First- and second-order piezoelectricity in III-V semiconductors

Abstract

We present the results of first-principles plane-wave pseudopotential calculations of piezoelectric coefficients of first and second order for a total of nine III-V binary phases (AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb) of zinc-blende semiconductors. These coefficients are used to calculate the piezoelectric fields for [111]-oriented quantum wells (QWs) with different well-barrier combinations and various dimensions. We derive an approximate analytic expression for the strain tensor in the case of pseudomorphic growth along an arbitrary growth direction. Together with the piezoelectric coefficients, this allows a simple calculation of the piezoelectric field up to second order in strain for an arbitrary growth direction and any material combination within the nine III-Vs presented here. Nonlinear contributions to the polarization are shown to be of significant magnitude for all the materials presented. In some cases the field is increased by the second-order terms; in some cases it is decreased. We analyze the chemical trends of the obtained coefficients. We compare our results to available experiments and find good agreement in one-third of the cases, while for the remaining cases the calculated field is larger to significantly larger than in the measurements. We discuss the popular experimental techniques and highlight possible reasons for the discrepancies.

Strain in crystalline core-shell nanowires

“…In other words, the c/a ratio, which represents the deviation from "ideal" wurtzite, is changed at almost constant volume. Note that a non-linear character of the piezoelectric effect has been measured in CdTe [24] and predicted for other semiconductors as well [25]. As it is attributed to a dependence of the piezoelectric coefficient on the hydrostatic strain, this non-linear character should not show up in a ZnO-(Zn,Mg)O NW.…”

“…Indeed, when calculating the stress corresponding to the cylindrical strain configuration, additional components appear through thec 14 terms in the stiffness tensor: for instance, at the interface in the y-direction (x = 0, y = r c ), a stress component normal to the interface and surface, σ yz =c 14 (ε xx − ε yy ) + 2c 44 ε zy , takes a finite value if we use the strain of equations (18) and (32), or (25) and (33). We thus expect an additional strain to appear,…”

“…-one with cylindrical symmetry (that with theĉ, note thatĉ 11 −ĉ 12 = 2ĉ 66 ); if we keep only this contribution, the strain configuration is that of equation (18) or equation (25), where the c ij 's are replaced by thê c ij 's; -one, proportional to c, with the expected fourfold symmetry around z. As mentioned earlier, with c < 0, a zinc-blende crystal is softer against a pure tetragonal stress (along a cubic axis, cos 4θ = 1) than against any other stress, in particular along a 1 1 0 axis (cos 4θ = −1).…”

Al4SiC4 wurtzite crystal: Structural, optoelectronic, elastic, and piezoelectric properties

“…25 To obtain the piezoelectric coefficients, the second-order derivatives of total energy have been calculated with respect to the strain and the electric field components 24 by DFPT. Small values are predicted for the linear piezoelectric coefficients (Table III): e 15 = −0.04 C m −2 , e 33 = +0.36 C m −2 , e 31 = +0.03 C m −2 by comparison with conventional semiconductors in zinc-blende [30][31][32][33] or wurtzite structures [34][35][36] using similar procedures. Indeed, these constants are one order of magnitude smaller than the ones of AlN, GaN, InN, and ZnO semiconductors 36 in wurtzite structure.…”

Exact Diagonalization Approach for Atomistic Calculation of Piezoelectric Effects in Semiconductor Quantum Dots

“…It should be noted that first calculations for self-assembled quantum dots using this approach were performed nearly two decades ago [16]. In recent years Bester, Zunger, and coworkers [17][18][19] proposed a non-linear approach using the linear e ij and quadratic B ijk piezoelectric tensors derived from the density functional theory (DFT):…”