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p n - Transverse Thermoelectrics:
A new class of Materials with
Possible Optoelectronic Applications
Matthew Grayson m-grayson@northwestern.edu
EECS, Northwestern U.
Chuanle Zhou (post-doc), Boya Cui, Yang Tang (PhD)
Stefan Birner (NextNano / TU Munich)
Karen Heinselman
Phys. Rev. Lett. 110, 227701 (2013)

p x n Transverse Thermoelectrics:
Outline:
I. Transverse Thermoelectricity
II. Type II broken-gap superlattices

The Dawn of Thermoelectricity
Edmund Altenkirch, Phys.Zeits. 10, 560 (1909); 12, 920 (1911).
Figure of Merit
2
ZT = T
INTENSIVE PARAMETERS
S – Seebeck coefficent r
– Electrical resistivity k
– Thermal conductivity

Z
||
T
= r
2
S xx xx k xx
T

T
H
C
T
PE

E
C
E
D
V
PE
=
E
V
Semi kT e h +
D
C
Metal Semi
D
PE
=
(
D
V
+D
C
)
T
H

T
H h + h + h +
Double-leg
T
C kT e e e -
T
H
I

Z
^
T
= r
2
S xz xx k zz
T

T
H e kT
C
T
PE

E
C
D
D
C
V
PE
=
E
V
Semi h +
Metal
D
PE
=
(
D
V
+D
C
)
=
E
G

Nernst-Ettingshausen effect
Single-leg
T
H h + h + e -
B e h +
C
T kT e -
I
Symmetry broken by B-field
DISADVANTAGE: REQUIRES LARGE B-field (1.5 T)
K.F. Cuff, Appl. Phys. Lett. 2, 145 (1963); C.F. Kooi, J. Appl. Phys. 34, 1735 (1963)

Stacked synthetic composites
Single-leg semi-metal p-type semi e h + h + e -
T
H h + e e h +
C
T kT
I
Symmetry broken by structure
DISADVANTAGE: Thick (~mm) layers cannot be scaled down
Labor intensive fabrication
V.P. Babin, Sov. Phys. Semicond. 8, 478 (1974); Reitmaier, Appl. Phys. A 99, 717 (2010)

p x n Transverse Thermoelectrics p n “n-type” in one direction….
h + h + h + e e e e h + h + h + e e e -
“p-type” orthogonal….
h + h + h + e e -
Symmetry broken by band structure anisotropy

p x n Transverse Thermoelectrics p e n e e -
J
Q h + h + h + e e e h + h + h + e e -
E h + h + h + e -
Symmetry broken by band structure anisotropy

p x n Transverse Thermoelectrics
I
T e -
C kT e h + e h + p n h +
Q
T
H
Symmetry broken by band structure anisotropy
ADVANTAGE: Scalable to cm or m m
No external B-field

Transverse Seebeck voltage generator
+V E

T p n
-V

Transverse Seebeck voltage generator
Meander structure:
Arbitrarily large Seebeck voltages V with small
D
T p n
E

T
H. J. Goldsmid, J. Elec. Mat.,40 5, 1254 (2010).

Transverse Peltier cooler
J
Q p n

Transverse Peltier cooler
Exponential Taper:
Arbitrarily large
D
T with finite current J
J
Q p n
C. F. Kooi et al.
, Appl. Phys. 34, 1735 (1963)

Annular Peltier cooler
Every angle of current takes heat away from center p n
J
Q

p x n Seebeck tensor
• Seebeck Tensor s n


 s n
0
0 s n

 , s p



 s
0 p
0 s p



• Electrical conductivity Tensor
σ n




 n
0
0
, xx

0 n , yy



,
σ p
• Total Seebeck Tensor
S

(
σ p
 σ n
)

1
(
σ




 p , xx
0 p s p


0 p
0
, yy



σ n s n
)
S


 s
0 p
0 s n


, s p

0 , s n

0
S
¢ =
R
-
1 q
é
ê s p
0
0 s n
ù
ú
R q
=
é
ê s aa s ba s ab s bb
ù
ú p n b y a q x

• Optimal angle cos
2 q


1

• Optimal transverse figure of merit
1 k yy r yy
/
/ k xx r xx
Z

T

Z ba
( q

) T
 
( S p , xx r xx k xx

S n , yy
)
2
T
 r yy k yy

2 p n b y a q x

p x n Transverse Thermoelectrics:
Outline:
I. Transverse Thermoelectricity
II. Type II broken-gap superlattices

Transverse thermoelectric figure of merit:
Z
^
T
= r
2
S xz xx k zz
T

InAs/GaSb Type II superlattice
 InAs/GaSb type II broken-gap superlattice (T2SL)
– Tunable bandgap
– Anisotropic electron-hole transport
– Fabrication challenge: strain, interface diffusion

Minimal Sb segregation
Up to 15 um superlattice growth with smooth morphology
M. Razeghi, Binh-Minh Nguyen, et al.
Proc. SPIE 6206, 0277-786X/06 (2006)
Type II superlattice photodetectors for MWIR to VLWIR Focal Plane Arrays

Thermal Conductivity: Experiment
Z
^
T
= r
2
S xz xx k zz
T

3 w
Thermal Conductivity
 Vertical thermal conductivity proportional to 3 rd harmonic
R +
D
R ( T )
GaSb substrate
Type II thin film
+I +V -V -I k =
D
D
4 p
R ~ (
V
LR
2 w
3
( V dR/dT
2
)
I ~ e i w t ln f
1
R ~ e
3 w
,1
/f
-
T ~ e
2 i2 i2 w
V w t t
3 w
,2
) dR dT
D
V = I
D
R ~ e i3 w t
D. G. Cahill, Rev. Sci. Instrum. 61(2) 802, (1990).
D. G. Cahill, Phys. Rev. B 50, 6077 (1994).
2 mm thin film substrate
Chuanle Zhou, MG, et al. J. Elect. Mat. (2012)

3 w
Thermal Conductivity
 Vertical thermal conductivity proportional to 3 rd harmonic
R +
D
R ( T )
GaSb substrate
Type II thin film
+I +V -V -I k =
V w
3 ln f
1
4 p
LR
2
( V
3 w
,1
/f
2
-
V
3 w
,2
) dR dT
D
V = I
D
R ~ e i3 w t
D. G. Cahill, Rev. Sci. Instrum. 61(2) 802, (1990).
D. G. Cahill, Phys. Rev. B 50, 6077 (1994).
l
~ d thin film substrate k film
D T f k out of phase
100 1000 10000 f (Hz)
Chuanle Zhou, MG, et al. J. Elect. Mat. (2012)

Type II Superlattice Thermal Conductivity
Thermal conductivity suppressed up to 2 orders of magnitude from
GaSb bulk value
1000
InAs[4]
GaSb[5]
+
GaSb
T2SL
100
10
1
1 10
T (K)
100
Chuanle Zhou, MG, et al unpublished

Power Factor: Theory
Z
^
T
=
2
S xz r xx k zz
T

InAs/GaSb Type II superlattice
 InAs/GaSb type II broken-gap superlattice (T2SL)
– Tunable bandgap
– Anisotropic electron-hole transport
– Fabrication challenge: strain, interface diffusion

Type II Superlattice
NextNANO 3 : Full-band envelope-function simulation InAs/GaSb superlattice dispersion
Positive gap:
Semiconductor
Zero gap
20
10
Ee (k
||
)
E hh
(k
||
)
Ee(k

)
Ehh(k

)
20
10
0 D
= 10.05 meV
0
-10 -10
5.4nm GaSb/7.5nm InAs
(21ML GaSb/22ML InAs) k
||
(Å
10
-0.005
)
8.53nm GaSb/7.87nm InAs
(28ML GaSb/26ML InAs) k
0.015

(Å
-1
10
)
0
D
= 0.13
meV
0 k
||
-10
-20
(Å
Ee (k
||
)
E
-0.005
) hh
(k
||
)
0.000
Ee(k

)
Ehh(k
0.005

)
0.010
k

-10
-20
0.015
(Å
-1
)

Deduce Conductivity & Seebeck Tensor
From band structure => m n , x
, m n , y
, m p , y
, E g
( m p , y
= ¥
)
For n -conductivity & Seebeck: anisotropic 3D dispersion s n , xx
=
2 2 e
2 g
3 p
2 3 m n , y
( k
B
T ) s
+
3/2 G
( s
+
3
2
) F
3/2
+ s è m -
E g k
B
T
ö
,
ø s n , yy
=
2 2 e
2 g
3 p
2 3
2 m n , x ( k
B
T ) s
+
3/2 m n , y
G
( s
+
3
2
) F
3/2
+ s è m -
E g k
B
T ø
For p -conductivity & Seebeck:
2D dispersion s p , xx s p , yy
= e
2 g p d
2
( k
B
T ) s
+
1 G
( s
+
2) F
1
+ s
m
è k
B
T ø
=
0 s n
= k e
B
ê
ê
ê
é
ê
ë
(
( s
+
5 / 2
)
F s
+
3
2 s
+
3 / 2
)
F s
+ 1
2
ç
æ
è
ç
æ
è m -
E g k
B
T m -
E g k
B
T
÷
ö
ø
÷
ö
ø
m -
E g k
B
T
ú
ú
ú
ù
ú
û s p
= k
B e
ê
ê
ê
é
ê
ë
( s
+
2
)
F
( )
F s
+
1 s
ç
æ
è
ç
æ
è
-
m m k
B
T k
B
T
÷
ö
ø
÷
ö
ø
+ m k
B
T
ú
ú
ú
ù
ú
û t = g
E s
(Power-law scattering, , where s = 0 observed for T2SL at 300 K)
Optimize transverse power factor S 2

=> deduce optimal chemical potential m
Chuanle Zhou, MG, submitted to PRL


Optimal T2SL




 d
E g q

GaSb
= 3.96 nm, d
InAs
= 28.3 meV,
= 32  m
= 7.88 nm
= 2.43 meV k = 4 W/ m∙K (measured 1 )
Z

T = 0.025 at T = 300 K p n b y a q x
1 C. Zhou et al., J. Elec. Mat. (2012)

Differential Transport Equations
 Transverse Thermoelectrics
0




E a
S ba
 dT db 

 2

( 1

Z ba
T )
Z ba d
2
T db
2
S ba

S ab
 Longitudinal thermoelectrics
0




E a
S ba


 2

1
Z d
2
T db
2
 Ettingshausen effect
0




E a
S ba


 2



 dT db 

 2

( 1

Z ba
T )
Z ba d
2
T db
2
S ba

S ab

0
S ba
 
S ab
39

Thermal distribution
 Different from longitudinal and Ettingshausen cooling
300

T
H
D
T = 4 K (ZT = 0.026)
= 300 K, b = 10 m m
290
280
ZT
H
= 0.50
D
D
T
T
=14 K (ZT = 0.1)
=56 K (ZT = 0.5)
270
260
250
240
Longitudinal
OATT
Ettingshausen
230
0.10
0 2 4 b (arb)
6 8
0.025
10

Exponentially tapering
 A competitive
D
T = 8 K ( b / L =2.77)
E
C
= -
S ba
T
H
L

p × n Type material
 Bulk materials ( monoclinic ) 1,2 : CsBi
4
Te
6
, ReGe x
Si
1.75−x ptype in a -direction and n -type in c -direction
1
ReSi
1.75
0.1
0.01
CsBi
4
Te
6
1E-3
1E-4
0 200 400 600 800 1000
T (K) age:
 Bulk material, geometric shaping
Low Z T at low temperature
1 Gu, Zhang, PRB 71, 113201 (2005)
2 Chyung, Mahanti, Kanatzidis,


MRS Proc 793 (2004)
1 J-J Gu, et al.,Mat. Res. Soc. Symp. Proc. 753, BB6.10.1 (2003) 2 D.-Y. Chung, Mat. Res. Soc. Symp. Proc. 793 S6.1.1 (2004)

p x n Transverse Thermoelectrics:
Outline:
I. Transverse Thermoelectricity
II. Type II broken-gap superlattices

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