EQUILIBRIUM CRITICAL THICKNESS FOR STRAINED-LAYER GROWTH

The critical thickness for two-dimensional layer growth of Si1-xGex on Si and InxGa1-xAs on GaAs is about 1-3 monolayers (ML) for x = 1, bey ond which islanding begins. Under certain growth conditions, this thic kness t would increase as some power of 1/x. The reason for this is no t clear; Snyder et al, argue that, under equilibrium conditions, this critical Stranski-Krastanov (SK) thickness t(c) is independent of x an d should remain at 1-3 ML, but that, under nonequilibrium growth condi tions, t similar to x(-4). However, Osten et al. showed, experimentall y, that even under equilibrium conditions there is an increase of SK t hickness with 1/x. We carry out calculations of energetics of large th ree-dimensional (3D) islands on substrates with varying thicknesses t of the epilayer and different coverages theta. We show that at low the ta or when islands are small (or both) then the SK thickness is small similar to 1-3 ML, in agreement with the results of Snyder et al. At i ncreasing coverages, when interisland separation l decreases to the po int where l-s (island size), we observe Delta E to decrease for the lo wer thicknesses t=3,4,5,...8...; until thicknesses t>3 become more fav orable. There is considerable tension going deep into the substrate di rectly below islands. The larger an island becomes, the more favorable it is for a:thicker layer beneath it to be of the same material as th e island. It is known that the critical size s(c) at which 3D islands first become favorable varies as x(-2). We argue from this that, at eq uilibrium, the average 3D island size increases with x(-p), p some exp onent, and at high enough coverages, when interisland separation is sm all, SK thickness t(c) increases. The experimental results of Osten et al. are consistent with exponents 2 less than or equal to p less than or equal to 4. (C) 1998 American Vacuum Society.