prof. junqiao wu department of materials science and engineering, u.c. berkeley

1

Prof. Junqiao Wu

Department of Materials Science and Engineering, U.C. Berkeley

wuj@berkeley.edu, 322 HMMB, 510-642-4391

Summer Lectures on

Semiconductor Physics for Engineers

Contents: 1. Semiconductor basis (2 lectures, 6/2, 6/4)

General trends, k-space, band structure, density of states and Fermi distributionkp theory, defects and effective mass approximationQuantum confinement and nanostructures

2. Electrostatics (2 lectures, 6/8, 6/11)Maxwell equations and Poisson’s equationBand bending and carrier equilibration

3. Electrodynamics (2 lectures, 6/16, 6/18)Drude’s model and classical dielectric theoryBoltzmann transport theory

4. Thermal effects (2 lectures, 6/23, 6/25)Phonons and thermal physicsThermoelectrics

5. Optical effects (1 lecture, 6/30)Light-semiconductor interactionsDevice physics of light emitting diodes and solar cells

Prerequisites:calculus, vectors, ordinary and partial differential equations, linear algebra, electromagnetism, optics basics, solid state physics basics, quantum mechanics basics

Time and location:Tuesday and Thursdays 5:00-6:30PM, June 2009. Rm350, HMMB.

Website: http://www.mse.berkeley.edu/~jwu/courses/semi.html

2

s2p2

cation and anion

Most common semiconductors: group IV (Si), III-V (GaAs), II-VI (CdSe), and their alloys

Insulators: group I-VII (NaCl)

3

General trends in semiconductors

1.0

1.5

2.0

2.5

3.0

3.5

0 10 20 30 40 50

ele

ctro

ne

ga

tivity

(e

V)

atomic number

Gordy, et. al.J. Chem. Phys.24(2), 439(1956)

O

SSe

N

B

C

P Te

Sb

As

Zn

Mg

Be

Si

GaAlSn

Ge

InCd

covalent

ionic

4

bandgap

Conduction bands

Valence bands

simple cubic face-center cubic zincblende

Brillouin zone(for fcc structure)

5You won’t regret visitinghttp://www.ioffe.ru/SVA/

6

n-doped

p-doped

Fer

mi

Si

7

Defects in semiconductors

8

9

Band offsets

10

Schottky Contact: example of M/nS with M>S

qM

qS q

ECB

EVB

EFM

EFS

before contact

qM

qS

q

ECB

EVB

EFM EFS

after contact

qVi=q(M-S)

qViqB

-

-

WD

i

qN

VW

2

-- + +-+

-+

vacuumlevel

- -+ +

-+

-+

11

Ohmic contact

Work function

12

net charge distribution

S D

nanowire

oxidegate

air

Nano Lett.; 7, 2778 (2007).

8

10

12

14

16

18

20

22

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

npN

d

log(

conc

entr

atio

n) (

cm-3

)

V (V)

DO

S (

1021

eV

-1cm

-3)

E (eV)

0

2

4

6

8

-2 -1 0 1

VBCB

Si @ 300K

13

p-n junction and depletion width

+ + + + +- - -

-----+ + +EF

-

-

+

+ ionized donor

ionized acceptor

free electron

free hole

+

- +-+-

+ -

-++ - +

--

--

---+++

++ +

-+

n-type p-type

ND NA

+

- +-+-

+ -++ - + -

--

---++

++ +

-dx

dnqDJ n

diffn diffusion current

+ + + + +- - - - -

-----+ + + + +

EFn

EFp

ED EA EgqV0

gi

DAB E

n

NNTkqV

20 ln

W DqN

VW 04

for ND=NA

drift current

dx

dEqn

EqnJ

cn

ndriftn

0

Total net current = 0 (unless externally biased)

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I

V0

forwardreverse

Biasing a diode

n p

Vf

n p

Vr

n p

pn

nn

P

P

TkqV

nL

pL

qAI

eII B

0

/0 ,1

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Hot carriers

resistivity

mobility

16

Phonon spectrum1D diatomic chain

Wavevector q

2xTA

1xLA

1xLO

2xTO

Si

17

Phys. Rev. 98, 940 (1955)

Bulk Si Seebeck coefficient

18

Natural Si(28Si=92%29Si=5%30Si=3%)

enriched Si(28Si=99.9%)

Majumdar, Science (2004)

Thermal conductivity and thermoelectric figure of merit

19

Reflected– Same energy (h) and

wavelength ()– Specular: 1’ = 1

Refracted then Absorbed– Snell’s law: n1sin1=n2sin2

– Frequency: 1 = 2 = = /2– Speed of light: n1c1 = n2c2

– Wavelength: n1 1=n2 2

– Intensity: I exp(-d)– Absorption: (h) (h-Eg)1/2

Transmitted 3 = 1

3 = 1, 3 = 1

Scattered– Rayleigh scattering, h = h1

– Raman and Brillouin scattering, h = h1 ħ

– not directional Emitted

– not directional– h Eg

incident

reflected

transmitted

scatteredabsorbed

emitted

1

21’

n1 n2

3

d

iir

ii

ir

ir

irir

ncnc

n

nn

nn

n

nR

iinnn

0

22

22

2

2

0000

22

2

,1

1

1

1

;1; EP

Optical process in semiconductors

20

k

kk

kk

k

cv

cvp

cv

p

m

P

m

e

di

2

0

2

22

2

0

2 where

,0

1

ħ

ri

0

GaAs

E1E0

E2

R

0

R

ħE0 E1 E2

(E-E0)1/2 for directbandgap semiconductors

Dielectric Functions of Semiconductors

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Absorptions in SemiconductorsA

bso

rptio

n co

effi

cien

t (cm

-1)

Photon energy (eV)

Wavelength (m)

10-3 10-2 10-1 100 101

100

102

104

106

103 102 101 100 10-1

bandgap

exciton

deeper-bands

free carrier

phonons (lattice vibration)

local impurity vibration

impurity electronic

cyclotron, spin, magnon

core levels

CB

VB+

-

-

+

-

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Fundamentals of photovoltaics

1. “Red” loss

2. Thermalization loss (“blue loss”)

3. Junction loss

4. Contact loss

5. Recombination loss

6. Reflection loss

usable qV

2

345

2

illumination1

6

23

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LED materials

InG

aN

AlG

aAs

AlG

aPA

lGaI

nPG

aAsP

GaP

N

GaN

ZnSe

,

AlN

AlG

aN

GaA

s