1. 半導體專題實驗 Fermi-Level Pinning & Schottky Barrier Height 蘇璟瑋、王騰漢
B , B 電機四 1

2. Schottky Barrier Ideal Condition
Φm: The work function of metal (about 2eV~6eV)
ΦS: The work function of n-type semiconductor
χ: The electron affinity (qχ=Ec – vacuum level)
ΦB0: Schottkey barrier height (ΦB0= Φm - χ)
In Sperated system
Thermal equilibrium 2

3. Schottky Barrier (cont’d)
Ideal Condition (Cont’d)
The work function of metal 3

4. Schottky Barrier (cont’d)
Ideal Condition (Cont’d)
The deviation of Schottky barrier height
The interface layer (oxide)
Image-force lowering
The presence of interface states 4

5. Schottky Barrier (cont’d)
Image-force lowering
Image-force lowering results the distortion of the potential barrier
The effect is very small since the reduction is about m-eV

6. Fermi-Level Pinning Interface States Metal / N-type semiconductor
If the density of bandgap states near is very large, then addition or depletion of electrons to semiconductor doesn’t alter the Fermi level position at the surface and Fermi level is said to be pinned
Netural level
Acceptor type
Donor type

7. Fermi-Level Pinning (cont’d)
The Schottky Barrier Height

8. Fermi-Level Pinning (cont’d)
The Schottky Barrier Height
When surface states → ∞
The Fermi level at the surface is pinned by large amount of surface states at the value above the valence band, and the barrier height is independent of the metal work function and is entirely determined by the surface properties of the semiconductor. (Bardeen limit)
When surface states → 0
Identical to the ideal condition
Generally, the number of surface states is hard to control, so the barrier height is determined by experiment.
Netural level
Acceptor type
Donor type

9. Fermi-Level Pinning (cont’d)
The Schottky Barrier Height
Metal/ n-type Si based semiconductor
Experimental Result
Reference: S. M. Sze, Physics of Semiconductor Devices, 3rd ed., Wiley, New York 2006, ch.3

10. Reference
Donald A.Neamen, Semiconductor Physics and Devices – Basic Principles, 3ed ed., McGRAW-HILL, 2003, ch1
S. M. Sze, Physics of Semiconductor Devices, 3rd ed., Wiley, New York 2006, ch.3
Jasprit Singh, Semiconductors Devices Basic Principle, Wiley, New York 2001, ch.6