Crack formation in GaAs heteroepitaxial films on Si and SiGe virtual substrates

We have determined the critical cracking thickness, or the thickness beyond which crack formation is favored, in GaAs films grown on Si and SiGe virtual substrates analytically and experimentally. The analytical model predicts a critical cracking thickness proportional to the biaxial modulus and the crack resistance of the GaAs film, and inversely proportional to the square of the thermal stress and a nondimensional crack resistance number Z. This Z number is determined by the mechanical properties of the GaAs film for a system without substrate damage, and is also determined by the mechanical properties of the substrate for a system with substrate damage. The experimentally determined critical thicknesses were in general greater than the analytically derived values due to the kinetic barriers to crack nucleation, which were not taken into consideration in the models. In addition, we have observed an asymmetric crack array formation, where arrays running in the [110] substrate off-cut direction are favored. We have also performed finite element modeling of the crack systems to study the evolution of thermal stress around crack planes in the GaAs film. (C) 2003 American Institute of Physics.