Importance of Second-Order Piezoelectric Effects in Zinc-Blende Semiconductors

We show that the piezoelectric effect that describes the emergence of an electric field in response to a crystal deformation in III-V semiconductors such as GaAs and InAs has strong contributions from second-order effects that have been neglected so far. We calculate the second-order piezoelectric tensors using density-functional theory and obtain the piezoelectric field for $[111]$-oriented ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum wells of realistic dimensions and concentration $x$. We find that the linear and the quadratic piezoelectric coefficients have the opposite effect on the field, and for large strains (large In concentration) the quadratic terms even dominate. Thus, the piezoelectric field turns out to be a rare example of a physical quantity for which the first-order and second-order contributions are of comparable magnitude.

Figure 1

Piezoelectric potential calculated from Eqs. (1, 2, 3, 4) (dashed line) and the Kohn-Sham potential obtained from self-consistent DFT calculations (solid line). Both calculations are for an $(\mathrm{InAs}{)}_6/(\mathrm{GaAs}{)}_9$ superlattice epitaxially strained on GaAs.

Figure 2

(a) Piezoelectric potential calculated from Eqs. (1, 2, 3, 4) for an 11 nm ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ well epitaxially strained to GaAs for $x=0.1–1.0$. (b) Same as (a) for $x=0.1–0.5$.

Figure 3

(a) Piezoelectric field as a function of $x$. Circles: Correct result with linear and nonlinear piezoelectric tensors from DFT. Triangles: Neglecting $B_{\mu jk}$ and using experimental $e_{\mu j}$. Squares: Neglecting $B_{\mu jk}$ and using LDA $e_{\mu j}$. (b) Magnification of the low-concentration region.