Theory of the anomalously low band-gap pressure coefficients in strained-layer semiconductor alloys

The band-gap pressure coefficients of III-V ternary semiconductor alloys within strained layers are significantly lower than the bulk binary values and the drop in pressure coefficient, of about $6x\mathrm{m}\mathrm{e}\mathrm{V}/\mathrm{k}\mathrm{b}\mathrm{a}\mathrm{r}$ for ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ grown on GaAs remains unexplained. Linear elasticity has been used to predict first-order (linear) effects of pressure, but for strained layers, this procedure fails to predict the pressure coefficients. We show that the nonlinear elasticity theory is necessary, and when evaluated with a consistent level of approximation throughout, it accounts for the pressure coefficients, largely through an approximately linear increase of Poisson’s ratio with pressure. Earlier experimental data and some photoabsorption results for ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ on InP are reviewed and they agree well with values predicted using our analysis.