Lundstrom ECE 305 S16

ECE-305: Spring 2015

Carrier Properties: I

Professor Mark Lundstrom Electrical and Computer Engineering

Purdue University, West Lafayette, IN USA lundstro@purdue.edu

1/19/15

Pierret, Semiconductor Device Fundamentals (SDF) pp. 32-40

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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

Lundstrom ECE 305 S16

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

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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)

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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

✔

✔