SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

24 CHAPTER 1. STRUCTURAL PROPERTIES OF SEMICONDUCTORS

while in the case of strained layer grown on a (111) substrate

σ =

c 11 +2c 12 +4c 44

2 c 11 +4c 12 − 4 c 44

xx =

[

2

3

−

1

3

(

2 c 11 +4c 12 − 4 c 44

c 11 +2c 12 +4c 44

)]

‖

yy = xx

zz = xx

xy =

[

− 1

3

−

1

3

(

2 c 11 +4c 12 − 4 c 44

c 11 +2c 12 +4c 44

)]

‖

yz = xy

zx = yz (1.4.4)

In general, the strained epitaxy causes a distortion of the lattice and, depending upon the
growth orientation, the distortions produce a new reduced crystal symmetry. It is important
to note that for (001) growth, the strain tensor is diagonal while for (111), and several other
directions, the strain tensor has nondiagonal terms. The nondiagonal terms can be exploited to
produce built-in electric fields in certain heterostructures as will be discussed in the next section.
An important heterostructure system involves growth ofhcplattice-based AlGaN or InGaN
on a GaN substrate along the c-axis. In this case the strain tensor is given by (aLis the substrate
lattice constant,aSis overlayer lattice constant)

xx = yy=

aS

aL

− 1

zz = − 2

c 13

c 33

xx (1.4.5)

This strain is exploited to generate piezoelectric effect based interface charge as discussed in
the next chapter. Such a charge can causeeffectivedoping in heterostructures as discussed in
Chapter 2. In table 1.1 we provide values of elastic constant of several important semiconductors.

1.5 TECHNOLOGY CHALLENGES

Metal and insulator (glass) technologies have been around for thousands of years. Com-
pared to these semiconductor technology is relatively new. Semiconductors need to be extremely
“pure” if they are to be useful. Defect densities of a percent may have minimal effect on metals
and insulators, but will ruin a semiconductor device. For most high performance devices, defect
densities of less than one part in 100 million are needed
Semiconductor substrate technology is available (i.e., bulk crystals can be grown in sufficient
size/purity) for a handful of materials. These include Si, GaAs, InP, and Ge, which are widely
available and SiC, Al 2 O 3 , and GaSb, etc., which are available only in small pieces (a few square
centimeters) and are very expensive. Since most semiconductors do not have a substrate available
from either bulk crystal growth or another lattice matched substrate, this severely restricts the