SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

50 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

6 5 4 3 2 1 0

–1

–2

–3

–4

0.3

L [111]Γ[100]X

k

(a)

ENERGY

(eV)

GERMANIUM

Indirect bandgap

Eg(300 K) = 0.66 eV

Eg(direct) = 0.9 eV

–1

–2

–3

–4

6 5 4 3 2 1 0

L [111]Γ[100]X

k

ENERGY

(eV)

(b)

ALUMINUM ARSENIDE

Indirect bandgap

Eg(300 K) = 2.15 eV

Eg(direct) = 2.75 eV

Figure 2.14: (a) Bandstructure of Ge and AlAs.

2.7 MOBILECARRIERS

From our brief discussion of metals and semiconductors in Section 2.5, we see that in a metal
current flows because of the electrons present in the highest (partially) filled band. As shown
schematically in figure 2.16a. The density of such electrons is very high (∼ 1023 cm−^3 ). In a
semiconductor, in contrast, no current flows if the valence band is filled with electrons and the
conduction band is empty of electrons. However, if somehow empty states or holes are created
in the valence band by removing electrons, current can flow through the holes. Similarly, if
electrons are placed in the conduction band, these electrons can carry current. This is shown
schematically in figure 2.16b. If the density of electrons in the conduction band isnand that of
holes in the valence band isp, the total mobile carrier density isn+p.

2.7.1 Mobileelectronsinmetals

In a metal, we have a series of filled bands and a partially filled band called the conduc-
tion band. The filled bands are inert as far as electrical and optical properties of metals are
concerned. The conduction band of metals can be assumed to be described by the parabolic
energy–momentum relation

E(k)=Ec+

^2 k^2

2 m 0

(2.7.1)

Note that we have used an effective mass equal to the free electrons mass. This is a reasonable
approximation for metals. The large electron density in the band “screens” out the background
potential and the electron effective mass is quite close to the free space value.