460
16 Polarized Semiconductors
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 16.12 Three-dimensional view of the a total, b longitudinal and c transverse polarization in uniaxially compressed
GaAs. Adapted from [1502]. d Transverse polarization P (parallel to the interface) and e longitudinal electric field
E ⊥ (perpendicular to the interface) in the InGaAs layer of a GaAs/In 0.2 Ga 0.8 As superlattice with joint in-plane lattice
constant (obtained from energy minimization, 1.4% lattice mismatch, the InGaAs is under compressive and the GaAs
under tensile strain). The layer thicknesses of the GaAs and InGaAs layers are identical. The quantities are shown for
various orientations of the growth direction. The vector of the growth direction varies in the (01–1) plane (φ = π/4)
with polar angle θ reaching from [100] (0 ◦ ) over [111] to [011] (90 ◦ ). Image (f) depicts the transverse polarization P
(P ⊥ = 0 in this geometry) for growth directions in the (001) plane (φ = 0). Parts d–f reprinted with permission from
[1503], ©1988 AIP
polarization is expected. For the [110] growth direction, the polarization is found to be parallel to the
interface (P ). The situation is shown for various orientations of the growth direction in Fig. 16.12.
16.4.3 Wurtzite Crystals
In wurtzite crystals, the piezoelectric polarization (with respect to x = [2–1.0], y = [01.0], z = [00.1])
is given by
4
4 In Voigt notation, P x = e 15 e 5 , P y = e 15 e 4
16 Polarized Semiconductors
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 16.12 Three-dimensional view of the a total, b longitudinal and c transverse polarization in uniaxially compressed
GaAs. Adapted from [1502]. d Transverse polarization P (parallel to the interface) and e longitudinal electric field
E ⊥ (perpendicular to the interface) in the InGaAs layer of a GaAs/In 0.2 Ga 0.8 As superlattice with joint in-plane lattice
constant (obtained from energy minimization, 1.4% lattice mismatch, the InGaAs is under compressive and the GaAs
under tensile strain). The layer thicknesses of the GaAs and InGaAs layers are identical. The quantities are shown for
various orientations of the growth direction. The vector of the growth direction varies in the (01–1) plane (φ = π/4)
with polar angle θ reaching from [100] (0 ◦ ) over [111] to [011] (90 ◦ ). Image (f) depicts the transverse polarization P
(P ⊥ = 0 in this geometry) for growth directions in the (001) plane (φ = 0). Parts d–f reprinted with permission from
[1503], ©1988 AIP
polarization is expected. For the [110] growth direction, the polarization is found to be parallel to the
interface (P ). The situation is shown for various orientations of the growth direction in Fig. 16.12.
16.4.3 Wurtzite Crystals
In wurtzite crystals, the piezoelectric polarization (with respect to x = [2–1.0], y = [01.0], z = [00.1])
is given by
4
4 In Voigt notation, P x = e 15 e 5 , P y = e 15 e 4