1. No category

Lattice Thermal Conductivity
for Bismuth Telluride
Dr. HoSung Lee
April 23, 2015
1
Satterthwaite and Ure (1957) – Westinghouse Research Laboratory, Pittsburg, Pennsylvania
2
Satterthwaite and Ure (1957) – Westinghouse Research Laboratory, Pittsburg, Pennsylvania
3
Wagner et al. (1978) – Physics Institute of University of Würzburg
4
Wagner et al. (1978) – Physics Institute of University of Würzburg
5
Rauh et al. (1981) – Physics Institute of University of Würzburg
6
Kullmann et al. (1990) - Physics Institute of University of Würzburg
7
Kullmann et al. (1990) - Physics Institute of University of Würzburg
8
Kullmann et al. (1990) - Physics Institute of University of Würzburg
9
Huang and Kaviany (2008) – University of Michigan
10
Huang and Kaviany (2008) – University of Michigan
11
Huang and Kaviany (2008) – University of Michigan
12
Qiu and Ruan (2009) – School of Mechanical Engineering, Purdue University
13
Qiu and Ruan (2009) – School of Mechanical Engineering, Purdue University
14
Chi et al. (2013) – Uhre’s group - Dept. of Physics, University of Michigan
15
Chi et al. (2013) – Uhre’s group - Dept. of Physics, University of Michigan
16
Chi et al. (2013) – Uhre’s group - Dept. of Physics, University of Michigan
17
Electronic Thermal Conductivity

 kB 
Le(  T n )   
 ec 
This Work

2 F 
e 2  1 T n
  2


  3

 Fe 0 2 1 T n
 


 kB 
Lh (  T n)   
 ec 
3

2 F 
h  2  1  T n
3
  2


  3

 Fh  0 2 1  T n
 

 F  1 3 1 T n 

 e 2



 Fe 0 3 1 T n 
  2

2





 F  1 3 1 T n 

 h  2



3
 Fh  0  1 T n 
  2

ke(  T n )  Le(  T n)  e(  T n)  T  Lh (  T n )  h (  T n )  T 
2





e(  T n )  h (  T n )
(  T n )
Lattice Thermal Conductivity
2
Drabble and Goldsmid (1961)
Melting point
TM  848K
 s  39

 T h (  T n )  e(  T n)
Strain parameter for point defects, Abeles (1963) used 39 for SiGe.
M  MBi  MTe
Vo  a
3
Mean atomic volume
18
This Work
a  aBi  aTe
 M 
a
s  y ( 1  y)  
  s  
 MBiTe 
 a


2
  1.79
 


2
Disorder parameter or mass-fluctuation-scattering parameter
Abeles (1963)
s  0.064
Gruneisen parameter, Madelung (1983)
γ = 2 is often used to describe the anharmonisity effects on the thermal conductivity.
  2
The ratio of Normal to Umklapp processes, β = 2 is used for SiGe by Steigmeier and Abeles (1964)
1




3  1  5  
 20 
2
2
3

 6   
9 

T  2

 

 U( xT)  
 NA  hp  


x

2  D 
 4   1   M
 3
 
BiTe a 


T1  300K
1
Phonon relaxation time for Umklapp process, Klemens
(1958), Steigmeier and Abeles (1964), and Vining (1991)
 N( xT)     U( xT)
4

 kB T  4

 Vo s   h   x 
 p  
 PD( xT)  
3


4   v s


x1  2


11
 U x1 T1  10
3
 9.587  10
s
1
Point defects ,Klemens (1955), Vining (1991)
and Klemens (1958)


11
 PD x1T1  10
5
 8.786 10
s
19
This Work
1 md_h  v s
Erc ( T)  
2
kB T
2
Reduced carrier energy
2




x
x   



1  exp Erc( T)   

2
3

16 Erc( T)
2   
 o  md_h  vs 



 EP(  xT)  
  x  ln
 
4
2

 4   hp  d  Erc( T) 

x
x   


 1  exp Erc( T)    16 E ( T)  2   
rc




  
 latt(  xT)    N( xT)

1
  U( xT)
1
  PD( xT)
1
  EP(  xT)
 1
1
Electron-phonon scattering,
Zieman (1956) and Vining (1991)
1
Combined phonon relaxation time

D
 kB T 
klatt(  T) 


2
h
2   v s  p 
kB
3 T





4 x
 latt (  xT) 
x e
ex  1
2
dx
x
h 
kB T
Debye-Callaway formula
0
k (  T n )  klatt (  T)  ke(  T n )
 150

200
Data_k_Goldsmid  
 250
 300

2.7 

2.2 
2.1 

2.3 
20
This Work
Prediction, this work
Experiments, Rauh (1981)
Debye cut-off freq.
  0.8
 1012  Hz   1
0.6
P_DOS t2 i
gph  i
1
 max
 1012  Hz   1
0.4
0.2
0
0
1
2
 i 10
 12
Hz
t2 i 
3
0  12
 max  10
4
5
Hz
150


 U xi T 2  f  xi
 
 EP   n1 T 2 xi T 2  f  xi
 latt    n1 T 2 xi T 2  f  xi
 PD xi T 2  f  xi
110
110
8
Cv (J/mol.K)
110
 10
 12
110
 14
110
 16
0.01
0.1
1
 i 10
10
 12
Hz
100
50
Prediction, this work
Experiment, Bessas et al. (2012)
100
0
0
100
200
T (K)
300
21
22