Residual Stress and BPD Density Evolution during Cooling

Unsteady module of VR-PVT can be applied to PVT of SiC and AlN. It enables simulation of transient heating/cooling for optimization of heating and cooling recipes in terms of the residual stress and the final density of dislocations in the crystal. The Alexander-Haasen (AH) model is applied during the unsteady cooling stage. It describes plastic deformation of a single crystal by slip mechanism, relaxation of elastic stress and multiplication of basal plane dislocations (BPD).

Simulation of the growth process with VR can include three stages:

  • Unsteady modeling of the growth system heating according to the user-defined recipe with Unsteady Module;
  • Crystal growth. Namely, simulation of the long-term heat and mass-transport within the quasi-steady state approach. This stage represents the conventional Virtual Reactor modeling as performed without the Unsteady Module;
  • Unsteady modeling of the growth system cooling according to the user-defined recipe. Simulation of the cooling stage can include prediction of the thermal stress and dislocation dynamics. At this stage, the thermal stress relaxation can be simulated using the Alexander-Haasen model.

There are two ways to specify heating/cooling recipe in the unsteady module. First approach is to specify programmed heater power. Alternatively, you can specify the evolution of temperature at a specific point (points). In the latter case, the software will automatically fit the power of the heater (heaters) to maintain that assigned temperature. 

Crucible and crystal cooling in PVT SiC

Modeling of the slow cool down of PVT furnace and SiC crystal

Application of the Unsteady Module to the development of cooling recipe of SiC crystal is illustrated below. The example shows residual stress (left) and final density of dislocations (right) in the crystal cooled down to the room temperature after the growth process using three different cooling recipes: 1) instantaneous switching off the heater (top), 2) decreasing the heater power linearly down to zero during 1 hour (middle), and 3) linear power decrease down to zero during 2 hours (bottom).

Effect of cooling recipe on residual stress in PVT SiC

Residual stress in SiC crystal for three different cooling recipes

Effect of cooling recipe on BPD density in PVT SiC

Final density of BP dislocations in SiC crystal for three different cooling recipes

Prediction of Warping of the Wafers Cut from the Bulk Crystal

When SiC boule is sliced, the wafers inherit plastic strain from the crystal, which affects their deformation after cutting. Based on the solution of the crystal plastoelastic deformation problem, expected radial distribution of the vertical displacement of the wafer, also known as warp, can be estimated for different vertical positions of the crystal.

Plot of the vertical displacement distribution along the wafer, found by integrating the plastic component of the shear strain. Wafer position is shown with red dash line above.


“Evolution of thermoelastic strain and dislocation density during sublimation growth of silicon carbide” by Zhmakin I.A., Kulik A.V., Karpov S.Yu., Demina S.E., Ramm M.S., Makarov Yu.N., Diamond and Related Materials, Vol.9, p.446-451, (2000)