Institute of Solid State Physics Technische Universität Graz 6. Photoemission Oct 18, 2018
Institute of Solid State PhysicsTechnische Universität Graz
6. Photoemission
Oct 18, 2018
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
Minimum of the conduction band
Free electron dispersion relation
k
E 22 0*2 c
k kE E
m
Ec
Conduction band minimum
Near the conduction band minimum, the bands are approximately parabolic.
Effective mass
2*
2
2( )x
md E k
dk
The parabola at the bottom of the conduction band does not have the same curvature as the free-electron dispersion relation. We define an effective mass to characterize the conduction band minimum.
This effective mass is used to describe the response of electrons to external forces in the particle picture.
22 0*2 c
k kE E
m
E
kxky
Top of the valence band
2*
2
2
0( )x
md E k
dk
In the valence band, the effective mass is negative.
Charge carriers in the valence band are positively charged holes.
m*h = effective mass of holes
E
k
2*
2
2( )h
x
md E k
dk
Holes
filled states
band empty states
empty states
( ) ( ) ( )
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
j ev k D k f k dk
ev k D k f k dk ev k D k f k dk
ev k D k f k dk
A completely filled band does not contribute to the current.
Holes have a positive charge and a positive mass.
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
-1 -3( ) 0 J m
cv
v
v c
vc
c
D E EE E
D E E E ED E E
E E
Ev Ec
Eg
2 20
*
( )2k kE
m
Semiconductors and insulators - 2d
-1 -3( ) 0 J mc v
v c
v c
D E ED E E E E
D E E
Ev Ec
Eg
Semiconductors and insulators - 3d
-1 -3( ) 0 J mc v v
v c
v c c
D E E E ED E E E E
D E E E E
Ev Ec
Eg
The electrical contribution to the thermodynamic properties of insulators depend on band edges
Silicon density of states
T = 300 K
1012
electrons in the conduction band
T = 300 K