High thermoelectric efficiency in lanthanum doped Yb
14
MnSb
11
Eric S. Toberer,
1
Shawna R. Brown,
2
Teruyuki Ikeda,
1
Susan M. Kauzlarich,
2
and
G. Jeffrey Snyder
1,a兲
1
Materials Science, California Institute of Technology, 1200 California Blvd., Pasadena, California 91125,
USA
2
Department of Chemistry, University of California, One Shields Ave., Davis, California 95616, USA
共Received 23 June 2008; accepted 24 July 2008; published online 15 August 2008兲
Lanthanum doping of the high-temperature p-type thermoelectric material Yb
14
MnSb
11
enhances
the figure of merit 共zT兲 through carrier concentration tuning. This is achieved by substituting La
3+
on the Yb
2+
site to reduce the free hole concentration as expected from the change in valence. The
high-temperature transport properties 共Seebeck coefficient, electrical resistivity, Hall mobility, and
thermal conductivity兲 of Yb
13.6
La
0.4
MnSb
11
are explained by the change in carrier concentration
using a simple rigid parabolic band model, similar to that found in Yb
14
Mn
1−x
Al
x
Sb
11
. Together, use
of these two dopant sites enables the partial decoupling of electronic and structural properties in
Yb
14
MnSb
11
-based materials. © 2008 American Institute of Physics. 关DOI: 10.1063/1.2970089兴
Thermoelectric generators have the potential to provide
clean, reliable electricity through waste heat recovery or co-
generation. As current generator efficiencies are insufficient
for widespread application, there is an interest in the devel-
opment of improved thermoelectric materials. Generator ef-
ficiency depends on both the Carnot efficiency and the ma-
terial thermoelectric figure of merit 共zT=
␣
2
T/
, where T is
absolute temperature兲. Material improvements have been
challenging because of the interdependent nature of the See-
beck coefficient 共
␣
兲, electrical resistivity 共
兲, and thermal
conductivity 共
兲 through the free carrier concentration 共n兲.
1
Several promising classes of materials
1
have been recently
identified for thermoelectrics. These include oxides and Zintl
phases and materials with complex crystal structures 共e.g.,
clathrates and zinc antimonides兲 or nanoscale microstruc-
tures
2
共nanowires, superlattices, or bulk nanostructures兲.
Zintl phases, in particular, have several features that make
them ideal candidates for thermoelectric materials,
3
this has
lead to the discovery of the high efficiency p-type material
Yb
14
MnSb
11
.
Yb
14
MnSb
11
has a peak zT of ⬃1.0 at 1223 K, which is
a significant gain over the state-of-the-art Si
0.8
Ge
0.2
共peak zT
0.6兲 thermoelectric material utilized by NASA in radioiso-
tope generators for deep space probes.
4,5
Yb
14
MnSb
11
be-
longs to a class of compounds of type A
14
MPn
11
, where A is
a heavier alkaline earth or 2+ rare earth element
共Ca
2+
,Sr
2+
,Ba
2+
,Yb
2+
,Eu
2+
兲, M is a group 13 element or
transition metal 共 Al
3+
,Mn
2+
,Zn
2+
兲, and Pn is a group 15
element 共P, As, Sb, Bi兲.
6
Zintl–Klemm formalism is used to
determine valence.
7
Group 13 containing compositions 共e.g.,
Ca
14
AlSb
11
兲 form diamagnetic semiconductors. In contrast,
Yb
14
MnSb
11
is a p-type metal with n=1.3⫻ 10
21
cm
−3
, cor-
responding to one hole per Mn
2+
.
8
Our prior work with the Yb
14
Mn
1−x
Al
x
Sb
11
solid solu-
tion found n to linearly follow the manganese concentration
共e.g., substitution of Al
3+
for Mn
2+
decreases n兲.
9
The opti-
mum range for n was found to be 共4–7兲 ⫻ 10
20
cm
−3
, which
gave a 30% enhancement in zT 共1.3 at 1223 K兲 when com-
pared to the original Yb
14
MnSb
11
compound. A particularly
appealing feature of this solid solution is that n can be ad-
justed without altering the band gap or effective mass, which
indicates that the material can be understood with a rigid,
parabolic band model.
Unlike the Yb
14
Mn
1−x
Al
x
Sb
11
solid solution, substitution
of Mn
2+
with isoelectronic Zn
2+
共Yb
14
Mn
1−x
Zn
x
Sb
11
兲 does
not lead to a continuous alloy.
10
For x
Zn
艋 0.7, substitution
with isoelectronic d
10
Zn
2+
lowers
without altering n or
␣
.
This decrease in
is attributed to the reduction in spin dis-
order scattering from the coupling of d
5
Mn
2+
and the itiner-
ant hole. The stable phase at high Zn concentrations has a
reduced
␣
attributed to valence fluctuations of Yb
2+/3+
.
11
Substitution of La
3+
for Yb
2+
in Yb
14−x
La
x
MnSb
11
should also decrease n linearly with x 关up to the solubility
limit of x = 0.7 共Ref. 8兲兴 much like the substitution of Al
3+
for Mn
2+
. In this system, La
3+
donates an additional electron,
moving the Fermi level closer to the band edge and reduces
the hole concentration n by one hole per formula unit
共Fig. 1兲. Sales et al. have measured the low T Hall resis-
tivity and magnetic properties of a single crystal of
a兲
Electronic mail: jsnyder@caltech.edu.
FIG. 1. 共Color online兲 A linear decrease in carrier concentration is expected
with increasing La
3+
substitution. The measured room temperature carrier
concentrations are shown for Yb
13.6
La
0.4
MnSb
11
and prior work by Sales et
al. 共see Ref. 8兲. The solid line indicated the reported maximum solubility of
La at x ⬇0.7. Similar carrier concentration dependence is found for the
Yb
14
Mn
1−x
Al
x
Sb
11
solid solution 共from Ref. 9兲.
APPLIED PHYSICS LETTERS 93, 062110 共2008兲
0003-6951/2008/93共6兲/062110/3/$23.00 © 2008 American Institute of Physics93, 062110-1
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Yb
13.3
La
0.7
MnSb
11
.
8
The reported n=4⫻ 10
20
cm
−3
for
Yb
13.3
La
0.7
MnSb
11
is consistent with this simple electron
counting approach.
In this work, we investigate the high T thermoelectric
properties of Yb
13.6
La
0.4
MnSb
11
. Our prior work on the
Yb
14
Mn
1−x
Al
x
Sb
11
共Ref. 9兲 enabled us to target the La con-
tent that should give the highest zT 共by tuning n兲 in the range
x= 0.6⫾0.2. Crystals were prepared by the Sn-flux method
as described in Ref. 4 with a Yb:La ratio of 13:1. The prod-
ucts were analyzed by x-ray diffraction and microprobe
analysis to verify purity before pulverizing and hot pressing.
The resulting ingot was sliced and three separate samples
were characterized to 1273 K. The composition of the pellet
was determined by microprobe analysis to be primarily
Yb
13.6
La
0.4
MnSb
11
, with a secondary phase 共51.5 Yb:1.6
La:2.2 Mn:44.7 Sb兲 that is likely one of the Yb–Sb binary
phases. Full
␣
and
versus T curves were measured on all
three samples with nearly identical results.
Room temperature Hall resistance 共R
H
兲 measurements of
Yb
13.6
La
0.4
MnSb
11
yield n=1/ R
H
e=6⫻ 10
20
cm
−3
. This
value is in good agreement with the expected n from the x
revealed in the microprobe measurements 共Fig. 1兲 and is
within the n = 共4–7兲⫻10
20
cm
−3
window expected for high
zT from Yb
14
Mn
1−x
Al
x
Sb
11
.
9
Figure 2共a兲 shows that
for
Yb
13.6
La
0.4
MnSb
11
共one representative sample兲 increases like
a metal or heavily doped semiconductor with increasing T up
to 1100 K due to its constant n and decreasing mobility,
=1/ ne
共proportional to T
−1
兲. Above 1100 K, the decrease in
is attributed to thermal excitation of carriers across the
band gap.
In the Yb
14
Mn
1−x
Al
x
Sb
11
system,
was found to be
dominated by acoustic phonon scattering, with an approxi-
mately n
−1/3
dependence.
9
Likewise, for Yb
13.6
La
0.4
MnSb
11
we find that decreasing n leads to an increased
共4.3 cm
2
V
−2
s
−1
at 300 K兲. Figure 2共b兲 superimposes the
room temperature
for Yb
14
Mn
1−x
Al
x
Sb
11
and the three
samples of Yb
13.6
La
0.4
MnSb
11
, with a n
−1/3
fit. The agree-
ment in
between the different alloys in Fig. 2共b兲 suggests
that 共a兲
is determined primarily by n and 共b兲
at the same
n are approximately equal. This second point is interesting,
as the scattering mechanisms are different between
Yb
13.6
La
0.4
MnSb
11
and Yb
14
Mn
1−x
Al
x
Sb
11
even with the
same n.Yb
1−x
La
x
MnSb
11
will exhibit more spin disorder
scattering than Yb
14
Mn
1−x
Al
x
Sb
11
because of the greater
content of magnetic Mn
2+
compared to nonmagnetic Al
3+
共Yb and La are nonmagnetic, with Yb expected to be all 2
+ and La, 3+ for this compound兲. The spin disorder scatter-
ing has been found to induce a T independent term in
that
can be reduced
10
with doping of nonmagnetic Zn
2+
. Simi-
larly, the charge difference of Al
3+
compared to Mn
2+
will
contribute impurity scattering that may also be T indepen-
dent. The charge disorder from having La on the Yb site is
expected to have little effect on the conduction because the
bands comprising the mobile holes should be mostly Sb and
transition metal character with very little rare earth 共Yb, La兲
character.
12
The similarity of
for Yb
13.6
La
0.4
MnSb
11
and
Yb
14
Mn
0.4
Al
0.6
Sb
11
共with the same n兲 suggests that the spin
disorder and impurity scattering may be of similar orders of
magnitude.
Figure 3共a兲 shows that
␣
for Yb
14
MnSb
11
and
Yb
13.6
La
0.4
MnSb
11
共one representative sample兲 increases lin-
early with increasing T through the extrinsic regime 共up to
about 1100 K兲. At high T, the thermal excitation of electrons
and holes leads to a compensated, reduced
␣
, which is more
noticeable in the lower n material. The peak in
␣
may be
FIG. 2. 共Color online兲共a兲 Yb
13.6
La
0.4
MnSb
11
is more resistive than the par-
ent compound Yb
14
MnSb
11
due to the decreased carrier concentration 共both
heating and cooling curves are shown兲. 共b兲 The Yb
13.6
La
0.4
MnSb
11
mobility
共for all the samples measured兲 at 300 K agrees with the previously observed
trend in mobility with carrier concentration for the Yb
14
Mn
1−x
Al
x
Sb
11
solid
solution 共from Ref. 9兲.
FIG. 3. 共Color online兲共a兲 The reduction in carrier concentration for
Yb
13.6
La
0.4
MnSb
11
compared to the parent compound Yb
14
MnSb
11
leads to
an increased Seebeck coefficient 共both heating and cooling curves are
shown兲. 共b兲 The Yb
13.6
La
0.4
MnSb
11
Seebeck coefficient at 600 K fits the
trend previously found for the Yb
14
Mn
1−x
Al
x
Sb
11
solid solution 共from Ref.
9兲.
062110-2 Toberer et al. Appl. Phys. Lett. 93, 062110 共2008兲
Downloaded 22 Aug 2008 to 131.215.225.137. Redistribution subject to AIP license or copyright; see http://apl.aip.org/apl/copyright.jsp
used to estimate the band gap 共E
g
=2e
␣
max
T
max
兲共Ref. 13兲 to
be 0.5 eV, a value identical to that found across the
Yb
14
Mn
1−x
Al
x
Sb
11
solid solution. Superimposing
␣
for
Yb
14
Mn
1−x
Al
x
Sb
11
at 600 K with the values obtained for
Yb
13.6
La
0.4
MnSb
11
reveals the La-doped samples fit the
Mn–Al trend with n. The Yb
14
Mn
1−x
Al
x
Sb
11
solid solution
was found to behave as a degenerate semiconductor with
energy independent scattering, resulting in
␣
proportional to
Tn
−2/3
关Eq. 共1兲兴. At the low T, degenerate limit, Eq. 共1兲 can
be used to calculate the effective mass 共m
*
兲 from n and the
slope of
␣
versus T plot. For Yb
13.6
La
0.4
MnSb
11
the effective
mass was found to be ⬃2.7m
e
, similar to the relatively con-
stant value of ⬃3m
e
found for Yb
14
Mn
1−x
Al
x
Sb
11
. The simi-
lar properties between the La
3+
and Al
3+
doped systems in-
dicate that the band structure is minimally altered by doping
either the cation or the transition metal site; doping simply
shifts the Fermi energy within a single parabolic band,
␣
=
8
2
k
B
2
3eh
2
m
*
T
冉
3n
冊
2/3
. 共1兲
The
=DdC
p
共Fig. 4兲 was calculated from laser flash
thermal diffusivity 共D兲 measurements, measured density 共d兲,
and heat capacity 共C
p
兲 estimated using the method of
Dulong–Petit. The Dulong–Petit method is consistent with
prior studies on the high T properties of Yb
14
MnSb
11
and its
alloys but is expected to be an underestimation of C
p
.To
determine the effect of alloying on the lattice thermal con-
ductivity 共
l
兲, the electronic component 共
e
兲 was subtracted
from
using the Wiedemann–Franz law 共
e
=LT/
;
=
l
+
e
+
b
; where L is the Lorenz factor. The remainder,
l
+
b
, 共Fig. 4兲 has a minimum value of ⬃0.3 W / m K. As seen
in the Yb
14
Mn
1−x
Al
x
Sb
11
solid solution, the rise in
l
+
b
at
high T is due to the excitation of mixed carriers enhancing
the bipolar 共
b
兲 term.
14
Figure 5 shows the zT of the parent compound,
Yb
14
MnSb
11
, and Yb
13.6
La
0.4
MnSb
11
, with a peak zT of 1.15
at 1150 K for the alloy. The magnitude of zT is lower than
the equivalent n sample from the Yb
14
Mn
1−x
Al
x
Sb
11
solid
solution 共Yb
14
Mn
0.4
Al
0.6
Sb
11
1.28 at 1200 K兲. This differ-
ence is due to ⬃3% differences in
␣
and
but well within
the expected uncertainty in these high T measurements.
Greater 共or different兲 La content may produce higher zT than
the composition studied here. However we expect the im-
provement to be minimal based on the broad maximum in zT
found for Yb
14
Mn
1−x
Al
x
Sb
11
.
Alloying Yb
14
MnSb
11
on the rare earth site with La
3+
permits the optimization of n and zT in a manner similar to
Al
3+
substitution on the transition metal site. For both the La-
and Al-doped systems, the same simple rigid parabolic band
model explains the behavior of the high T transport proper-
ties. The development of two separate dopant sites permits
the partial decoupling of n, spin disorder scattering, and im-
purity scattering. Such control should lead to further im-
provements in zT through simultaneous doping of different
elements on both sites.
We thank NASA/JPL, the Beckman Foundation, and
NSF 共Contract No. DMR-0600742兲 for funding and B. C.
Sales for useful discussions.
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FIG. 4. 共Color online兲 Thermal conductivity from flash diffusivity measure-
ments for Yb
13.6
La
0.4
MnSb
11
and Yb
14
MnSb
11
. The electronic component
may be subtracted 共Wiedemann–Franz law兲 to leave the lattice 共
l
兲 and
bipolar 共
b
兲 components of the thermal conductivity.
FIG. 5. 共Color online兲 Thermoelectric figure of merit 共zT兲 for
Yb
13.6
La
0.4
MnSb
11
and the parent compound Yb
14
MnSb
11
共from Ref. 4兲.
062110-3 Toberer et al. Appl. Phys. Lett. 93, 062110 共2008兲
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