The size-dependence of the thermoelectric power factor of thin-films and nanowires is theoretically investigated from the electric quantum limit (EQL) to the bulk-like regime. Different functional forms of the energy-dependent relaxation time τ(E) are incorporated in the model to account for carrier scattering mechanisms typical in semiconductor nanostructures. The calculations show that the steeper the increase in the relaxation time with carrier energy, the higher the power factor-to-average scattering time ratio, PF/〈τ〉, confirming the benefits of the preferential scattering of low-energy carriers to thermoelectric performance. However, outside the EQL, the power factor values are lower in the low-dimensional structures than in their three-dimensional counterparts. Thus, the power factor is more readily improved by modifications of the scattering rates than by quantization of the energy states.

1.
G.
Joshi
,
H.
Lee
,
Y.
Lan
,
X.
Wang
,
G.
Zhu
,
D.
Wang
,
R. W.
Gould
,
D. C.
Cuff
,
M. Y.
Tang
,
M. S.
Dresselhaus
,
G.
Chen
, and
Z.
Ren
,
Nano Lett.
8
,
4670
(
2008
).
2.
B.
Poudel
,
Q.
Hao
,
Y.
Ma
,
Y.
Lan
,
A.
Minnich
,
B.
Yu
,
X.
Yan
,
D.
Wang
,
A.
Muto
,
D.
Vashaee
,
X.
Chen
,
J.
Liu
,
M. S.
Dresselhaus
,
G.
Chen
, and
Z.
Ren
,
Science
320
,
634
(
2008
).
3.
A. I.
Hochbaum
,
R.
Chen
,
R. D.
Delgado
,
W.
Liang
,
E. C.
Garnett
,
M.
Najarian
,
A.
Majumdar
, and
P.
Yang
,
Nature
451
,
163
(
2008
).
4.
J. M. O.
Zide
,
D.
Vashaee
,
Z. X.
Bian
,
G.
Zeng
,
J. E.
Bowers
,
A.
Shakouri
, and
A. C.
Gossard
,
Phys. Rev. B
74
,
205335
(
2006
).
5.
J. P.
Heremans
,
C. M.
Thrush
, and
D. T.
Morelli
,
J. Appl. Phys.
98
,
063703
(
2005
).
6.
J. P.
Heremans
,
V.
Jovovic
,
E. S.
Toberer
,
A.
Saramat
,
K.
Kurosaki
,
A.
Charoenphakdee
,
S.
Yamanaka
, and
G. J.
Snyder
,
Science
321
,
554
(
2008
).
7.
C. M.
Jaworski
,
V.
Kulbachinskii
, and
J. P.
Heremans
,
Phys. Rev. B
80
,
233201
(
2009
).
8.
O.
Rabin
,
Y.-M.
Lin
, and
M. S.
Dresselhaus
,
Appl. Phys. Lett.
79
,
81
(
2001
).
9.
T.
Koga
,
X.
Sun
,
S. B.
Cronin
, and
M. S.
Dresselhaus
,
Appl. Phys. Lett.
73
,
2950
(
1998
).
10.
A. J.
Minnich
,
M. S.
Dresselhaus
,
Z. F.
Ren
, and
G.
Chen
,
Energy Env. Sci.
2
,
466
(
2009
).
11.
C. J.
Vineis
,
A.
Shakouri
,
A.
Majumdar
, and
M. G.
Kanatzidis
,
Adv. Mater.
22
,
3970
(
2010
).
12.
L. D.
Hicks
and
M. S.
Dresselhaus
,
Phys. Rev. B
47
,
16631
(
1993
).
13.
L. D.
Hicks
and
M. S.
Dresselhaus
,
Phys. Rev. B
47
,
12727
(
1993
).
14.
N.
Mingo
,
Appl. Phys. Lett.
84
,
2652
(
2004
).
15.
N.
Mingo
,
Appl. Phys. Lett.
85
,
5986
(
2004
).
16.
D. A.
Broido
and
T. L.
Reinecke
,
Phys. Rev. B
64
,
045324
(
2001
).
17.
D. A.
Broido
and
T. L.
Reinecke
,
Appl. Phys. Lett.
77
,
705
(
2000
).
18.
D. A.
Broido
and
T. L.
Reinecke
,
Appl. Phys. Lett.
70
,
2834
(
1997
).
19.
J. E.
Cornett
and
O.
Rabin
,
Appl. Phys. Lett.
98
,
182104
(
2011
).
20.
J. E.
Cornett
and
O.
Rabin
,
Phys. Rev. B
84
,
205410
(
2011
).
21.
Y.-M.
Lin
, M. Sc. thesis,
Massachusetts Institute of Technology
,
2000
.
22.
N. W.
Ashcroft
and
N. D.
Mermin
,
Solid State Physics
(
Holt, Rinehart and Winston
,
New York
,
1976
).
23.
J.
Zhou
,
R.
Yang
,
G.
Chen
, and
M. S.
Dresselhaus
,
Phys. Rev. Lett.
107
,
226601
(
2011
).
24.
V. I. i.
Fistul
,
Heavily Doped Semiconductors
(
Plenum
,
1969
).
25.
D.
Chattopadhyay
and
H. J.
Queisser
,
Rev. Mod. Phys.
53
,
745
(
1981
).
26.
W.
Zawadzki
and
W.
Szymanska
,
J. Phys. Chem. Solids
32
,
1151
(
1971
).
27.
R. A.
Stradling
and
R. A.
Wood
,
J. Phys. C: Solid State Phys.
3
,
L94
(
1970
).
28.
O.
Madelung
,
Semiconductors: Group IV Elements and III-V Compounds
(
Springer-Verlag
,
1991
).
29.
See supplementary material at http://dx.doi.org/10.1063/1.4729381 for calculated PF1D(τCRTA/τ1D) values (Fig. S1) and a plot of Ef,max and the first 7 subband energies as a function of film thickness (Fig. S2).
30.
D.
Vashaee
and
A.
Shakouri
,
J. Appl. Phys.
95
,
1233
(
2004
).

Supplementary Material

You do not currently have access to this content.