SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

122 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS

E l ectri c f i el d

E(x)

Position in space, x

UNIFORM ELECTRIC FIEL D

(a)

+ve

–ve

0

U(x)

Energy band,

Ec, Ev

Ec

EFi

Ev

x

(b)

x

(c)

POT E NT IA L ENERGY PR OFI L E

ENER GY BAND PR OFI L E

Figure 3.17: (a) Electric field profile in a semiconductor. (b) Plot of the potential energy associ-
ated with the electric field. (c) Electron energy band profile. The negative charge of the electron
causes the energy band profile to have the opposite sign to the potential energy profile.

To find the relation between diffusion parameters and drift parameters (i.e. between D and
μ) we assume that the system is in equilibrium and the total electron and hole currents are