processes

Abstract In this paper an advanced numerical approach for the simulation of epitaxial growth in metalorganic chemical vapor deposition reactors (MOCVD) is presented. The mathematical model is based on the conservation equations for momentum and heat transfer combined with mass transfer including thermodiffusion and chemical reactions. The thermal radiation analysis assumes a non-participating medium and semi-transparent quartz walls. The radiation heat transfer is coupled with convection and conduction. The heat conduction includes thermal solid/fluid interactions between the gas and solid parts of the reactor. The model is implemented in a finite volume numerical solution procedure on block-structured non-orthogonal grids for two-dimensional (plane and axisymmetric) laminar flows. To speed up the convergence of the computations, a “full approximation scheme” multigrid technique is employed. In order to demonstrate the ability of the present method to analyze complex problems, investigations for horizontal CVD reactor configurations are presented. These problems include very complicated radiative heat transfer, buoyancy-driven flow, combined heat transfer in the reactor walls and the susceptor, as well as the transport of chemically reacting components. The simulated temperature distribution is compared with well-known temperature measurements [1] [L. Stock and W. Richter, J. Crystal Growth 77 (1986) 144] and good agreement with them is achieved. The growth of GaAs from trimethylgallium (TMGa), arsine, and hydrogen was considered where the deposition process is assumed to be in the transport-limited regime. The predicted deposition rates in the reactor fairly well compare with the available experimental results from literature.

Development of advanced mathematical models for numerical calculations of radiative heat transfer in metalorganic chemical vapour deposition reactors

Abstract The effect of radiative heat transfer in a horizontal chemical vapour deposition (CVD) reactor on the upper wall temperature is studied in detail. A three-band model for the quartz absorption coefficient is introduced and the wall emittance, reflectance, and transmittance are calculated for the cases of specular and diffuse walls, and also for walls covered by a film. Numerical simulation of the heat transfer in the horizontal reactor has shown that the upper wall temperature varies about up to 40–70 K depending on the type of the wall and the emissivity of the susceptor.