SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

84 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

2.12DEFECTSTATESINSOLIDS...........................

The band theory discussed in this chapter is valid only for perfect crystals. Even in good-
quality crystals there are defects, which break the periodicity of the structure. Typical defects in
crystalline materials are: (i) defects in the structure arise from missing atoms (vacancies), atoms
at the wrong sites, unintended impurities, etc. (ii) We may also have dislocations at surfaces of a
crystal the arrangement of atoms does not have the same periodicity as in the bulk. (iii) We could
also have absorbed atoms or molecules at the surface; disordered solids such as amorphous or
polycrystalline materials.

Defects and surface states

In figure 2.38 we show a schematic of a perfectly periodic material and one with a defect. A
deep potential region indicates the region of defect. In the case of the periodic system we have
seen the electrons see a bandedge and are described by simple a effective mass equations near
the bandedge. There are no allowed states in the bandgap region. In the case of a defect the deep
level causes new electronic states, which can have energies in the bandgap.

Bound state trapped near the

grain boundary

Perfectly periodic material Defect in a material

ATOMIC

POTENTIALS

ψψ

Schematic of electron states

in a perfect crystal

Schematic of a defect

r

"free" states

r

Defect

(a) (b)

ATOMIC

POTENTIALS

Figure 2.38: A schematic of the structural and electronic properties of (a) crystals and of (b) a
material with a defect.