At the critical thickness, it can be assumed that a two-dimensional dislocation
ID: 3161414 • Letter: A
Question
At the critical thickness, it can be assumed that a two-dimensional dislocation network with equal spacings is produced at the substrate-epilayer interface. The dislocation energy can therefore be represented by a line of atoms with broken bonds. Show, from energy minimization conditions, that the critical thickness hc = a/2f, where the symbols have their usually meanings. Calculate hc for InxGa1-xAs (0 x 1) on GaAs and compare the results with those of Figure 1.18
103 0.0 02 Figure 1.18 Calculated variation of 0.4 0.6 0.8 1.0 critical thickness with InGa -As composition (misfit f for epitaxy of InGaAs on GaAs substrate.Explanation / Answer
Defect free (but lattice strained) epitaxial films (commensurate) can be obtained with thickness d which is lesser than dcas per the Mattews theory
It is also seen that extended dislocation arrays do not form instantaneously with welldefined spacings; rather, dislocations nucleate individually
Surface ripples arise because the film is under compressive stress
Thus the latticeplane spacing of the film shrinks near thecusplike troughs (shown as )and expandsat the rounded peaks () (Note: Flat filmsurface expected corr. to the minimum energy configuration) .
However, when relievalof film strainenergy outweighsthe tendency of surface energy (which tend to smooth/flatten out the film) the roughening occurs.
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