Download Doped Semiconductors - UT Mechanical Engineering

ME 381R Lecture 13:
Semiconductors
Dr. Li Shi
Department of Mechanical Engineering
The University of Texas at Austin
Austin, TX 78712
www.me.utexas.edu/~lishi
[email protected]
1
Free Electron Bands
Free electron band
• Origin of Energy Bands
R
0
3p
V(r) ˜ -1/r
Discrete Electronic
Energy States
Atom 2
Atom 1
Energy (eV)
-5
3s
-10
-25
R
Split Energy
Levels
-30
-35
Atom 1
Atom 2
Pauli’s Exclusion Principle
2p
0
3.67 5
10
Interatomic Distance (Å)
Na: 1s22s22p63s1
2
Semiconductors
X (real space)
3
K Space
Semiconductor
Forbidden
gap
Metal
E
k
k
4
Band Gap Energy: Eg
5
How is the Band Gap formed?
•For free electron in metals: U 0 because of high electron density
and short electrostatic screening length
•Electron wavefunction scattered by periodic potentialstanding
wave when K= np/a (think about interference of light)
6
Multiple Bands
7
Bandgap Formation
8
Bandstructure of Si and GaAs
9
Electrons and Holes
10
Charge Carrier Density
Parabolic approx (free electron):
Electron:
Hole:
m*: effective mass
11
f(E) and D(E)
Intrinsic Semiconductor
Doped Semiconductor
12
Law of mass action:
13
Intrinsic Semiconductors
14
Doped Semiconductors
15
Dopant Energy Level
16
Carrier Densities in Doped Semiconductors
“Law of Mass Action” for semiconductors
Charge accounting:
17
Charge Density in Doped Semiconductors
Charge neutrality
(accounting):
Occupation of donors by electrons:
Occupation of acceptors by holes:
From now on: pure n-type semiconductor (pure p-type is similar)
Approximation
= 0 (Only one type of dopant at a time)
18
where
19
Temperature Dependance of Carrier Concentration
I) Low temperature limit
Carrier freeze-out
II) Higher temperature limit
Saturation
III) Muy caliente limit: n ~ ni  intrinsic region
20
Carrier Density
vs. Temperature
HOT
COLD
21
Carrier Transport in Semiconductors
• Current Density:
• Mobility:
• Electrical Conductivity:
• Drift Velocity:
22
Carrier Scattering
Carrier Scattering Mechanisms
• Defect Scattering
• Phonon Scattering
• Boundary Scattering (Film Thickness,
Grain Boundary)
Grain
Grain Boundary
23
Carrier
Scattering
•Intra-valley
•Inter-valley
•Inter-band
24
Defect Scattering
(i) Ionized defects
Perturb potential
periodicity
Charged defect
(ii) Neutral defects
25
Scattering from Ionized Defects (“Rutherford Scattering”)
•Average Carrier Velocity in Semiconductors
(not the drift velocity):
•Mean Free Time:
1/  <v>-3  T-3/2
•Mobility:
26
Carrier-Phonon Scattering
• Phonon modulates the periodic potential
1/ph~
Carrier scattered by moving potential
27
Mobility
28
Electrical Conductivity
29