Is grown pseudomorphically on GaAs

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction · Semiconductor physics and devices

Solid State Physics, Ch Heterostructures, quantum wells and the two-dimensional electron gas

Problem

\mathrm{In_{0.1}Ga_{0.9}As}

is grown pseudomorphically on GaAs. The unstrained lattice constants are

a_{\mathrm{InAs}}=0.6058\,\mathrm{nm}

and

a_{\mathrm{GaAs}}=0.5653\,\mathrm{nm}

. ((a)) Using Vegard's law, find the misfit

f=(a_l-a_s)/a_s

of the layer on the GaAs substrate. ((b)) Using the single-layer force balance for

60^\circ

dislocations,

h_c=\frac{b(1-\nu\cos^2\alpha)}{8\pi |f|(1+\nu)\cos\lambda}\left[\ln(h_c/b)+1\right],

with

b=0.40\,\mathrm{nm}

\nu=0.31

\alpha=\lambda=60^\circ

, solve iteratively for the critical thickness

h_c

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