Electronic Band Structures
for Tin Selenide
Dr. HoSung Lee
April 2, 2015
1
Car et al. (1978) – Istituto di Fisica del Politecnico, Milano
Calculated bandgap: 2.1 eV
Experimental value (Albers et al. (1962)): 0.9 eV
2
Soliman et al. (1995) – Dept. of Physics, Ain Shams University, Cairo
3
Lefebvre et al. (1998) – IEMN and LPMC, France
4
Makinistian and Albanesi (2009) – Universidad Nacional de Entre Rios, Argentina
Indirect bandgap, C1-V1: 1.05 eV
5
Chen et al. (2012) – Tongji University, China
Polycrystalline SnSe
The band gap can be
adjusted by doping
element Te from
0.643 (no doping) to
0.608 eV (doping).
Band gap: 0.643 eV
6
He et al. (2013) – Dept. of Material Science and Engineering, Nanjing Institute of Technology, China
Direct energy gap: 0.8 eV
Debye temperature: 215 K
Gruneisen parameter: 2.98
7
Sun et al. (2013) – Chinese Academy of Sciences, China
8
Zhao et al. (2014) – Dept. of Chemistry, Northwestern University
9
Zhao et al. (2014) – Dept. of Chemistry, Northwestern University
10
Shi and Kioupakis (2015) – Dept. of Material Science and Engineering, University of Michigan
11
Shi and Kioupakis (2015)
12
Park et al. (2010) – Dept. of Physics, Missouri University of Science and Technology
Scheidemantel et al. (2003) – Dept. of Physics, Pen State University
13
Shi and Kioupakis (2015)
14
Shi and Kioupakis (2015)
15
Experiments,
Soliman et al.
(1995)
Ab initio
Calculation,
Chen et al.
(2012)
Experiments,
Zhao et al.(2014)
Ab initio
Calculations, Shi and
Kioupakis (2015)
Semiclassical
Nonparabolic Two-Band
Kane Model
(fit to measurements of
Zhao et al. (2014))
Band edge
LCB
HVB
LCB
HVB
LCB
HVB
LCB
HVB
LCB
HVB
First band,
Second band
-
-
-
-
1
1
1
1
1
1
1
1
Degeneracy of first band,
Degeneracy of second
band,
-
-
-
-
-
-
2
2
2
2
2
(4)
2
(4)
DE (eV) =
First band – second band
-
-
-
-
-
Band gap, Eg (eV)
0.895
0.643
0.61-0.39
0.83-0.46
0.74 – 0.95x10-4T
Single DOS effective
mass (md)
-
-
4.02mo
1.06mo
-
-
-
2.4mo
3.0mo
0.74mo
0.34mo
5.35 mo
(3.3mo)
0.47 mo
(0.3mo)
Integral DOS effective
mass (m*)
-
-
-
-
-
-
-
-
8.5 mo
0.75 mo
LCB: Lowest conduction band
HVB: Highest valence band
Note: This work assumes that the multiple bands are equal to multiple valleys. The effective
masses are calculated using the relationship of md = (mxmymz)1/3 and m* = Nv2/3 md.
16
Nonparabolic two-band model for p-type SnSe by Dr. HoSung Lee on 7/26/2014
 23 J
 19
ec  1.6021 10
kB  1.3806 10
C
 34
h p 
6.6260810

J s
 31
me  9.1093910

K
23
NA  6.02213710

2 
 o  290  0
2 4
 12 A  s
kg
Maldelung (1983)
Thomas (1991) used 90 for Bi2Te3
density-of-state effective mass of hole for multiple valleys
meff_e  8.5 me
density-of-state effective mass of electron for multiple valleys
meff_h0
( 300K )

md_h ( T)  Nv
0
T
3
m  kg
Nv  2
meff_h0  0.75 me
meff_h ( T) 
 0  8.854  10
Bejenari (2008) used exponent 0.2 for Bi2Te3 and exponent 0.2 for Si by Barber (1967) and
exponent of 0.8 for PbTe by Lyden (1964)
0
2
3
 meff_h ( T)
mI_h ( T)  md_h ( T)

md_e  Nv
2
3
 meff_e
Lyden (1964) and Pei et al. (2012)
mI_e  md_e
Chen et al. (2014)
Nv
2
m* h
0.75
This work
2
0.75
m*e
SPB model calculation
Calculation
Nv: multiplicity of valleys
17
Debye temperature θ =65K by Zhao et al. (2014), θ =215 K for SnSe by He et al. (2013)
D  155K
gm
d Sn  5.76
d Se  4.81
3
cm
MSn  118.71gm
gm
Mass density= mass/volume = molar mass/(NA*a^3),
Goldsmid (1964) and Maldelung (1983)
3
cm
MSe  78.96gm
Atomic (molecular) masses, Periodic table
y  0.5
1
 MSn 
aSn  

 NA  d Sn 
1
3
 10
aSn  3.247  10
 MSe 
aSe  

 NA  d Se 
m
3
 10
aSe  3.01  10
m
1
a  aSn  ( 1  y )  aSe  y


3
3
3
 10
a  3.133  10
m
Atomic size, Vining (1991)
Atomic size, 2.9x10^-8 cm used by Larson et al. (2000)
Mean atomic mass
M SnSe  M Sn  ( 1  y )  M Se y
d 
M SnSe
NA  a
d  5.339
3
gm
mass density, d = 8.219 gm/cm^3 by Malelung (1983)
3
cm
1
v s 
kB
hp
 2 3 Da
 6 
5 cm
v s  1.631  10 
s
Speed of sound, Zhao et al. (2014) gives 2.0 x 10^5 cm/s.
18
Carrier density (cm^-3)
110
 

nh  n1 T i T i n1

110
20
19
Holes (This work)
Electrons (This work)
Holes, Zhao et al. (2014))
2
3
3
cm
 


ne  n1 T i T i n1
110

18
3
cm
p_data
 1
4
19
 10
110
17
5
200
110
16
200
400
600
T i T i p_data
800
 0
110
3
400
600
800
3
110
Temperature (K)
n = 3.3 x10^17 cm^-3
T (K)
19
600
0.8
  400
k (W/m*K)
(
V/K)
500
This work
Zhao et al. (2014)
300
200
400
600
3
0.2
0 o  4.5 ec V
400
200
100

1

1
cm

0.4
110
800
T (K)
80
0.6
Z  0.1
This work
Zhao et al. (2014)
Ka  1
600
800
3
110
T(K)
Total thermal conductivity
Electronic thermal conductivity
Lattice thermal conductivity
Zhao et al. (2014)
60
40
20
0
200
400
600
800
110
3
20
800


300 K
900 K
300 K
900 K

  ni T 1 T 1 ni 600
V
K


  ni T 3 T 3 ni
V
K
 400


  ni T 1 T 1 ni
1
1
600
  cm
400
  ni T 3 T 3 ni


1


1
  cm
200
0
16
110
800
200
17
110
110
18
19
110
0
20
110
ni
3
cm
Shi and Kioupakis (2015)
This work
21
3
3
This work
Experiment, Zhao et al. (2014)
  

ZT    ni T 2 T 2 ni
ZT    ni T 3 T 3 ni
1
ZT  ni T 1 T 1 ni 2
ZT
2
1
0
16
110
0
200
400
600
110
800
300 K
600 K
900 K
17
110
3
18
110
19
110
20
110
ni
3
cm
Temperature (K)
0.3
1.5

gSPM Ei
a
3


 ec V

1
gSKM Ei

E_DOS t i
a
3

 ec V
0.2
Cv (J/g.K)

Parabolic model
Kane model
Ab Initio calc. He et al. (2013)
1

1
0.1
0.5
Prediction, this work
Experiment, Zhao et al. (2014)
0
3
0
2
1
0
Ei

Ei
1

ti
ec V ec V ec V
2
3
0
200
400
600
T (K)
800
110
3
22
The End
23