M. Selder

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.

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.

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.

Impact of source material on silicon carbide vapor transport growth process

We have studied the impact of morphological changes of the source material during physical vapor transport growth of silicon carbide (SiC). Digital X-ray imaging (P.J. Wellmann et al., Mat. Res. Soc. Symp. Proc. 572 (1999) 259) was carried out to visualize the ongoing processes inside the SiC source material and numerical modeling was performed in order to study the impact on the crystal growth process. According to numerical modeling there is a large impact of the SiC powder compression and morphology on the global heat transfer and mass transfer inside the growth cell. Two different SiC sources containing microscopic SiC powder and macroscopic SiC pieces, respectively, were investigated. Although the SiC source material undergoes fundamental transitions during growth (i.e. evolution from powder to compressed SiC block) it was found that self-stabilizing of the growth process occurred by formation of a disk-like structure on the top of the source material, independent of the initial source morphology. The experimental results were confirmed by the numerical simulation of the global growth process.

Numerical simulation of global heat transfer in reactors for SiC bulk crystal growth by physical vapor transport

A modeling approach for the numerical simulation of heat transfer during SiC sublimation growth in inductively heated PVT-reactors is introduced. The physical model takes into account the volume heat sources induced by the electromagnetic field and the main processes contributing to the conservation equations for mass, momentum and energy. Results of calculations are compared to experimental observations to discuss the validity of the modeling approach. The computed isotherms and their temporal evolution agree with the shape of grown SiC crystals during a growth run.