SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

48 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

6 5 4 3 2 1 0

–1

–2

–3

–4

Eg

(a)

ENERGY

(eV)

(b)

kz

kx (100) (010)

(001)

(010) (100)

(001)

ky

Constant energy

surfaces of six

equivalent valleys

at conduction

bandedge

Γ

[110] [111]

L X

SILICON

Indirect gap

Eg= 1.1 eV

Direct gap

3.4 eV

Figure 2.12: (a) Bandstructure of Si. (b) Constant energy ellipsoids for the Si conduction band.
There are six equivalent valley in Si at the bandedge.

where we have two masses, the longitudinal and transverse. The constant energy surfaces of Si
are ellipsoids according to Eq. 2.6.2. The six surfaces are shown in figure 2.12
The longitudinal electron massm∗l is approximately 0. 98 m 0 , while the transverse mass is
approximately 0. 19 m 0.
The next valley in the conduction band is theL-point valley, which is about 1.1 eV above the
bandedge. Above this is theΓ-point edge. Due to the six-fold degeneracy of the conduction
bandedge, the electron transport in Si is quite poor because of the very large density of states
near the bandedge, leading to a high scattering rate in transport.

GaAs
GaAs is a direct gap material with small electron effective mass. The near bandedge bandstruc-
ture of GaAs is shown in figure 2.13. The bandstructure can be represented by the relation
(referenced toEc)

E=

^2 k^2

2 m∗

(2.6.3)

withm∗=0. 067 m 0. A better relationship is the non-parabolic approximation

E(1 +αE)=

^2 k^2

2 m∗

(2.6.4)

withα=0. 67 eV−^1.
For high electric field transport, it is important to note that the valleys aboveΓ-point are the
L-valleys. There are eightL-points, but, since half of them are connected by a reciprocal lattice
vector, there are four valleys. The separationΔEΓLbetween theΓ-andL- minima is 0.29 eV.