SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

2.9. DOPING IN POLAR MATERIALS 69

ZINC BLENDE

Material e 14 (C/m^2 )

AlAs –0.23

GaAs –0.16

GaSb –0.13

GaP –0.10

InAs –0.05

InP –0.04

WURTZITE (c-axis growth)

Material e 31 (C/m^2 ) e 33 (C/m^2 ) Psp (C/m^2 )

AlN –0.6 1.46 –0.081

GaN –0.49 0.73 –0.029

InN –0.57 0.97 –0.032

Table 2.4: Piezoelectric constants in some important semiconductors. For the nitrides the spon-
taneous polarization values are also given. (Data for zinc-blende material from S. Adachi,J.
Appl.Phys. vol. 58,R1(1985). For nitrides see E. Bernardini, V. Fiorentini, and D. Vanderbilt,
Phys.Rev.B vol. 56,R10024(1997).)

the appropriate grading scheme. This polarization induced channel charge can be modulated by
a gate in a structure called a polarization-doped FET or PolFET can be used to tailor the gm-Vgs
profile of the PolFET. This is analogous to impurity doped MESFETs, where the gm-Vgsprofile
is modified by dopant profile design. In figure 2.29, we show experimentally measured electrical
characteristics of doped GaN, GaN 2DEG structures, and GaN 3DEG structures.

Piezoelectric Effect
As noted above, when a structure is under strain a net polarization can arise—a phenomenon
calledpiezoelectriceffect. The value of the polar charge induced by strain depends upon the
strain tensor. In the previous section we have discussed the nature of the strain tensor in strained
epitaxy (i.e., in the coherent growth regime).
Nitride heterostructures have polarization charges at interfaces because of strain related piezo-
electric effect as well as from spontaneous polarization. For growth along (0001) orientation the
strain tensor for coherently strained wurtzite crystals is given in Chapter 1. The piezoelectric
polarization is related to the strain tensor by the following relation

Ppz=e 33 zz+e 31 (xx+yy) (2.9.2)

Piezoelectric effect is also present in zinc blende structures. However, the piezoelectric effect
only occurs when the strain tensor has off-diagonal components. The polarization values are
given by

Px = e 14 yz

Py = e 14 xz

Pz = e 14 xy (2.9.3)