Photoemission

Semiconductors

Measure the density of states with photoemission spectroscopy

Photoemission spectroscopy

UPS - Ultraviolet photoemission spectroscopy

XPS - X-ray photoemission spectroscopy

From: Ibach & Lueth

Angle resolved photoemission spectroscopy (ARPES)

Measure the dispersion relation with angle resolved photoemission

http

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http

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Bi2Te3

Topological insulator

Inverse photoemission spectroscopy (IPES)

http://iopscience.iop.org/0034-4885/51/9/003

k-resolved Inverse Photoemission Spectroscopy (KRIPES)

http://iopscience.iop.org/0034-4885/51/9/003

Handbook of X-ray photospectroscopyJohn F. Moulder

XPS: Chemical identificationUPS: Valence electrons

XPS

XPS

XPS

Cu

ARPES

GaN

1st Brillioun zone of hcp

E

kxky

Free electron Fermi gas

-1 -12 2

2( ) J m2 F

m nD EE E E

1 - d

-1 -22( ) J m

F

m nD EE

2 - d

3 / 2-1 -3

2 2 3 / 2

2 3( ) J m2 2 F

m nD E E EE

3 - d

Semiconductors and insulators - 1d

*

2 2

-1 -3

*

2 2

2

( ) 0 J m

2

hv

v

v c

ec

c

m E EE E

D E E E E

m E EE E

Ev Ec

Eg

2 20

*

( )2k kE

m

Semiconductors and insulators - 2d

*

2

-1 -3

*

2

( ) 0 J m

hv

v c

ec

m E E

D E E E Em E E

Ev Ec

Eg

Semiconductors and insulators - 3d

32

32

*

2 3

-1 -3

*

2 3

22

( ) 0 J m

22

hv v

v c

ec c

mE E E E

D E E E E

mE E E E

Ev Ec

Eg

The free electron density of states is modified by the effective mass.

3 / 2*

2 2

2( )2 c

mD E E E

Density of electrons in the conduction band

1( ) exp1 exp B

B

Ef Ek TE

k T

Ev Ec

f(E)

3 / 2*

2 2

2( ) ( ) exp2

c c

cBE E

m En D E f E dE E E dEk T

BoltzmannapproximationEc - > 3kBT

Density of electrons in the conduction band

3 / 2*

2 2

2( ) ( ) exp2

c c

cBE E

m En D E f E dE E E dEk T

3 / 2*

222

Bc

m k TN

02xxe dx

exp cc

B

En Nk T

= effective density of states

Density of holes in the valence band

3 / 2*

2 2

2( )2

hv

mD E E E

11 ( ) 1 exp

1 exp B

B

Ef Ek TE

k T

Ev Ec

1- f(E)

3 / 2*

2 2

2( ) 1 ( ) exp2

v vE Eh

vB

m Ep D E f E dE E E dEk T

Boltzmannapproximation Ev > 3kBT

Density of holes in the valence band

3 / 2*

3 2 2

21 ( ) 1 ( ) exp2

v vE Eh

vB

m Ep N E f E dE E E dEL k T

exp vv

B

Ep Nk T

3 / 2*

222

h Bv

m k TN

= Effective density of states inthe valence band

Semiconductors

3 / 2

300 exp300

vv

B

ETp Nk T

3 / 2

300 exp300

cc

B

ETn Nk T

Conduction band

heavy hole band

light hole band

Eg k

E

The thermodynamic properties of insulators depend on band edges

Narrow bandgap semiconductors

Ev Ec

Use the programs for metals for small bandgap semiconductors.