Y. Obayashi et K. Shintani, DIRECTIONAL DEPENDENCE OF SURFACE MORPHOLOGICAL STABILITY OF HETEROEPITAXIAL LAYERS, Journal of applied physics, 84(6), 1998, pp. 3141-3146
Surface morphological stability in coherent heteroepitaxial layers is
analyzed focusing on the directional dependence of surface undulations
created by surface diffusion. The critical stability condition is def
ined in terms of the free energy of the system which is assumed to be
the sum of the elastic strain energy and the surface free energy. The
displacement and stress fields of the semi-infinite anisotropic solid
with the slightly undulating surface are calculated by using the surfa
ce admittance tensor and the vector complex potential function. Numeri
cal results for the Si1-xGex/Si systems show that the critical wavelen
gth of the [100] surface undulations is smaller than that of the [110]
surface undulations, which means that surface undulations are likely
to be formed in the [100] directions. It is also found that the critic
al wavelength decreases with the increase of Ge fraction. These tenden
cies are in good agreement with the observations in annealing experime
nts for the Si1-xGex/Si systems in the literature. If the substrate is
assumed to be rigid, the range of layer thickness where the system is
absolutely stable against a surface undulation of any wavelength exis
ts. Finally, the growth rate of the amplitude of surface undulations i
s estimated from an evolution equation for the surface shape. It is sh
own that even if anisotropy is taken into account, the growth rate of
the amplitude takes the maximum value when the wavelength is 4/3 times
the critical wavelength, which is the same as in the isotropic approx
imation. (C) 1998 American Institute of Physics.