Upload
others
View
7
Download
0
Embed Size (px)
Citation preview
Recent Progress in Nanostructured Thermoelectric
Materials
Author: Tian Liu1
1Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4,
9747 AG Groningen,The Netherlands
E-mail: [email protected]
Supervisor: Graeme R. Blake1
1Zernike Institute for Advanced Materials, University of Groningen, Nijenborgh 4,
9747 AG Groningen, The Netherlands
E-mail: [email protected]
Abstract. Thermoelectrics have long been recognized as a cost-effective and
pollution-free technology due to their ability to convert heat energy directly into electric
energy. The research on thermoelectric materials keeps exhibiting rapid improvement
and exciting breakthroughs in the past twenty years due to the extensive investigation
on nanostructured thermoelectric materials.More than ten percent in efficiency has
been gained from changes in structural features on a length scale seven orders smaller
than that of the devices. This paper sets out to explore the basic mechanisms of
the thermoelectric effect, summarizes the main methodology for improving the energy
conversion efficiency, critically analyzes measurement accuracy issues, and proposes
thermoelectric systems with novel nanostructures that should exhibit better efficiency.
A discussion of structural design in nanostructured thermoelectric materials is aimed
at enhancing the thermoelectric figure of merit in practical applications.
Keywords: Nanostructured thermoelectric materials, Nanoscience
CONTENTS 2
Contents
1 Introduction 2
1.1 Thermoelectric Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Basic Theory for Improving ZT . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Measurement Accuracy in Thermoelectrics . . . . . . . . . . . . . . . . . 7
2 Thermoelectric Materials in Low Dimensional systems 8
2.1 Quantum Well Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 One Dimensional Nanowires . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 Bulk Nanostructured Thermoelectric Materials 11
3.1 Progress in Bulk Nanostructured Thermoelectric Materials . . . . . . . . 11
3.2 A Strategy to Improve ZT in Nanocomposites . . . . . . . . . . . . . . . 13
4 Conclusion 15
5 Acknowledgement 16
6 Reference 16
1. Introduction
1.1. Thermoelectric Materials
The global demand for fossil fuels, such as coal and oil, is continuing to increase,
meanwhile the growing speed of non-renewable energy consumption results in inevitable
environmental degradation. The limits of conventional energy and the environmental
concerning both point to find new ways of improving the energy utilization rate.
Thermoelectric materials have attracted increasing attention both from the energy and
environmental aspects over the past few decades due to the promising high efficiency of
converting waste heat into electric energy.
A schematic diagram of the structure of a typical thermoelectric device is shown
in Figure 1. The electrons in the n-type material and the holes in the p-type material
CONTENTS 3
Figure 1. A thermoelectric device with n-type and p-type legs electrically in series
and thermally in parallel. From Shakouri [1].
all carry heat away from the bottom metal-semiconductor contact, by which the hot
side metal-semiconductor junction is cooled[1], and that is the Seebeck effect. Practical
devices are fabricated of multiple pairs of p-type and n-type semiconductor legs to obtain
both high current densities and low voltages. The conversion efficiency of thermoelectric
materials is related to a quantity named the figure of merit (ZT) which is defined by
Altenkirch in 1911 as the relation in Eq. (1).
ZT =S2σT
κ=
S2σT
κl + κe(1)
S is the Seebeck coefficient, σ and κ are the electrical and thermal conductivity of the
materials respectively. Thermal conductivity consists of two contributors (κ): lattice
thermal conductivity (κl) and electron thermal conductivity (κe). The relation between
ZT and efficiency of a thermoelectric device is plotted in Figure 2, where a higher ZT
value is directly related to a high device efficiency.
The first functioning thermoelectric devices were built in the 1950s and 1960s,
with ZT around 1.0 and efficiency about 4%-6% [2]. In the 1990s, materials with
high ZT values were explored in the form of low-dimensional systems and on the
nanoscale [3]. Until now, two different approaches have been investigated to search
for high ZT thermoelectric materials over the past two decades: one is finding and using
new classes of bulk thermoelectric materials with complex crystal structures, and the
other is studying materials in low dimensional systems and bulk structures embedded
CONTENTS 4
Figure 2. Thermoelectric energy conversion as a function of ZT when the cold side
temperature is 300K. A higher ZT is directly related to a high device efficiency. From
Chen [7].
with nanomaterials. Bulk structures embedded with nanomaterials are usually called
bulk nanostructured thermoelectric materials [4, 5, 6].
Nanostructured materials and thermoelectrics have been the subject of significant
research in recent years [5], and it is a challenging topic combining materials science,
nanoscience and physics. Exploring nanostructured thermoelectric materials is not only
useful searching for the next generation of thermoelectric materials exceeding ZT=2.4,
and it is also an inspiration for other research areas of nanoscience by gaining better
material performance from small features [8].
In this review paper, firstly the basic theory and methodology for improving
ZT is introduced, including a discussion of measurement accuracy. After that,
the performances of thermoelectric materials in low dimensional systems and bulk
nanostructured thermoelectric materials are reviewed. Finally, a designed approach
for improving ZT in nanocomposites is proposed.
CONTENTS 5
1.2. Basic Theory for Improving ZT
Enhancing the figure of merit (ZT) is the common idea for improving efficiency of
thermoelectric materials [9], as explained in Figure 2. From the definition of ZT
in Equation (1), three correlated quantities need to be taken into consideration for
optimizing the value of ZT, and these three factors are a large Seebeck coefficient (S ),
a high electrical conductivity (σ) and a low thermal conductivity (κ). These quantities
are interconnected by the charge carrier concentration n, as plotted in Figure 3. S2σ
is defined as the power factor of thermoelectric devices, which denotes the contribution
of the Seebeck coefficient and electronic conductivity to ZT. The relation between the
Seebeck coefficient and the charge carrier concentration n can be expressed as
S =8π2σk2B
3eh2m∗T(
π
3n)2/3 (2)
where kB is the Boltzmann constant, e is the carrier charge, h is Plancks constant and
m∗ is the effective mass of the charge carrier. Here the charge carriers can be either
electrons or holes. According to Drude’s model, electrical conductivity can be denoted
as
σ = neµ (3)
where µ is the mobility of the charge carrier. The electronic component of thermal
conductivity can be denoted as
κe = LTσ = LTneµ (4)
which follows the Wiedemann−Franz Law. Decreasing the electronic thermal
conductivity results in idecreasing the electrical conductivity, and does not affect ZT
much. The lattice component of thermal conductivity can be estimated as
κl =1
3Cvl (5)
where C is heat capacity of materials, v is the average sound velocity for phonons, and l
is the phonon mean free path (mfp). Compared to the electronic thermal conductivity,
lattice conductivity contributes to the change of ZT much more significantly. There
is a trade-off between the improvement of thermopower and the reduction of thermal
conductivity by charge carrier concentration. Typically, good thermoelectric materials
CONTENTS 6
Figure 3. Illustration of the variation of the Seebeck coefficient (S ), electrical
conductivity (σ), power factor (S2σ), electronic thermal conductivity (κe), and lattice
(κl) thermal conductivity on the charge carrier concentration n, for a bulk material.
From Shakouri [1].
.
are heavily doped semiconductors with carrier concentration of 1019 − 1021 cm−3 (also
in Figure 3) [10, 7].
As we mentioned before, there are mainly two methods for improving ZT. For
the first appoach, i.e. complex crystal structures, a basic phonon-glass electron-
crystal (PGEC) as a high performance thermoelectric material was proposed by Slack
in 1995 [11, 12]. This idea implies that high thermoelectric performance materials
behave like glass materials regarding their thermal properties and demonstrate electrical
properties as crystalline materials. Materials with ZT>1 have been discovered based
on this idea, for example in skutterudites, clathrates and β-Zn4Sb3 structures [7]. In
particular, a high ZT=1.7 is realized in Ba0.08La0.05Yb0.04Co4Sb12, which is a n-type
skutterudite structure. [13].
However, materials with higher ZT (even more than 2) are normally prepared by
the second approach, i.e. nanostructuring. In the nanostructuring method, the phonon
mfp decreases while the power factor S2σ is maintained at the same level or becomes
even higher than in the original bulk materials. The connection among the above
three factors: Seebeck coefficient S, electrical conductivity σ and thermal conductivity
κ is weaken by the design of nanostrucures. In most cases, only the lattice thermal
conductivity is significantly reduced. Comparing the two approaches, the basic idea for
CONTENTS 7
the first one is trying to find an optimized balance point in the tade-off between these
three factors, while the second approach changes the manner of this trade-off.
1.3. Measurement Accuracy in Thermoelectrics
Nevertheless, before starting the introduction to exciting and high performance
nanostructured thermoelectric materials, the author would like to mention that there
are serious measurement issues for most thermoelectrics. The measurement issues arise
because of the complexity of fabricating devices, measurement uncertainty and materials
complications [14]. Moreover, inaccurate carrier concentration measurement can also
result in wrong Seebeck factor enhancement [8, 15]. Direct efficiency measurements
require nearly as much complexity as building an entire device [14].Therefore the figure
of merit is obtained by measuring thermal conductivity κ, Seebeck coefficient S and
electrical conductivity separately.
Thermal conductivity values κ are normally calculated from thermal diffusivity α,
while thermal diffusivity measurement exhibits considerable inaccuracy. The relation
between thermal conductivity and thermal diffusivity is defined as
α =κ
ρCp
(6)
where ρ is the material density and Cp is the specific heat capacity. Furthermore, in this
calculation, there is also an approximation that the specific heat capacity constant in the
material according to the Dulong−Petit Law.. This approximation brings uncertainty
to the final result, especially in complex nanosctructured materials. The inaccurate
measurement in thermal diffusivity and and the approximation of a constant specific
heat results in uncertainty around 15%-20% in thermal conductivity calculation. The
error for the Seebeck coefficient is around 5% (it may be up to 10%), and the inaccuracy
for electric conductivity measurement is also 2%-3%. The final ZT value therefore
exhibits significant uncertainty, which can be up to around 30%.
Besides the simple superposition of errors due to measurements and the
approximation, the final result can be more inaccurate because it originates from
the process of separate measurements. Firstly, the inside grain sizes and shapes of
thermoelectric materials are changed by annealing, which occurs after each measurement
CONTENTS 8
is performed. Therefore separate measurements do not measure the properties of the
exact same sample, and there are slightly difference in each measurement. Secondly,
the grains in a ceramic material can align in a preferential direction, and the physical
properties can exhibit anisotropy such that the sample exhibits better performance when
measured along a particular direction. These preferred directions also add difficulties to
the ZT measurements. The final errors of ZT can be up to even 50% in some cases.
These measurement inaccuracies are directly linked to the reproducibility of
experimental results. Currently, the reproducibility of thermoelectric materials with
high performance is poor and many excellent results haven’t been proved by a second
research group [2]. As Snyder and his coworker mentioned, one should be encouraged
by results of ZT exceeding 1.5 but remain wary of the uncertainties involved to avoid
pathological optimism [14].
2. Thermoelectric Materials in Low Dimensional systems
The great pioneers Hicks and Dresselhaus proposed a few types of thermoelectric
materials in low dimensional systems, including 1D conductors, quantum wells and
semimetal-semiconductor transition in quantum-well superlattices in 1993 [3, 16, 17].
Later in 1996, they experimentally realized a ZT of 2.0 in 2D multiple-quantum-well
structures (PbTe/Pb1−xEuxTe) by Molecular Beam Expitaxy (MBE) [18]. That value
of ZT iis still one of the highest reported until now. This excellent research guided the
journey toward nanostructured thermoelectric materials in the past twenty years.
2.1. Quantum Well Superlattices
The original idea of applying quantum well structures to thermoelectric materials is that
an enhancement of the power factor S2σ could be realized through quantum confinement.
Additionally the lattice thermal conductivity could be significantly reduced by the
interface scattering in the direction perpendicular to the quantum wells , especially in
atom thick layers. The predicted ZT in 2D as a function of layer thickness is plotted in
Figure 4. Based on this idea, high ZT values are realized not only in PbTe/Pb1−xEuxTe
systems [18], but also in PbTe/PbSe0.2Te0.8 by MBE [19]. In 2001, Venkatasubramanian
CONTENTS 9
Figure 4. Calculated ZT as a function of layer thickness a in a quantum well structure
for layers parallel to the ab plane (1)and b-c plane (2). The dashed line represents the
optimized ZT forbulk Bi2Te3. From Hicks[16] and Chen[7].
and his coworkers reported the highest ZT=2.4 in Bi2Te3/Sb2Te3 (p-type) quantum well
superlattices [20]. Further explanation about the increased power factor is proposed by
Shakouri. The improvement of power factor is due to sharp features in the electronic
density of states of quantum-confined structures (Figure 5(b)). It enables a doping-level-
tunable increase in the asymmetry between hot and cold electron transport, leading
to a large average transport energy and a carrier concentration (i.e., a large Seebeck
coefficient and electrical conductivity) [21].
MBE is not the only frabrication technique in quantum well superlattices for
thermoelectric materials. Ohta and his coworkers reported ZT=2.4 in a two-dimensional
electron gas in SrTiO3/SrTi0.8Nb0.2O3 superlattices [22], where this sample was
fabricated by pulsed laser deposition (PLD). The quantum well thickness was only
0.3905nm. One should note that this high value of ZT is calculated from the assumption
that electrons are strictly confined in that thin layer [1].
Although high ZT values have been discovered in artificial superlattice structure,
there is still a long way to go for practical applications for waste heat power generation,
since it is difficult to fabricate large area devices for fitting in practical devices. Moreover
the stability of the thin layer needs to be investigated for real applications [11].
Larger area and lower cost techniques than MBE and PLD such as Chemical Vapour
CONTENTS 10
Figure 5. Schematic illustration of the density of states (DOS) as a function of energy
for: (a) a bulk material (3-D), (b) a quantum well (2-D), (c) a nanowire (1-D)
Deposition (CVD) have not been well developed for allowing high quality film growth
with atomic precision. Fabrication techniques like CVD need to be improved in the
fulture especially for the growth of crystalline chalcogenides, which is necessary for
many high-performance thermoelectric materials.
Thermal conductivity reduction is found to be the main reason behind the enhanced
ZT in superlattices. Studies on the heat-conduction mechanisms in superlattices
demonstrate that periodic structures are not necessary for thermal conductivity
reduction [23]. To overcome the scaling-up problems and find materials for commercial
applications, combining bulk nanomaterials and nanostructures seems to be a reasonable
solution, which will be introduced later in this paper.
2.2. One Dimensional Nanowires
Theoretical calculations predict a large improvement of ZT in one-dimensional
nanowires, even higher than in 2D quantum well superlattices. The reasons for
this enhancement are the change of DOS (Figure 5(c)) due to the strong quantum
confinement and the reduced lattice thermal conductivity due to the high surface to
volume ratio [3]. The thermoelectric figure of merit of a one-dimensional conductor or
quantum wire depends strongly on the radius of the wire [3]. Theoretical studies on III-
V semiconductor nanowires also indicate that InSb seems to be a promising candidate
for a reasonably high figure of merit for nanowires around 10nm thick. Some materials
(such as GaAs) show calculated high ZT values with diameters which are experimentally
unattainable [24]. However, in experiments InSb nanowires exhibit even lower ZT values
CONTENTS 11
than their bulk materials [25, 26]. The unexpected reduction of ZT also arises in Bi2Te3
nanowires [27]. The reason for this unexpected reduction has not been fully understood,
but may originate from the impurities in nanowires [28, 29, 30].
Improved ZT values are found for some nanowires in experiments, but in general
high ZT materials as 2D quantum well superlattice systems have not yet been
fabricated.. For example, silicon nanowires demonstrate a ZT=0.25 [31] for rough silicon
nanowires of 50 nm in diameter and 0.6 [32] for rough silicon nanowires of 50 nm in
diameter, while the bulk ZT for silicon is only around 0.01[33, 34]. Cylindrical Bi
nanowires are predicted to have a significantly improved Seebeck coefficient, because
a semimetal-semiconductor transition can occur below a critical wire diameter due to
quantum confinement [35]. The critical wire diameter at 77 K is found to be between
39nm and 55nm, and it depends on the crystal orientation of the wire axis [35]. High-
quality Bi nanowires are difficult to fabricate and they are often fabricated in porous
anodic aluminium oxide (AAO) or quartz (SiO2) templates [30]. Large enhancement
in the thermoelectric power of Bi nanowires embedded in porous alumina and porous
silica was reported by Heremans [36] in 2002, where the nanowires are with diameters
of 9nm and 15nm and the thermoelectric power is enhanced by two or three orders in
the temperature range of 100-300K.
High quality nanowires of these materials are generally quite challenging to
synthesize. Moreover, the unexpected reduction of ZT also needs to be investigated
to find the mechanisms behind it.
3. Bulk Nanostructured Thermoelectric Materials
3.1. Progress in Bulk Nanostructured Thermoelectric Materials
Bulk nanostructured thermoelectric materials[23] are bulk materials embedded with
nanoparticles or interfaces with nanometer size. These materials demonstrate improved
thermoelectric properties similar to the low dimensional systems, where the lattice
thermal conductivity is reduced due to designed phonon scattering. Compared to those
thermoelectricswith low dimensions, bulk nanostructured thermoelectric materials can
CONTENTS 12
be produced in a form suitable for current thermoelectric device configurations [5]. This
type of materials are also called nanostructured composite materials or nanocomposites.
In some high performing thermoelectric nanocomposites, the main contribution
to improved ZT is the reduction of lattice thermal conductivity. The mfps of phonons
typically range from several nanometers up to a few hundred nanometers, while the mfps
of carriers are much shorter, only a few nanometers [37]. Therefore, nanocomposites offer
the possibility for the effective scattering of phonons with long mfps without hindering
charge current conduction. Additionally, the Seebeck coefficient can also be lifted due to
electron filtering at grain boundaries in nanocomposites [11]. Furthermore, it is desirable
to have nanostructural features on different size scales, ranging from single atomic point
defects to nanoscale second phase inclusions to grain boundaries / twin boundaries on
the hundreds of nm scale. This helps to scatter phonons over their entire wavelength
range. A strategy based on this idea is illustrated later in this paper.
There have been three main strategies for bulk thermoelectric nanocomposites, as
demonstrated schematically in Figure 6[11]. One strategy is to form thermoelectric
nanocomposites with single-phase nanograins, which only involves reduction of the
thermal conductivity. The other two stratigies are to form second-phase nanoinclusions
(Figure 6 (b), (c)), where a large number of interfaces are formed between the
thermoelectric material and the nanoinclusions. The interfaces can be either incoherent
or coherent, which corresponds to the second and third strategies respectively. A
coherent nanoinclusion demonstrates good lattice matching with the matrix phase due
to similar lattice constants, while an incoherent nanoinclusion shows a clear boundary
between the matrix phase and the dispersed phase for the embedded nanostructures [11].
The Seebeck coefficient is enhanced for the last two approaches, in addition to the
reduction of thermal conductivity.
Typical strategies to synthesize nanocomposite thermoelectric materials are the
powder metallurgy method and melt metallurgy method, which are inspired by classic
metallurgical approaches. The powder metallurgy method is to prepare pre-synthesed
nanoparticles by physical or chemical routes with fast powder compaction to avoid grain
growth. For example spark plasma sintering is a direct current induced hot pressing
CONTENTS 13
Figure 6. Approaches for bulk thermoelectric nanocomposites: (a). nanograined
composite, (b). nanoinclusion composite with an incoherent interface, and (c).
nanoinclusion composite with a coherent interface[11]
technology, and it can create extensive interfaces between the neighbouring nanoparticles
and lower the thermal conductivity. The melt metallurgy method usually applies melting
and quick cooling to obtain small grain size or even amorphous powders [11, 7, 38].
The improvement of ZT has been investigated in a wide range of bulk
nanostructured material families, including Bi2Te3-based nanocomposites, PbTe-based
nanocomposites and SiGe-based nanocomposites. For a detail overview of these three
families of bulk nanostructured thermoelectric materials, the reader is referred to the
recent review article by Chen et al [7]. In this paper, the author proposes an idea for
improving ZT by the detailed design of a more efficient way of scattering phonons, i.e.
by adjusting the distribution of the nanosize dots or interfaces along the temperature
gradient in practical devices.
3.2. A Strategy to Improve ZT in Nanocomposites
Current research in nanostructured composites for thermoelectric materials combines
low-dimensional and bulk materials for thermoelectric applications. As we mentioned
before, nanocomposites (in Figure 6) contain a high density of second-phase
nanoinclusions, and they are powerful tools for improving ZT. For example, Girardin
et al. reported PbTe bulk materials with homogeneous distributed PbS nano-size dots
that improves ZT into 1.4 at 750K in the PbS(8%)-PbTe materials system by lattice
thermal conductivity reduction [38]. Biswas et al reported a figure of merit of 1.7 at
800K in PbTeSrTe (SrTe=0.52mol%) materials doped with 1mol% Na2Te [39]. Also in
CONTENTS 14
Na1−xPbmSbyTem+2 systems, ZT=1.7 at 700 K was reported by Poudeu [40]. These
nanostructured thermoelectric systems exhibit better ZT than simple bulk materials
mainly due to the scattering of long mfp phonons by nano-scale features.
The mean free path of phonons in nanocomposites based on bulk materials is
determined by two factors:one is scattering from nanosize particles and grain boundaries
of the sample and the other is scattering with other phonons.. Current studies
have focused on the first factor and improve ZT by optimizing compositions of the
materials that can scatter phonons more effectively. In the second factor, the interaction
between phonons can also change the mfp by the Umklapp process. The probability
that a phonon undergoes a collision is directly proportional to the number of other
phonons present and the number of phonons at high temperature is proportional to
kBT/~ω, according to the Bose-Einstein Distribution. Therefore the mfp l in the
system is approximately proportional to 1/T. In thermoelectrics, a pronounced gradient
of temperature is required, meanwhile phonon mfps increase along the temperature
gradient. Therefore it is reasonable to propose a model which varies the nano-size
features of thermoelectrics along the temperature gradient and gains better scattering
results for phonons over their entire mfp range corresponding to different temperatures.
A schematic figure is plotted to illustrate this idea in Figure 7, where an increased
trend in size for nanoparticles is demonstrated. The homogeneous size distribution (in
Figure 7.a) only obtains an average optimized scattering rate for phonons with different
mfps. Our designed system (in Figure 7.b.) can optimize the scattering of phonons over
their entire mfp range along the temperature gradient, and therefore it could achieve a
higher ZT value in the end.
One reasonable way to realize this model is applying ferromagnetic nanoparticles
with a wide range of sizes in bulk materials. By applying a magnetic field in the
molten state of the bulk matrix, a size distribution can be established. For example,
one can control the size distribution of magnetite (Fe3O4) nanoparticles embedded in
GST (Ge2Sb2Te5) matrices. There are two shortcomings of this idea. One is that the
ferromagnetic nanoparticles need a high melting point, which limits the materials that
CONTENTS 15
Figure 7. Schematic pictures of: (a). homogeneous size distribution for nanoparticles
in a bulk thermoelectric material compared with (b). increased size distribution along
the thermal gradient for nanoparticles in a bulk thermoelectric material. The latter
model can scatter phonons over their entire mfp range.
can be combined with each other.Another difficulty is that the crystal types (or space
groups) of the nanoparticles and matrices need to be same or compatible.
4. Conclusion
Over the past twenty years, thermoelectric nanomaterials and materials embedded
with nanostructures have been extensively investigated and and have shown promising
potential promising potentials for waste heat utilization. ZT values of thermoelectric
materials have been increased from 1.0 in the 1950s to around 2.4 nowadays. In this
paper, an idea of adjusting nano-scale structures along the temperature gradient is
proposed. This strategy could be a fruitful way to enhance thermoelectric device
performance for practical applications. Measurement accuracy and reproducibility of
high-performance thermoelectrics are also critically analyzed. Measurement issues of
thermoelectrics are very serious (even with errors around 30%-50%) and worth attracting
attention from academia for bridging the gap from high-performance materials to
practical devices. Moreover, applying thermoelectric materials with a ZT value
exceeding 2.0 in commercial devices is still a challenging topic, especially for materials in
CONTENTS 16
low dimensional systems. To solve the measurement inaccuracy and apply the excellent
breakthrough of ZT into waste heat utilization, scientists from academia and industry
need cooperate together for fabricating practical devices and improving efficiency in an
accurate way.
5. Acknowledgement
This review paper is finished under the guidance of Dr. Blake. The author thanks
him for his supervision and suggestions during very useful discussions. The author also
appreciates the workshops given by Prof. Chiechi and Dr. Pchenitchnikov and especially
thanks Dr. Kaverzin for his teaching in writing skills.
6. Reference
[1] A. Shakouri, “Recent Developments in Semiconductor Thermoelectric Physics and Materials,”
Annual Review of Materials Research, vol. 41, no. 1, pp. 399–431, 2011.
[2] L.-D. Zhao, V. P. Dravid, and M. G. Kanatzidis, “The panoscopic approach to high performance
thermoelectrics,” Energy & Environmental Science, vol. 7, no. 1, p. 251, 2014.
[3] L. D. Hicks and M. S. Dresselhaus, “Thermoelectric figure of merit of a one-dimensional conductor,”
Physical Review B, vol. 47, no. 24, pp. 16631–16634, 1993.
[4] G. J. Snyder and E. S. Toberer, “Complex thermoelectric materials,” Nature materials, vol. 7,
no. 2, pp. 105–114, 2008.
[5] a. J. Minnich, M. S. Dresselhaus, Z. F. Ren, and G. Chen, “Bulk nanostructured thermoelectric
materials: current research and future prospects,” Energy Environ Sci, vol. 2, no. 5, pp. 466–479,
2009.
[6] M. G. Kanatzidis, “Nanostructured thermoelectrics: The new paradigm?,” Chemistry of Materials,
vol. 22, no. 3, pp. 648–659, 2009.
[7] Z. G. Chen, G. Hana, L. Yanga, L. Cheng, and J. Zou, “Nanostructured thermoelectric materials:
Current research and future challenge,” Progress in Natural Science: Materials International,
vol. 22, no. 6, pp. 535–549, 2012.
[8] C. J. Vineis, A. Shakouri, A. Majumdar, and M. G. Kanatzidis, “Nanostructured thermoelectrics:
Big efficiency gains from small features,” Advanced Materials, vol. 22, no. 36, pp. 3970–3980,
2010.
[9] H. Goldsmid, “Thermoelectric refrigeration. 1964.”
[10] P. Vaqueiro and A. V. Powell, “Recent developments in nanostructured materials for high-
performance thermoelectrics,” Journal of Materials Chemistry, vol. 20, no. 43, p. 9577, 2010.
CONTENTS 17
[11] K. Koumoto and T. Mori, Thermoelectric nanomaterials. Springer, 2015.
[12] D. M. Rowe, CRC handbook of thermoelectrics. CRC press, 1995.
[13] X. Shi, J. Yang, J. R. Salvador, M. Chi, J. Y. Cho, H. Wang, S. Bai, J. Yang, W. Zhang, and
L. Chen, “Multiple-filled skutterudites: high thermoelectric figure of merit through separately
optimizing electrical and thermal transports,” Journal of the American Chemical Society,
vol. 133, no. 20, pp. 7837–7846, 2011.
[14] G. J. Snyder and E. S. Toberer, “Complex thermoelectric materials,” Nature materials, vol. 7,
no. 2, pp. 105–114, 2008.
[15] C. J. Vineis, T. C. Harman, S. D. Calawa, M. P. Walsh, R. E. Reeder, R. Singh, and a. Shakouri,
“Carrier concentration and temperature dependence of the electronic transport properties of
epitaxial PbTe and PbTe/PbSe nanodot superlattices,” Physical Review B - Condensed Matter
and Materials Physics, vol. 77, no. 23, pp. 10–12, 2008.
[16] L. D. Hicks and M. S. Dresselhaus, “Effect of quantum-well structures on the thermomagnetic
figure of merit,” Physical Review B, vol. 47, no. 19, pp. 727–731, 1993.
[17] L. D. Hicks, T. C. Harman, and M. S. Dresselhaus, “Use of quantum-well from nonconventional
to obtain a high figure of merit thermoelectric materials,” Applied physics letters, vol. 63, no. 7,
pp. 3230–3232, 1993.
[18] L. Hicks, T. Harman, X. Sun, and M. Dresselhaus, “Experimental study of the effect of quantum-
well structures on the\nthermoelectric figure of merit,” Fifteenth International Conference on
Thermoelectrics. Proceedings ICT ’96, vol. 53, no. 16, pp. 493–496, 1996.
[19] H. Beyer, J. Nurnus, H. Bottner, a. Lambrecht, T. Roch, and G. Bauer, “PbTe based superlattice
structures with high thermoelectric efficiency,” Applied Physics Letters, vol. 80, no. 7, pp. 1216–
1218, 2002.
[20] R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O’Quinn, “Thin-film thermoelectric devices
with high room-temperature figures of merit.,” Nature, vol. 413, no. 6856, pp. 597–602, 2001.
[21] M. Christensen, A. B. Abrahamsen, N. B. Christensen, F. Juranyi, N. H. Andersen, K. Lefmann,
J. Andreasson, C. R. H. Bahl, and B. B. Iversen, “Avoided crossing of rattler modes in
thermoelectric materials.,” Nature materials, vol. 7, no. 10, pp. 811–815, 2008.
[22] H. Ohta, S. Kim, Y. Mune, T. Mizoguchi, K. Nomura, S. Ohta, T. Nomura, Y. Nakanishi,
Y. Ikuhara, M. Hirano, H. Hosono, and K. Koumoto, “Giant thermoelectric Seebeck coefficient
of a two-dimensional electron gas in SrTiO3.,” Nature materials, vol. 6, no. 2, pp. 129–134, 2007.
[23] M. S. Dresselhaus, G. Chen, M. Y. Tang, R. Yang, H. Lee, D. Wang, Z. Ren, J. P. Fleurial, and
P. Gogna, “New directions for low-dimensional thermoelectric materials,” Advanced Materials,
vol. 19, no. 8, pp. 1043–1053, 2007.
[24] N. Mingo, “Thermoelectric figure of merit and maximum power factor in iii–v semiconductor
nanowires,” Applied Physics Letters, vol. 84, no. 14, pp. 2652–2654, 2004.
[25] F. Zhou, A. L. Moore, M. T. Pettes, Y. Lee, J. H. Seol, Q. L. Ye, L. Rabenberg, and L. Shi, “Effect
CONTENTS 18
of growth base pressure on the thermoelectric properties of indium antimonide nanowires,”
Journal of Physics D: Applied Physics, vol. 43, no. 2, p. 025406, 2009.
[26] A. I. Persson, Y. K. Koh, D. G. Cahill, L. Samuelson, and H. Linke, “Thermal conductance of inas
nanowire composites,” Nano letters, vol. 9, no. 12, pp. 4484–4488, 2009.
[27] A. Mavrokefalos, A. L. Moore, M. T. Pettes, L. Shi, W. Wang, and X. Li, “Thermoelectric and
structural characterizations of individual electrodeposited bismuth telluride nanowires,” Journal
of Applied Physics, vol. 105, no. 10, p. 104318, 2009.
[28] J. H. Seol, A. L. Moore, S. K. Saha, F. Zhou, L. Shi, Q. L. Ye, R. Scheffler, N. Mingo, and
T. Yamada, “Measurement and analysis of thermopower and electrical conductivity of an indium
antimonide nanowire from a vapor-liquid-solid method,” Journal of applied physics, vol. 101,
no. 2, p. 023706, 2007.
[29] F. Zhou, J. Seol, A. Moore, L. Shi, Q. Ye, and R. Scheffler, “One-dimensional electron transport and
thermopower in an individual insb nanowire,” Journal of Physics: Condensed Matter, vol. 18,
no. 42, p. 9651, 2006.
[30] J. R. Szczech, J. M. Higgins, and S. Jin, “Enhancement of the thermoelectric properties in
nanoscale and nanostructured materials,” Journal of Materials Chemistry, vol. 21, no. 12,
pp. 4037–4055, 2011.
[31] A. I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J.-K. Yu, W. A. Goddard Iii, and J. R. Heath, “Silicon
nanowires as efficient thermoelectric materials,” Nature, vol. 451, no. 7175, pp. 168–171, 2008.
[32] A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and
P. Yang, “Enhanced thermoelectric performance of rough silicon nanowires,” Nature, vol. 451,
no. 7175, pp. 163–167, 2008.
[33] L. Weber and E. Gmelin, “Transport properties of silicon,” Applied Physics A, vol. 53, no. 2,
pp. 136–140, 1991.
[34] O. Caballero-Calero and M. Martın-Gonzalez, “Thermoelectric nanowires: A brief prospective,”
Scripta Materialia, vol. 111, pp. 54–57, 2016.
[35] Y.-M. Lin, X. Sun, and M. Dresselhaus, “Theoretical investigation of thermoelectric transport
properties of cylindrical bi nanowires,” Physical Review B, vol. 62, no. 7, p. 4610, 2000.
[36] J. P. Heremans, C. M. Thrush, D. T. Morelli, and M.-C. Wu, “Thermoelectric power of bismuth
nanocomposites,” Physical Review Letters, vol. 88, no. 21, p. 216801, 2002.
[37] D. G. Cahill, W. K. Ford, K. E. Goodson, G. D. Mahan, A. Majumdar, H. J. Maris, R. Merlin,
and S. R. Phillpot, “Nanoscale thermal transport,” Journal of Applied Physics, vol. 93, no. 2,
pp. 793–818, 2003.
[38] S. N. Girard, J. He, C. Li, S. Moses, G. Wang, C. Uher, V. P. Dravid, and M. G. Kanatzidis,
“In situ nanostructure generation and evolution within a bulk thermoelectric material to reduce
lattice thermal conductivity,” Nano Letters, vol. 10, no. 8, pp. 2825–2831, 2010.
[39] K. Biswas, J. He, Q. Zhang, G. Wang, C. Uher, V. P. Dravid, and M. G. Kanatzidis, “Strained
CONTENTS 19
endotaxial nanostructures with high thermoelectric figure of merit.,” Nature chemistry, vol. 3,
no. 2, pp. 160–166, 2011.
[40] P. F. P. Poudeu, J. D’Angelo, A. D. Downey, J. L. Short, T. P. Hogan, and M. G. Kanatzidis,
“High thermoelectric figure of merit and nanostructuring in bulk p-type Na1-xPbmSbyTem+2,”
Angewandte Chemie - International Edition, vol. 45, no. 23, pp. 3835–3839, 2006.