Recent developments in thermoelectric materials

G. Chen, M. S. Dresselhaus, G. Dresselhaus, J.-P. Fleurial and T. Caillat

F Fermi–Dirac integral deŽ ned by equation (8)

Efficient solid state energy conversion based on f distribution function
the Peltier effect for cooling and the Seebeck effect ò Planck’s coeYcient divided by 2p, J s
for power generation calls for materials with high I current, A
electrical conductivity s, high Seebeck coefficient k thermal conductivity, W m – 1 K – 1
S, and low thermal conductivity k. Identifying kB Boltzmann’s constant, J K – 1
materials with a high thermoelectric figure of merit L functions deŽ ned by equation (4)
Z(=S2 s/k) has proven to be an extremely m* eVective mass, kg
challenging task. After 30 years of slow progress,
thermoelectric materials research experienced a
Q heat current, W
resurgence, inspired by the developments of new S Seebeck coeYcient, V K – 1
concepts and theories to engineer electron and T temperature, K
phonon transport in both nanostructures and bulk V voltage, V
materials. This review provides a critical summary v velocity, m s – 1
of some recent developments of new concepts and Z Ž gure of merit, K – 1
new materials. In nanostructures, quantum and ZT non-dimensional Ž gure of merit
classical size effects provide opportunities to tailor
the electron and phonon transport through Q azimuthal angle
structural engineering. Quantum wells, h polar angle
superlattices, quantum wires, and quantum dots L mean free path, m
have been employed to change the band structure, m chemical potential, J
energy levels, and density of states of electrons, j chemical potential divided by k B T
and have led to improved energy conversion P Peltier coeYcient, V
capability of charged carriers compared to those of s electrical conductivity, S m
their bulk counterparts. Interface reflection and the t relaxation time, s
scattering of phonons in these nanostructures
v angular frequency, Hz rad
have been utilised to reduce the heat conduction
loss. Increases in the thermoelectric figure of merit
based on size effects for either electrons or Introduction
phonons have been demonstrated. In bulk
materials, new synthetic routes have led to Solid state cooling and power generation based on
engineered complex crystal structures with the thermoelectric eVects have been known since the
desired phonon–glass electron–crystal behaviour. Seebeck eVect (for power generation) and the Peltier
Recent studies on new materials have shown that eVect (for cooling and heat pumping ) were discovered
dimensionless figure of merit (ZÖ temperature) in the 1800s.1 The Seebeck eVect is associated with
values close to 1·5 could be obtained at elevated the generation of a voltage along a conductor when
temperatures. These results have led to intensified it is subjected to a temperature diVerence. Charged
scientific efforts to identify, design, engineer and carriers (electrons or holes) diVuse from the hot side
characterise novel materials with a high potential to the cold side, creating an internal electric Ž eld that
for achieving ZT much greater than 1 near room
temperature. IMR/397
opposes further diVusion. The Seebeck coeYcient is
deŽ ned as the voltage generated per degree of temper-
© Dr Chen is in the Mechanical Engineering Department, ature diVerence between two points
Massachusetts Institute of Technology, Cambridge, MA
V1 2
02139, USA (gchen2@mit.edu). Dr M. S. Dresselhaus is S =­ . . . . . . . . . . . . (1)
in the Department of Physics, Department of Electrical DT1 2
Engineering and Computer Science, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA. Dr G. The Peltier eVect re ects the fact that when carriers
Dresselhaus is in the Francis Bitter Magnet Laboratory,  ow through a conductor, they also carry heat. The
Massachusetts Institute of Technology, Cambridge, MA heat current Q is proportional to the charge current I
02139, USA. Dr Fleurial and Dr Caillat are in the Jet
Propulsion Laboratory, California Institute of Technology, Q =PI . . . . . . . . . . . . . (2)
4800 Oak Grove Drive, MS 277–207, Pasadena, CA 91109,
USA. and the proportionality constant P is called the
© 2003 IoM Communications Ltd and ASM International.
Peltier coeYcient. When two materials are joined
Published by Maney for the Institute of Materials, Minerals together and a current is passed through the interface,
and Mining and ASM International. there will be an excess or deŽ ciency in the energy at
the junction because the two materials have diVerent
Peltier coeYcients. The excess energy is released to
the lattice at the junction, causing heating, and the
List of symbols deŽ ciency in energy is supplied by the lattice, creating
C phonon volumetric speciŽ c heat per unit cooling. The Seebeck and the Peltier coeYcients are
frequency interval, J m – 3 K – 1 Hz – 1 related through the Kelvin relation P=ST, where T
E electron energy, J is the absolute temperature. 1 A typical thermoelectric
e electron unit charge, C cooler is shown in Fig. 1a. P-type and n-type semi-
DOI 10.1179/095066003225010182 International Materials Reviews 2003 Vol. 48 No. 1 45
46 Chen et al. Recent developments in thermoelectric materials

the units of inverse Kelvin and it often appears as a

product with an absolute temperature T , such as the
average device temperature. Thus, the dimensionless
numerical Ž gure of merit Z T is often cited rather
than Z by itself.
The central issue in thermoelectrics materials
research is to increase Z T. The best Z T materials are
found in heavily doped semiconductors. Insulators
have poor electrical conductivity. Metals have rela-
tively low Seebeck coeYcients. In addition, the ther-
mal conductivity of a metal, which is dominated by
electrons, is in most cases proportional to the electri-
cal conductivity, as dictated by the Wiedmann–Franz
law. It is thus hard to realise high Z T in metals. In
semiconductors, the thermal conductivity has contri-
butions from both electrons k e and phonons k p , with
the majority usually coming from phonons. The
phonon thermal conductivity can be reduced without
causing too much reduction in the electrical conduct-
ivity. A proven approach to reduce the phonon
thermal conductivity is through alloying.2 The mass
diVerence scattering in an alloy reduces the lattice
thermal conductivity signiŽ cantly without much
degradation to the electrical conductivity. The com-
mercial state of the art thermoelectric cooling mater-
ials are based on alloys of Bi2 Te3 with Sb2 Te3 (such
as Bi0 ·5 Sb1 ·5 Te3 , p-type) and Bi2 Te3 with Bi2 Se3 (such
as Bi2 Te2 ·7 Se0 ·3 , n-type), each having a Z T at room
a cooler; b power generator; c actual device temperature approximately equal to 1. Refrigerators
1 Illustration of thermoelectric devices based on such materials typically have a coeYcient
of performance (COP) of about 1,1 compared to
compressor based refrigerators with a COP between
conductor elements are interconnected on the cold 2 and 4 operating over a comparable working temper-
and the hot sides, such that a current  ows through ature range. Their low COP has limited thermo-
all the elements in series, while the energy they carry electric coolers to niche market sectors, such as
(by electrons and holes) leaves the cold side in parallel. temperature stabilisation of semiconductor lasers and
Thermoelectric power generators work in reverse to picnic coolers. The market for thermoelectric coolers,
thermoelectric coolers, as shown in Fig. 1b. Because however, is rapidly increasing, partly due to the
the hot side has a higher temperature, electrons and explosive growth of optical telecommunication. State
holes are driven to the cold side through diVusion of the art power generation materials are PbTe and
and  ow through an external load to do useful work. Si 0 ·8 Ge0 ·2 , which have been used in deep space radio-
Practical devices are made of many pairs of p–n legs isotope thermoelectric power generators that operate
(Fig. 1c), usually arranged such that current  ows in at ~900°C with a maximum eYciency of about 7%.
series through all the legs and energy  ows in parallel From equation (3), one can infer that the best
from the cold side to the hot side. thermoelectric devices should have a thermal conduct-
In addition to the temperatures of the hot and cold ivity close to zero. One possibility is using vacuum
sides, which are important to all thermal engines, the between the cold and the hot side. Electrons can be
eYciency of actual thermoelectric devices is deter- emitted through a thermionic emission process from
mined by the thermoelectric Ž gure of merit a metal surface and  ow through a vacuum. This is
S2 s the principle behind thermionic power generators,
Z= . . . . . . . . . . . . . (3) which were developed in the 1950s.3 In a vacuum
k
based thermionic power generator, the emitter is held
where s is the electrical conductivity and k is the at a high temperature. Electrons with energy higher
thermal conductivity. The appearance of S in Z is than the work function can escape from the emitter
self-explanatory. The reason that the electrical con- surface and reach the collector. Conceivably, rather
ductivity s enters Z is due to Joule heating. When a than for power generation, vacuum thermionic emis-
current passes through the thermoelectric elements, sion can also be used for cooling, if a current drives
Joule heat is generated which can be conducted back electrons from the emitter to the collector, as in a
to the cold junction. The thermal conductivity k vacuum tube. The major problem, however, is that
appears in the denominator of Z because, in thermo- most metals have a large work function value, which
electric coolers or power generators, the thermoelec- makes room temperature refrigeration based on
tric elements also act as the thermal insulation vacuum thermionic emission impractical.4
between the hot and the cold sides. A high thermal The progress since the 1960s in improving Z T had
conductivity causes too much heat leakage between been very slow before the 1990s. The value of maxi-
the hot and the cold sides. The Ž gure of merit Z has mum Z T had essentially remained around 1 and
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 47

published three volume series.1 3 A few other reviews

and introductory reports have also been published,
emphasising bulk thermoelectric materials.1 4 – 1 7
Proceedings of International Conferences on
‘Thermoelectrics’,1 8 which are held annually, and sev-
eral volumes1 9 of the MRS proceedings on this topic
give broad coverage of progress made in recent years.
This review is directed more towards low-dimensional
materials, although bulk materials are also covered
to provide readers with a quick overview of current
thermoelectric materials research. The selection of the
coverage was in uenced by the research focus of
the present authors and re ects their assessment
of the Ž eld. The above mentioned references should
be consulted for more comprehensive coverage.

Directions in search of high ZT

2 Non-dimensional figure of merit ZT as function
of temperature for state of the art materials materials
Expressions for thermoelectric properties are often
derived from the Boltzmann equation under the relax-
research funding in this area dwindled. The landscape ation time approximation2 0
in thermoelectrics research changed quite signiŽ cantly
L( 2 ) L(1 ) L(1 ) L(1 )
in the 1990s due to several new conceptual devel- s= L(0 ) , ke = ­ , S =­ (4)
opments and renewed interested from several e2 T e2 T L(0 ) eT L(0 )
US research funding agencies. New developments where
occurred both in bulk materials and in low-dimen-

P A B
sional materials. The best thermoelectric materials d3k ç fF D
L( a) = e 2 ­ t [E (k)][ v ( k)]2 [E ( k) ­ m]a
were succinctly summarised as ‘phonon–glass elec- 4 p3 ç E
tron–crystal’ (or PGEC in short ), which means that . . . . . . . . (5)
the materials should have a low lattice thermal con-
ductivity as in a glass, and a high electrical conduct- In the above expressions, fF D is the Fermi–Dirac
ivity as in crystals.5 In bulk materials, the major new distribution, t is the electron (hole) relaxation time,
concept that was developed is the use of ‘phonon k is the electron wave vector, k e is the electronic
rattlers’ to reduce the lattice thermal conductivity. contribution to thermal conductivity, v is the electron
These phonon rattlers are normally interstitial atoms group velocity, and e is the unit charge. If the relax-
inserted into empty spaces in the host materials. Their ation time is assumed to be a constant and a three-
vibration is not in harmony with the atoms in the dimensional (3D) parabolic electronic energy band is
host material, thus scattering the phonons in the assumed, Z T can be expressed as1 , 2 1
original lattice. In this connection, several classes of [(5F3 /2 / 3F1 /2 ) ­ j* ]2 (3F1 /2 / 2 )
materials have been discovered and/or re-investigated Z3 D T = (6)
with regard to their potential for high Z T, such as 1/ B3 D + 7F5 /2 / 2 ­ (25F 23 /2 / 6F1 /2 )
skutterudites and clathrates. In low-dimensional where
materials, such as thin Ž lms, superlattices, and quan-

A B
tum wires, several approaches have been proposed. (m* )3 /2 2kB T 3/2 k2B Tm
B3 D = . . . . . (7)
For transport along the Ž lm plane (wire axis) direc- 3 p2 ò 2 ekp
tion, quantum size eVects are considered to increase
the electronic power factor S 2 s and boundary scat- and m*=(mx my mz )1 /3 is the eVective density of states
tering to reduce k.6 ,7 For transport in the direction mass of electrons in the band, k p is the phonon
perpendicular to the Ž lm plane, several possibilities contribution to the thermal conductivity, k B is
were suggested. One was to use the band-edge dis- Boltzmann’s constant, m is the electron mobility, j*
continuity as a Ž lter for cold electrons. 8 This was is the chemical potential normalised by k B T, and Fi is
later developed into a thermionic emission cooling the Fermi–Dirac integral deŽ ned as

P
approach.9 , 1 0 Another approach was based on ?
x i dx
phonon re ection at interfaces to reduce the lattice F (j* ) = . . . . . . (8)
i exp (x ­ j* ) + 1
thermal conductivity. 1 1 , 1 2 Figure 2 shows a ‘snapshot’ 0
of the reported Z T values. The Z T values of low- In equations (6) and (7), the subscript 3D is used to
dimensional structures are subject to higher uncer- indicate that those expressions are derived considering
tainty and should be taken cautiously, primarily due the density of states of 3D bulk crystals. In low-
to the diYculties involved in characterising the Z T dimensional structures, these expressions must be
of low-dimensional materials. reformulated. 2 1 In equation (6), the reduced chemical
In this paper, it is intended to provide a concise potential j* is a free variable that can be controlled
critical review of some recent developments in ther- by doping. The optimum value for the chemical
moelectrics research. An extensive review of most of potential is chosen to maximise Z T. Therefore, ther-
the topics discussed here is contained in a recently moelectric materials development involves careful
International Materials Reviews 2003 Vol. 48 No. 1
48 Chen et al. Recent developments in thermoelectric materials

control and optimisation of doping. The only other weight material. Its success relies on its multiple
variable that aVects the Z T value in equation (6) is carrier pockets that give a reasonably high density of
the B factor, which depends on the electron eVective states and, more importantly, on the alloying method
mass, the carrier mobility, and the phonon thermal that signiŽ cant lowers its thermal conductivity com-
conductivity. The larger the B factor, the larger is Z T. pared to that of bulk Si or Ge. High temperature
Thus, thermoelectric materials research is often operation also helps to increase the Z T of Si1 – x Gex .
guided by Ž nding materials that have a large B factor, While the general Z T formulation for bulk mater-
which include a large electron (hole) eVective mass ials has played and will continue to play an instrumen-
and a high mobility, and a low lattice thermal con- tal role in developing strategies in the search for
ductivity. Such materials are succinctly called highly eYcient thermoelectric materials, it should be
phonon–glass electron–crystal materials by Slack.5 It kept in mind that these expressions are derived by
should be pointed out that the requirements of a high using a set of approximations. Those related to the
mobility (which needs a low mobility eVective mass) present discussion are given below.
and a high density of states (which demands a large 1. Bulk density of states for electrons and holes.
density of states eVective mass) are not necessarily Expressions such as (6) and (7) are derived by
mutually exclusive. In anisotropic media, either in assuming 3D parabolic bands. Quantum structures
bulk form or in superlattices, it is possible to have a to be discussed later have a drastically diVerent
small eVective mass in the current  ow direction to density of states and expressions (6) and (7) will
give a high mobility and large eVective masses in the change correspondingly.
directions perpendicular to the current  ow to give a 2. Local equilibrium approximation. Expressions
high density of states. for the transport coeYcients, equations (4) and (5),
It should be mentioned that the derivation of are derived by assuming that electrons deviate only
equation (6) is based on the constant relaxation time slightly from their equilibrium distributions. This is
approximation. A more realistic form of the relaxation valid only when the characteristic length along the
time has an energy dependence t! E c, which depends transport direction is much longer than the electron
on the scattering mechanisms. For example, c=1/2 mean free path. This assumption will not be valid for
for optical phonons, and c=­ 1 for acoustic transport at the interfaces and for carrier transport
phonons. 1 It can be shown that Z T also depends on in the direction perpendicular to very thin Ž lms. In
c. Thus, one strategy that is sometimes used to addition, the electrons and phonons are typically
improve Z T is to control the scattering mechanism. assumed to be in thermal equilibrium. This assump-
The thermal conductivity of phonons is also often tion is not necessarily true, as in the well known hot
modelled from the Boltzmann equation under the electron eVect in semiconductor electronics.
relaxation time approximation, i.e. 3. Isotropic relaxation time for both electrons and
phonons. Many low-dimensional structures, such as

P
d 3k ç fp superlattices, are highly anisotropic. Expressions such
kp = æ [vp x ( k)]2 t ò v
8p3 ç T p as equation (9) for the thermal conductivity are no
p
longer correct.

P
1 Much of the development in low-dimensional struc-
= C(v)vp (v)Lp (v) dv . . . . . . (9) tures can be attributed to relaxing one or several of
3
these approximations. This allows for more independ-
for an isotropic bulk material, where fp is the phonon ent control of S, s, or k, as will be seen in the
distribution function, C is the speciŽ c heat of phonons following discussion.
at frequency v, vp is the phonon group velocity, tp is
the phonon relaxation time, Lp is the free path of
phonons at v and the summation is over the diVerent
Low-dimensional thermoelectric
phonon polarisations. To reduce the thermal conduct- materials
ivity, materials with a small phonon group velocity Low-dimensional materials, such as quantum wells,
and a short relaxation time are desired. Roughly superlattices, quantum wires, and quantum dots oVer
speaking, the phonon group velocity is proportional new ways to manipulate the electron and phonon
to (K /m)1 /2 , where K is the spring constant between properties of a given material. In the regime where
the atoms and m is the mass of the atom. Thus, quantum eVects are dominant, the energy spectra of
materials with high atomic mass are often used for electrons and phonons can be controlled through
thermoelectric materials. The phonon relaxation time altering the size of the structures, leading to new ways
can be reduced by scattering, such as through to increase Z T. In this regime, the low-dimensional
alloying2 and by adding phonon rattlers.1 5 structures can be considered to be new materials,
Successful bulk thermoelectric materials that were despite the fact that they are made of the same atomic
developed in the past were directed by the principles structures as their parent materials. Each set of size
derived from the above general discussion for bulk parameters provides a ‘new’ material that can be
materials. For example, Bi2 Te3 was tested because of examined, to a certain extent, both theoretically and
its high atomic weight.2 2 Other important character- experimentally, in terms of its thermoelectric prop-
istics of Bi2 Te3 that were discovered later, such as its erties. Thus, searching for high Z T systems in low-
multiple carrier pockets, high mobility, and low ther- dimensional structures can be regarded as the equival-
mal conductivity, all contributed to its high Z T value ent of synthesising many diVerent bulk materials and
because all these factors work favourably to increase measuring their thermoelectric properties. Because
the B factor. In contrast, SiGe is not a high atomic the constituent parent materials of low-dimensional
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 49

structures are typically simple materials with well

known properties, the low-dimensional structures are
amenable to a certain degree of analysis, prediction
and optimisation. In contrast, theoretical predictions
for bulk materials properties are often diYcult2 3 and
the investigation of each new material presents a
diVerent set of experimental and theoretical chal-
lenges. When quantum size eVects are not dominant,
it is still possible to utilise classical size eVects to alter
the transport processes, as for example the exploi-
tation of boundaries to scatter phonons more eVec-
tively than electrons. Investigations over the past
decade on low-dimensional structures have exploited
both quantum and classical size eVects for electrons
and phonons. The focus of discussion here is along
three directions. One is for electron transport parallel 3 Calculated dependence of non-dimensional
to the plane of thin Ž lms or along the axis of figure of merit ZT (within quantum well or
nanowires. Another is for the electron transport per- within quantum wire) on well or wire width for
Bi2 Te3-like material at optimum doping
pendicular to the Ž lm plane. The third emphasises concentration for transport in highest mobility
phonon transport. Although no devices based on low- direction: also shown is ZT for bulk (3D) Bi2 Te3
dimensional structures are close to commercialisation, calculated using corresponding 3D model 6,25
research on low-dimensional thermoelectricity has
been stimulating to recent developments in thermo-
electrics research, and new research groups worldwide 4, and that the model calculations were in good
are now starting to bring new ideas to the Ž eld based agreement with the experimental observations. Soon
on nanostructures. thereafter, it was shown that an enhanced thermoelec-
tric Ž gure of merit could also be observed for p-type
Electron band gap engineered materials: PbTe quantum wells,3 0 , 3 1 which is, of course, an
transport parallel to film plane or nanowire important consideration for thermoelectric devices,
axis which depend on having both n-type and p-type legs.
These modelling calculations and experimental
The development of band gap engineering in quantum
data are based on the consideration of transport
structures for thermoelectric applications started with inside the quantum wells only, and thus the reported
the modelling of single quantum wells6 and soon
Z T values are referred to as (Z T )2 D . Theoretical
moved on to the consideration of superlattices. 2 1 It
modelling pointed out that when the barrier regions
was soon recognised that quantum wires would oVer of the superlattices are also considered, the overall
more quantum conŽ nement and therefore would have
gain in Z T of the whole structure is considerably
advantages over quantum wells for thermoelectric
reduced 3 2 , 3 3 because the barriers do not contribute
applications, 2 4 , 2 5 as shown in Fig. 3. In due course, to the electrical transport, but do contribute to the
researchers also began to consider the beneŽ ts of
reverse heat conduction. In the limit that the barrier
quantum dot systems for thermoelectric applications.
is thin, it was also suggested that tunnelling between
The key idea is to use quantum size eVects to increase quantum wells reduces the Z T enhancement inside
the electron density of states at the Fermi level and
an individual quantum well. How to address this
in this way to optimise the power factor. Further
issue is very important for the utilisation of quantum
beneŽ ts to thermoelectric performance can be realised size eVects on the electron transport along the Ž lm
by exploiting boundary scattering to reduce the ther-
plane. One possible approach, suggested by the
mal conductivity preferentially, without much loss to
Dresselhaus group, is to use both the quantum wells
the electrical conductivity. and barriers for thermoelectric transport along the
Quantum wells and superlattices Ž lm plane.3 4 For example, by proper choice of the
The most elementary generic calculations, 6 , 2 4 , 2 5 and widths of the quantum wells and barriers for
also more sophisticated calculations on speciŽ c mater- GaAs/AlAs superlattices, the carriers in the C-point
ials,2 6 both predict enhanced thermoelectric perform- and L-point valleys contribute to transport in the
ance within the quantum wells of multiwell GaAs regions, while the X-point valleys can contrib-
superlattices relative to bulk materials of the same ute to transport in the AlAs regions. 3 5 Furthermore,
stoichiometry. To show proof of principle experimen- for a given superlattice system, such as Si/Ge superlat-
tally, special superlattices were designed by the tices and their alloys,3 6 model calculations can be
Dresselhaus group and fabricated by the Harman used to optimise the superlattice geometry to achieve
group at MIT Lincoln lab for PbTe based superlat- the maximum Z T of the whole superlattice structure.
tices2 7 and by the Wang group at UCLA to make Although there are limited experimental data suggest-
Si/Ge superlattices. 2 8 , 2 9 The Ž rst proof of principles ing this possibility, more experimental eVorts are
experiment to conŽ rm the enhancement of Z T within needed to demonstrate the eVectiveness of this carrier
a quantum well was reported for n-type PbTe quan- pocket engineering approach.
tum wells within PbTe/Eux Pb1 – x Te superlattices. 2 7 The theoretical work has inspired experimental
The results showed that the power factor within the studies of thermoelectric eVects in superlattices. The
PbTe quantum well could be increased by a factor of past few years have seen steady improvements in the
International Materials Reviews 2003 Vol. 48 No. 1
50 Chen et al. Recent developments in thermoelectric materials

5 Cross-sectional view of Bi nanowires in

4 Thermoelectric non-dimensional figure of merit cylindrical channels of 65 nm average diameter
versus carrier concentration for high quality within anodic alumina template, shown as
bulk PbTe material in comparison to much transmission electron microscope (TEM) image:
higher ZT for PbSeTe/ PbTe quantum dot template has been mostly filled with Bi, and
superlattice structure at 300 K7 (courtesy T. TEM image was taken after top and bottom
Harman) sides of sample had been ion milled with 6 kV
Ar ions 44,48

thermoelectric performance of speciŽ c superlattices.

nels from 7 to 100 nm in diameter and 50 mm in
For example, experimental thermoelectric data from
length with packing densities of 101 0 channels cm – 2
Harman’s group demonstrated that for PbTe/Te
(Refs. 44, 45). These pores within the channels can
superlattices, obtained by the addition of a few nano-
then be Ž lled with promising thermoelectric materials,
metres of Te above the PbTe layer before the barrier such as Bi or Bi1 – x Sbx alloys. Because of the low
layer is added, the Z T increased from 0·37 to 0·52 at
eVective masses and large anisotropy of the constant
room temperature and this increase in Z T was associ-
energy surfaces of these materials, quantum conŽ ne-
ated with the formation of a quantum dot structure ment eVects at 77 K are predicted for wire diameters
at the interface.3 1 The Harman group further disco-
as large as 50 nm, 4 6 as discussed further below. These
vered experimentally that quantum dot superlattices
eVects have been veriŽ ed experimentally by transport
based on PbTe/PbSeTe have an even higher Z T. For measurements. 4 4 , 4 7
example, PbSeTe/PbTe quantum dot superlattices
Figure 5 shows an example of an anodised alumina
show a large enhancement in the Seebeck coeYcient
template which is Ž lled with Bi using the pressure
relative to bulk PbTe samples with the same carrier injection method. 4 8 One important advantage of these
concentration. 7 At this stage, detailed mechanisms for
Bi nanowires is their crystal properties which can be
the reported Seebeck coeYcient enhancements in
seen in the X-ray and electron diVraction patterns
these quantum dot superlattices are not clear. Among shown in Fig. 6 for an array of Bi nanowires 52 nm
the speculations are both quantum conŽ nement eVects
in average diameter, indicating that each wire has a
and a more favourable scattering mechanism associ-
similar crystal orientation along the nanowire axis.
ated with quantum dots. Furthermore, an estimation This is veriŽ ed in Fig. 6 by comparison of the X-ray
of Z T for such quantum dot superlattices, based on
diVraction pattern with the corresponding electron
the phonon thermal conductivity of equivalent alloys
diVraction pattern for a typical nanowire, showing a
that are considered by the authors as conservative, unidirectional orientation of the nanowires along the
yields a room temperature value of 0·9, which is more
wire axes. In principle, the crystalline orientation can
than a factor of 2 greater than has been achieved
be controlled, but thus far the preferred growth
with the best bulk PbTe material (see Fig. 4). EVorts direction for a given growth method has dominated
are presently underway by several groups worldwide
the nanowire crystalline orientation. As a result of
to obtain reliable measurements of the in-plane ther-
the high crystallinity of these nanowires, high carrier
mal conductivity of small superlattice samples.3 7 – 4 1 mobility and long mean free paths are achievable,
The growth by molecular beam expitaxy of PbTe
which is of direct beneŽ t for thermoelectric
based superlattices and quantum dot superlattices
applications.
can be relatively fast, making it feasible to grow very In addition to pressure injection, physical vapour
thick superlattices (50–100 mm total thickness) for
deposition 4 9 has also been used to Ž ll the templates
simple device testing.4 2
and to make Bi nanowires with single crystal prop-
Quantum wires erties, having the same crystal structure and lattice
General theoretical considerations suggest that, constants as bulk Bi. Electrodeposition is very attract-
because of their increased quantum conŽ nement ive for Ž lling the pores of an alumina template,
eVects, 1D quantum wires could have an even larger because of the ease in making good electrical contacts.
enhancement in Z T 2 4 , 4 3 than 2D quantum wells (see The  exibility of the electrodeposition approach has
Fig. 3). To fabricate controlled arrays of quantum allowed nanowire arrays of Bi, CoSb3 , and Bi2 Te3 to
wires, anodic alumina (Al2 O3 ) templates have been be produced. The nanowire arrays thus far produced
developed and these templates can be made to have by electrodeposition are polycrystalline and are there-
regular triangular arrays of porous nanoscale chan- fore expected to have lower carrier mobilities than
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 51

6 X-ray diffraction pattern for anodic alumina/ Bi

nanowire composites (average wire diameter of
Bi nanowires is about 52 nm) and selected
area electron diffraction pattern (inset) taken
from same sample: these two experimental
results indicate that Bi nanowires are highly
crystalline and possess strongly preferred
growth orientation 44,45

the arrays prepared by Ž lling from the vapour phase

or by pressure injection.
Bismuth has a highly anisotropic band structure
with some very small eVective mass tensor com-
ponents (~10 – 2 free electron masses), and high a subband structure at 77 K of Bi quantum wires oriented
mobility carriers making it a very attractive thermo- along [011Â 2] growth direction, showing energies of highest
electric material, except that in bulk form, Bi is a subbands for T-point hole carrier pocket, L-point electron
semimetal with equal concentrations of electrons and pockets (A, B and C) as well as L-point holes, which are
indicated in Brillouin zone shown on right (zero energy
holes, thus leading to a nearly complete cancellation refers to conduction band edge in bulk Bi): as wire diameter
between the positive and negative contributions to decreases, conduction subbands move up in energy, while
the Seebeck coeYcient. However, for Bi as a quantum valence subbands move down; at d c =49·0 nm, lowest
well or a quantum wire, the band edge for the lowest conduction subband edge formed by L(B,C) electrons
subband in the conduction band rises above that for crosses highest T-point valence subband edge, and
semimetal–semiconductor transition occurs (D0 is band
the highest subband in the valence band (see Fig. 7) overlap and EgL is L-point band gap);45 b Fermi surfaces of
thereby leading to a semimetal–semiconductor trans- Bi, shown in relation to Brillouin zone corresponding to
ition. This is predicted to occur at a wire diameter of fifth-band hole pocket about T-point and three sixth-band
49 nm for Bi nanowires oriented along the favoured L-point electron pockets labelled A, B, and C: mirror plane
symmetry of bulk bismuth structure results in
growth direction. Bismuth nanowires are of interest crystallographic equivalence of L-point carrier pockets B
for thermoelectric applications when in the semicond- and C; however, L-point carrier pocket A is not equivalent
ucting regime, under heavy doping conditions. crystallographically to carrier pockets B or C
Temperature dependent resistance measurements 7 Diameter dependence of band edges for Bi
(see Fig. 8a) in conjunction with model calculations nanowires: 3D Brillouin zone in b shows
(see Fig. 8b) show that these bismuth nanowires are important band edges participating in semi-
converted from a semimetal into a semiconductor due metal–semiconductor transition
to quantum size eVects.5 0 This is seen by the mono-
tonic temperature dependence of the resistance in the the resistance of both nanowire arrays and of single
semiconducting phase for wire diameters below 48 nm nanowires. These diYculties arise from problems with
and the non-monotonic behaviour with temperature making good ohmic contacts to all the nanowires of
for wires with diameters larger than 70 nm, above a nanowire array and with the oxidation of the
which the wires are in the semimetallic regimes, in individual nanowires, when they are removed from
agreement with theoretical predictions (Fig. 8b). The their templates.
non-monotonic dependency of resistance on the The Bi1 – x Sbx alloy system is interesting as a
nanowire diameter is due to the extrinsic carriers method for obtaining a low-dimensional p-type semi-
contributed by uncontrollable impurities, which conductor with very low eVective masses and high
becomes more important as band gap increases. So mobility carriers, which is important because thermo-
far, there exists no conclusive experimental data show- electric devices require both n-type and p-type legs.
ing an enhanced power factor in Bi nanowire arrays, Since Sb is isoelectronic with Bi and has the same
due to diYculties in measuring the absolute value of A15 crystal structure as Bi, bulk Bi1 – x Sbx alloys
International Materials Reviews 2003 Vol. 48 No. 1
52 Chen et al. Recent developments in thermoelectric materials

SM=regions where alloy is semimetal; SC=region where

alloy is semiconductor
9 Schematic diagram for energy bands near Fermi
level for Bi1 – x Sbx bulk alloys as function of x at
low T (à 77 K):51 when highest valence band is
at L-point, direct gap semiconductor results; for
x values where highest valence states are at T
or H, indirect semiconductor is obtained

a experimental temperature dependence of normalised

resistance for Bi nanowire arrays of various wire diameters
prepared by vapour deposition method, in comparison with
corresponding data for bulk Bi: measurement of resistance 10 Phase diagram of electronic band structure of
was made while Bi nanowires were in their alumina Bi1 – x Sbx nanowires: 52 bold arrow in centre
templates using two-probe measurement technique;49
b calculated temperature dependence of resistance for Bi indicates condition where 10 hole pockets
nanowires of 36 and 70 nm, using semiclassical transport (about T-point, 3 L-points and 6 H-points in
model45 Brillouin zone) coalesce in energy
8 Temperature dependence of resistance
measurements for Bi nanowires concentration, the wires are predicted to be semimet-
allic, a direct gap semiconductor, or an indirect gap
provide a high mobility material, but with electronic semiconductor. The calculations of Fig. 10 show how
properties that can be varied considerably as the Sb variation of the nanowire diameter can be used to
concentration is varied (see Fig. 9). Of particular change the electronic structure quite dramatically
interest for thermoelectric applications is the low with no basic change occurring in the crystal struc-
Sb concentration range ( below x =0·07) where the tures. Of particular interest in this diagram for the
bulk material is semimetallic, the regions for Bi1 – x Sbx nanowires is the point at x =0·13, and a
0·07<x <0·09 and 0·16<x <0·22 where bulk wire diameter of 60 nm, where the L-point, T-point
Bi1 – x Sbx is an indirect gap semiconductor and Ž nally and H-point hole subband edges are all degenerate
the region 0·09<x <0·16 where bulk Bi1 – x Sbx is a with one another, leading to a very large density of
direct gap semiconductor. 5 1 Calculations for the elec- hole states. Such a system, where all 10 hole subband
tronic structure for Bi1 – x Sbx nanowires (see Fig. 10)5 2 edges are degenerate in energy, is predicted to exhibit
show that variation of the wire diameter leads to an enhanced Seebeck coeYcient and an increased
another important degree of freedom in the control Z T.5 2 , 5 3 The feasibility of observing interesting trans-
of the electronic structure, showing regions where, port properties in Bi1 – x Sbx nanowires has been
depending on the nanowire diameter and Sb alloy demonstrated by showing that the high degree of
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 53

crystallinity of the Bi nanowires is preserved upon Sb Bowers predicted that solid state thermionic coolers
alloying as is the high carrier mobility. have a larger cooling power than that of thermoelec-
Thus far, progress in the fabrication and measure- tric devices. Mahan and co-workers 5 7 , 5 8 followed up
ment of the thermoelectric performance of test with a thermionic cooling and power generation
samples is most advanced for 2D systems where model for multiple layer structures. In this case, the
superior performance has already been demonstrated. advantage of the non-uniform heat generation inside
The excellent Z T3 D for these superlattices is attributed a double heterojunction structure 9 due to the ballistic
to the presence of quantum dot structures at the electron transport is lost. Their initial calculation5 7 , 5 8
nanoscale, 7 whose behaviour is not yet understood in suggests that multilayer thermionic coolers can have
detail, nor has the structure yet been optimised for a high eYciency. Yet in another paper, Vining and
thermoelectric performance. The 1D quantum wires Mahan5 9 compared the equivalent B factor that deter-
have in contrast been modelled in detail, though mines the Z T for thermionic multiple layer structures
materials problems involving surface oxidation and and similar thermoelectric multiple layer structures
with the formation of good individual contacts to the and found that the B factor of thermionic structures is
nanowires have slowed the experimental evaluation not larger than that for thermoelectric structures.
and optimisation of the thermoelectric performance Their conclusion is that the thermal conductivity
of the quantum wires. It is thus expected that further reduction 1 1 ,1 2 will be the major beneŽ t of multiple
emphasis will be given to materials science issues, layer structures, which is consistent with the studies
before the construction of reliable quantum wire carried out by the Ehrenreich group.5 5 In addition to
thermoelectric devices will be seriously undertaken. an all solid state cooling strategy, vacuum thermionic
refrigeration based on resonant tunnelling through
triangular wells and small spatial gaps in the vacuum
Electron transport perpendicular to film plane has been proposed recently.6 0 , 6 1 Theoretical calcu-
Most of the eVort so far has been focused on thin lations predict operation at room temperature and
Ž lms and superlattices. There are two lines of consid- below, with a cooling power density of 100 W cm – 2 .
eration for electron transport perpendicular to the No net cooling based on such vacuum thermionic
thin Ž lm plane: (i) control of the density of electron coolers has been reported experimentally.
states using quantum size eVects, and (ii) energy Theoretically, the modelling of electron transport
Ž ltering through thermionic transport. Two theo- perpendicular to the conŽ nement direction is con-
retical papers considered quantum size eVects siderably more diYcult compared to that along the
on thermoelectric properties for electron transport Ž lm plane, because the Ž lm thickness may be compar-
perpendicular to the superlattice plane.5 4 ,5 5 A slight able to several characteristic lengths of the charge
increase in Z T for Si/SiGe superlattices made of carriers, including the wavelength and the mean free
extremely thin layers (~5 A) is predicted. 5 4 Radtke path. Thus far, quantum based models, which consider
et al.5 5 studied Hgx Cd1 – x Te superlattices, and their the electrons as totally coherent, and thermionic
calculation shows that a 20% increase in power factor emission models, which consider the electrons as
is possible in narrow-well narrow-barrier superlattice totally incoherent, have been constructed. But there
systems, but suggested that the gain in Z T will most is no theory so far for the overlapping region. In
likely come from a thermal conductivity reduction addition, there are also thermoelectric eVects inside
rather than from a power factor increase. So far, there the Ž lm, which may be coupled with thermionic eVects
seems to be no experimental eVort aimed at pursuing at the interface to yield a total Z T of the structure.
a power factor increase due to quantum size eVects There have been a few studies that treat both eVects
for transport perpendicular to superlattice planes. and phonon size eVects by Zeng and Chen.6 2 – 6 4 Their
In the limit that the quantum size eVect is not modelling suggests that when the Ž lm is very thin,
important, for this case, there is still a possibility for energy conversion is dominated by the thermionic
increasing Z T. It was proposed that the energy bar- emission and when the Ž lm is thick, thermoelectric
riers at the junctions of diVerent materials be used as transport governs the energy conversion eYciency. In
an energy Ž lter to increase the thermoelectric energy the intermediate Ž lm thickness range, both eVects
conversion eYciency.8 Electron transport over such contribute to the Ž nal Z T. Their work also suggests
barriers is described by thermionic emission theory. that the thermal conductivity reduction will contrib-
In a theoretical paper, Mahan5 6 considered the cool- ute more to the Z T enhancement compared to the
ing power of vacuum based thermionic coolers, which thermionic emission, Z T which is consistent with
are based on the same principle as vacuum based previous studies that inferred the importance of the
thermionic power generators. His calculation showed thermal conductivity reduction based on experimental
that vacuum based thermionic coolers will not be results. 5 5 , 5 9
able to run at room temperature because of the large Experimentally, Shakouri and co-workers have
work function of known materials and because of fabricated thin Ž lm thermoelectric coolers based on
space charge eVects. Shakouri and Bowers9 suggested single heterojunction structures 6 5 and superlattice
that this could be circumvented using double hetero- structures 6 6 – 7 0 based on InP and Si/Ge superlattices.
junction structures. The barrier height between two The maximum temperature rise measured on a single
materials can be precisely tailored in theory as well element device is 12 K at a 200°C substrate temper-
as in practice for certain materials systems. Another ature from Si/Ge superlattices. 7 0 Mahan1 0 pursued
advantage of this approach is that Joule heating is metal–semiconductor superlattice structures for cool-
mostly rejected at the hot side due to the ballistic ing. No cooling eVect has yet been reported from
transport. Based on a simpliŽ ed model, Shakouri and such structures. It should be emphasised that testing
International Materials Reviews 2003 Vol. 48 No. 1
54 Chen et al. Recent developments in thermoelectric materials

a single device is very diYcult and involves many removal of the substrate. 3 7 – 3 9 , 8 3 Very few studies have
forms of losses that may degrade the device perform- reported thermal conductivity in both the in-plane
ance. Thus, these devices may have better performance and cross-plane directions. 3 8 , 4 0 All these experiments
if successfully developed as arrays, rather than as conŽ rmed that the thermal conductivities of the super-
individual devices. So far, there are no systematic lattices in both directions are signiŽ cantly lower than
experimental investigations on whether the observed the predictions based on the Fourier law and the
cooling is due to thermionic or thermoelectric mech- properties of their bulk parent materials. In the cross-
anisms, or both. Field emission coolers based on plane direction, the thermal conductivity values can
GaAs are also being investigated, but no cooling deŽ nitely be reduced below that of their correspond-
eVect has been observed so far.7 1 ing alloys.1 2 ,8 1 In the in-plane direction, the reduction
is generally above or comparable to that of their
Engineering phonon transport equivalent alloys,4 0 although a few experimental data
Phonon transport in low-dimensional structures is indicate that k values lower than those of the corres-
also aVected by size eVects and can be utilised to ponding alloys are possible. 1 1
increase Z T. Size eVects in the thermal conductivity A few groups have developed theoretical expla-
are a well known phenomenon that is important at nations for the thermal conductivity of superlattices,
low temperatures for bulk materials.7 2 Several studies for both in-plane and cross-plane directions. Two
of the thermal conductivity of thin Ž lms were carried schools of thought are apparent from the literature.
out in the 1970s and 1980s, mostly for polycrystalline One starts from the phonon spectrum calculation and
metallic or semiconductor thin Ž lms. The Ž rst experi- attributes the thermal conductivity reduction to
ment on superlattices was performed by Yao3 7 for the changes in the group velocity, density of states, and
thermal conductivity along the Ž lm plane. He scattering mechanics.8 8 – 9 3 The other approach starts
observed that the thermal conductivity of the super- from the simple picture of interface re ection and
lattices investigated was higher than that for their treats phonon transport in terms of particles.9 4 – 9 7 The
compositionally equivalent alloys. One can easily former assumes that phonons are totally coherent
infer that the reported values are also signiŽ cantly and the latter treats phonons in each layer as totally
lower than the values calculated from bulk properties incoherent. The coherent phonon picture is accurate
according to the Fourier theory. The Ž rst experiment if the interfaces and internal scattering do not destroy
in the cross-plane direction was reported by Chen the coherence of the phonons. Compared to the
et al.3 8 They measured the thermal conductivity of a coherent picture, the particle approach does not treat
semiconductor laser structure, which contained short the following mechanisms correctly: (i) phonon inter-
period superlattices, in both directions and observed ference, which gives minigaps in the superlattice
a factor of 10 reduction of k in the cross-plane phonon spectrum, (ii) phonon tunnelling, which
direction compared to predictions by the Fourier occurs for very thin layers above the critical angle for
theory. The reduction in the in-plane direction is total internal re ection of phonons, and (iii) long
smaller but also signiŽ cant. In a review paper, Tien wavelength phonons, which do not ‘see’ the existence
and Chen7 3 suggested that the new spectrum in of the interfaces. These three factors, however, do not
superlattices can potentially lead to super thermal seem to be dominant in the observed thermal conduct-
insulators. The studies by Yao3 7 and Chen and ivity behaviour of superlattices. This is because heat
co-workers 3 8 , 3 9 were mainly geared towards thermal conduction involves the contribution from all allow-
management applications for semiconductor lasers.7 4 able phonons covering the entire phonon frequency
Venkatasubramanian proposed to use the potentially range. Minigaps created by interference eVects cover
low cross-plane thermal conductivity of superlattices only a small fraction of the total thermal energy.
for thermoelectric devices.1 1 ,7 5 The idea is to use the Tunnelling is important only when each layer is only
phonon re ection at interfaces to reduce the thermal 1–3 monolayers thick due to the small phonon wave-
conductivity, while maintaining the electron trans- length. In addition, the diVuse interface scattering
mission at the interfaces by combining materials with occurring at most interfaces, which seems to be a very
small or, ideally, zero band-edge oVset. Such struc- important factor, destroys the phonon coherence.
tures are called electron-transmitting phonon-block- Comparison of lattice dynamics,9 2 acoustic wave
ing structures. This strategy on the Bi2 Te3 /Sb2 Te3 propagation, 9 8 and Boltzmann equation 9 4 , 9 6 , 9 7 simu-
system seems to have led to a signiŽ cant increase of lations with experimental data, by Chen and
Z T 1 1 ,7 6 as indicated in Fig. 2. As a word of caution, co-workers, leads to the conclusion that the major
because the characterisation of Z T is extremely reason for the observed thermal conductivity
diYcult in this direction, the values should be sup- reduction in the cross-plane direction is the phonon
ported by more research, preferably by diVerent re ection, particularly the total internal re ection.1 2
groups. Although phonon conŽ nement due to the spectral
Extensive experimental data on the thermal con- mismatch can potentially contribute signiŽ cantly to
ductivity of various superlatttices, including Bi2 Te3 / the thermal conductivity reduction, it is likely that
Sb2 Te3 ,7 5 ,7 7 ,78 GaAs/AlAs,3 7 – 3 9 ,7 9 ,8 0 Si/Ge,4 0 ,8 1 – 8 3 InAs/ many phonons leak out due to inelastic scattering.
AlSb,8 4 InP/InGaAs,8 5 CoSb3 /IrSb3 ,8 6 and PbTe For both the in-plane and the cross-plane directions,
based superlattice 4 1 have been reported in recent diVuse interface scattering of phonons seems to play
years. Most of these measurements are in the cross- a crucial role. As an example, in Fig. 11a the simulated
plane direction, 7 5 , 8 1 – 8 6 using the 3v method 8 7 or the thermal conductivity reduction in Si/Ge superlattices
optical pump-and-probe method. 8 0 Measurements in both the in-plane and the cross-plane directions
along the Ž lm plane direction relied heavily on the based on lattice dynamics modelling of the phonon
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 55

a lattice dynamics simulation of thermal conductivity normalised to bulk values;92 b temperature dependence of thermal
conductivity of Si/Ge (20/20 A) superlattice along (subscript x) and perpendicular (subscript z) to film plane;40 c thickness
dependence of thermal conductivity of GaAs/AlAs superlattices along film plane (GaAs and AlAs layers are of equal layer
thickness);94 d period thickness dependence of thermal conductivity of Si/Ge superlattices in cross-plane direction97 (also
plotted in b–d are fittings based on solutions of Boltzmann equations with p representing fraction of specularly scattered
phonons at interface, and values calculated based on Fourier law and measured bulk thermal conductivities of Si and Ge)
11 Results indicating crucial role of diffuse interface scattering of phonons

spectrum in superlattices 9 2 is shown in comparison is contrary to most experimental observations on

to experimental results (Fig. 11b–11d)4 0 on a Si/Ge GaAs/AlAs superlattices and Si/Ge superlattices,
superlattice. The simulation based on the phonon as shown in Fig. 11c and 11d,9 4 , 9 7 except in the very
group velocity reduction leads to only a small thin layer region where experimental data on
reduction in k in the in-plane direction, while the Bi2 Te3 /Sb2 Te3 superlattices indeed show a recovery
cross-plane direction shows a relatively large drop trend with decreasing period thickness. 1 1 Acoustic
(Fig. 11a). The lattice dynamics models imply perfect wave simulation suggests that the recovery in the
interfaces and thus no diVuse interface scattering. thermal conductivity at the very thin period limit is
Experimentally, the thermal conductivity reductions due to the tunnelling of phonons from one layer into
in both directions are much larger, as shown in another for incidence above the critical angle.9 8 In
Fig. 11b. In addition, the lattice dynamics simulation reality, however, there also exists the possibility that
leads to a thermal conductivity that Ž rst decreases such a recovery is due to interface mixing that creates
with increasing superlattice period thickness and then alloys rather than superlattices. In the thicker period
approaches a constant that is signiŽ cantly lower than regime, the Boltzmann equation based modelling that
that of its corresponding bulk values. Such behaviour treats phonons as particles experiencing partially
International Materials Reviews 2003 Vol. 48 No. 1
56 Chen et al. Recent developments in thermoelectric materials

specular and partially diVuse scattering at the He proposed that the correct starting point should
interfaces, can lead to a reasonable Ž t to the experi- be from the following expression for the thermal
mental data, as shown in Fig. 11b–11d. The parameter conductivity
p in Fig. 11b–11d represents the fraction of specularly

P GP CP
1 vmax 2p p
scattered phonons at the interface and (1­ p) that of kp = sin2 Q dQ C(v)n (v, h, Q)
the diVuse scattering that may be caused by interface 4p
0 0 0
mixing and roughness, or anharmonic forces at the
interface. The agreement between modelling and
experimental results suggests that the phonon coher-
ence length in superlattices is short and the loss of
Ö L (v, h, Q) cos2 h sin h dh
DH dv . . . (10)

coherence is probably due to diVuse interface where h and Q are the polar and azimuthal angles
scattering. formed with the heat  ux direction. The task of
To exhibit signiŽ cant size eVects, the phonon mean reducing the thermal conductivity is to reduce the
free path in the bulk material should be larger than value of the above integral. Low-dimensional struc-
the Ž lm thickness or other characteristic lengths of tures oVer several new ways to reduce the thermal
the structure. The estimation of the phonon mean conductivity integral in equation (10). First, the group
free path, however, must be done carefully. Often, velocity can be altered in nanostructures. The forma-
one tends to estimate the phonon mean free path L tion of standing waves in nanostructures means that
from the simple kinetic formula k =CvL/3, using the the group velocity becomes smaller, thus reducing the
speciŽ c heat and speed of sound in bulk materials. thermal conductivity. In superlattices, the bulk acous-
The mean free paths of phonons that actually carry tic phonons can be changed into optical phonons,
the heat could be much longer, because: (i) optical thereby drastically reducing their group velocity.
phonons contribute to the speciŽ c heat but not much Second, it is possible to induce anisotropic scattering
to thermal conductivity due to their small group in low-dimensional structures. For example, interface
velocity, and (ii) the acoustic phonon group velocity re ection and transmission are highly angle depen-
can be much smaller than the speed of sound due to dent. Total internal re ection means that phonons
dispersion eVects. For example, a careful estimation above the critical angle will be re ected backwards.
of the phonon mean free path in silicon leads to As another example, the optical phonons in two
2500–3000 A,9 7 , 9 9 compared to the kinetic theory materials have totally diVerent frequencies. It is likely
value of ~400 A. Because of this, some apparently that the scattering of optical phonons at the interface
low thermal conductivity materials, such as will be highly directional, i.e. the optical phonons will
Bi2 Te3 /Sb2 Te3 and CoSb3 /IrSb3 superlattices, can be preferentially scattered backwards. In the context
actually be engineered to have lower values by explor- of the phonon dispersion curve, this is called phonon
ing size eVects. Another important point is that typi- conŽ nement. The eVects of total internal re ection
cally the thermal conductivity reduction in the cross- and the phonon conŽ nement on the thermal conduct-
plane direction is larger than in the in-plane direction ivity can also be interpreted as reducing the angle
because interfaces impede the phonon transport more and frequency integration limits of equation (10),
in the cross-plane direction than along the Ž lm plane, thus decreasing the thermal conductivity. Third, the
as is suggested by Fig. 11b. For polycrystalline mater- speciŽ c heat of nanostructures can be changed by
ials this may not necessarily be true, because the changing: (i) the density of states and (ii) the degrees
columnar grain structures can actually cause a more of freedom of the atomic vibrations. Theoretical stud-
signiŽ cant reduction in the in-plane direction, as is ies on superlattices, however, suggest that these
observed in diamond thin Ž lms.1 0 0 Other factors such changes are not strong, except at low temper-
as the dislocation orientation (occurring in threading atures.1 0 3 – 1 0 5 Based on these arguments, Chen1 2 sug-
dislocations) may also create more scattering in the gested that low-dimensional structures may have a
in-plane direction, although there have been neither smaller minimum thermal conductivity. Figure 12
detailed theoretical nor experimental studies. shows the experimental thermal conductivity of a
Existing experimental data have clearly shown that Si/Ge superlattice compared to predictions based on
the thermal conductivity of superlattices can be made the minimum theoretical thermal conductivity of bulk
smaller than that of their corresponding alloys. Si and Ge. The Ž gure suggests the possibility of
Remember that alloying has been used in thermoelec- reaching values lower than that theoretically attain-
tric materials research as an eVective way to reduce able in bulk materials.
the lattice thermal conductivity. This raises the ques- Thus, it seems that the following strategies may be
tion of what is the minimum thermal conductivity of pursued to engineer the phonon transport in order
superlattices. Slack1 0 1 proposed that the minimum to reduce the lattice thermal conductivity.
thermal conductivity one can reach for a material is 1. For transport along the interfaces, i.e. along the
when the phonon mean free path in equation (9) is Ž lm plane and wire axis, the thermal conductivity can
replaced by the wavelength. Later, Cahill et al.1 0 2 be reduced by creating diVuse interface scattering and
further limited it to half the wavelength. The more reducing the interface separation distance. In addition
fundamental question is whether low-dimensional to the naturally existing interface roughness due to
structures are subject to the same limit or not. Chen1 2 the mixing of atoms at the interfaces, other possibil-
argued that the same minimum may not be applicable ities are artiŽ cially corrugated interfaces, such as thin
to low-dimensional materials which are highly aniso- Ž lms grown on step-covered substrates, and quantum
tropic, because anistropy causes directional depen- dot interfaces. In controlling the interface structures
dence of the relaxation time and of the group velocity. for phonon thermal conductivity reduction, the
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 57

than periodic superlattices, or composite superlattices

with diVerent periodicities, may provide methods to
localise some, if not all, of these long wavelength
phonons.
4. Defects, particularly dislocations, can provide
another vehicle to reduce the lattice thermal conduct-
ivity in low-dimensional systems. Clearly, whether all
or some of these strategies will work for the improve-
ment of the energy conversion eYciency will depend
on their impacts on the electron/hole energy conver-
sion capabilities. More studies of these eVects should
be done.
The phonon size eVects in quantum wires and quan-
tum dots are conceivably more signiŽ cant than in
thin Ž lms and superlattices due to their increased
12 Comparison of measured thermal conductivity surface/interface area. Up to now, studies of the
of highly dislocated Si/ Ge superlattice with thermal conductivity of quantum wires have been
predictions of minimum thermal conductivity scarce. There are a few experimental and theoretical
theory for bulk Si and Ge and their multilayer
composite, latter is calculated based on Fourier
studies on the thermal conductivity of quantum dot
theory:12 solid and dashed lines are from arrays and nanostructured porous media.1 0 7 ,1 0 8
minimum thermal conductivity theories by Theoretically, one can expect a larger thermal con-
Slack101 and Cahill et al.102 respectively ductivity reduction in quantum wires compared to
thin Ž lms.1 0 9 ,1 1 0 The measurements of the thermal
interface eVects on the electron transport must also conductivity in quantum wires have been challenging.
be considered. It may, however, be possible to capital- Recent measurements on the thermal conductivity of
ise on the diVerent wavelengths of electrons and individual carbon nanotubes 1 1 1 provide a possible
phonons, such that phonons are scattered more approach for related measurements on thermoelectric
diVusely at the interface than electrons, because the nanowires of interest. Nanowires for thermoelectrics,
dominant phonon wavelength is typically shorter however, have very low k compared to carbon nano-
than the electron wavelength. tubes, and this large diVerence in behaviour will create
2. For transport perpendicular to the interfaces, new challenges for measurements on nanowires of
increasing the phonon re ectivity is the key strategy interest to thermoelectricity.
for reducing the thermal conductivity. This could be
realised by increasing the mismatch between the Bulk materials
properties of the two constituents, such as the density,
group velocity, speciŽ c heat, and the phonon spectrum The search for ‘phonon–glass electron–crystal’ bulk
between adjacent layers. The eVects of interface rough- materials has now moved beyond the traditional
ness can be positive or negative, depending on Bi2 Te3 based binary system. Several classes of bulk
whether the diVuse phonon scattering actually materials have been discovered or re-investigated as
decreases or increases the phonon re ectivity at the interesting for potential thermoelectric applications.
interfaces. Experiments and modelling so far seem to Representative among them are skutterudites, clath-
indicate that diVuse scattering is more eVective when rates, b-Zn4 Sb3 , half-Heusler intermetallic com-
the mismatch in the material properties is not large. pounds, and complex chalcogenides. The phonon
Phonon conŽ nement occurs due to the mismatch rattler concept developed by Slack has proven to be
between the bulk phonon dispersion relations, and a very eVective in reducing the thermal conductivity of
large diVerence in the dispersion favours more phonon materials with open cages, such as skutterudites and
conŽ nement. How much phonon conŽ nement can be clathrates. The highest Z T in Ž lled skutterudites
achieved, however, is an open question. Needless to reached 1·4 at ~600°C, as shown in Fig. 2. In this
say, however, in pursuing the phonon thermal con- section, several promising bulk thermoelectric mater-
ductivity reduction, the eVects of interfaces on the ials will be brie y reviewed.
electron transport must be considered. Past studies
on electron transport, particularly in the development Skutterudites
of vertical-cavity surface-emitting lasers (VCSELs), Existence and composition
indeed suggest the possibility of much stronger In the early 1990s, a systematic search for advanced
reduction in the thermal conductivity than in the thermoelectric materials resulted in the ‘rediscovery’
electrical conductivity. For example, digitally or con- of a family of attractive semiconducting materials
tinuously graded interfaces are often used to reduce with the skutterudite crystal structure. 1 1 2 For state of
the electrical resistivity of Bragg re ectors used for the art thermoelectric materials, such as PbTe and
VCSELs,1 0 6 while it is likely that such graded Bi2 Te3 alloys, the number of isostructural compounds
interfaces can create more phonon back re ection is limited and the possibilities to optimise their bulk
and thus a larger thermal conductivity reduction. 3 8 properties for maximum performance at diVerent
3. Some long wavelength phonons may not ‘see’ temperatures of operation are also very limited. This
the interfaces in structures, such as superlattices. The is not the case for the skutterudite family of materials,
localisation of these phonons can further decrease the where 11 binary compounds and many solid solutions
lattice thermal conductivity. Using aperiodic rather and related phases are known to exist.1 1 3 These
International Materials Reviews 2003 Vol. 48 No. 1
58 Chen et al. Recent developments in thermoelectric materials

materials cover a large range of decomposition tem-

peratures and band gaps, which oVer the possibility
to adjust the composition and doping level for a
speciŽ c temperature range of application. An excellent
in-depth review of skutterudites as novel thermoelec-
tric materials was recently written by Uher.1 1 4
The unit cell of the skutterudite structure (cubic,
space group Im3, prototype CoAs3 ) contains square
radicals [As4 ]4 – . This anion, which is located in the
centre of the smaller cube, is surrounded by 8 trivalent
transition metal Co3 + cations. The unit cell consists
of 8 of these smaller cubes, or octants, two of them
empty, and six of them containing the anions [As4 ]4 –
in the centre. This arrangement is necessary to main-
tain the stoichiometric ratio Co3 + : [As4 ]4 – =4 : 3.
Taking into account one-half of the full 32 atom unit
cell and its empty octant, one can represent the
skutterudite formula as h T4 Pn1 2 , where h is the
empty octant, T is the transition metal and Pn is the 13 Schematic of filled skutterudite 34 atom unit
pnicogen atom. If considering a simple bonding cell of novel thermoelectric materials – each
scheme,1 1 5 each transition metal contributes 9 elec- cell contains 8 transition metal atoms: Fe, Ru,
trons and each pnicogen contributes 3 electrons to Os, Co, Rh, Ir, Ni, Pd or Pt; 24 pnicogen atoms:
P, As, Sb (substitution by S, Se or Te possible);
the covalent bonding, for a valence electron count 2 rare earth atoms filling vacant octants in
(VEC) total of 72 for each h T4 Pn1 2 unit. The VEC skutterudite structure: La, Ce, Pr, Nd, Sm, Eu,
is a useful number in determining the skutterudite Gd, Th and U
compositions that are semiconducting. The valence
electron count of 72 corresponds to a diamagnetic
It should be noted, however, that even if a simple
semiconductor for the skutterudite materials. Uher1 1 4
VEC scheme may be used to explain the various
gave a detailed discussion on the bonding scheme
that favours the semiconducting behaviour. There are atomic composition permutations in skutterudites,
the actual picture is certainly quite a bit more compli-
eleven h T4 Pn1 2 binary skutterudites reported in the
cated, especially when trying to explain the transport
literature. The nine semiconducting compositions are
formed with all nine possible combinations of T = properties of the more complex skutterudites, in view
of some doping and compositional limitations. Much
Co, Rh, Ir and Pn=P, As, Sb. Two additional
eVort has been devoted in recent years to understand-
skutterudite phosphides were reported, NiP3 and
PdP3 . However, in these two compounds, the total ing the valence of transition metals and some rare
earth Ž lling atoms in ternary and Ž lled skutterudites
VEC is 73, resulting in metallic behaviour.1 1 6
but results are somewhat inconclusive at this point. 1 1 4
The existence of many ternary skutterudites has
been determined. Nine ternary compounds have been Transport properties
reported in the literature, and at least 17 more have The transport properties of both n-type and p-type
been discovered.1 1 7 Ternary skutterudite compos- conductive binary skutterudite compounds, mostly
itions are derived from binary compounds by keeping antimonides and arsenides, have been thoroughly
a total VEC of 72. Using h Co4 Sb1 2 (CoSb3 ) as an characterised in the past few years (see e.g. Refs.
example, substituting trivalent Co (Co3 + ) by divalent 124–126). Associated with a low hole eVective mass,
Fe (Fe2 + ) and tetravalent Pd (Pd4 + ), results in very high hole mobilities, low electrical resistivities
h Fe2 Pb2 Sb1 2 (Fe0 ·5 Pb0 ·5 Sb3 ). If instead, Sb is and moderate Seebeck coeYcients are obtained in
replaced by Sn and Te, then h Co4 Sn6 Te6 p-type skutterudites (Fig. 14). Most of the samples
(CoSn1 ·5 Te1 ·5 ) is obtained. If substitutions occur on shown in this Ž gure were not nominally doped. They
both the transition metal and pnicogen sites, then were grown using a gradient freeze technique from
h Fe4 Sb8 Te4 (FeSb2 Te) is obtained. non-stoichiometric, Sb rich melts.1 2 7 One should note
A Ž lled skutterudite structure is simply derived that the room temperature mobility values of p-type
from the skutterudite structure by inserting one atom skutterudites are very high (Fig. 14a), about 10 to
in each empty octant, as illustrated in Fig. 13. A large 100 times higher than those for p-type Si and GaAs
number of these compounds have been known for at similar carrier concentrations. RhSb3 exhibits the
some time (see e.g. Refs. 116, 118–121), where the greatest hole mobility, 8000 cm2 V – 1 s – 1 for a carrier
Ž lling atom is typically a rare earth lanthanoid, concentration of 2·5 Ö 101 8 cm – 3 , which is about 70
though other compositions with actinoids Th and times higher than p-type GaAs and still 5 times higher
U,1 2 1 ,1 2 2 as well as alkaline earths Ca, Sr and Ba1 2 1 ,1 2 3 than n-type GaAs. For a comparable doping level,
have also been reported. For a typical Ž lled skutterud- the carrier mobilities of n-type samples are about an
ite composition, such as LaFe4 P1 2 , the rare earth order of magnitude lower than the values achieved
element contributes 3 electrons, but due to the on p-type samples. However, the much larger electron
divalent Fe (Fe2 + ), the total VEC is only 71. This eVective masses and Seebeck coeYcients make n-type
deŽ cit results in metallic behaviour for most simple skutterudites promising candidates as well.
Ž lled ternary compounds. Only CeFe4 P1 2 , UFe4 P1 2 Unfortunately, the room temperature thermal con-
and CeFe4 As1 2 have been reported as semiconductors. ductivity of binary skutterudites (10–25 W m – 1 K – 1 )
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 59

order of magnitude lower in some ternary unŽ lled or

Ž lled compositions. Also, as shown in the table, high
doping levels in n-type CoSb3 result in a 70%
reduction in lattice thermal conductivity, an eVect
comparable to that obtained by forming solid solu-
tions. As a result, Z T values as high as 0·85 are
obtained in the 850–900 K temperature range in
heavily doped n-type CoSb3 ,1 2 8 as shown in Fig. 2.
These experimental results thus demonstrate that
the skutterudite family of compounds and alloys oVer
extremely attractive possibilities for the search for
high Z T materials. Skutterudites have excellent elec-
trical transport properties and the thermal conduct-
ivities can be reduced by a factor of 20, down to
nearly glassy characteristics. Since the work of
Chasmar and Stratton, 1 2 9 it has been obvious that
high Z T values require materials with a high mobility,
high eVective mass and low lattice thermal conduct-
ivity, where ideally one can separately optimise the
power factor and minimise the thermal conductivity,
or as summarised by Slack,5 fabricate a PGEC. While
the conceptual approach to high Z T has been known
for over 40 years, much eVort has been devoted into
Ž nding out if skutterudites could truly be such PGEC
materials, that is conserving the excellent electrical
properties of the binary compounds while reducing
the thermal conductivity to values substantially lower
than that of state of the art of Bi2 Te3 alloys.
However, a number of experimental and theoretical
results published in recent years on both ternary
unŽ lled and Ž lled skutterudite compounds indicate
that their electronic band structure and transport
properties are vastly diVerent from the pure binary
compounds. 1 3 0 , 1 3 1 For example, the study of such
ternary compounds as FeSb2 Te, Fe0 ·5 Ni0 ·5 Sb3 and
Ru0 ·5 Pd0 ·5 Sb3 derived from high carrier mobility
CoSb3 and RhSb3 shows that they are heavily doped
semiconductors with carrier concentration values
ranging from 1Ö 102 0 to 1 Ö 102 1 cm – 3 . Comparing
these compounds to CoSb3 at such high carrier
concentrations, they are characterised by signiŽ cantly
lower carrier mobility, and lattice thermal conduct-
14 a Hall mobility variation as function of carrier ivity values as much as 50 to 75% lower. Such low
concentration and b Seebeck coefficient as lattice thermal conductivity values are somewhat
function of temperature for binary skutterudite
compounds: samples were not nominally
doped 127 Table 1 Room temperature conductivity type,
carrier concentration N, and lattice
thermal conductivity kp of various
is too high to result in high Z T values. Substantial skutterudite compounds and alloys,
reductions in the lattice thermal conductivity must including filled compositions
be obtained to achieve values comparable to those
Compound Conductivity N, cm – 3 kp , W m – 1 K – 1
of state of the art thermoelectric materials
(1–4 W m – 1 K – 1 ). Several approaches to the CoP3 p 3Ö 1019 23·7
reduction of the lattice thermal conductivity in skut- CoAs3 p 4Ö 1018 14·0
terudites have been pursued: heavy doping, and for- CoSb3 p 9Ö 1018 10·3
CoSb3 n 1Ö 1021 3·4
mation of solid solutions and alloys, as well as the
CoP1·5 As1·5 p 5Ö 1018 3·8
study of novel ternary and Ž lled skutterudite com- Co0·88 Ir0·12 Sb3 p 1Ö 1019 2·9
pounds. All those approaches have resulted in skut- FeSb2 Te p 5Ö 1020 2·3
terudite compositions with substantially lower OsSb2 Te p 4Ö 1018 2·1
thermal conductivity values. The room temperature RuGe0·2 Sb2 Te0·8 p 9Ö 1019 1·4
lattice thermal conductivity and carrier concentration Ru0·5 Pd0·5 Sb3 p 1Ö 1020 1·5
values of selected skutterudite compounds and alloys IrSn1·5 Se1·5 p 3Ö 1019 2·7
are reported in Table 1 for comparison. It is interes- CeRu4 P12 p 1Ö 1020 8·0
ting to note that, compared to binary compounds, CeFe4 Sb12 p 3Ö 1021 1·6
the lattice thermal conductivity values can be one Nd0·7 Ru2 Co2 Sb12 p 2Ö 1020 1·8

International Materials Reviews 2003 Vol. 48 No. 1

60 Chen et al. Recent developments in thermoelectric materials

surprising considering that the atomic mass and

volume diVerences introduced by the substituting
anion/cation are fairly small: Fe and Ni for Co, Ru
and Pd for Rh, Te for Sb. A possible explanation
given for the unusually high phonon scattering rate
is that transition metal elements have mixed valence
states and electrons are transferred between the
diVerent ions, thus scattering the phonons in this
process. 1 3 2 ,1 3 3 This would be consistent with low
carrier mobilities as well as with the experimental
diYculties encountered in controlling their electrical
properties since changes in carrier concentration are
not easy to achieve because dopants can be compen-
sated by small  uctuations in the overall valence of
the transition metals.
Interestingly enough, the search for high Z T values
in skutterudites has been most successful so far in
compounds that do not share the exceptional carrier
mobilities of the pure binary compounds, but rather
have a combination of high degeneracy, unusually 15 Room temperature lattice thermal con-
large Seebeck coeYcient values and low lattice ther- ductivity as function of filling atom rattling
mal conductivities: Ž lled and partially Ž lled skutterud- amplitude for various fully filled and fully dense
ites. A maximum Z T value of 1·4 has been achieved filled skutterudite compounds: carrier con-
to date at a temperature of 875 K in Cef Fe4 – x Cox Sb1 2 centrations are also reported to account for
and Laf Fe4 – x Cox Sb1 2 , where f<1 and 0<x < additional charge carrier scattering of phonons
4.1 3 4 ,1 3 5
The initial appeal of introducing a Ž lling atom into itions has proven quite challenging from a materials
the skutterudite structure was to substantially reduce synthesis standpoint. Electron microprobe analysis of
the lattice thermal conductivity of the original binary a series of Cef Fe4 – x Cox Sb1 2 compounds has demon-
compound with minimal decrease in the carrier strated that the fraction of Ce Ž lling f decreases with
mobility, and thus to achieve a ‘PGEC’. The heavy increasing substitution of Fe by Co. In addition to
Ž lling atom would ‘rattle’ within its octant ‘cage’ and Co, substitution of Fe by Ni and Ru, and the substi-
thus scatter phonons quite eVectively. Also because it tution of Ru by Pd have also been investigated
is Ž lling an empty octant, its contribution to the recently. The variations of the Ž lling fraction f as a
electrical transport would be minimal, though the function of x are plotted in Fig. 16 for the four
increased phonon scattering rate should somewhat diVerent ranges of compositions. The two solid lines
impact the carrier scattering rate (carrier–phonon represent the expected transition for Ni and Co from
interaction). However, it became rapidly clear that p-type to n-type (when the VEC reaches 72), taking
Ž lled skutterudites are quite diVerent from their into account both f and x variations. When Fe is
binary relatives, and that their low lattice thermal totally replaced by Co, only a very small amount
conductivities result from a combination of eVects, of Ce remains in the sample ( f=0·07). The chain
often quite diYcult to separate from each other: dotted line was calculated based on a CeFe4 Sb1 2 –
rattling, carrier–phonon scattering (high doping Ce0 ·0 6 5 Co4 Sb1 2 range of ‘solid solution’ compo-
levels), mixed valence of the transition metals, point sitions. Cef Fe4 – x Nix Sb1 2 compositions with x >1·5
defect scattering. have not yet been synthesised, but it is clear that
If comparing fully Ž lled compositions and taking at equivalent concentrations, Ni substitution res-
into account charge carrier concentration levels, how- ults in less Ce Ž lling than Co substitution. However,
ever, it can be shown that the lattice thermal conduct- because Ni donates two electrons instead of only one
ivity does indeed decrease signiŽ cantly with increasing for Co when replacing Fe, the decrease in carrier
rattling amplitude of the Ž lling atom, as shown in concentration and the corresponding change in prop-
Fig. 15. The rattling amplitude is deŽ ned as the erties with increasing x is much stronger for
diVerence between the void Ž ller covalent radius and Cef Fe4 – x Nix Sb1 2 . One can see from these results that
the radius of the cage.1 3 6 The rattling amplitude semiconducting compositions can be obtained for Co
increases are the largest when going from the phos- rich compositions. However, they typically show
phides to the antimonides which have larger unit cells mixed conduction eVects at room temperature. 1 1 7
and cage sizes, and very little when going from Fe Recent theoretical studies on n-type Ž lled skutteru-
based to Ru based compositions. dites1 3 7 and new experimental materials preparation
The most recent research eVorts on skutterudites approaches through high pressure, high temperature
have focused on improving Z T over a wide temper- synthesis or the use of thin interdiVusing layers1 3 8 ,1 3 9
ature range by attempting to conserve the excellent may eventually allow for the characterisation of
semiconducting behaviour of the unŽ lled binary skut- ‘optimised’ skutterudite compositions with perhaps
terudites when introducing a ‘compensating’ atom for high Z T values at room temperature. In the mean-
the addition of the ‘Ž lling’ atom into the structure, time, skutterudites are now being actively pursued
and going back to a VEC of 72. However, preparing for introduction into advanced thermoelectric power
lightly doped extrinsic p-type and n-type compos- generation devices and systems with the potential
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 61

frequency phonons by the Sr atoms that are loosely

bonded inside the structure and are free to rattle
around their atomic positions. A good indicator of
the possible motion of the guest atoms is the atomic
displacement parameter (ADP) that is a measure of
the mean-square displacement amplitude of an atom
around its equilibrium site. Unusually large ADP
values have been measured for guest atoms, such as
Cs and Sr in Ge based clathrates. 1 4 3 Sales et al. have
recently proposed a model to estimate the lattice
thermal conductivity based on ADP values.1 4 5 At
room temperature, the thermal conductivity of
Sr8 Ga1 6 Ge3 0 is close to that of amorphous Ge. Low
thermal conductivity values have also been observed
in other Ge based clathrates. Silicon based clathrates
tend to have higher thermal conductivity values. A
good thermoelectric material must combine a low
lattice thermal conductivity with good electronic
properties. The electronic properties of several Si, Ge,
solid lines represent expected transition for Ni and Co
from p-type to n-type (when VEC reaches 72), taking into and Sn based clathrates have been measured. Metallic
account both f and x variations: when Fe is totally replaced to semiconducting behaviour can be achieved by
by Co, only very small amount of Ce remains in sample varying the doping and/or composition. Both n- and
(f=0·07); chain dotted line was calculated based on p-type materials can be obtained by the same process.
CeFe4 Sb12 –Ce0·065 Co4 Sb12 range of ‘solid solution’
compositions (Cef Fe4 – x Nix Sb12 compositions with x>1·5 Good Seebeck coeYcient values up to ­ 300 mV K – 1
have not yet been synthesised, but it is clear that at have been achieved. To date, the best dimensionless
equivalent concentrations, Ni substitution results in less Ž gure of merit Z T obtained for n-type clathrate
Ce filling than Co substitution) compounds is about 0·34 with a projected value >1
16 Ce filling fraction f for Cef Fe4 – x Mx Sb12 samples above 700 K. The ability of engineering clathrate
as function of x, Fe substitution by M, with compounds with glass-like thermal conductivity com-
M=Co, Ni, and Ru bined with their relatively good electronic properties
has ranked clathrates among PGEC materials,
for 15% conversion eYciency in the 25–700°C tem- although full decoupling between their electronic and
perature range.1 4 0 thermal properties remains to be demonstrated in
these materials. Nevertheless, the encouraging results
obtained to date combined with the numerous options
Other novel bulk materials for optimisation warrant further investigations of
Clathrates these interesting materials.
Among other materials of interest as potential new
thermoelectric materials are clathrates. A clathrate b-Zn4 Sb3
material can be deŽ ned as one with a lattice that Another material re-investigated recently for thermo-
contains voids that can be Ž lled with guest atoms or electric power generation is b-Zn4 Sb3 with a hexag-
molecules. Silicon, Ge, and Sn based clathrates Ž lled onal rhombohedric crystal structure, and space group
with alkaline atoms have been reported 1 4 1 ,1 4 2 and R3C, as shown in Fig. 17. Caillat et al.1 4 6 have
have recently been investigated for their thermoelec- measured the thermal conductivity of polycrystalline
tric properties. 1 4 3 They can be divided into two major b-Zn4 Sb3 samples. The lattice thermal conductivity
groups: type I and type II. Both types have a cubic is nearly temperature independent between 300 and
unit cell, but diVer according to the number and size 650 K, with a room temperature lattice thermal con-
of the voids present in the structure. Ternary com- ductivity of 0·65 W m – 1 K – 1 at 300 K, nearly 2 times
pounds have also been reported. There are numerous lower than that of Bi2 Te3 alloys. This remarkably low
possible compositional, structural, and Ž lling vari- value and unusual temperature dependence (a 1/T
ations in those materials, resulting in vastly diVerent temperature dependence is usually observed ) can be
electronic properties ranging from semimetallic to attributed to the relatively complex crystal structure,
semiconducting. Recently, Nolas et al.1 4 4 have meas- as well as the presence of vacancies in the lattice. The
ured the thermal conductivity of semiconducting electronic transport properties are typical of a semi-
Sr8 Ga1 6 Ge3 0 polycrystalline samples and observed a metal with low electrical resistivity that increases with
temperature dependence typical of amorphous mater- increasing temperature. The Seebeck coeYcient also
ial. These results have triggered extensive theoretical increases with increasing temperature and peaks at
and experimental research eVorts to synthesise several 675 K with a value of about 200 mV K – 1 . This rela-
of these materials and further understand their pecul- tively high Seebeck value for a metal is the result of
iar transport properties. A comprehensive review of a fairly large eVective mass.1 4 6 The best Z T obtained
these materials has recently appeared in the to date on polycrystalline samples is about 1·4 at
literature.1 4 3 675 K (Fig. 2).1 4 6 Above 765 K, b-Zn4 Sb3 transforms
The low temperature T 2 temperature dependence into c-Zn4 Sb3 that has poorer thermoelectric prop-
observed by Nolas et al.1 4 4 for Sr8 Ga1 6 Ge3 0 polycrys- erties. Band structure calculations1 4 7 predict a metallic
talline samples was attributed to the scattering of low behaviour with improved thermoelectric performance
International Materials Reviews 2003 Vol. 48 No. 1
62 Chen et al. Recent developments in thermoelectric materials

coeYcient values. Large power factors on the order

of 25–30 mW cm – 1 K – 2 have since been experimen-
tally obtained for several of these materials, e.g.
ZrNiSn and HfNiSn. The impact on the electronic
properties of compositional variations and/or atomic
substitutions on the various sublattices has been
investigated, showing that both doping level and
conductivity type can be altered. While the power
factors are promising, the thermal conductivity of
ternary compounds, such as ZrNiSn and HfNiSn, is
rather high. The total thermal conductivity (which is
essentially the lattice thermal conductivity for these
materials) ranges from 5·9 to 17 W m – 1 K – 1 for
ZrNiSn.1 5 1 The spread in the values was primarily
due to the diVerence of structural quality introduced,
for example, by annealing the samples. Attempts to
reduce the lattice thermal conductivity of these mater-
ials using mass-defect scattering on the various sub-
lattices were made. Although lattice thermal
conductivity values of 5–6 W m – 1 K – 1 were obtained
for alloys, these values are still too high compared to
those obtained for state of the art thermoelectric
17 Schematic representation of Zn4 Sb3 crystal alloys, such as Bi2 Te3 alloys. EVorts should therefore
structure illustrating various Sb and Zn focus on further reducing the lattice thermal conduct-
atomic sites ivity of these materials that otherwise possess impress-
ive electronic properties that can be tuned through
for lower doping levels. Little success has however doping and alloying. Possible schemes for reducing
been obtained experimentally to optimise the doping the thermal conductivity may however be somewhat
level of this compound. b-Zn4 Sb3 forms a full range limited apart from the introduction of point defect
of solid solutions with the isostructural compound scattering, since these materials are not ‘cage-like’
Cd4 Sb3 . Low temperature thermal conductivity materials, such as skutterudites or clathrates. Most
measurements on Zn4 – x Cdx Sb3 mixed crystals transport property measurements on half-Heusler
showed a nearly temperature independent variation alloys to date have been limited to low temperatures
of the thermal conductivity, which is lower than for but these materials may actually be quite interesting
b-Zn4 Sb3 (Ref. 148) mostly due to point defect scat- at temperatures up to 800–900 K, considering that
tering. Zn4 – x Cdx Sb3 mixed crystals appear to be less they typically behave as semimetals at temperatures
stable than b-Zn4 Sb3 itself and a Z T maximum of below 300 K and semiconductors above that temper-
1·4 at about 400 K was obtained for these mixed ature. Transport property measurements above 300 K
crystals. EVorts to incorporate b-Zn4 Sb3 into would therefore be of interest to fully assess the
advanced, high eYciency thermoelectric unicouples potential of these materials for thermoelectric
are in progress.1 4 9 Further optimisation of the prop- applications.
erties of these compounds is limited because of the Complex chalcogenides
diYculties to dope them and the restricted compos- While several materials with Z T >1 have been ident-
itional variations possible. iŽ ed above room temperature, there is a great need
Half-Heusler intermetallic compounds for new thermoelectric materials with Z T >1 for
Half-Heusler intermetallic compounds with the gen- cooling applications. At and below room temperature,
eral formula MNiSn (M=Zr, Hf, Ti) have also only two materials have been known for many years
attracted considerable interest as potential new ther- to have decent thermoelectric properties: Bi–Sb and
moelectric materials.1 5 0 These materials possess the Bi2 Te3 alloys. Past studies suggest new low temper-
MgAgAs structure and are closely related to the full ature semiconducting thermoelectric materials are
Heusler compounds MNi2 Sn which are metals. likely to be found in narrow band gap materials.1 4
Replacing one Ni atom by an ordered lattice of An extensive eVort at Michigan State University
vacancies leads to a gap formation in the density of has focused on a number of new chalcogenides com-
states and to a semiconducting character with band posed mostly of heavy elements. As a result, a number
gap values on the order of 0·1 to 0·2 eV. As a result of potential new materials for low temperature ther-
of the large electron eVective mass in these materials, moelectric applications have been identiŽ ed. A com-
high Seebeck coeYcients are typically obtained at prehensive review of these materials has recently
300 K and higher. EVective masses of 2–3 m0 were appeared in the literature. 1 5 3 A number of complex
estimated by Uher et al.1 5 1 for ZrNiSn, and Seebeck phases have been prepared preferably by a  ux tech-
coeYcients as high as ­ 300 mV K – 1 were measured nique and several new compounds have been ident-
at 300 K for this material. It was originally suggested iŽ ed. Among the materials investigated are the
by Cook et al.1 5 2 that these materials might be good sulphides KBi6 ·3 3 S1 0 and K2 Bi8 S1 3 , the selenides b-
thermoelectric materials, considering their combi- K 2 Bi8 Se1 3 and K2 ·5 Bi8 ·5 Se1 4 , A1 + x Pb4 – 2 x Bi7 + x Se1 5
nation of low electrical resistivity with large Seebeck (A =K, Rb) compounds, and the tellurides A/Bi/Te
International Materials Reviews 2003 Vol. 48 No. 1
 Chen et al. Recent developments in thermoelectric materials 63

and A/Pb/Bi/Te. A common feature for most of these Thermoelectric materials require high doping with
materials is their low thermal conductivity, compar- carrier concentrations of ~101 9 cm – 3 . Careful
able or even lower than that of Bi2 Te3 alloys. Many optimisation of the doping concentration is necessary.
of these compounds show very anisotropic transport Thus an experimental thermoelectric research pro-
properties. Perhaps the most promising compound gramme must be prepared in the synthesis and
identiŽ ed to date is CsBi4 Te6 . This compound has a optimisation, as well as fast characterisation turn-
layered anisotropic structure with Cs ions between around capability.
[Bi4 Te6 ] layers. The ADPs of the Cs ions are 1·6 Most thin Ž lms in electronic devices are on the
times greater than those of the Bi and Te atoms. order of submicrometres in the Ž lm thickness.
Crystals of CsBi4 Te6 grow with a needlelike morph- Thermoelectric thin Ž lms should typically be thicker,
ology and are stable in air and water. The crystals both for characterisation purposes and for device
are amenable to doping and SbI3 , BiI3 , and In2 Te3 applications. For thermoelectric devices in the cross-
have been successfully used to optimise the carrier plane direction, Ž lms thicker than a few micrometres
concentration of this material. The power factor can or even much thicker are desirable in terms of sustain-
be maximised through doping and a maximum power ing a reasonable temperature diVerential. For thermo-
factor value of about 50 mW cm – 1 K – 2 was obtained electric devices intended for use for in-plane transport
at 185 K for the p-type material.1 5 3 The total thermal applications, the reverse heat  ow from the supporting
conductivity along the growth axis is about substrate must be minimised. This means either the
1·5 W m – 1 K – 1 at 300 K and is essentially constant removal of the substrate or depositing very thick
down to 100 K. This atypical temperature dependence Ž lms. Thus, both in-plane and cross-plane devices
suggests again that the rattling Cs ions signiŽ cantly demand relatively thick Ž lms, while quantum or
contribute to phonon scattering in this compound. classical size eVects typically require individual layers
The best Z T to date obtained along the needle of the order of several tens of angstroms. Such con-
direction is 0·82 for the p-type material (Fig. 2),  icting requirements impose a severe limit for the
slightly better than p-type Bi2 Te3 at this temperature. practical scale up of materials synthesis methods,
The In2 Te3 ‘doped’ n-type material has poorer ther- although in research, many thin Ž lm deposition
moelectric properties. Nevertheless, p-type CsBi4 Te6 methods, such as molecular beam epitaxy, metallo-
is the Ž rst compound identiŽ ed in the low temperature organic chemical vapour deposition, pulsed laser
range to match or even outperform Bi2 Te3 alloys. deposition, and sputtering, are all being explored.
Whether or not this compound can be further Thermoelectric materials employ relatively large
optimised through doping and/or alloying will need numbers of alloy compositions. For example,
to be determined in the future as well as its mechanical Si 0 ·8 Ge0 ·2 is typically used in bulk thermoelectric
stability under thermal stresses to warrant its practical generators. For comparison, electronic devices based
use in devices. on SiGe alloys, such as heterojunction bipolar transis-
Pentatelluride materials such as HfTe5 and ZrTe5 tors, use 1–5%Ge concentration. A larger concen-
and their alloys have been considered promising new tration of Ge is required for thermoelectrics
thermoelectric materials at low temperatures because applications to create more thermal conductivity
of their relatively large Seebeck coeYcient values at reduction. Even in superlattices, a relatively large
low temperatures which, combined with relatively low equivalent Ge concentration is needed for suYcient
electrical resistivity values, result in large power factor thermal conductivity reduction. For superlattices
values.1 5 4 Their electronic properties can be tuned made of materials with a large mismatch in their
through alloying and doping, but the challenge for lattice constants, buVer layers are needed. To grow
these materials is to reduce their lattice thermal 20/20 A Si/Ge superlattices, for example, graded
conductivity. Another challenge lies in the very aniso- buVer layers of SiGe alloys from 1 to 5 mm with
tropic nature of these materials that requires the continuously varying Ge concentrations have been
growth and characterisation of single crystals for used. These buVer layers complicate the characteris-
transport properties. Single crystal whiskers were ation and usually degrade the device performance.
obtained by a vapour transport technique, but The characterisation of thermoelectric properties
measurements on these small crystals oVer great of potentially interesting thermoelectric materials,
challenges. Further investigations will be required to particularly samples consisting of low-dimensional
determine whether or not the transport properties of structures, imposes an even greater challenge. Even
these materials can be further optimised and if thermal for bulk materials, thermal conductivity measure-
conductivity values close to those for state of the art ments are never easy and are prone to large uncer-
thermoelectric materials can be obtained without tainty. For low-dimensional structures, thermal
signiŽ cantly degrading their electronic properties. conductivity measurements are much trickier. The
most widely used method for cross-plane thermal
conductivity measurements is the 3v method that
Special challenges in materials relies on the deposition of small heaters that also act
synthesis and characterisation as temperature sensors. 8 7 The principle of the 3v
Compared to semiconductor materials for electronic method is simple, but when applied to speciŽ c low-
and optoelectronic devices, thermoelectric materials dimensional structures, it can be quite involved, due
impose diVerent sets of materials requirements, which to the following factors.
in turn create new challenges in their materials syn- 1. Thermoelectric Ž lms are conducting, thus an
thesis and characterisation. Some of these special insulator is needed for electrical isolation between the
challenges will be brie y discussed here. sensor and the sample. The insulator has unknown
International Materials Reviews 2003 Vol. 48 No. 1
64 Chen et al. Recent developments in thermoelectric materials

thermal conductivity. Often, a diVerential method electric transport in both low-dimensional and bulk
is used.1 5 5 materials. However, there is much left to be done, in
2. Superlattices are grown on substrates and new materials syntheses, characterisation, physical
buVers, whose properties are not exactly known. understanding, and device fabrication. It is hoped
Although the principle of the 3v method allows the that this review will arouse broader interest in thermo-
measurements to be made on the thermal conductivity electrics research from the materials research com-
of the substrate, the determination of a high thermal munity. Meanwhile, the authors would like to
conductivity substrate is actually subject to quite emphasise that thermoelectric materials research is a
large uncertainties. The buVer layers typically have multidisciplinary endeavour and requires close collab-
unknown and anisotropic thermal conductivities that oration between researchers in diVerent Ž elds to
cannot be easily determined. address issues in materials, theory, characterisation,
3. Superlattices also have anisotropic properties, and eventually, devices.
and thus care must be taken to ascertain which
direction is being measured. Through careful model- Acknowledgements
ling, both the in-plane and cross-plane direction ther-
mal conductivity can be determined. 4 0 Several other Two of the authors (GC and MSD) gratefully
factors, such as the thermal property contrast between acknowledge their collaborators in thermoelectric
the Ž lm and the substrate and the Ž lm heat capacity research, including Professors R. Gronsky, J.-P. Issi,
eVects, are discussed in detail by Borca-Tasciuc T. D. Sands, K. L. Wang, Dr J. Heremans, and
et al.1 5 5 In addition to the 3v method, other methods T. Harman, and contributions from all students in
that have been used often are the ac calorimetry their respective research groups. The authors are
method for determining the thermal conductivity grateful for support for this work by DoD MURI:
along the Ž lm plane direction, 1 5 6 and the pump-and- N00014–97–1–0516 (GC and MSD), US Navy
probe method for determining the cross-plane thermal Contract N00167–98–K–0024 (MSD), DARPA
conductivity.8 0 Contract N66001–00–1–8603 (MSD), DARPA
The determination of the Seebeck eVect is usually not HERETIC Project (J-PF and GC), JPL: 004736–001
considered to be a big challenge for bulk materials, (J-PF and GC), and NSF Grant DMR 01–16042
but it can be quite tricky for superlattices that are (MSD).
grown on substrates and buVers because the substrate
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International Materials Reviews 2003 Vol. 48 No. 1