16.4 Piezoelectricity
459
Table 16.1 Piezoelectric coefficients (in C m −2 ) for various zincblende and wurtzite semiconductors. Data from [165,
1501, 1504], for zb-ZnO from [1505], for zb-GaN from [1506]
Zincblende
Wurtzite
III–V
e 14
II–VI
e 14
e 33
e 31
e 15
InSb
−0.123
CdTe
0.054
CdSe
0.347
−0.16
−0.138
InAs
−0.078
ZnSe
0.049
CdS
0.385
−0.262
−0.183
GaSb
−0.218
ZnS
0.254
ZnS
0.265
−0.238
−0.118
GaAs
−0.277
ZnO
0.69
ZnO
0.89
−0.51
−0.45
AlSb
−0.118
GaN
0.375
GaN
0.73
−0.49
−0.3
AlN
1.46
−0.60
−0.48
BeO
0.02
−0.02
16.4 Piezoelectricity
16.4.1 Piezoelectric Effect
External stress causes atoms in the unit cell to shift with respect to each other. In certain directions,
such a shift can lead to a polarization. Generally, all ferroelectric materials are piezoelectric. However,
there are piezoelectric materials that are not ferroelectric, e.g. quartz, GaAs and GaN. Piezoelectricity
can occur only when no center of inversion is present. Thus, e.g., GaAs is piezoelectric along 111, but
Si is not. Also, the cubic perovskite structure (in the paraelectric phase) is not piezoelectric. Generally,
the piezoelectric polarization is related to the strains via the tensor e i jk of the piezoelectric modules
3
P i = e i jk jk .
(16.15)
16.4.2 Zincblende Crystals
In zincblende semiconductors, the polarization (with respect to x = [100], y = [010], z = [001]) is
due to shear strains only and is given as
P pe = 2 e 14
⎛
⎝
yz
xz
xy
⎞
⎠ .
(16.16)
The values of e 14 for various zincblende compound semiconductors are listed in Table 16.1. We note
that the sign of e 14 reverses from negative in cubic III–V to positive in cubic II–VI semiconductors.
This non-trivial behavior involves strain effects on ionic and electronic polarization and ionicity as
discussed in [184, 1501]. The coefficient e 33 , the equivalent to e 14 in wurtzite semiconductors (see
below), is positive for III–V and II-VI semiconductors.
The strain in pseudomorphic heterostructures (cf. Sect. 5.3.3) can cause piezoelectric polarization
in a piezoelectric semiconductor. In zincblende, the main effect is expected when the growth direction
is along [111] and the strain has a purely shear character. In this case, the polarization is in the [111]
direction, i.e. perpendicular to the interface (P ⊥ ). For the [001] growth direction, no piezoelectric
3 Another formulation is used with parameters d i jk and P i = d i jk σ jk .
459
Table 16.1 Piezoelectric coefficients (in C m −2 ) for various zincblende and wurtzite semiconductors. Data from [165,
1501, 1504], for zb-ZnO from [1505], for zb-GaN from [1506]
Zincblende
Wurtzite
III–V
e 14
II–VI
e 14
e 33
e 31
e 15
InSb
−0.123
CdTe
0.054
CdSe
0.347
−0.16
−0.138
InAs
−0.078
ZnSe
0.049
CdS
0.385
−0.262
−0.183
GaSb
−0.218
ZnS
0.254
ZnS
0.265
−0.238
−0.118
GaAs
−0.277
ZnO
0.69
ZnO
0.89
−0.51
−0.45
AlSb
−0.118
GaN
0.375
GaN
0.73
−0.49
−0.3
AlN
1.46
−0.60
−0.48
BeO
0.02
−0.02
16.4 Piezoelectricity
16.4.1 Piezoelectric Effect
External stress causes atoms in the unit cell to shift with respect to each other. In certain directions,
such a shift can lead to a polarization. Generally, all ferroelectric materials are piezoelectric. However,
there are piezoelectric materials that are not ferroelectric, e.g. quartz, GaAs and GaN. Piezoelectricity
can occur only when no center of inversion is present. Thus, e.g., GaAs is piezoelectric along 111, but
Si is not. Also, the cubic perovskite structure (in the paraelectric phase) is not piezoelectric. Generally,
the piezoelectric polarization is related to the strains via the tensor e i jk of the piezoelectric modules
3
P i = e i jk jk .
(16.15)
16.4.2 Zincblende Crystals
In zincblende semiconductors, the polarization (with respect to x = [100], y = [010], z = [001]) is
due to shear strains only and is given as
P pe = 2 e 14
⎛
⎝
yz
xz
xy
⎞
⎠ .
(16.16)
The values of e 14 for various zincblende compound semiconductors are listed in Table 16.1. We note
that the sign of e 14 reverses from negative in cubic III–V to positive in cubic II–VI semiconductors.
This non-trivial behavior involves strain effects on ionic and electronic polarization and ionicity as
discussed in [184, 1501]. The coefficient e 33 , the equivalent to e 14 in wurtzite semiconductors (see
below), is positive for III–V and II-VI semiconductors.
The strain in pseudomorphic heterostructures (cf. Sect. 5.3.3) can cause piezoelectric polarization
in a piezoelectric semiconductor. In zincblende, the main effect is expected when the growth direction
is along [111] and the strain has a purely shear character. In this case, the polarization is in the [111]
direction, i.e. perpendicular to the interface (P ⊥ ). For the [001] growth direction, no piezoelectric
3 Another formulation is used with parameters d i jk and P i = d i jk σ jk .