SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

20 CHAPTER 1. STRUCTURAL PROPERTIES OF SEMICONDUCTORS

(a)

(b)

(c)

n bonds: substrate

n+ 1 bonds: epilayer

Substrate

Overlayer

aL > aS aL < aS

GROWTH WITH DISLOCATIONS

n bonds: substrate

n–1 bonds: epilayer

DISLOCATION FREE

n~^1 ε

Figure 1.16: (a) An overlayer with one lattice constant is placed without distortion on a substrate
with a different lattice constant. (b) Dislocations are generated at positions where the interface
bonding is lost. (c) The case is shown where the overlayer is distorted so that no dislocation is
free and coherent with the substrate.

constant of the overlayer to that of the substrate. This causes the overlayer to be under strain
and the system has a certain amount of strain energy.Thisstrainenergygrowsastheoverlayer
thicknessincreases. In the strained epitaxy, the choice between the state of the structure shown
in figure 1.16b and the state shown in figure 1.16c is decided by free energy minimization con-
siderations. The general observations can be summarized as follows:
For small lattice mismatch (<0.03), the overlayer initially grows in perfect registry with
the substrate, as shown in figure 1.16c. However, as noted before, the strain energy will grow
as the overlayer thickness increases. As a result, it will eventually be favorable for the overlayer