1. Lecture 7 OUTLINE Poisson’s equation Work function
Metal-Semiconductor Contacts
Equilibrium energy band diagrams
Depletion-layer width
Reading: Pierret 5.1.2, ; Hu 4.16

2. Poisson’s Equation Gauss’ Law: E(x) E(x+Dx) s : permittivity (F/cm)
area A
E(x)
E(x+Dx) Dx
s : permittivity (F/cm)
 : charge density (C/cm3)
EE130/230M Spring 2013
Lecture 7, Slide 2

3. Charge Density in a Semiconductor
Assuming the dopants are completely ionized:
r = q (p – n + ND – NA)
EE130/230M Spring 2013
Lecture 7, Slide 3

4. Work Function E0: vacuum energy level FM: metal work function
FS: semiconductor work function
EE130/230M Spring 2013
Lecture 7, Slide 4

5. Metal-Semiconductor Contacts
There are 2 kinds of metal-semiconductor contacts:
rectifying
“Schottky diode”
non-rectifying
“ohmic contact”
EE130/230M Spring 2013
Lecture 7, Slide 5

6. Ideal M-S Contact: FM > FS, n-type
Band diagram instantly
after contact formation:
qVbi = FBn– (Ec – EF)FB
Equilibrium band diagram: n
Schottky Barrier Height: W
EE130/230M Spring 2013
Lecture 7, Slide 6

7. Ideal M-S Contact: FM < FS, n-type
Band diagram instantly
after contact formation:
Equilibrium band diagram:
EE130/230M Spring 2013
Lecture 7, Slide 7