SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

2.7. MOBILE CARRIERS 53

Evac

EF

Ec

ENERGY

Electrons in the

conduction band

can carry current

Evac

Ec

E EV

NERGY

Conduction band electrons

(density, n) are mobile

Holes (density, p) are mobile

Mobile carrier density = n + p

(a)

(b)

• –––––––––––––


• –––––––––––––
  
  
  • ––––––
  
  
  
  

Core electrons do

not carry current

Work function

SEMICONDUCTORS

METALS

• ––––

+ + +

EF

Figure 2.16: (a) In metals the highest occupied band is partially filled and electrons can carry
current. (b) A schematic showing the valence band and conduction band in a typical semicon-
ductor. Only electrons in the conduction band and holes in the valence band can carry current.

kF,called the Fermi vector, and a velocityvF,called the Fermi velocity as

kF =

(

3 π^2 n

) 1 / 3

vF =

(



m 0

)(

3 π^2 n

) 1 / 3

(2.7.4)

It is important to note that even at 0 K, the velocity of the highest occupied state isvFand not
zero, as would be the case if we used classical statistics. At finite temperatures, the Fermi level
is approximately given by

EF(T)=EF(0)

[

1 −

π^2

12

(kBT)^2

(EF(0))^2

]

(2.7.5)

whereEF(T)andEF(0)are the Fermi levels at temperaturesTand 0 K, respectively. In Metals
there is very little change in the Fermi level with temperature.