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 eVExperimental value (Albers et al. (1962)): 0.9 eV

2

3

Soliman et al. (1995) – Dept. of Physics, Ain Shams University, Cairo

4

Lefebvre et al. (1998) – IEMN and LPMC, France

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

6Band gap: 0.643 eV

Polycrystalline SnSe

The band gap can be adjusted by doping element Te from 0.643 (no doping) to 0.608 eV (doping).

He et al. (2013) – Dept. of Material Science and Engineering, Nanjing Institute of Technology, China

Direct energy gap: 0.8 eVDebye temperature: 215 KGruneisen 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

13

Park et al. (2010) – Dept. of Physics, Missouri University of Science and Technology

Scheidemantel et al. (2003) – Dept. of Physics, Pen State University

14

Shi and Kioupakis (2015)

15

Shi and Kioupakis (2015)

16

Experiments, Soliman et al.

(1995)

Ab initio Calculation, Chen et al.

(2012)

Experiments, Zhao et al.(2014)

Ab initio Calculations, Shi and

Kioupakis (2015)

SemiclassicalNonparabolic 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 11

11

1 1

Degeneracy of first band,Degeneracy of second

band,

- - - - - - 22

22

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 bandHVB: Highest valence bandNote: 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.

Nonparabolic two-band model for p-type SnSe by Dr. HoSung Lee on 7/26/2014

Maldelung (1983) Thomas (1991) used 90 for Bi2Te3

density-of-state effective mass of hole for multiple valleys

density-of-state effective mass of electron for multiple valleys

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)

Lyden (1964) and Pei et al. (2012)

0 8.854 1012

A

2s4

m3

kg

ec 1.602110

19C kB 1.380610

23

J

K me 9.1093910

31kg

hp6.6260810

34 J s

2 NA 6.02213710

23 Nv 2

o 290 0

meff_h0 0.75 me

meff_e 8.5 me

meff_h T( )meff_h0

300K( )0

T0

md_h T( ) Nv

2

3

meff_h T( )

md_e Nv

2

3

meff_e

mI_h T( ) md_h T( ) mI_e md_e

Nv m*h m*e

Chen et al. (2014) 2 0.75 SPB model calculation

This work 2 0.75 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)

Mass density= mass/volume = molar mass/(NA*a^3),

Goldsmid (1964) and Maldelung (1983)

Atomic (molecular) masses, Periodic table

Atomic size, Vining (1991)

Atomic size, 2.9x10^-8 cm used by Larson et al. (2000)

Mean atomic mass

mass density, d = 8.219 gm/cm^3 by Malelung (1983)

Speed of sound, Zhao et al. (2014) gives 2.0 x 10^5 cm/s.

D 155K

dSn 5.76gm

cm3

dSe 4.81gm

cm3

MSn 118.71gm MSe 78.96gm y 0.5

aSn

MSn

NA dSn

1

3

aSn 3.247 1010

m aSe

MSe

NA dSe

1

3

aSe 3.01 1010

m

a aSn3

1 y( ) aSe3

y

1

3

a 3.133 1010

m

MSnSe MSn 1 y( ) MSe y

dMSnSe

NA a3

d 5.339gm

cm3

vs

kB

hp

6 2

1

3

D a vs 1.631 105

cm

s

18

200 400 600 800 1 103

1 1016

1 1017

1 1018

1 1019

1 1020

Holes (This work)

Electrons (This work)

Holes, Zhao et al. (2014))

T (K)

Carr

ier

den

sity

(cm

^-3)

nh n1 Ti Ti n1

cm3

ne n1 Ti Ti n1

cm3

p_data1

1019

Ti Ti p_data0

200 400 600 800 1 103

5

4

3

2

n = 3.3 x10^17 cm^-3

Temperature (K)

19

200 400 600 800 1 103

300

400

500

600

This work

Zhao et al. (2014)

T (K)

( V/K

)

200 400 600 800 1 103

0

20

40

60

80

100

This work

Zhao et al. (2014)

o 4.5 ec V

Z 0.1

Ka 1

1

cm1

200 400 600 800 1 103

0

0.2

0.4

0.6

0.8

Total thermal conductivity

Electronic thermal conductivity

Lattice thermal conductivity

Zhao et al. (2014)

T(K)

k (

W/m

*K

)20

21

1 1016

1 1017

1 1018

1 1019

1 1020

0

200

400

600

800

0

200

400

600

800

300 K

900 K

300 K

900 K

ni T1 T1 ni V

K

ni T3 T3 ni V

K

ni T1 T1 ni

1

cm1

ni T3 T3 ni

1

cm1

ni

cm3

Shi and Kioupakis (2015)

This work

200 400 600 800 1 103

0

1

2

3

This work

Experiment, Zhao et al. (2014)

Temperature (K)

ZT

1 1016

1 1017

1 1018

1 1019

1 1020

0

1

2

3

300 K

600 K

900 KZT ni T1 T1 ni

ZT ni T2 T2 ni

ZT ni T3 T3 ni

ni

cm3

3 2 1 0 1 2 30

0.5

1

1.5

Parabolic model

Kane model

Ab Initio calc. He et al. (2013)gSPM Ei

a3

ec V 1

gSKM Ei

a3

ec V 1

E_DOS ti

Ei

ec V

Ei

ec V

ti

ec V

0 200 400 600 800 1 103

0

0.1

0.2

0.3

Prediction, this work

Experiment, Zhao et al. (2014)

T (K)

Cv

(J/

g.K

)

22

The End

23