SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

2.6. BANDSTRUCTURE OF SOME IMPORTANT SEMICONDUCTORS 47

Valence

band

III

II

I

I Heavy Hole Band

II Light Hole Band

III Split-Off Band

Δ = Split-Off Energy

DIRECT GAP INDIRECT GAP

Conduction

band

Conduction

bandedge

Valence

band

III

II

I

k = 0 k = 0

Figure 2.11: Schematic of the valence band, direct bandgap, and indirect bandgap conduction
bands. The curves I, II, III in the valence band are called heavy hole, light hole, and split-off
hole states, respectively.

whereEcis the conduction bandedge, and the bandstructure is a simple parabola. The equation
for theE–krelation looks very much like that of an electron in free space as noted in the previous
section.

Silicon
The most important semiconductor is silicon. Silicon has an indirect bandgap as shown in
figure 2.12. The bottom of the conduction band in Si is at point (∼(2π/a)(0. 85 , 0 .0);i.e., close
to theX-point. There are six degenerateX-points and, consequently, six conduction bandedge
valleys. The near bandedge bandstructure can be represented by ellipsoids of energy with simple
Evs.krelations of the form (for examples for the [100] valley)

E(k)=

^2 kx^2

2 m∗l

+

^2

(

k^2 y+k^2 z

)

2 m∗t

(2.6.2)