SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

22 CHAPTER 1. STRUCTURAL PROPERTIES OF SEMICONDUCTORS

:Missing rows of atoms

Region with few

dislocations

Dislocations are

confined

Substrate Substrate

Figure 1.17: Strained epitaxy above critical thickness. The left hand side figure shows a desir-
able structure in which the dislocations are confined near the overlayer-substrate interface. On
the right hand side, the dislocations are penetrating the overlayer.

The lattice constant of the epitaxial perpendicular to the substrate will be changed by the Poisson
effect. These two cases are depicted in figure 1.16c. This type of coherently strained crystal is
called pseudomorphic.
For layer-by-layer growth, the epitaxial semiconductor layer is biaxially strained in the plane
of the substrate, by an amount‖, and uniaxially strained in the perpendicular direction, by an
amount⊥. For a thick substrate, the in-plane strain of the layer is determined from the bulk
lattice constants of the substrate material,aS, and the layer material,aL:

e‖ =

aS

aL

− 1

=  (1.4.1)

Since the layer is subjected to no stress in the perpendicular direction, the perpendicular strain,
⊥, is simply proportional to‖:

⊥=

−‖

σ

(1.4.2)

where the constantσis known as Poisson’s ratio.
Noting that there isnostress in the direction of growth it can be simply shown that for the
strained layer grown on a (001) substrate (for anfcclattice)

σ =

c 11

2 c 12

(1.4.3)

xx = ‖

yy = xx

zz =

− 2 c 12

c 11

‖

xy =0

yz =0

zx =0