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Lundstrom ECE 305 S16
ECE-305: Spring 2015
Carrier Properties: I
Professor Mark Lundstrom Electrical and Computer Engineering
Purdue University, West Lafayette, IN USA [email protected]
1/19/15
Pierret, Semiconductor Device Fundamentals (SDF) pp. 32-40
Lundstrom ECE 305 S16 2
outline
1. Effective mass and bandstructure
2. Doping
3
free electron mass
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F t( ) υ t( )
F = m0 a
x t( )
m0 = 9.11×10−31 kg
q= 1.6×10−19 C
charge= −q
“effective mass” of electrons
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F = m0 a → mn* a
“effective mass” for electrons
Si: GaAs:
mn* = 1.18m0
mn* = 0.066m0
“crystal potential”
effective mass of holes
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F = m0 a → mp
* a
effective mass for holes
Si: GaAs:
mp
* = 0.81m0
mp
* = 0.52m0
energy and momentum (free electron)
6 Lundstrom ECE 305 S16
F t( ) υ t( )
F = m0 a
x t( )
E = 1
2m0υ
2 = p2
2m0
E
p = m0υ
energy and “crystal momentum”
7 Lundstrom ECE 305 S16
E
p = !k
E = p2
2m0
→ E = EC +p2
2mn*
“band structure”
EC
EV
E = p2
2m0
→ E = EV −p2
2mp*
“direct bandgap”
k = 2πλ
energy and “crystal momentum”
8 Lundstrom ECE 305 S16
E
p = !k
E = p2
2m0
→ E = EC +p2
2mn*
EC
EV
E = p2
2m0
→ E = EV −p2
2mp*
“indirect bandgap”
charge carriers in semiconductors
9 Lundstrom ECE 305 S16
1) Electrons in the conduction band (“electrons”):
Free to move about within the crystal Can be treated as Newtonian particles with an effective mass.
2) Holes in the conduction band (“holes”):
Free to move about within the crystal Can be treated as Newtonian particles with a different effective mass.
Lundstrom ECE 305 S16 10
outline
1. Effective mass and bandstructure
2. Doping
✔
doping
11
Phosphorus or Arsenic
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Gallium or boron
dopants
12 Lundstrom ECE 305 S16
column IV
n-type doping
13
Phosphorus or Arsenic
Weakly bound Easily broken at room temperature
EB = −13.6 eV
EB = −m0q
4
2 4πε0!( )2 eV
KS = 11.8
EB ≈ −0.1eV
mn* = 1.18m0
Lundstrom ECE 305 S16
n-type doping
14
Phosphorus or Arsenic
“Ionized donor” + N D cm-3
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N D+ ≈ n
energy band view (n-type)
15
n-doped Si
EC
EV
EG = 1.1eV
n ≈1018cm−3
p = ?cm−3
ED ≈ 0.05 eV
1014 ≤ N D ≤1020 cm−3
Lundstrom ECE 305 S16
N D = 1018cm−3
N D+ = 1018cm−3
n ≈ N D+ = 1018cm−3
p ≈ ?
(T = 300 K)
p-type doping
16
Gallium or boron
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p-type doping
17
Gallium or boron
Missing bond
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p-type doping
18
Gallium or boron
Ionized acceptor
N A cm-3
_
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N A− ≈ p ≈ N A
energy band view (p-type)
19
p-doped Si
EC
EV
EG = 1.1eV
n = ?cm−3
EA ≈ 0.05 eV
N A = 1018cm−3
N A− = 1018cm−3
p ≈ N A− = 1018cm−3
n ≈ ?
p ≈1018cm−3
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question
20
1) Which of the following atoms would be an n-type dopant in Si?
a) Ga (a column III) element) b) Si (a column IV element) c) As (a column V element) d) O (a column VI element) e) F (a column VII element)
Lundstrom ECE 305 S16
Another question
21
2) What type of dopant is Si in GaAs?
a) n-type b) p-type c) either n-type or p-type d) neither n-type nor p-type e) don’t know
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temperature dependence
22 Pierret, SDF, Fig. 2.13
N-type
P-type
carrier concentration vs. temperature
23 23 Fig. 2.22 from R.F. Pierret, Semiconductor Device Fundamentals
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outline
1. Effective mass and bandstructure
2. Doping
✔
✔