Pressure Dependence of AlN Growth Rate

Slack developed a thermodynamic model to predict how AlN crystal growth would vary with system pressure. He concluded growthrate increases proportionally to the square root of the nitrogen partial pressure. Thus he predict that increasing the pressure by a factor of 100 would increase the growthrate by a factor of 10. However, to date, the effect of the pressure on the growthrate has not been experimentally determined. A counter argument can be made that the growthrate should increase by reducing the pressure. Slack based his arguments on the supposition that the process is in equilibrium, but more realistically, the growthrate is limited by either the kinetics of sublimation (at the AlN powder source) or condensation (at the seed crystal) and mass transport between the source and seed. If the condensation rate is rapid and nearly irreversible, the AlN growthrate will be limited by the sublimation process. The sublimation process is analogous to evaporation, for which it has been established that the evaporation rate is directly proportional to the pressure above the melt. Thus, the evaporation rate is enhanced with a reduction in the system pressure. Furthermore, mass transfer rates are increased as the pressure is reduced since gas phase diffusion coefficients are directly proportional to the pressure. High pressures may in fact be detrimental to crystal growth, as gas-phase convection increases with pressure, and convection can lead to nonuniform growthrates of the crystal. In the analogous SiC bulk crystal growth technique, the crystal growthrate does indeed increase as the system pressure is reduced. Because the sublimation - recondensation crystal processes are similar for both AlN and SiC, it is reasonable to assume that AlN crystal growthrate also increases with a decrease in pressure.