THERMOELECTRICS:

MATERIALS RESEARCH

AND DEVICE ASPECTS. University of Twente

ABSTRACT An essay on the aspects of state of the art semiconductor material research and applicability of Thermoelectric technology suitable for waste heat energy harvesting.

Anastasios Englezos, S1463144 Advanced Semiconductor devices

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Contents 1. Introduction.................................................................................................................................. 1

2. Theory on thermoelectricity ........................................................................................................ 3

2.1. Thermoelectricity and the Seebeck effect............................................................................. 3

2.2. Electrical conductivity ........................................................................................................... 5

2.3. Thermal conductivity ............................................................................................................ 6

2.4. The Thermoelectric Figure of Merit zT .................................................................................. 7

3. The thermoelectric module concept .......................................................................................... 10

3.1. Thermoelectric generator design concepts ......................................................................... 10

3.2. Working principles of a common design thermoelectric generator .................................... 12

3.3. Filling factor ........................................................................................................................ 15

4. Thermoelectric Materials Research ........................................................................................... 18

4.1. General Framework ............................................................................................................ 18

4.2. Enhancing the Thermoelectric power factor ....................................................................... 18

4.3. The search for glasslike thermal conductivity ..................................................................... 24

4.4. Other parameters that affect material performance: Application considerations. ............. 26

5. Overview of Thermoelectric material families .......................................................................... 29

5.1. Silicon-based composites .................................................................................................... 29

5.2. Chalcogenides ..................................................................................................................... 32

5.2.1. Lead Chalcogenides ..................................................................................................... 32

5.2.2. Bismuth chalcogenides ................................................................................................ 33

5.2.3. Tin Selenide, Copper selenide and Copper sulfide ...................................................... 34

5.2.4. Oxychalcogenide compounds...................................................................................... 35

5.3. TAGS and LAST Compounds ................................................................................................ 37

5.4. Skutterudites ....................................................................................................................... 37

5.5. Thermoelectric half-Heusler compounds ............................................................................ 40

5.6. Cobaltite-Oxides .................................................................................................................. 41

6. Short overview of fabrication and shaping techniques ............................................................. 43

6.1. Upscaling material fabrication – nanobulk materials .......................................................... 43

6.1.1. Melt Spinning (MS) ...................................................................................................... 43

6.1.2. Ball Milling ................................................................................................................... 44

6.1.3. Spark erosion .............................................................................................................. 44

6.2. Thermal Processing Techniques .......................................................................................... 45

6.2.1. Solution phase synthesis ............................................................................................. 45

6.3. Powder to Bulk Densification Methods ............................................................................... 47

7. Outlook ....................................................................................................................................... 49

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8. Bibliography ............................................................................................................................... 50

List of figures Figure 1: Waste heat and potential recovery into usable energy by various fields in industry through the use of thermoelectrics. ................................................................................................................... 1 Figure 2: Schematic comparison of various thermoelectric materials for waste heat recovery and refrigeration applications with respect to (a) the operational temperature and ecological friendliness and (b) in terms of abundancy. Adapted from ...................................................................................... 2 Figure 3: Schematic representation of a one level semiconductor device the energy difference between the chemical potential μ and the energy of the conduction level is of the order of a few kT.3 Figure 4: Schematic representation of the interaction between the Fermi function and the density of states for a hypothetical one level n-type semiconductor device......................................................... 5 Figure 5: Optimizing zT through carrier concentration tuning. The value range for the other parameters plotted against the y-axis are: α (0-500μVK-1), σ(0-5000Ω-1cm-1),λ(0-10Wm-1K-1),adapted from ...................................................................................................................................................... 8 Figure 6: Lower lattice thermal conductivity directly increases the zT and increases the Seebeck coefficient due to lower electronic thermal conductivity λe. Plot is based on a model system (Bi2Te3), adapted from ........................................................................................................................................ 9 Figure 7: Schematic diagram of a typical thermoelectric module for electrical power generation. Components of n-type (red) and p-type (blue) materials are connected in series and then contained between ceramic substrates. Heat is applied to one side of the module, causing the charge carriers to diffuse across the module and generating an electrical current .................................................... 10 Figure 8: Illustration of the Two FGTM concepts: left: Ideal functionally graded leg. Right: segmented leg design. ........................................................................................................................................... 11 Figure 9: Illustration of segmented generator design (left) and cascaded generator design (right). Color code indicator of the different material components (middle). ................................................ 12 Figure 10: Illustration of the concept of regulating the filling factor according to geometrical characterization of the heat propagation. .......................................................................................... 16 Figure 11: Electronic density of states in relation to system dimensions ........................................... 19 Figure 12: Electron energy filtering mechanism schematic. The energetic barrier filters low energy carriers. Adapted from ........................................................................................................................ 20 Figure 13: Schematic of the density of states over energy depicting the resonance effect. Adapted from19.................................................................................................................................................. 21 Figure 14: Illustration of band bending effect due to metallic nanoinclusions (a) semiconductor host with the metallic spheres (b) Example of the calculated potential V(r). Adapted from ..................... 24 Figure 15: Example of chimney-ladder structure of HMS ................................................................... 30 Figure 16: Illustration of the concept of hieratically ordered system ................................................. 33 Figure 17: Representative example of the crystal structure of BiTe, BiSe compounds. Bi2Se3 is shown. ............................................................................................................................................................ 33 Figure 18: Visual representation of SnSe Crystal lattice ...................................................................... 34 Figure 19: Crystal structure of Cu2Se at high temperatures (β-phase) ................................................ 35 Figure 20: Tetragonal unit cell of BiCuSeO .......................................................................................... 36 Figure 21: elemental composition and structural characteristics of filled skutterudites. ................... 38 Figure 22: Structural characteristics of HH materials. They can be formed by combination of the different elements from the periodic table in accordance to the color coding. ................................. 40

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1. Introduction

Motivation The global human population is steadily increasing and with it the demand for energy

resources is escalating. Moreover, recent reports on the global warming phenomena have

dramatically outlined the fact that there is imminent need to limit the consumption of fossil fuels for

our energy needs since the greenhouse gasses and pollution produced in the process, irreversibly

harm the earth’s environment and contribute to the global warming.

Evolution of nuclear power generation has contributed towards limiting the use of fossil fuels.

However high maintenance and equipment costs, issues related to the safe disposal of the toxic waste

by-products as well as the risks of nuclear meltdown, limit the use of nuclear power generation as an

alternative power source.

Other promising renewable power generation alternatives such as wind turbines and solar

panel power plants are becoming more and more efficient. However a large scale implementation is

usually needed in the form of “wind parks” or “solar power farms” in order to achieve adequate power

output towards the main power grid. This fact renders the implementation costly and environmentally

challenging.

One factor that is common in almost every energy production and energy consumption

method is heat losses. Commonly known as Waste heat, it is the dominant energy loss factor in the

majority of industrial applications nowadays. Loss of heat caused by friction, hot exhaust gasses,

resistances etc. can more than 60% (figure 1). This energy could potentially be harvested and recycled

into electricity directly by using the capability of thermoelectric energy conversion. This way the

output of the current power generation technologies can be improved and energy lost into heat during

consumption can be partially recovered into the main power grid. Moreover, standalone

thermoelectric power generators could be used wherever sufficient temperature gradients are

possible providing another alternative sustainable power source which can decrease the consumption

rates of fossil fuels.

Figure 1: Waste heat and potential recovery into usable energy by various fields in industry through the use of thermoelectrics.1

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Thermoelectric (TE) power generation has been successfully used in some niche applications

and cheap low output TE modules are nowadays commercially available. Large scale application

however has been prohibited by factors such as poor output efficiency, material complications, high

temperature incompatibility, and costs related to the rarity and treatment required for thermoelectric

materials. The fact that thermoelectric modules do not involve any moving parts significantly lowers

the maintenance costs due to the increased reliability while also permits for scalability and makes

implementation much easier. To date, promising application of TE energy recovery has been in

automobiles, where a lot of waste heat is produced in the engine coolant or exhaust gas, which could

be recycled directly into energy for the car. TE power generation has also been widely used in space

technology where energy recovery is of the outmost importance.

The best performing thermoelectric materials, however, are either scarce or therefore

expensive, or contain toxic elements such as lead, tellurium or antimony, which pose danger and may

degrade when exposed to high temperature air. Finding materials suitable for thermoelectric research

that are abundant in nature, nontoxic, and have a wide temperature range of applicability is not a

trivial task (figure 2). Novel fabrication methods from a nanoscopic perspective can be utilized to

improve thermoelectric performance.

Figure 2: Schematic comparison of various thermoelectric materials for waste heat recovery and refrigeration applications with respect to (a) the operational temperature and ecological friendliness and (b) in terms of abundancy. Adapted from2

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2. Theory on thermoelectricity

2.1. Thermoelectricity and the Seebeck effect

The Seebeck effect is the direct conversion of temperature differences into a voltage

differential and hence into electricity. In 1821, Thomas Seebeck, a German physicist, realized that

when two different metallic elements which are joined in two places forming a closed circuit, while at

the same time they are held in different temperatures (ΔΤ) , a compass needle would be deflected.

The phenomenon was attributed to the different response of the metals. Due to their compositional

difference, to the temperature gradient formed between them, generating a current loop and a

magnetic field. The effect was termed "thermoelectricity" and it can be described as the way a

material responds to the temperature gradient applied to it in order to maintain its electronic balance.

Figure 3: Schematic representation of a one level semiconductor device the energy difference between the chemical potential μ and the energy of the conduction level is of the order of a few kT.

A relatively easy way to explain this effect is by using the bottom up approach for a small scale

one level device (elastic resistor) where the free electron approximation is valid (figure 3). The two

sides of the device in this example is the same material with its two sides held at different

temperature. The energy level (E) of the conduction band can be approximated by the parabolic

dispersion relation with respect to the electron wave number (κi) and the directional effective mass

of the electron (𝑚𝑖∗) with (i=x,y,z):

𝐸3𝑑(𝜿) =ħ2

2(∑

𝜅𝑖2

(𝑚𝑖∗)

2

𝑖

)

And the density of the electronic states corresponding to that energy, D(E), is given by:

𝐷(𝐸) =1

2𝜋2 (2⟨𝑚∗⟩

ħ2 )

3/2

𝛦1/2

Where:

⟨𝑚∗⟩ = √𝑚𝑥𝑚𝑦𝑚𝑧3 ,

and (ħ = ℎ/2𝜋) is the reduced Plank constant.

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Using expression for the Fermi distribution function f(E,μ,T), where (E) is the energy level of the

conduction band, (μ) is the chemical potential (T) is the temperature and (k) the Boltzmann constant;

𝑓(𝐸, 𝜇, 𝑇) =1

𝑒(𝐸−𝜇)

𝑘𝑇 + 1

and the overall electronic conductance (G):

𝐺 = ∫ 𝑑𝐸 (−𝜕𝑓

𝜕𝐸) 𝐷(𝐸)

We can estimate the current (I) running through the device:

𝐼 =1

𝑞∫ 𝑑𝐸 𝐷(𝐸)(𝑓1 − 𝑓2)

With (q) being the charge of the carrier.

For the hypothetical device with one conduction level and for very small variations in temperature

and chemical potential between the two contacts, the current can be approximated through Taylor

expansion as:

𝐼 ⋍ 𝐺 (𝜇1 − 𝜇2

𝑞) + 𝐺𝑠(𝑇1 − 𝑇2) = 𝐺𝛥𝑉 + 𝐺𝑠𝛥𝛵

With the indicators 1,2 referring to contact 1 and 2 respectively and with (Gs) being the conductance

attributed to the temperature gradient:

𝐺𝑠 = ∫ 𝑑𝐸 (−𝜕𝑓

𝜕𝐸) 𝐷(𝐸)

𝐸 − 𝜇

𝑞𝑇

Expressed in terms of voltage difference we get:

𝛥𝑉 =1

𝐺𝐼 −

𝐺𝑠

𝐺𝛥𝛵

Where the ratio between (Gs) and (G) is the Seebeck coefficient:

𝛼 =𝐸 − 𝜇

𝑞𝑇

It is clear from the derivation above that due to the nature of the Fermi function, current flow

can be obtained not only by differing the chemical potential, but also by different temperature without

application of external voltage. The physical aspects of this derivation are explained in figure 4.

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Figure 4: Schematic representation of the interaction between the Fermi function and the density of states for a hypothetical one level n-type semiconductor device.

At higher temperatures the Fermi distribution function is changing gradually over a range of

a few kβT, from zero to one; figure 4.a. At very low temperatures close to zero Kelvin the Fermi

distribution changes abruptly from zero to one along the chemical potential; figure 4.b. When these

two states are in contact, figure 4.c, the electrochemical potential is initially at the same level but the

difference of the Fermi function due to the temperature gradient, enables current flow from contact

1 to contact 2 (hot to cold in this example), for conducting states above the chemical potential and

from contact 2 to contact 1 (cold to hot), for conducting states below the chemical potential.

For a typical semiconductor the chemical potential lies roughly in the middle of the forbidden

energy band between the valence and conduction band which lies at energy (E). Due to the nature of

the density of states D(E) in semiconductors usually resembling a parabola, the interaction of the

Fermi distribution function with D(E) allows for conduction in the hot contact while it prohibits

conduction in the cold contact figure 4.d and when two sides are connected, current is allowed to flow

between them and the conduction electron population is the product of (f1-f2) and the Density of

states D(E) figure 4.e.

Therefore semiconductor materials with the conduction band way above the chemical

potential (large bandgap) are found to have a high Seebeck coefficient. However a very large bandgap

would significantly hinder electron conductance. This is the reason why usually the materials chosen

for thermoelectric research have a bandgap such that it allows for high Seebeck without limiting the

conductivity. I.e. materials with increased carrier mobility.

2.2. Electrical conductivity

The electrical conductivity (σ) is used to measure the freedom of charge carriers to move

through a material. For a crystal lattice it is given as the interaction between the electron charge (e),

the relaxation time between electron collisions (τ), the electronic carrier density (n) and the electron

effective mass (m*), by the Drude equation:

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𝜎 =𝑒2𝜏𝑛

𝑚∗ =1

𝜌

Where ρ is the resistivity of the material. A relation between the charge, the collision time and the

effective mass is also expressed as the carrier mobility (μ):

𝜇 =𝑒𝜏

𝑚∗

By combining the two equations the conductivity can be expressed as a function of the carrier density

and carrier mobility:

𝜎 = 𝑛𝑒𝜇

2.3. Thermal conductivity

Thermal conductivity is a measure of the ability of a material to allow the flow of heat from

its warmer surface through the material to its colder surface. Understanding the mechanism of

thermal conductivity is a major factor in the research on thermoelectric materials. Thermal

conductivity is the parameter that affects the time under which the induced thermal gradient can be

maintained throughout a sample’s geometry as well as the magnitude of the temperature difference

that can be achieved. According to the theory by Debye and Peierls for a crystal, at the lowest

temperatures the thermal conductivity depends on the size and shape of the crystal and increases

with temperature in relation to the specific heat. The maximum thermal conductivity is limited by the

scattering of phonons and is characteristic of the material. Near the maximum, the thermal

conductivity is sensitive to the imperfections and impurities in the crystal lattice3.

Like electrical conductivity where the associated charge carriers are electrons or holes, the

parameter attributed to thermal conductivity is (λ), and it has contribution from the electronic charge

carriers (λe) as well as the lattice vibration modes (phonons) (λL).

𝜆 = 𝜆𝑒 + 𝜆𝐿

Where λe can be related to the Electrical conductivity through the Lorentz factor (L) and the

temperature (T). This relation is given by the Wiedermann-Franz law4:

𝜆𝑒 = 𝐿𝜎𝑇 = 𝑛𝑒𝜇𝐿𝑇

The Lorentz factor for free electrons is:

𝐿 =𝜋2

3(

𝑘𝐵

𝑒

2

) = 2.45 ∗ 10−8 𝑊𝛺𝛫2

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Since the lattice contribution λL cannot directly be measured, it is calculated as the difference between

the measured λ and the electronic contribution. Hence there is need for accurate estimation of λe.

Electronic thermal conductivity

The electronic contribution to the thermal conductivity of a material is given by:

𝜆𝑒 =1

3𝐶𝑒𝑣𝑓𝑙𝑒 =

𝜋2𝑛𝑘𝛣2 𝑇𝜏𝑒

3𝑚𝑒∗

Where (Ce) is the electron specific heat, (νf) is the Fermi velocity, (le) is the electron mean free path

and (τe) is the average collision time of electrons.

Lattice thermal conductivity

Lattice thermal conductivity of a crystal is attributed to phonons and is determined by three

contributions: The frequency dependent specific heat of phonons (Cph), the phonon group velocity

(vph) and the mean free path of phonons (lph). It can be modeled by:

𝜆𝐿 = 𝜆𝑝ℎ =1

3𝐶𝑝ℎ𝑙𝑝ℎ𝑣𝑝ℎ

The mean free path of phonons is determined by two factors: the rate of scattering with other

phonons at high temperatures and by scattering with static impurities or boundaries in the crystal

lattice at lower temperatures. The transition between the two contributions is dependent on the

Debye Temperature (TD) of the material which can vary between 100-1000K. At high temperatures

lph is decreasing with 1/T.

The phonon specific heat at temperatures exceeding the Debye limit is given in its classical

form from the Dulong Petit law:

𝐶𝑝ℎ = 3𝑁𝑘𝛽

With 3N being the number of normal phonon modes, and is independent of temperature

2.4. The Thermoelectric Figure of Merit zT

The efficiency of energy conversion of a thermoelectric material is determined primarily by three

properties: (α) Seebeck coefficient, (σ) the electrical conductivity and (λ) the thermal conductivity of

the material. A simplified way to quantify this efficiency is through the connection of all the properties

and the temperature of application (T) in the dimensionless figure of merit (zT).

𝑧𝑇 =𝛼2𝜎

𝜆𝛵

Where the nominator is also called the Power factor and it is indicative of how well a thermoelectric

material performs with respect to its electronic properties:

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𝑃 = 𝛼2𝜎

In more detail the electronic conductivity / resistivity can be connected by the equation:

𝜎 = 𝑛𝑒𝜇 =1

𝜌

The Seebeck coefficient expressed in more detail as function of the effective mass and carrier density:

𝛼 =8𝜋2𝑘𝛽

2

3𝑒ℎ2 𝑚∗𝑇 (𝜋

3𝑛)

23⁄

Where (𝑚∗) is the electron effective mass and (𝑘𝛽), (ℎ) the Boltzmann constant and Plank’s constant

respectively.

It can be easily understood that in order to enhance the thermoelectric efficiency there are

three different paths to follow. Enhancing the Seebeck coefficient, enhancing the electrical

conductivity or lowering the thermal conductivity. However it has been proven that this is not a minor

task. The three properties are not by default decupled from each other and most of the time,

optimizing one factor comes at the cost of diminishing another. This fact is depicted in figure 5, where

it is noted that the zT factor is optimal at a different carrier concentration value than the power factor.

Another approach for enhancing the Seebeck coefficient is by increasing the effective mass

m* of the carriers i.e. by narrowing the bands via designing the density of states5 or via nanostructure

engineering6. However this approach may significantly reduce the mobility of the carriers, while there

are also studies supporting that higher performance can be achieved through an effective mass

reduction7.

Figure 5: Optimizing zT through carrier concentration tuning. The value range for the other parameters plotted against the y-axis are: α (0-500μVK-1), σ(0-5000Ω-1cm-1),λ(0-10Wm-1K-1),adapted from4

Thermoelectric materials are usually heavily doped semiconductors and with carrier

concentrations in the range of 1019-1021 per cm3. A reduction in the lattice thermal conductivity can

significantly increase the figure of merit zT. Figure 6 denotes this fact.

λ

α2σ

α

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Figure 6: Lower lattice thermal conductivity λL over λe ratio, directly increases the zT and increases the Seebeck coefficient due to lower overall thermal conductivity λ. Plot is based on a model system (Bi2Te3), adapted from4

Through the above analysis of the thermoelectric properties, three paths leading to a potential

increase of the zT factor and thus the energy conversion efficiency of devices made of nanostructures

can be derived. 1) Introduce Interfaces and boundaries of nanostructures to constrain the electron

and phonon waves, which lead to a change in their energy states and correspondingly, their density

of states and group velocity. 2) Use of quantum size effects and classical interface effects to influence

the symmetry of the differential conductivity with respect to the Fermi level. 3) Utilize interface

scattering and induce variations of the phonon spectrum in low-dimensional structures in order to

reduce the phonon thermal conductivity.

λ|=

λL=

λe

λL=0.8

λL=0.2

λ

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3. The thermoelectric module concept

A typical thermoelectric module for power generation consists of both n-type and p-type

thermoelectric materials connected in series with a conductive material. A temperature gradient

applied across the module causes the charge carriers to diffuse towards the cold side, generating a

thermoelectric voltage. This way the electron and hole transport from the n-type and p-type materials

respectively, is additive and leads to the generated current. A Schematic diagram representing the

concept of such a module is presented in figure 7.

Figure 7: Schematic diagram of a typical thermoelectric module for electrical power generation. Components of n-type (red) and p-type (blue) materials are connected in series and then contained between ceramic substrates. Heat is applied to one side of the module, causing the charge carriers to diffuse across the module and generating an electrical current8.

It has to be clarified that the figure of merit zT described in the previous chapter, is only

referring to the material’s thermoelectric performance and not to the overall efficiency of the

thermoelectric module which contains those materials. This is primarily because the material

properties (α, κ, σ) are also dependent on temperature and due to factors related to the

interconnectivity and cumulative performance of all the parts co-existing in TEG module. A good

approximation of the overall performance of a thermoelectric generator described by the combined

Carnot efficiency and the averaged material efficiency as (η):

𝜂 =𝛥𝛵

𝛵ℎ

√1 + 𝑍�̅� − 1

√1 + 𝛧�̅� +𝑇𝑐𝑇ℎ

Where (Z) is the averaged material figure of merit, (Tc) and (Th) are the effective temperatures in

the cold side and the hot side of the active part of the module respectively, (ΔΤ) is the difference

between them and (T̅) is the average working temperature of the generator4.

3.1. Thermoelectric generator design concepts

Research towards optimization of material thermoelectric properties is essential to the overall

goal of improving performance of thermoelectric energy conversion. However, a research direction of

equal significance is the optimal design of the thermocouples and modules. This procedure involves

taking into account the material properties for a given temperature regime and working towards

optimizing performance by changing the leg material composition and dimensioning.

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Since the thermoelectric properties (σ, λ, α) are temperature dependent they can all be

optimized at a certain unique temperature T and this is giving the best material performance factor Z.

When a thermoelement leg of length 0<x<L, composed of one material is operating under a

temperature gradient Tc(0)<T(x)<Th(L) (one dimensional), it is evident that the material

performance will be varying in every x-position of the leg. This fact is more pronounced when

considering application of thermoelectrics under larger temperature gradients or when the design

optimization leads to legs of larger length.

In literature there are two solutions for this problem, which could be referred to as the optimal

and the averaged approach. The optimal approach is the development of thermocouple legs consisting

of one material doped in such that the resulting carrier concentration (n) gradient is fitted for the

given temperature gradient to yield the optimal material properties combination in every x-position

along the leg length. This kind of leg design is described as Functionally Graded Thermoelectric

Material (FGTM)

The averaged FGTM approach or segmented design is to have thermoelectric legs consisting

of segments of different materials along the leg length. Each segment then needs to be composed of

a material which performs optimally for the temperature gradient that exists across its length. The

materials selection and combination is then important as they need to be compatible with each other

both in terms of thermoelectric properties and in terms of thermo-elastic behavior (I.e matching

thermal expansion coefficients). A visual illustration of both concepts is given in figure 8. Another

concern related to the segmented leg approach is the electrical and thermal resistances that may arise

in the interfaces between the segments. According to a study by Rasmus BØrk9, If the efficiency

benefits from segmentation in terms of efficiency is in the order of 30%, then an electrical contact

resistance of 30% or a thermal contact resistance of 20% can be tolerated.

A different design concept that avoids compatibility issues between the combinations of

materials for the different temperature stages is the cascaded generator. In this design there is an

independent electric circuit for each temperature stage thus allowing for an independent current

flowing for each temperature stage. In principle independent circuits would require an electric

connector between a high temperature stage and an external load at ambient temperature. This

situation is not practical however, since such connections cannot have very low or very high electric

resistance. Low resistance, according to Wiedermann Franz Law, would cause heat conduction away

from the hot side, high resistance on the other hand would induce large joule heat losses. The loss

from such connections is inversely proportional to the number of couples (~1/𝑁𝑐𝑜𝑢𝑝𝑙𝑒) for each

connector and thus the greater the number of couples the lower the loss.

In order for such loses to be avoided entirely the current should pass from the high

temperature stage to the load after passing through the p, n elements of the lower temperature stage.

The current (I) can be the same while its density (J) and thermal behavior can be adjusted by the

n

x

n

x x=0

Figure 8: Illustration of the Two FGTM concepts: left: Ideal functionally graded leg. Right: segmented leg design.

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different cross-sectional geometries and amount of thermocouples per temperature stage. Since the

current is the same, by equating the Heat in each stage (Ui):

𝑈𝑖 = 𝐼𝑁𝑖(𝛷𝑝,𝑖 − 𝛷𝑛,𝑖) = 𝐼𝑁𝑖+1(𝛷𝑝,𝑖+1 − 𝛷𝑛,𝑖+1) ,

where (Φp,i) and (Φn,I) are the potentials of the n and p-type elements at the ith stage, the ratio

𝑁𝑖+1/𝑁𝑖 of couples between the stages can be calculated. Under optimal conditions the overall

efficiency of a cascaded generator is the sum of the efficiencies of each individual stage. A schematic

illustration of both generator designs is given in figure 9.

3.2. Working principles of a common design thermoelectric generator

In existing literature there are many variations regarding derivations of the equations that

apply in thermoelectric generator systems which follow the common thermocouple design structure,

each with their own set of formulation, assumptions, simplifications and boundary conditions10-13. For

reasons of thoroughness of explanation the derivation process explained in this chapter is adapted

from14.

The basic unit of a thermoelectric generator is a thermocouple, consisting two semiconducting

legs: a p-type and an n-type. These are connected electrically in series and thermally in parallel and

they operate between a heat source at temperature Th and a heat sink at temperature Tc. The rate of

heat flow from the heat source towards the thermocouple is denoted as Qh and the rate at which heat

exits the thermocouple is denoted as Qc.

The operation of a thermoelectric generator is based on the Seebeck effect. However three

additional effects take place at the same time: a) leak of heat due to temperature difference between

the hot and cold junction; b) Joule heat as a result of the electrical current; and c) Thomson heat

attributed to both the temperature gradient and the current flow. From principles of non-equilibrium

thermodynamics, for electrical current with density J that passes through a conductor that is forced

into a temperature gradient:

𝜵 ∙ 𝑱𝑼 = −𝜵 ∙ (𝜆𝜵𝛵) + 𝑇𝑱 ∙ 𝜵𝛼 − 𝑱 ∙𝑱

𝜎 ,

With JU the current density of energy of density in the conductor.

Figure 9: Illustration of segmented generator design (left) and cascaded generator design (right). Color code indicator of the different material components (middle).

n p

n p n p

n p

n p

n

n

p

p

Electrical insulator

Electrical/Thermal insulator or gap

Electrical contact

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The set of variables for the case of homogeneous semiconducting elements being thermally and

electrically insulated from each other and their surroundings everywhere except the junction reservoir

contacts are as follows:

The temperatures inside the elements Tn(x) and Tp(x) in (K). They are a function of the

element length considering one directional heat flow.

Total length (of n- and p-type) element legs Ln and Lp in (m),

The cross-sectional areas An and Ap in (m2),

The thermal conductivities λn and λp in (W/mK),

The electrical conductivities σn and σp in (S/m),

The Seebeck coefficients αn and αp in (V/K),

The Thomson coefficients τn and τp in (V/K), which show the dependency of α over T :

τ=Τda/dΤ

From there on we can define for (i= n or p):

The thermal conductance Ki=λiAi/Li in (W/m)

The electrical resistance Ri=Li/(σiΑi) in (Ω)

Then for stable operation we have for each leg the equations of heat conduction:

𝐾𝑛𝐿𝑛

𝑑2𝑇𝑛

𝑑𝑥2 − 𝜏𝑛𝐼𝑑𝑇𝑛

𝑑𝑥+

𝑅𝑛𝐼2

𝐿𝑛= 0, 0 ≤ 𝑥 ≤ 𝐿𝑛

𝐾𝑝𝐿𝑝

𝑑2𝑇𝑝

𝑑𝑥2 − 𝜏𝑝𝐼𝑑𝑇𝑝

𝑑𝑥+

𝑅𝑝𝐼2

𝐿𝑝= 0, 0 ≤ 𝑥 ≤ 𝐿𝑝

Where I=J in one dimension

We can now set the boundary conditions:

𝑇𝑛(0) = 𝑇𝑝(0) = 𝑇𝑐

𝑇𝑛(𝐿𝑛) = 𝑇𝑝(𝐿𝑝) = 𝑇ℎ

𝑄𝑐 = (𝑎𝑝𝑐 − 𝛼𝑛

𝑐 ) 𝑇𝑐𝐼 + 𝐾𝑛𝐿𝑛

𝑑𝑇𝑛

𝑑𝑥|

𝑥 = 0 + 𝐾𝑝𝐿𝑝

𝑑𝑇𝑝

𝑑𝑥|

𝑥 = 0

𝑄ℎ = (𝑎𝑝ℎ − 𝛼𝑛

ℎ) 𝑇ℎ𝐼 + 𝐾𝑛𝐿𝑛

𝑑𝑇𝑛

𝑑𝑥|

𝑥 = 𝐿𝑛 + 𝐾𝑝𝐿𝑝

𝑑𝑇𝑝

𝑑𝑥|

𝑥 = 𝐿𝑝

𝑇𝑛 = 𝑇𝑐 +𝑅𝑛𝐼

𝜏𝑛𝐿𝑛𝑥 +

𝑇ℎ − 𝑇𝑐 −𝑅𝑛𝐼

𝜏𝑛𝐿𝑛𝐿𝑛

𝑒𝜏𝑛𝐼

𝐾𝑛𝐿𝑛 𝐿𝑛 − 1

(𝑒𝜏𝑛𝐼

𝐾𝑛𝐿𝑛 𝑥

− 1) , 0 ≤ 𝑥 ≤ 𝐿𝑛

𝑇𝑝 = 𝑇𝑐 −𝑅𝑝𝐼

𝜏𝑝𝐿𝑝𝑥 +

𝑇ℎ − 𝑇𝑐 +𝑅𝑝𝐼

𝜏𝑝𝐿𝑝𝐿𝑝

𝑒

𝜏𝑝𝐼𝐾𝑝𝐿𝑝

𝐿𝑝− 1

(𝑒−

𝜏𝑝𝐼

𝐾𝑝𝐿𝑝 𝑥

− 1) , 0 ≤ 𝑥 ≤ 𝐿𝑝

14

To ease the formulation we can compact some geometric parameters by setting:

𝜔𝑛 =

𝜏𝑛𝐼

𝐾𝑛𝐿𝑛, 𝜔𝑝

=𝜏𝑝𝐼

𝐾𝑝𝐿𝑝

𝑌𝑛 =

𝑅𝑛𝐼

𝜏𝑛𝐿𝑛, 𝑌𝑝

=𝑅𝑝𝐼

𝜏𝑝𝐿𝑝

And rewrite the above equations:

𝑇𝑛 = 𝑇𝑐 + 𝑌𝑛 𝑥 +

𝑇ℎ − 𝑇𝑐 − 𝑌𝑛 𝐿𝑛

𝑒𝜔𝑛 𝐿𝑛 − 1

(𝑒𝜔𝑛 𝑥 − 1), 0 ≤ 𝑥 ≤ 𝐿𝑛

𝑇𝑝 = 𝑇𝑐 − 𝑌𝑝 𝑥 +

𝑇ℎ − 𝑇𝑐 − 𝑌𝑝 𝐿𝑝

𝑒−𝜔𝑝 𝐿𝑝 − 1

(𝑒−𝜔𝑝 𝑥 − 1), 0 ≤ 𝑥 ≤ 𝐿𝑛

𝑄𝑐 = 𝛼𝑐𝑇𝑐𝐼 + (𝐾𝑛∗ + 𝐾𝑝

∗)(𝑇ℎ − 𝑇𝑐) + [𝑅𝑛∗ + 𝑅𝑝

∗ ]𝐼2

𝑄ℎ = 𝛼ℎ𝑇ℎ𝐼 + (𝐾𝑛∗ + 𝐾𝑝

∗)(𝑇ℎ − 𝑇𝑐) − (𝜏𝑝 − 𝜏𝑛)(𝑇ℎ − 𝑇𝑐)𝐼 + [𝑅𝑛∗ + 𝑅𝑝

∗ − (𝑅𝑛 + 𝑅𝑝)]𝐼2

Where we have used for abbreviations:

𝐾𝑛∗ =

𝜏𝑛𝐼

𝑒𝜔𝑛 𝐿𝑛 − 1

, 𝐾𝑝∗ =

𝜏𝑝𝐼

1 − 𝑒𝜔𝑝 𝐿𝑝

𝑅𝑛∗ = 𝑅𝑛 {

1

𝜔𝑛 𝐿𝑛

−1

𝑒𝜔𝑛

𝐿𝑛 − 1} , 𝑅𝑝

∗ = 𝑅𝑝 {1

1 − 𝑒−𝜔𝑝

𝐿𝑝

−1

𝜔𝑝 𝐿𝑝

}

And 𝛼 ℎ = 𝛼𝑝

ℎ − 𝛼𝑛ℎ in the hot side and 𝛼𝑐 = 𝛼𝑝

𝑐 − 𝛼𝑛𝑐 in the cold side

Then we can have the formula for the power output:

𝑃 = 𝑄ℎ − 𝑄𝑐 = (𝑎ℎ𝑇ℎ − 𝑎𝑐𝑇𝑐)𝐼 − 𝜏(𝛵ℎ − 𝑇𝑐)𝐼 − 𝑅𝐼2

Setting P=0 we get two solutions for I:

𝐼 = 0, 𝐼 =𝑎ℎ𝑇ℎ − 𝑎𝑐𝑇𝑐 − 𝜏(𝛵ℎ − 𝑇𝑐)

𝑅= 𝐼𝑚𝑎𝑥

Deriving 𝑑𝑃/𝑑𝐼 = 0 we get the current required for the maximum power output:

𝐼𝑃𝑚𝑎𝑥=

𝑎ℎ𝑇ℎ − 𝑎𝑐𝑇𝑐 − 𝜏(𝛵ℎ − 𝑇𝑐)

2𝑅=

1

2𝐼𝑚𝑎𝑥

The corresponding maximum power is

15

𝑃𝑚𝑎𝑥 =1

4𝑅[𝑎ℎ𝑇ℎ − 𝑎𝑐𝑇𝑐 − 𝜏(𝑇ℎ − 𝑇𝑐)]2

And the efficiency:

𝜂 = 1 −𝑄𝑐

𝑄ℎ=

(𝑎ℎ𝑇ℎ − 𝑎𝑐𝑇𝑐)𝐼 − 𝜏(𝛵ℎ − 𝑇𝑐)𝐼 − 𝑅𝐼2

𝛼ℎ𝑇ℎ𝐼 + (𝐾𝑛∗ + 𝐾𝑝

∗)(𝑇ℎ − 𝑇𝑐) − 𝜏(𝑇ℎ − 𝑇𝑐)𝐼 + [𝑅𝑛∗ + 𝑅𝑝

∗ − 𝑅]𝐼2

With 𝑅 = (𝑅𝑛 + 𝑅𝑝), the sum of the two legs and 𝜏 = (𝜏𝑝 − 𝜏𝑛) , the combined Thomson coefficient.

From the equations for 𝐼𝑃𝑚𝑎𝑥 and 𝑃𝑚𝑎𝑥 and the relation: 𝑃 = 𝐼2𝑅𝐿, It is derived that for a

thermoelectric generator to be running at maximum power the load resistance has to be matched

with the resistance of the generator (𝑅𝐿 = 𝑅). This is known as the load resistance matching condition

for a thermoelectric generator.

Using the derivation above the thermoelectric figure of merit can be expressed as

𝑍 = 𝛼2/(𝑅𝐾)

with 𝐾 = 𝐾1 + 𝐾2 the sum of the two thermal conductances.

Provided that the material parameters λn and λp, σn and σp, can be calculated or approximated for a

given temperature gradient profile then the optimal geometric configuration for the thermoelectric

generator leg length and cross-sectional area is given by the following ratio:

𝐿𝑛 𝐿𝑝⁄

𝐴𝑛 𝐴𝑝⁄= √

𝜆𝑛𝜎𝑛

𝜆𝑝𝜎𝑝

And with that, the minimum combined resistance factor (electrical and thermal), RK is attained when:

(𝑅𝐾)𝑚𝑖𝑛 = (√𝜆𝑛

𝜎𝑛+ √

𝜆𝑝

𝜎𝑝 )

2

These two last equations drive the geometrical characteristics when designing a thermoelectric

device.

3.3. Filling factor

The filling factor for a thermoelectric device is the ratio between the total area of the

thermoelectric legs (electrically active area) over the total area of the structural insulating

substrate/cover plate (i.e. ceramic layer). It is commonly described with the letter (F).

16

𝐹 =𝑁𝐴𝑝 + 𝑁𝐴𝑛

𝐴𝑡𝑜𝑡

Where N is the number of legs and Ap, An, the areas of the p-leg and the n-leg respectively.

In literature there are at least two ways of optimizing the filling factor. The first method is

described hereafter and is an outcome of modelling the effective heat spreading region in dependence

to the substrate thickness and the geometry of the legs15. The area outside of the spreading region

does not influence the heat flow in the thermoelectric elements. It is therefore natural to consider

filling of the elements until the boundaries of the spreading regions (figure)

Assuming uniform temperature at the heat transfer surface the boundary of spreading limit

in the form of an angle is up to 46.45 deg. (model by Vermeersch et al.16) and assuming equal

spreading thermal resistance for the hot and cold substrates and equal substrate thermal conductivity

βs (W/mK) we have:

𝜓𝑠ℎ = 𝜓𝑠𝑐 =𝛬

𝛽𝑠𝛿(1 + 2𝛬 𝑡𝑎𝑛𝜑)

Where: {𝜑 = 5.86 ln(𝛬) + 40.4 𝑓𝑜𝑟 0.0011 < 𝛬 ≤ 1

𝜑 = 46.45 − 6.048𝛬−0.969 𝑓𝑜𝑟 𝛬 ≥ 1, is the heat spreading angle in reference to

the leg normal vertical boundaries against the substrate.

and

𝛬 =𝑑𝑠

𝛿 ,

Is the ratio between the substrate thickness (ds) and the leg width dimension (δ) (in 2D) under the

assumption that we have equal square cross-sectional legs.

The limit condition is given when:

𝐹 = (1 −2𝑑𝑠𝑡𝑎𝑛𝜑

𝛿)

2

Substrate

φ

δ

TE leg

TE leg

Spreading region

Spreading

region

Heat in

Heat in

ds

Figure 10: Illustration of the concept of regulating the filling factor according to geometrical characterization of the heat propagation.

17

In a more specific approach, the heat propagation geometry would have to be modelled in accordance

to the geometrical characteristics of the module’s compartments.

The second approach takes into consideration material, manufacturing and implementation

procedures costs in combination with efficiency, power output calculations and optimal geometry

estimations. The optimal Fill factor is then given as cost/power-output optimization for chosen

geometries17.

18

4. Thermoelectric Materials Research

The following entry contains an overview of the most important parameters which influence

the performance of thermoelectric materials. Focusing on strategies and theoretical aspects that are

applied in new methods of material design and fabrication.

4.1. General Framework

As indicated in the introduction all the parameters involved in the performance factor (z) of

a thermoelectric material are interdependent apart from the lattice thermal conductivity (𝜆𝑙𝑎𝑡).

However even though the lattice thermal conductivity is a decoupled parameter, it is challenging to

be reduced without affecting the electron mobility since the way to decrease it is usually by lattice

complexity, defects, boundaries and interfaces, and therefore the same features that could potentially

also scatter electrons and hider the material electrical conductivity.

In most cases, a general framework of rules to follow when selecting or synthesizing materials

for thermoelectric research and applications is given below18.

1. Choose a compound with narrow band gap and high symmetry crystalline structure to have high

degenerate energy valley and therefore high power factor.

2. Choice of heavier atoms reduces the lattice thermal conductivity. As an example: Sn-atom is

heavier than Si-atom therefore between the isoelectronic compounds Mg2Si and Mg2Sn, the later

should have should have smaller phonon group velocity, and thus lower Lattice thermal

conductivity (λlat)

3. Compounds with smaller electronegativity difference between anions and cations show higher

carrier mobility (𝜇).

4. There has to be a balance on the effect of the alloying element(s) on decreasing λlat and

corresponding decrease on carrier mobility. As an Example: Most of the best thermoelectric

materials are compounds with a sublattices filled by two or three isoelectronic atoms to counter

balance the effects. On Mg2Sn, when replacing the Sn, the atomic size of Ge is closer to Sn than

that of Si, and therefore it has less impact on the carrier mobility, so it should be better for

enhancing the power factor.

5. Compositional band-crossing effect is important to optimize the weighted mobility: μ(m*/me)3/2,

and hence achieve high power factor.

6. Application of nano features to micro features in a hierarchical manner to create selective phonon

scattering barriers and interfaces.

4.2. Enhancing the Thermoelectric power factor

In this section an overview of methods established to enhance the power factor in

thermoelectric materials will be given19. As discussed in the introduction, the power factor is a

contribution of the Seebeck coefficient and the electronic conductivity of the materials, as such it

describes the overall electronic material performance decoupled from the thermal attributes and it

plays a major role towards enhancing the zT value.

19

4.2.1. Methods to enhance the Seebeck:

Quantum confinement approach

The electronic density of states is a function of the dimensions of the system (crystal), as the

system size decreases to nanometer length scales sharp features are induced to the electronic density

of states as a function of the dimensions as depicted in the formula:

𝑔(𝐸) =𝑁𝑣

𝑔𝐷𝑎3−𝐷 (2𝑚𝑑

ℎ2 )

𝐷2

(𝐸 − 𝐸0)𝐷2−1

With md the geometrical average of the band effective masses, D = 2π2 for 3d, 2π for 2d and π for

1d systems and Nv the number of valence states visually depicted in figure 11.

The differential conductivity is then given by:

𝜎(𝛦) ≡ 𝑒2𝑔(𝐸)𝑣𝑥2(𝐸)𝜏(𝛦, 𝛵)

It measures the contribution of electrons with energy E to the total conductivity as a function of i)

band structure parameters g(E) and v(E) and ii) the carrier scattering time τ(Ε,Τ) which is not only

related to the band structure alone. If we are in the degenerate limit where (𝐸𝑐 − 𝐸𝐹) > 𝑘𝐵𝑇, then

the Seebeck coefficient is given by the Mott formula:

𝛼 =𝜋2𝑘𝛣

2 𝛵

3𝑒

1

𝜎(𝛦)

𝑑𝜎(𝛦)

𝑑𝐸|

𝐸 = 𝐸𝐹+ 𝑂[𝑇3]

Following the derivation we have:

𝛼 =𝜋2𝑘𝛣

2 𝛵

3𝑒{

1

𝑔(𝛦)

𝑑𝑔(𝛦)

𝑑𝐸

1

𝜏(𝛦)

𝑑𝜏(𝛦)

𝑑𝐸

2

𝜈(𝛦)

𝑑𝜈(𝛦)

𝑑𝐸} |

𝐸 = 𝐸𝐹

Sharp features in the electronic density of states increase the factor: 𝑑𝑔(𝐸)/𝑑(𝐸), and therefore

increase the Seebeck coefficient.

Figure 11: Electronic density of states in relation to system dimensions19

20

Electron energy filtering

Considering a quasi-equilibrium and diffusive electron transport process, the Seebeck

coefficient is to the first order proportional to the mean excess energy: ⟨E − EF⟩. Thus for a given

carrier concertation the larger the difference between the two energies the larger the Seebeck. In

total for a high power factor a large and energy asymmetric differential conductivity is required within

the Fermi window. If the electrons with lower mean excess energy are filtered out a higher Seebeck is

obtained. However this effect comes at the cost of a decreased carrier concentration which in turn

degrades the electronic conductivity (σ). Therefore for energy filtering to be effectively applied the

rise of the Seebeck compensates for the reduction of σ.

In practice the filtering effect can be achieved by the introduction of energetic barriers in the

order of a few kBT in the conduction band of an n-type material or in the valence band of a p-type

material. Carriers of lower energy are being filtered while those of higher energy are selectively

transmitted. The phenomenon can be visualized in figure 12.

Resonance levels – resonant scattering

In this approach the scattering parameter (r) which is strongly energy dependent also

resonates at certain energies. Resonance levels induce a narrow Lorentzian line shaped peak in the

electronic density of states that centers on the energy with value ED, as shown in figure 3. At the same

time current is conducted while electrons resonantly scatter, in a dephasing process unlike the normal

momentum relaxation mechanism for typical scattering effects. In physical explanation the phase

change (δl) is associated with the delay the carrier experiences due to an impurity before it resumes

its conduction, known as Wigner delay time:

𝜏𝑤 = 2ℏ (𝜕𝛿𝑙(𝛦)

𝜕𝛦)

Since the delay time is energy dependent RLs are usually implemented via hetero-electron doping and

resonant dopant impurities must have electron energy levels residing inside the conduction band or

the valence band, rather than inside the band gap.

A B

Energetic barrier

E

X Figure 12: Electron energy filtering mechanism schematic. The energetic barrier filters low energy carriers. Adapted from19

21

4.2.2. Enhancement of the electrical conductivity

Modulation doping

Most of the materials used in thermoelectrics are heavily doped semiconductors with carrier

concentrations in the order of 1018-1020 cm-3. On the one hand sufficient level of doping is needed in

order to achieve high enough carrier density to conduct electricity, on the other hand high carrier

mobility is also crucial to ensure efficient current flow. While the addition of doping centers provides

the required number of conduction carriers, they disturb the optimal crystal formation with ionized

impurity centers which in turn diminish the mobility of the carriers.

The concept of modulation doping is to selectively dope regions of the material rather than

the material as a whole. The main benefit of modulation doping compared to normal doping is that it

spatially separates the doping impurities from the conductive channel thus reducing the

backscattering of carriers and increasing the overall carrier mobility. This concept has been effectively

applied in two dimension systems by applying a thin concentrated dopant material layer and

separating it from the conduction channel by a spacer material i.e. modern transistor technology. In

(2D) structures, this separation is achievable via smooth material interface engineering using for

instance Molecular Beam Epitaxy (MBE) technology.

In thin film (2D)20 and nanowire (1D)21 systems, modulation doping has been successfully

demonstrated as an outcome of an effective spacer layer and as a result of field-effect doping

correspondingly. Researchers have investigated the possibility to embed metallic or semi-metallic

nanoparticles inside an intrinsic bulk sample in a form of clustered doping centers22-24 in the form of a

modulation doping. Charge carriers spill over from the clusters into the host material with theoretically

reduced ionized impurity scattering, this way enhancing the mobility and overall the power factor.

Although significant enhancement of the power factor was achieved, the coulomb interaction

between the clusters and the charge carriers is still in the same order as single impurities and charge

carriers, since due to lack of the spacer layer there is no complete decoupling between charge carriers

and their parent atoms.

In order for the modulation doping theory to be effectively applied in the bulk semiconductors

used in thermoelectrics, the concept of a spacer material between dopant and “main” semiconductor

material has to be applied in 3D systems. A conceptual approach is the addition of a coating layer to

the dopant nanograins, before the doping procedure, however this has not been successfully

demonstrated yet, according to existing literature.

E

ED

DOS

Figure 13: Schematic of the density of states over energy depicting the resonance effect. Adapted from19.

22

Alignment of the crystallites

Many of the materials used in thermoelectric research, including the chimney ladder

structured HMS and layered oxides such as NaxCoO2 and Ca3Co4O9, have crystal structures that are

highly anisotropic along different crystallographic directions. The charge carrier mobility is highly

coupled with the level of anisotropy thus having some high and low mobility directions. In

polycrystalline thermoelectric samples the carrier mobility could be significantly enhanced if the

crystallites (grains) where aligned along the preferred transport direction. A measure of the degree of

orientation is given by the Lotgering factor (F)25:

𝐹 =𝑝 − 𝑝0

1 − 𝑝0 , 𝑤ℎ𝑒𝑟𝑒 𝑝 =

∑ 𝐼(00𝑙)

∑ 𝐼(ℎ𝑘𝑙)

And I (hkl) is the intensity of the X-ray diffraction pattern. For p=p0, F=0 and the sample is totally

randomly oriented.

In order to achieve this preferentially oriented grain alignment, one of the simplest

approaches is mechanical alignment under uniaxial compression which is achieved during hot pressing

and spark plasma sintering techniques. The degree of alignment depends, among other parameters,

on the initial mechanical properties of the powder, its morphology and size distribution as well as the

compressional load applied. Methods of severe plastic deformation such as Hot Area Reduction

Extrusion (HARE), Equal Channel Angular Extrusion/Pressing (ECAE or ECAP), and hot forging are also

techniques used to manufacture strongly textured materials with high degree of alignment. Another

technique of alignment to prepare highly textured samples from materials that have anisotropic

magnetic susceptibility is via high magnetic field alignment. Here the material grains held in a colloidal

solution are aligned according to the magnetic field and while in that state they are consolidated using

SPS or Hot pressing methods.

Composite engineering

The concept of composite engineering is based on the idea that under certain strict conditions,

a multicomponent material system may have enhanced performance compared to its individual

constituents. This theoretical model considers a homogeneous medium over the length scales of the

legs, without crystallite effects and boundary charge transfer. Therefore this approach cannot be used

when investigating the thermoelectric properties of a segmented or graded material with nanoscale

inhomogeneities.

Ideally when employing the composite engineering concept, the end material should have

enhanced electrical conductivity, in combination with a Seebeck coefficient close to the high Seebeck

coefficient composite. The characteristic lengths such as crystallite lengths of the components,

phonon and carrier mean free path as well as energy relaxation length define the increase of the

electrical conductivity and the drop in Seebeck coefficient over that of the best component.

23

4.2.3. Combined approach for simultaneous enhancement of both Conductivity and

Seebeck

Carrier pocket engineering

On the one hand the Seebeck coefficient is proportional to the effective mass (m*) on the

other hand materials with band structure leading to large band effective mass (mb*) tend to have

lower conductivity values, since In general the carrier mobility is dependent on the weighted mobility

of the carriers: μ(m*/me)3/2. However, the convergence of multiple degenerate valleys has been

studied to increase m* by a factor of Nv2/3 (m*= Nv

2/3 mb*), with intervalley scattering having limited

negative influence towards the mobility.

The concept of carrier pocket engineering is to induce merging of symmetrically equivalent

valleys thus increasing the amount of degenerate bands (Nv) near the Fermi level. This way the density

of states increases, effectively inducing more pathways for the carriers transport higher conductivity

while concomitantly enhancing the Seebeck coefficient thanks to the larger effective mass. To identify

bands as effectively equivalent, their energy separation must be in the order of KΒT.

The theory for this approach for improvement of the thermoelectric power factor was

proposed by Konga et al.26,27 and results have been investigated for low dimensional thermoelectric

nanostructures Si/Ge superlattices26 with successful demonstration and Bi0.87Sb0.13 nanowires28.

Furthering the concept to bulk thermoelectrics favorable for up-scaled applicability, Zaitsev et al29

,successfully enhanced the performance of n-type bulk polycrystalline Sb-doped Mg2Si1-xSnx solid

solutions while Pei et al30 , achieved convergence of 12 valleys in the valence band of Se doped PbTe

reaching a zT of 1.8 at 859K.

In summary, high valley degeneracy produced by carrier pocket engineering in both low

dimension and bulk material is an effective strategy to enhance thermoelectric performance through

the convergence of conducting electronic bands, provided that the doping is properly tuned.

“Invisible” dopants

This approach is similar to the modulation doping, taking a step further as it involves dopant

engineering in such a way that the doping centers do not scatter the charge carriers as much thus

limiting the deteriorating effect on the mobility. This concept can be theoretically achieved by

modifying the dopant material in terms of size, shape and chemical potential.

The idea of invisible dopants was a result of the observation by Ramsauer and Townsend that

for noble gases the collision probability between electrons and gas atoms is minimized at a certain

amount of kinetic energy. Zebarjadi et al31, having the same principle idea in thermoelectric materials,

designed core-shell nanoparticles-dopants in such a way that electrons within a specific energy range,

effectively observe a smaller scattering area compared to the real physical area of the nanoparticles.

If this energy range is set to overlap with the Fermi energy window (energy level at which conduction

takes place) then the doping centers will be invisible to the conduction electrons and the mobility will

be significantly enhanced.

Similarly this theory is backed by the achievements in optical cloaking under a range of

wavelength. Due to the wave nature of the electrons there is a belief that electronic cloaking should

be possible. The feasibility of this idea has been recently studied for both artificial32,33 and real34

materials. Although there is no experimental proof and the application of the idea is very difficult due

24

to the required precision in size and uniformity of the core-shell nanoparticles, the predicted

enhancement of the power factor is promising and worthwhile of further future research.

Effects of interfaces

Since most of the thermoelectric materials that are suited for large scale application are

polycrystalline due to the significant cost reduction there is an ample amount of interfaces formed

between the grains of crystallites. Engineering of these interfaces in thermoelectric materials plays a

key role in tuning of the scattering and the carrier filtering mechanisms. In general, interface effects

can be used to decouple the resistivity, Seebeck and thermal conductivity factors which are otherwise

interdependent in a bulk material

Defect physics, describe an interface as a planar “2D” defect with its characteristic length scale

ranging from nanometers to millimeters. Hence interfaces are more efficient in scattering longer mean-

free-path electrons and phonons (lower energy). Manipulation of the interface roughness factor can

also influence the range of energies that can be filtered through the scattering mechanism, increasing

the effectiveness of high mobility carriers in a similar manner as the other filtering methods.

Interfaces may also be charged and as such they behave differently than a simple

superposition of a point charge and a neutral 2D grain boundary. They can tune the carrier

concentration inside the grains suppressing the bipolar effect and enabling the Seebeck potential to

reach higher values, while also acting as obstacles that scatter minority carriers with higher probability

than majority carriers. An indication of this concept was observed for p-type and n-type nano-bulk

Bi2Te3 35,36.

Interface effects between metal/semiconductor nano inclusions been modeled in a study by

Sergey V. Faleev and François Léonard37. They consider spherical metallic nanoinclusions of radius (R)

and fraction (x) of the total volume of the system at a random distribution in a PbTe host material. Due

to charge transfer between the metal and the semiconductor, the bands tend to bend away from the

interface, and this behavior it characterized by an electrostatic potential V(r). The presence of this

extra potential leads energy-dependent carrier scattering and causes the electron filtering effect

described earlier. An illustration of the concept can be visualized in figure 1

4.3. The search for glasslike thermal conductivity

The concept idea of a Phonon-glass electron crystal (PGEC) material introduced by G.A. Slack38,

is that a crystalline material has certain lattice structure conditions that affect the phonon thermal

conductivity in a way similar to amorphous materials, however maintaining electronic structures that

Figure 14: Illustration of band bending effect due to metallic nanoinclusions (a) semiconductor host with the metallic spheres (b) Example of the calculated potential V(r). Adapted from37

.

25

can be described as for crystalline solids. The aim for high performance thermoelectric materials

therefore is to maintain high electrical conductivity while at the same time having thermal

conductivity like an amorphous solid. In terms of thermal conductivities this goal can be quantified in

reducing the thermal conductivity ratio λlatt/λel. The reduced thermal conductivity in an amorphous

solid is a result of the small phonon mean free paths (between scattering processes), due to dampened

localized oscillators compared to the normal phonons in a crystalline lattice. Since in most materials

the electronic properties can be affected through doping modifications, intrinsic phonon glass

materials are considered as excellent candidates in the research for efficient thermoelectrics.

The main attributes of such materials where studied by Cahill et al.39 , and in their conclusions

it is noted that:

They possess “loose” atoms or molecules with not clearly defined translational and

rotational locations which have two or more metastable positions.

There is no long range correlation between the locations of the “loose” atoms or

molecules.

The mass of these loose atoms and molecules accounts for at least 3% of the total

mass of the crystal.

Disorder which results from point defect scattering alone, cannot induce glass-like

lattice vibrations; and residing only on this approach cannot reach the minimum

lattice thermal conductivity.

In lattices consisting of more than two atoms in the primitive unit cell, phonon vibrational

modes can be discretized in acoustic and optical. Acoustic phonons are coherent movements of atoms

of the lattice out of their equilibrium positions, while optical phonons are out-of-phase movements of

the atoms in the lattice, one atom moving to the left, and its neighbor to the right.

In a nanobulk material the interfacial resistance due to the grains is expected to limit the

phonon group velocity and the phonon relaxation time related to the mean free path. The reduction

of the relaxation time can be achieved via phonon scattering at lattice point defects and grain

boundaries. As indicated from the simple kinetic theory, neglecting the normal interactions between

phonons, the lattice thermal conductivity is a contribution of the frequency dependent heat capacity

C(ω), Group velocity vg(ω) and the total relaxation time τ(ω) in the formula:

𝜆𝑙𝑎𝑡𝑡 =1

3∫ 𝐶(𝜔)𝑉𝑔(𝜔)2𝜏(𝜔)𝑑𝜔

𝜔𝑐

0

Where ωc is the cutoff frequency.

In order to design thermoelectric materials with low thermal conductivity a frequency

dependent analysis of λlatt is essential, due to the complex interdependence of the three influence

factors. A short explanation of the mechanisms influencing the lattice thermal conductivity is given.

26

Effect on Group velocity

According to the one-dimensional Born-Von Karman model, where a chain of atoms is considered

connected by springs having a linear restoring force, the reduction of the group velocity occurs in three

ways:

By increasing the number of atoms in the primitive unit cell, the velocity of optical vibrational

modes is decreased and vg(ω) is significantly reduced.

By increasing the mass contrast, the optical mode is flattened and at higher temperatures

where Umklapp scattering process (reflection or a translation, of a wave vector to another

Brillouin zone) is dominant, vg(ω) is reduced.

In open framework compounds i.e. Clathrates and Skutterudites, the introduction of guest

atoms in the host lattice, blocks the crossing in the area of their vibrational modes and reduces

the acoustic contribution, in turn limiting vg(ω)

Effect on the Relaxation Time

Phonon reflection and refraction resulting from the difference of the group velocities in

adjacent grains.

Phonon diffusive scattering at the interfaces due to impurities or roughness.

Wave diffraction when the particle sizes are comparable to the wavelength. In the case when

the excited phonon wavelengths are much larger than the interface region, then the problem

is treated as diffraction process (Rayleigh scattering).

Strain effects as a result of different lattice constants at interfaces influence vibrational modes

and relaxation times.

Deformation potential as a result of lattice mismatch effects at interfaces. This potential

accounts for the interaction between charge carriers and phonons.

Anharmonic effects attributed to inelastic scattering processes or unharmonic coupling at the

interface of two grains. They can be modeled, considering specific ranges of phonon frequency

interactions and the conservation of the density of the phonons. Unharmonic bands are

characterized by the Gruneisen parameter γ, which can be microscopically defined as the

volume (V) dependence of the ith vibrational mode of the lattice (ωi): 𝛾𝑖 = −𝑉

𝜔𝑖

𝜕𝜔𝑖

𝜕𝑉 and

macroscopically through its thermodynamic definition as: 𝛾𝑡ℎ =𝛼𝑉𝛫𝛵

𝐶𝑣 . Where α is the thermal

expansion, KT is the isothermal bulk modulus and CV is the heat capacity at constant volume.

4.4. Other parameters that affect material performance: Application considerations.

When transitioning from thermoelectric material research and fabrication, to module

implementation, the three parameters: Thermal conductivity, electrical conductivity and Seebeck

coefficient that define the material performance factor zT, are not the only ones that mater. More

specifically it is crucial for the selected materials to have certain mechanical and chemical behavior

under the considered temperature of application so that they are stable and do not hinder the

performance. In this chapter these parameters are explained.

27

Thermomechanical performance

The way materials behave mechanically under the application of temperature gradient can be

described with the term Thermomechanical performance. This in turn can be summarized by three

factors namely: the material strength, hardness and toughness according to a review paper by Weishu

Liu et al40.

The mechanical strength of the material in the elastic region is defined by Young’s modulus E

(Pa) while in the non-elastic regime it is defined by the critical stress. The higher the value of E the

more resistant the material is to fracturing during elastic deformation. Low mechanical strength in

thermoelectric materials can result in complications and failures during leg cutting while it can also

limit the size of processing. Typical ways to improve the mechanical strength of materials is to

decrease the average grain size as well as adding nanoparticles and or nanowires to limit fracture

propagation. However these methods usually come at the expense of a reduced zT.

The (Vickers) hardness value Hv (Pa) of a material is indicative of how easily can the surface

of the material be damaged during handling and device assembly the value is proportional to the

material’s modulus E and also found to be decreasing with an increase of the material’s porosity

The fracture-toughness value for a thermoelectric module is an indicator of how many thermal

cycles, mechanical fatigue cycles and shocks it can withstand before breaking down. These repetitive

processes, typical for the working conditions of a thermoelectric module, enhance the formation of

micro-cracks and hence the damage formation. For a typical bulk material the fracture toughness is

given as 𝛫𝑐 = 𝑌𝜎𝑓(𝜋𝛼𝑐)0.5 in [Pa m0.5] and indicates the flaw tolerance, dependent on the fracture

strength (σf [Pa]) and on the length of the largest preexisting flaw (αc [m]). (𝑌) is a dimensionless

geometric factor.

Thermal shock is present when a thermal gradient causes different parts of a material to

expand by different amounts. A material’s resistance to thermal shock, based the thermoelectric

approach is given by 𝑅 = 𝜎𝑓(1 − 𝜈)𝜆 𝛼𝛦⁄ in [W m-1], with (𝛼 [𝐾−1]) here being the thermal

expansion coefficient, (𝑣) the Poisson’s ratio and (𝜆 [𝑊𝑚−1𝛫−1]) the thermal conductivity. It is

intuitive to observe that the requirement for thermoelectric materials to have low 𝜆 values in order

to enhance the 𝛧𝑇 already reduces its thermal shock tolerance.

The coefficient of thermal expansion (CTE) or α as mentioned earlier is defined as the

fractional change in length or volume with a unit change in temperature: 𝑎 = ((𝛥𝐿/𝐿0 ))/(𝑇2 − 𝑇1 ).

A large CTE mismatch between the active TE material and the metallic connections, would lead to high

shear stresses and higher risk of damaging the thermoelectric legs. Moreover thermoelectric materials

with large CTE experience geometrical changes within the applied temperature gradient which leads

to divergence from the expected performance41. Matching the CTE is also critical when considering

segmented leg design.

Thermochemical performance

Another important parameter to account for when considering thermoelectric materials and

their temperature of operation is their thermochemical behavior, which is related to the chemical

stability of the atomic defects, dislocations and grain boundaries. The procedures that influence the

chemical stability of a thermoelectric material are sublimation and diffusion of the atoms and the

movement of dislocations and grain boundaries. If we consider the 10 years of stable operation limit

for thermoelectric technology then the maximum sublimation rate allowed is in the order of 10-7 (gcm-

1h-1), leading to a maximum of 5% cross-sectional area decrease of the TEG leg over 10 years of

operation.

28

Apart from the effective area reduction of the TEG, sublimation may also affect its

stoichiometric composition, due to the concentration gradient of vacancies left behind by the atomic

species leaving the surface. These vacancy defects can diffuse into the remaining material degrading

its thermoelectric performance at a faster rate, while also affecting its mechanical strength42.

Chemical stability is also influenced by the oxygen and nitrogen diffusion from the air into the

TE materials and the reactivity of the TE with these elements at the operating temperature. The

reactivity with the ambient species can be minimized through use of protective cover layer or by

treating the surface of the TE material to alter its chemical composition rendering it more resistive to

oxidation. Another way is to seal the material inside inert environment eg. Argon, a method which

however makes application more difficult.

Diffusion properties

Diffusion of particles43-45, describes their migration from regions of high concentration to

regions of low concertation. It can occur at interfaces between different material types i.e. metal-

semiconductor, same material types but with different carrier concentrations and at empty sites

within a single material type (Self diffusion). In semiconductor technology carrier diffusion is

dependent on the bandgap energy window and the ratio between electron and hole conductivity. It

is therefore crucial to be able to understand and model carrier diffusion characteristics in relation to

dimensions and temperature as it influences their performance through altering the carrier mobility

and concentration density.

Diffusion effects in undoped semiconductors are more apparent at higher temperatures

where the compounds begin to dissociate at temperatures of approximately 80–90% of the absolute

melting point of the materials. The process depends on the existing temperature gradients as well as

the level of dissociation that has already occurred. In binary compounds the higher amount of

probable native point-defects and complexities in the crystal structure compared to elemental

semiconductors, also influence self-diffusion.

Taking into account these facts, semiconducting thermoelectric materials can be considered

homogenous and with well-defined properties only within a very small temperature range and there

is an optimum temperature at which the values of the properties give the maximum thermoelectric

performance for a homogeneous element. When the temperature range increases diffusion processes

alter the material properties deteriorating its maximum performance.

Diffusion is also a factor to consider upon the selection of the metallic contacts between the

p and n-type semiconductor thermoelectric legs especially for the hot side of application. In many

occasions a diffusion barrier layer is needed to counter the diffusion of electrons from the contact to

the semiconductor material and prevent unwanted doping effects. However in many cases, a lower

application temperature range than the maximum that can be sustained by the device, is allowed, in

order to prevent unpredicted diffusion phenomena.

29

5. Overview of Thermoelectric material families

Novel fundamental research on thermoelectrics was made possible over the last two decades

due to the rise of nanotechnology. Lowering the size limit of material observation and intervention

capabilities to the nanoscale, provided an improved understanding of the interrelation between

structural properties and transport coefficients involved, which in turn lead to a significant increase in

the zT. This chapter contains an overview of the thermoelectric material research outlining some of

the most important progress and results. Research involving nanowires, quantum dot superlattices

and thin films is also mentioned since it underlines the capabilities of quantum effects towards

enhancing the thermoelectric properties, however it has to be mentioned in advance that these

fundamental methods are still far from large scale practical implementation.

5.1. Silicon-based composites

Bulk crystalline silicon has high lattice thermal conductivity values and is thus not favorable

for thermoelectric applications. Despite this fact however, its abundancy as an earth element as well

as the well-established knowledge on the material processing, doping methods, synthesis and

fabrication techniques as well as utilization of existing infrastructure, render silicon based materials

promising as thermoelectric candidates. In a recent theoretical modeling study46, thin film silicon has

been calculated to achieve thermoelectric conversion able to generate a harvested power density up

to 7 [𝑊/𝑐𝑚2] for ΔT=30 K.

Silicon films, and membranes with nanostructured porosity and defects (absence of silicon

atoms in the lattice), as well as nanowires and nanowire arrays wave been investigated by several

groups denoting the significant enhancement of the zT compared to bulk, for un-doped silicon

(examples47-50). The influence is on the thermal conductivity by filtering out and blocking heat carrying

phonons. The modes/frequencies blocked and the overall influence, is dependent on the

homogeneity, the size and diameter of the nanowires and on the density of the porosity and defects

for the films and membranes. Although these approaches lead the way towards the fundamental

understanding on improving the performance of Si-thermoelectrics, their applicability is limited to

small scale due to the rigidness of the structures the complexity of manufacturing and

implementation. Therefore use of dopant species to enhance the power factor and utilization of other

means of “nano to bulk” fabrication are essential towards upscaling and improving applicability.

One of the common methods of improving the intrinsic thermoelectric properties of Silicon is

by alloying it with Germanium. Ge-atoms, being larger in size act as phonon scattering centers as they

are distributed in the silicon crystal. Furthering the research through nano-micro structuring the silicon

high zT values of (~1.5 at 900) have been reported for optimal SiGe nano-bulk alloys. However, use

of germanium in high content hinders large scale application considerations due to rarity and cost.

Thus researchers tend to focus on reducing the Germanium content sacrificing some performance in

favor of a less costly product with zT values close to 1 i.e. using nanofabrication methods which

generically reduce thermal conductivity through similar phonon scattering effects. In both approaches

however a certain balance needs to be kept since inducing a lot of scattering boundaries and defects

will reduce the electronic conductivity as an unwanted side effect51,52.

30

Within the silicon-based family of thermoelectric materials, higher manganese silicides (p-

type) and magnesium silicides (n-type) have long been recognized to yield adequate figures of merit

in the medium-high temperature regime, but at very low materials costs.

Higher Manganese Silicides (HMS) MnSix (x=1.72-1.8), are the highest silicon rich intermediate

phases in the manganese-silicon binary phase diagram. Structurally they are tetragonal Nowotny

chimney ladder phases with the Mn-sublattice forming a rigid chimney like structure while the Si-

atoms are arranged within this chimney structure helically (figure 15). This helical Si-structure tends

to be quite flexible and adaptive to different geometries according to the ratio between Mn/Si. The

in-plane a parameter is similar for all HMS compositions. The out-of-plane c-axis parameter is what

varies drastically with the composition and thus forming the tall chimney like structure. In the

undoped HMS crystals a strong anisotropy of the thermoelectric parameters (σ, α, λ) is observed and

related to traits of crystal-chemical structure of HMS. MnSi phase precipitated along (001) planes also

reduces electric conductivity in the direction of с-axis, as macro- and micro-cracks often form in these

planes. Doped crystals possess considerably lower anisotropy of thermoelectric properties in these

crystallographic directions with the most evident example germanium-doped crystals. The hole

concentration ranges between 1020-1021 between doped and undoped HMS with the doped showing

a reduction in mobility53.

Low-lying optical vibration modes, low group velocities and polarization effects that undergo

avoided crossings with the acoustic branches near the Brillouin zone are believed to be the causes of

the intrinsically low thermal conductivity54. Further reduction of the thermal conductivity is studied to

be achievable by introducing grain boundaries of length scales around 10nm without influencing the

carrier mobility since the mean free path is estimated to be around 1-2nm.

They are cheap, non-toxic and they are stable in air up to 1023K. Moreover they have

properties such as large Seebeck coefficient, low resistivity and high oxidation resistance, which

render them suitable for a variety of applications including the field of thermoelectric power

generation55. M. Saleemi et al56 reported an increase in the HMS performance by inclusion of

Ytterbium (Yb) Which creates nano-inclusions at the grain boundaries, While D.Y. Nhi Truong et al57

in recent work have shown that through the wet milling procedure the both the electrical resistivity

and the thermal conductivity can be significantly reduced by achieving finer initial particles. The use

of a liquid medium during high energy ball milling is well known to prevent welding between particles

during collisions, and decrease the final particle size. According to their measurements, the sample

prepared by wet milling shows a better thermoelectric performance, with 20% higher Seebeck

Figure 15: Example of chimney-ladder structure of HMS.31

31

coefficients, 23% lower electrical resistivity, and 30% lower thermal conductivity than the one

synthesized by dry milling for the whole temperature range.

There is a variety of methods found in literature to synthesize HMS. Alloying and SPS, Solid

phase reaction, sputtering, reactive deposition epitaxy, chemical reaction, ribbon-growth-on-

substrate (RGS) technology. In general the production methods for bulk HMS can be split into two

main categories: Melting process, and Solid state reaction. For the first method the main challenges

are the high melting points of the manganese and silicon compounds as well as maintaining the correct

composition in order to minimize the creation of secondary phase monosilicided MnSi which study

results indicate to be detrimental to the overall performance. However the procedure is quite straight

forward and fast and when optimized the results can be adequate for application58. The solid state

reaction lowers the initial energy consumption needed and usually offers a more consistent and

homogenous end product. However the conditions required for mechanical alloying are quite tough

and they involve high ball to powder ratio, high rotation speeds and long time for the milling process

which may require up to weeks. One of the biggest challenges is loss of product in the form of powder

accumulation on the walls of the containers which could in turn lead to stoichiometric errors.

One way of enhancing the power factor of these materials is to introduce metallic compounds

into the HMS compounds. By doing so the thermal conductivity of the end product is reduced due to

phonon scattering on the metallic inclusions56. Moreover the carrier concertation can be tuned in the

same manner.

Intermetallic n-type compounds of Mg2X (X=Si, Ge, Sn) have been considered as candidates

for high performance thermoelectric materials in for the medium-high temperature range 500-800K.

In comparison to other thermoelectric materials in the same range of application such as PbTe and

CoSb3, Mg2X compounds score high in competitiveness not so much due to their zT value, which

achieves average high values, but more due to the abundancy and non-toxicity of the comprising

elements as well as the well-established means of fabrication which render them antagonistic cost

wise. Moreover partial substitution of Si1-z with z-amount of Snz has been shown to drop the thermal

conductivity significantly and thus increasing their figure of merit59. Recently H. Ning et al60 have

shown that by creating a less dense magnesium tin silicide element via pressure-less SPS they were

able to further enhance the low to medium temperature performance of the material (zT~1.6) due

to an increase of the Seebeck coefficient and concomitant decrease of the thermal conductivity while

the resistivity was only slightly increased due to the porosity. In another high performance example,

Weishu Liu et al18 achieved peak zT of 1.4 at 723K for n-type Mg2Sn0.75Ge0.25 through ball milling and

hot pressing method. The Mg2Sn1-xGex system increases phonon scattering and the Seebeck

coefficient while the decrease in carrier mobility sets the peak performance limit and determines the

optimal composition.

Manganese silicide is quite sensitive to the formation of MgO. In a recent case study Johannes

de boor et al,61 denote the deterioration of the performance of Mg2X compounds due to the formation

of MgO phase which is enhanced as a result of an increase of the surface/interface area in ball milled

samples (since MgO is formed at the grain boundaries). The message of this observation is that upon

treatment of a material in order to decrease the size of the grains in order to enhance phonon

scattering, one should be aware of insulating secondary phases, which upon formation diminish the

electronic properties of the final compound.

32

5.2. Chalcogenides

Metal chalcogenides such as lead and bismuth based selenides and tellurides have been

showing better and more reliable performance compared to other TE materials. Commercially

available modules have zT values of around 1 while values up to 3 have been achieved in the laboratory

via nanotechnology, chemical doping and electronic structure engineering.

5.2.1. Lead Chalcogenides

Lead chalcogenides are compounds of lead Pb with Sulphur S, selenium Se and tellurium Te.

They form a narrow bandgap semiconductor with Eg at room temperature in the range of 0.3-0.4 eV

and they are recognized for their performance in optics and thermoelectrics. Lead is one of the most

used elements in thermoelectric material research, due to its abundance its ease of processing and its

inherent low lattice thermal conductivity due to its heavy atomic weight. PbTe has the best

thermoelectric properties of the Chacogens and it has been used commercially for a couple decades

already. Its crystal structure is rocksalt-type (Face centered cubic). As-grown it is always p-type due to

the naturally occurring Pb vacancies however non-stoichiometric compounds can switch to n-type of

carriers. (Pb-rich compounds are n-type while Te-rich are p-type). Its high melting point, above

1150K, permits a high performance in the mid-high temperature range (500-900K)62.

Doping PbTe with halogens produces donor centers that can greatly increase its electrical

properties. Such doping can be achieved via PbCl2, PbBr2 and PbI2. Other n-type doping agents such

as Bi2Te3, TaTe2, MnTe2, when added to PbTe, they substitute Pb atoms and thus create uncharged

vacant Pb-sites. These vacant sites are subsequently replenished by atoms from the lead excess. The

valence electrons of these vacant atoms are free to diffuse through the crystal, since they are not

involved in the formation of chemical bonds. On the other side p-Type doping agents such as Na2Te,

K2Te, Ag2Te can be used to replace Te-atoms and similarly induce empty uncharged Te-sites. These

sites are then Re-filled by Te atoms which when ionized they create additional positive holes. The final

free carrier concentration (electron or hole) in PbTe is the sum of the electrons or holes originating

from Pb or Te in solution plus the electrons or holes introduced by the donor or acceptor species 63.

One of the highest figure of merit values to date zT of 3 at 550K, has been reported by Harnan

et al64 for PbTe/PbTeSe quantum dot superlattice grown by Molecular Beam Epitaxy (MBE). While

for bulk p-type Na-doped PbTe and n-type I-doped PbTe, zT was risen to 1.5 and 1.4 at 750K,

respectively65. The largest lattice thermal conductivity reduction followed by an increase of the zT

factor up to 2.2 at 915K was achieved for powder processed and SPS treated p-type PbTe doped with

4% SrTe, 2% Na (molar concentration) by Kanishka B. et al66. Their methodology was to improve the

phonon scattering mechanism in all the relevant length scales, in a hieratically ordered system starting

from atomic-scale lattice disorder to nanoscale endoaxial precipitates to grain boundary formation in

the mesoscale. In principle the hierarchical logic of this method can be applied in any bulk

thermoelectric system. A visual representation of the method is shown in Figure 16.

33

Figure 16: Illustration of the concept of hieratically ordered system66.

In another research by Kanishka B et al67, the focus was to increase the power factor by

chemical doping. A zT of 1.7 was achieved for P-type Na0.02Pb0.98Te0.85Se0.15 at 815 K, and the mobility

increase without simultaneous decrease of the carrier concentration was attributed to the

convergence of the electronic bands. Avoiding the use of rare and expensive Tellurium, n-type PbSe

was obtained via doping with Al by K.Zhang et al68 with a zT value of 1.3 at 850K.

Successful as a thermoelectric material as it may be, the toxicity of lead in combination with

new regulations (inside the E.U), prohibit it from being used in large scale thermoelectric applications.

I.e industrial waste heat recovery units.

5.2.2. Bismuth chalcogenides

One of the most studied and used elemental or simple compound semiconductors for low

temperature TE technology is Bi2Te3. Crystals of Bi2Te3 can be readily cleaved in planes perpendicular

to the trigonal or c-axis. Proceeding towards the c-direction, there are layers atoms that follow the

sequence: Te[1]-Bi- Te[2]- Bi-Te[1] ,repeated until a crystal boundary is reached. Tellurium and bismuth

layers are held together by strong ionic-covalent bonds, leaving no electrons remaining to connect the

adjacent Te[1] layers which are instead bound by weaker van der Waals forces making it easier for the

crystal to be cut at this facet. The compound has a high atomic weight, a low melting point, and a small

Debye temperature. The highest figure of merit is reached when the Seebeck coefficient is around

±200 [𝜇𝑉/𝐾]. It presents a multivalley band structure and thus a density of states dependent

effective mass effective mass significantly larger than the inert mass. The acoustic-mode lattice

scattering is the dominant parameter in determining carrier mobility.

Figure 17: Representative example of the crystal structure of BiTe, BiSe compounds. Bi2Se3 is shown.

34

In order to obtain the required concentration of charge carriers in Bismuth Telluride and its

solid solutions, a certain deviation from stoichiometry is required. This is usually achieved by

introducing an excess of bismuth or tellurium atoms into the melt or by dopant impurities. In the n-

type solid solutions Bi2Te3-Bi2Se3, halogen compounds are used to adjust the carrier concentration

as they replace tellurium atoms in the lattice and donate one additional atom to the conduction band.

For p-type BixSb2-xTe3 the concentration of holes due to the Sb is balanced by introducing Te-atoms

to the native melt.

Bi2Te3 and its alloys with Sb and Se, with a zT of 0.6 at 300 K, have been commercialized and

used in thermoelectric refrigerators. Nanostructured superlattices of Bi2Te3-Sb2Te3 have achieved a

zT of 2.4 at room temperature69. The zT of p-type BixSb2-xTe3 has been increased from 1 to 1.4 by

inducing Sb nano-inclusions during powder metallurgy synthesis70, while for n-type Bi2Te2.7Se0.3, zT

was increased to 0.94-0.9971

In Theoretical studies the zT value of Bi2Te3 thin films of precisely 5 atomic layers of

thickness, can be as high as 7.2 at room temperature72, as an outcome of quantum confinement which

leads to a change of distribution of the valence band density. N-type Bi2Te3 nanowires with uniform

dimensions 8nm where synthesized by Zhang et al73 reaching a zT value of 0.96 at 380K. In theory

nanowires with diameters smaller than 5nm are predicted to be able to yield zT values of 6 and over.

5.2.3. Tin Selenide, Copper selenide and Copper sulfide

Toxicity concerns and restrictions for Pb, cost considerations for Te as well as need for higher

temperature implementation capabilities drive the research for other binary metallic chalcogenide

compounds with respect to thermoelectric performance.

One recent study By Li-Dong Zhao et al74 reports the unexpectedly low thermal conductivity

of SnSe single crystals 0.35 [𝑊/𝑚𝐾], leading to record high zT values of 2.62 at 923K measured

along the b-axis of the crystal lattice of the compound (figure 19). It has to be noted that due to the

anisotropy in the crystal structure the properties are dependent on the measuring direction. Further

theoretical studies75 are found to predict such observations of anisotropic behavior of the compound

and its high thermoelectric performance. SnSe does not have high molecular weight, nor a complex

crystal structure or a large unit cell, therefore these results were unexpected considering the

attributes sought after in novel thermoelectric research.

Copper selenide (Cu2Se) is a binary compound which due to its unique properties is being

studied as a “green energy material” for generation of renewable green energy, initially for efficient

Figure 18: Visual representation of SnSe Crystal lattice.47

35

photovoltaic devices and later for efficient thermoelectric energy conversion. Cu2Se is typically a p-

type semiconductor with an indirect band gap of 1.23 eV while for non-stoichiometry of copper atoms,

x > 0, Cu2-xSe is a p-type electrical conductor with a high Seebeck and its conductivity increases with

decreasing Cu content attributed to an equivalent concentration of holes, as indicated by transport

measurements76.

At room temperature Cu2Se is stable at its monoclinic a-phase with the copper atoms being

localized and not very conductive. The compound undergoes a phase transition into (β-phase)

crystalizing in a FCC lattice (figure 20) at temperatures above 400K where the Cu atoms become

delocalized, with high mobility and behave like an ionic fluid, thus enhancing the conductivity by

becoming a superionic conductor77. The liquid like behavior of the Cu atoms contributes also to a

decrease in the lattice thermal conductivity, with the total thermal conductivity reaching values lower

than 1 [𝑊/𝑚𝐾] at 973K. The maximum zT value reaches 1.6 at that temperature78.

Research and studies up to date indicate that the thermoelectric properties of Cu2Se seem to

rely mainly on the intrinsic structural characteristics of the compound79, since utilizing different hot

pressing techniques does not seem to drastically improve the performance.

Figure 19: Crystal structure of Cu2Se at high temperatures (β-phase)78

Similar to copper-selenide, copper sulfide Cu2-xS presents ionic conduction with freely mobile

Cu atoms at its a-phase which is reached above 700K. This type of conduction is an outcome of the

two ions of copper (I) comprised in the β-phase Cu2S unit cell randomly occupy and the 12 interstitial

sites within the rigid, hexagonal-closed-packed sulfur lattice, with equal probability80. The maximum

reported figure of merit for this compound is 1.7 at 1000K for Cu1.97S 81 , the benefit however being

the grater abundancy and much lower cost of Sulfur against Selenium.

For both compounds there are concerns regarding the diffusivity of Cu when in contact with

the electrodes, as well as the stability of the phases over long term high temperature exposure82,83.

These studies have indicated the formation of cracks and copper whiskers due to the migration of Cu

in the Cu2S sample, while this degradation effect was not observed for CuS and Cu1.8S under similar

stress test conditions. The later compounds however show lesser thermoelectric performance.

Even though the thermoelectric properties and the cost of these compounds are appealing,

results are still at early stage. Further research both on performance and stability is required before a

clearer opinion is formed regarding the suitability of these compounds for thermoelectric applications.

5.2.4. Oxychalcogenide compounds

Oxychalcogenide compounds84 have the general formula RMChO (R= trivalent cation, M=Ag

or Cu, Ch=chalcogen). Among properties such as potential as transparent conducting materials for

36

optoelectronic applications and high-Tc superconductivity in some of them, these materials exhibit a

large peak of the thermopower around 100K, which makes them promising for thermoelectric cooling

applications in the cryogenic temperature range. Research into several materials and compositions

that share similar crystallographic structures aiming to find new superconducting phases or potential

thermoelectric materials, promising High temperature thermoelectric properties where found in ox

chalcogenide materials with parent compound BiCuSeO. With reproducible zT values that exceeded

exceed 1 above 600○C, and room for improvement, this family of materials may be promising for large

scale thermoelectric applications.

Oxychalcogenides [1111] crystalize in a layered tetragonal structure as shown in the figure.

Alternating bismuth oxide (Bi2O2) and copper selenide (Cu2Se2) layers are stacked along the c-axis.

The Bi2O2 layer in non-conductive and acts as the charge reservoir, and the electrical properties of the

materials are mainly directed by the Cu2Se2 layer which comprise of slightly distorted CuSe4

tetrahedra linked by their edges.

Figure 20: Tetragonal unit cell of BiCuSeO.84

The parent compound BiCuSeO has a moderate band gap semiconductor of 0.8 [𝑒𝑉] 85 and it

does not exhibit ionic conductivity. Polycrystalline samples however, usually show a metallic electrical

behavior. Polycrystalline BiCuSeO samples can be easily unintentionally p-type doped if little amounts

of copper vacancies are induced. The synthesis conditions influences the vacancy concentration. For

example, a copper vacancy fraction as low as 10−4 [𝑐𝑚−3] leads to the introduction of

1. 5𝑥1018 [𝑐𝑚−3] holes in the valence band. The Seebeck coefficient and electrical resistivity values

of unintentionally doped BiCuSeO polycrystalline samples are dispersed and dependent on the

synthesis conditions, with mean room temperatures values of the order of 400 [𝜇𝑉/𝐾] and

100[𝑚𝛺𝑐𝑚] correspondingly.

In general the BiCuSeO compounds do not show very high power factor and this is commonly

attributed to the low holes mobility (< 2 [𝑐𝑚/𝑉𝑠]) in optimally doped compounds. However, the zT

reaches high values due to the low thermal conductivity of the compound which is lower than

1 [𝑊/𝑚𝐾] at room temperature and 0.5 [𝑊/𝑚𝐾] at high temperature. These values can be further

reduced by tuning the material grain size down to sub-micrometer scale, or by phonon point defect

scattering when partially substituting Bi with Ba or Sr. It is believed that these values of the thermal

conductivity originate from the weak interlayer bonding, and from the large anharmonicity of the Bi

bonding, due to the lone pair of electrons from the Vb group elements which results in a large

Gruneisen parameter.

Jing Li et al86 investigated the role of Na doping in Bi1-xNaxCuSeO (0.0 ≤ x ≤ 0.02) resulting

in an increased zT value or 0.91 at 923K for x=0.015 due to the enhancement of the hole

37

concentration. From simple valence electron counting, each Na+ atom is expected to induce two

holes.

In conclusion BiCuSeO-based materials are very promising p-type thermoelectrics with an

average zT value that exceeds 1.2 in the medium-high temperature range. Although this zT values is

still lower compared to the nanostructured PbTe based materials, they are lead-free, which is an

advantage for large scale applications, taking into account European Union regulations. Moreover,

from a material-cost point of view, due to the absence of tellurium, BiCuSeO precursors are 50% less

expensive than PbTe precursors.

A fast way of synthesizing BiCuSeO based materials at room temperature in the form of single

phase nanocrystalline powder has been shown to be possible via Mechanical alloying87. The samples

fabricated this way do not show degradation of properties compared to the conventional synthesis

approach. The powders can later be densified using SPS.

5.3. TAGS and LAST Compounds

The acronym LAST is used for compounds containing Pb, Ag, Sb, Te, with the general formula:

AgnPbmSbnTem+2n also encountered as LAST-m. These compounds have a NaCl-like structure with the

elements Ag, Pb and Sb disordered in the structure on the Na-sites while Te occupies the Cl-sites. In

general the AgnPbmSbnTem+2n materials are derived by isoelectronic substitution of Pb2+ ions for Ag+

and Sb3+ in the lattice. The substitution generates local distortions both in the structure and in the

electronic behavior, which are critical in determining the properties of the end material. In a research

by M. G. Kanatzidis88 two variations of the n-type compound where explored: LAST-10 and LAST-18

with the later exhibiting a high thermoelectric figure of merit of 2.1 at 800K.

Similarly the acronym TAGS stands for alloys containing elements Te, Ag, Ge, and Sb. They

are alloys between compounds AgSbTe2 and GeTe and structurally they resemble Lead-Telluride since

the solid solution has partially the same sodium chloride structure. The compounds are subjected to

a phase transformation when the concentration of GeTe becomes lower than 80%. Close to this phase

transformation the figure of merit is higher and this effect is attributed to lattice strains affecting the

lattice thermal conductivity. TAGS-85 (85%GeTe) gives a zT value of 1.4 at 750K, associated to a

minimum in the thermal expansion coefficient and the minimum lattice parameter, even higher

values for zT=1.7 at 700K have been reported for the AgSbTe2 alloy that contains 80% GeTe,

however this composition shows inferior mechanical strength.

The use of Silver, Germanium and Tellurium renders these compounds significantly expensive

for large scale commercial use. A thorough cost/performance evaluation over time of use is needed

in order to decide upon large scale application.

5.4. Skutterudites

Binary skutterudites89, based on the mineral 𝐶𝑜𝐴𝑠3 have the general formula 𝑇𝑋3 (T = Co, Rh,

or Ir and X = P, As, or Sb), forming intrinsic nanoscale cages in their crystal structure brought about by

corner sharing TX6 octahedra. Structurally they form a Body Centered Cubic Crystal with low Laue

Symmetry as characterized by Oftedal for binary CoAs3. The unit cell reveals a three dimensional As-

Metal framework (As in sites 24 g), Co-atoms are enclosed at the centers of tilted As-octahedra (sites

8c) and a vast icosahedral space (in sites 2a) for the inclusion of atoms as fillers. A large variety of

38

compounds and solid solutions can be derived from this structure type. The filled skutterudites, such

as YbFe4Sb12 shown in figure 22 have a structural chemical formula EPyT4X12, where EP is usually an

electropositive element species enclosed by the cage structure formed by the pnicogen atoms X, and

transition metals T, at the octahedral centers52.

In the medium to high temperature regime of application Skutterudites show very promising

features. With respect to thermoelectric research CoSb3 has received significant attention. It has a

band gap of 0.2 eV, high carrier mobility and the composing elements are relatively inexpensive and

environmentally benign. CoSb3 binary component however has high thermal conductivity and in turn

low conversion efficiency due to low zT value.

Figure 21: Elemental composition and structural characteristics of filled skutterudites.52

The electronic structure of the host lattice is tunable either by chemical substitution in the T-

site or by the nature of the guest EP-atom and its filling level. Depending on the electron concentration

tuned by chemical substitution and filling level (in general fillers are effective n-type dopants, with the

exception of iodine which acts as an electron acceptor), filled skutterudites solutions may change from

an n-type to a p-type semiconductor. Due the variety of combinations, a wide range of physical

properties can be found within the Skutterudites such as heavy Fermion superconductivity in metallic

systems, Kondo scattering, intermediate valence when involving unstable electronic configuration of

rare earth elements, strongly correlated electrons, or hopping conductivity, metal to insulator

transitions, pronounced crystal field splitting, and long range magnetic ordering.

Filler atoms are studied to be loosely bound to the Sb host atoms in the nanocages, thus

leading to Einstein-like vibrational modes and large atomic displacement parameters that scatter

phonons and can significantly reduce the lattice thermal conductivity. Studies and DFT calculations

have shown that frequencies of the phonons blocked are dependent on the resonant frequencies of

the fillers, thus suggesting that by carefully selecting different fillers and defining their filling

concentration, there is interaction with a broader phonon spectrum leading to further reduction of

the lattice thermal conductivity90. Partial replacement of Co atoms with Fe atoms is also an effective

way of reducing the thermal conductivity91.

The filler atoms are believed to have minimal influence to the conduction band edge and the

density of states near the Fermi level and therefore to not alter the transport properties significantly,

the latter being mainly confined to the Co-Sb framework. However, they do significantly increase the

total carrier concentration, which is predominantly determined by the filling fraction and the ionic

charge state of the fillers90. In several studies it was repetitively observed that when 0.5 electrons per

39

unit cell are introduced into the conduction band, the filled skutterudites reach their maximum power

factor92.

The general approach of synthesizing Skutterudite thermoelectric materials is through

densification via SPS or hot pressing after optimizing the elemental composition and grinding the

elements into powders. As an example J. Q. Guo et al91 were using pure >99% metals Sb, La, Yb, Al,

Ga, In, Ti, Ba and Ca, as the raw materials to synthesize the p/n-type skutterudites. The materials are

held in high temperature in a vacuum quartz tube, then grinded to powders with sizes <150 μm and

sintered to pellet form by SPS. One of the important observations was that the thermal conductivity

was significantly lowered upon the addition of Ga, and Ti, increasing the zT to 0.75 for p-type

La0.7Ba0.1Ga0.1Ti0.1Fe3Co1Sb12 moreover the addition of Al, Ga, and In enhanced the zT value

Yb0.3Ca0.1Co3.75Fe0.25Sb12 from 0.65 to 1 for Yb0.3Ca0.1Al0.1Ga0.1In0.1Co3.75Fe0.25Sb12 in the same

temperature.

In recent work Rogl et al93, focused not only in increasing the zT figure of merit , but also in

using Ni as a cheaper alternative instead of Co and in finding the right balance in the thermal expansion

coefficient of both p-type and n-type filled skutterudites. Both are crucial steps towards upscaling

module fabrication and enhancing stability. n-type Ba0.09Sr0.02DD0.22Yb0.02Fe2.4Ni1.6Sb12 and P-type

Ba0.15DD0.28Yb0.05Fe3NiSb12 were found to have average zT values of 0.9 and 0.8 in the temperature

range 400-700K thermal conductivities of 1.7 [𝑊/𝑚𝐾] and 2 [𝑊/𝑚𝐾] and almost identical thermal

expansion coefficients of 11.9 and 11.8 [x10-6K-1] in correspondence, rendering them a viable option

for a module approach. In later work form the same group94 demonstrated an increase from zT of 1.1

to 1.3 at 775K for p-type DDy(Fe1-xCox)4Sb12 and from zT 1.0 to 1.6 at 825K for n-type

(Mm,Sm)yCo4Sb12 by tuning of the grain size , which result in corresponding max-efficiencies (300–

800 K) of η > 13% to η≈16%, respectively.

Scaling up and commercialization Skutterudite thermoelectrics is hindered by the scarcity and

cost of the constituent elements when the more exotic variations are considered. However the more

abundant elemental varieties of skutterudites look promising for the future of thermoelectric

applications. In a recent publication, Yinglu Tang et al95 , focused on the use of Cerium (Ce) as an

alternative , relatively abundant and thus less costly rare earth element as a single filler element in n-

type CexCo4Sb12 Skutterudite. They used higher annealing temperatures to increase the filling fraction

limit of Ce-CoSb3 and the optimized sample with composition Ce0.17Co4Sb12 reached a zT value of 1.3

at 850K (zT>0.9 between 600 – 850K) and thermal conductivity of λ≈3.1 W/m*K. Their results are

comparable with those of the more expensive Yb filled compounds which proves that this could be a

step towards lowering the cost of High zT Skutterudites.

In studies by J.R. Salvador et al.90,96 conducted a complete evaluation on filled Skutterudite

thermoelectrics, starting from the material synthesis and characterization proceeding to densification

and pellet formation and then to module fabrication. They report a reproducible, within sufficient

accuracy, scaled up method of synthesis of n-type Yb0.09Ba0.09La0.05Co4Sb12 and p-type

Mm0.28Fe1.52Co2.48Sb12 up to 3 kilograms through composition matching and melting procedures. The

materials where then grinded to powder and subjected to SPS under the same conditions forming

cylindrical pucks which were sliced into 4mm thick wafers. A thin metallic layer was applied to both

sides of the wafers to act as a diffusion barrier preventing the antimony from directly reacting with

the metallic interconnections that connect the p-n legs. Two types of modules where created one with

no extra filling in between the legs and one with aerogel filling concluding that the encapsulated

version performed better both in the power output and degradation tests.

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5.5. Thermoelectric half-Heusler compounds

The so-called Heusler compounds were discovered in 1903 by Fritz Heusler and have in

general the elemental formula X2YZ. The half-Heusler (HH) compounds are a variant of the Heusler

compounds with the elemental formula XYZ and are among a few materials that are semiconducting

despite containing exclusively metallic elements HH materials consist of three interlaced face-

centered cubic sub-lattices. Many of the compounds have narrow band gaps, suitable for

thermoelectric properties. The structure of HH compounds promotes the possibility to dope each of

the three occupied fcc sublattices individually in order to optimize the thermoelectric properties. For

example, by doping on the Z position it is possible to alter the number of charge carriers while

concomitantly reducing the thermal conductivity through disorder and mass fluctuations introduced

by doping X and Y positions52.

So Far HH compounds are known to have high power factor as a combined result of high

Seebeck coefficient and high electrical conductivity. The thermal conductivity values however still

remain high against other material candidates in thermoelectric research.

Research is mainly focused in both n-type and p-type intermetallic compounds with

elemental formula XNiSn and XCoSb respectively with (X=Ti,Zr,Hf). In these systems, a typical

approach it to optimize the conductivity by altering the number of charge carriers with doping on the

Z-site (Sn and Sb), while simultaneously introduce disorder to influence the lattice thermal

conductivity by isoelectronic alloying on the X and Y -sites97. Those compositions display potential for

high zT values if as discussed, the thermal conductivity is radically reduced, currently it is in the order

of 10 [W/m*K].

In a recent review paper on Half-Heusler Thermoelectrics by Jan-willem G.Bos and Ruth A.

Downie98, it is argued that due to the enhanced doping potential for the HH-compounds enhancement

of the power factor can be achieved relatively easy and zT values close to unity where possible without

significant reduction of the thermal conductivity. If however values down to 1W/m*K for the thermal

conductivity are achieved while maintaining the optimal electronic properties the zT can be boosted

to values above 2.

Figure 22: Structural characteristics of HH materials. They can be formed by combination of the different elements from the periodic table in accordance to the color coding52.

41

Reduction of the thermal conductivity to values of 2-3 W/m*K for HH compounds has been

linked to multiphase behavior for samples with mixtures of Ti, Zr and Hf, note that all three elements

had to be present in the sample to achieve the optimal enhancement. Although the mechanism of the

reduction is not clearly explained, it is believed that it is and effect of strong alloy scattering of

phonons. zT value of 1.2 at 830K was achieved for n-type Ti0.5Zr0.25Hf0.25NiSn underlining the

importance of phase separation towards the enhancement of the thermoelectric properties99. A zT of

1 at 873 K was possible for n-type Hf0.75Zr0.25NiSn0.99Sb0.01 via mechanical reduction of the grain

size100. For p-type HH compounds a zT of 0.45 at 850 K for TiFe0.15Co0.85Sb101.The highest zT achieved

in literature was 1.5 at 700K for n-type Ti0.5(Zr0.5Hf0.5)0.5NiSn0.998Sb0.002 by alloying and carrier

doping.

Half-Heusler compounds are usually prepared by conventional solid state methods involving

arc-melting and annealing at high temperatures for an extended period of time. One possible step

towards upscaling quickening the synthesis of the HH compounds was indicated by Christina S. Birkel

et al102, by using microwave assisted preparation of TiNiSn and TiCoSb. The TiNiSn samples prepared

this way also showed an enhancement in the zT compared to the same samples synthesized with the

conventional methods. For the TiCoSb however the zT was lower due to the presence of a metallic

second phase.

HH-compounds already fulfill fundamental industrial demands for TE materials, i.e.

environmental-friendliness, low cost and availability of raw materials, industrial scale manufacturing

and chemical and mechanical resistance at high temperatures. Since research however is quite novel

the long-term stability and long term chemical and mechanical resistance at high temperatures have

to be thoroughly studied before considering device production52.

Half-heusler based thermoelectric module fabrication, long term stability measurements and

performance reproducibility has been performed by K. Bartholome et al103. They focused on large

quantity production, thus without using the most optimized compositions or nano-interventions to

have an overview of the performance. The materials used were Zr0.4Hf0.6NiSn0.98Sb0.02 (n-type) with

peak zT 0.7 and Zr0.5Hf0.5CoSb0.8Sn0.2 (p-type) with peak zT 0.5 and they were produced in kilogram-

batches. The conversion efficiency and ZT value of the module were determined by simulations,

resulting in a maximum efficiency of 5% and a mean ZT value of 0.44 at ΔT = 500K.

5.6. Cobaltite-Oxides

Metal oxides are ionic compounds consisting of metal cations and oxygen anions alternately

paced and held together via attractive Coulombic interaction between them. In such ionic compounds,

the charge carriers (electrons or holes) polarize the surrounding crystal lattice by strongly interacting

with it, localizing themselves on the lattice points while inducing lattice distortion and limiting the

overlap of the atomic orbitals. Transport of such localized carriers known also as small polarons, is

done by a hopping mechanism accompanied by the surrounding lattice distortion. Due to this

transport mechanism results in carrier mobility values much lower than that for the band conduction

in the range of 1 − 0.1 [𝑐𝑚2/𝑉𝑠]. These attributes result in a stronger coupling of the three factors

(electrical conductivity, thermal conductivity and Seebeck coefficient). The mean free path of phonons

in oxides ranges between 0.2-2nm and thus, for effective phonon scattering to be achieved,

patterning and nano features induced in the materials should be of comparative length scales.

Initially oxides where believed to be inadequate as thermoelectric materials due to low

motility values. However they have other inherent properties that render them a good candidate for

42

thermoelectric material research. They are non-toxic and environmentally friendly while attributes

such as large thermal and chemical stability allow for their application over a wide temperature

gradient in air environment. Due to the large temperate gradient tolerance not only a high Carnot

efficiency and can be achieved but also, nonlinear, nonlocal TE effects (such as the benedicks effect)104

may me induced, playing also a positive role towards the thermoelectric potential.

Moreover oxides can be chemically adaptive and structurally complex which makes them

suitable for nanoscale material engineering both in aspects of composition and structure. Finally they

can be found in abundancy in nature thus radically decreasing the cost of raw material. Although the

evaluated zT values of the researched oxides are still lower that of state of the art thermoelectric

materials, the positive factors mentioned previously indicate that research on oxides from the

thermoelectric point of view is certainly worthwhile2.

Cobaltite-oxides and more specifically NaxCoO2 and Ca3Co4O9 as well as variations with

different dopant elements105-107 have been reported to yield significant thermoelectric properties

reaching zT values that exceed unity2. Research on cobaltite oxides is also focused on epitaxially grown

single crystal thin films If those performance values can be confirmed through further testing and

reproducibility these two materials can be probable candidates for the next generation high

temperature thermoelectric applications.

Thermoelectric properties of cobaltite oxides have been also researched in high quality

epitaxial thin film form i.e.108-112 grown on different crystal substrates, in an attempt to study the size

effects due to different lattice induced stress, in combination with the interface boundary formation.

The concept is that the electronic transport properties and the high Seebeck coefficient are retained

as high as in single crystals due to the high quality epitaxy while the thermal conductivity can be

influenced due to phonon scattering at the interface boundaries.

43

6. Short overview of fabrication and shaping techniques

Intrinsically low-dimensional structures achieved in thin films, membranes and nanowires can

be mainly used in micro-systems applications. High zT thermoelectric nanomaterials turned into bulk

form broaden the options of applicability and the effectiveness of the modules as well as decreasing

significantly the complexity of implementation approaches and system design.

6.1. Upscaling material fabrication – nanobulk materials

As investigated in the previous chapter, there is significant ongoing research on all the

thermoelectric material families, and in the lab-scale and under academic perspective there is

undeniable progress in increasing the materials thermoelectric performance. This outcome is

dependent upon the scientists better understating of the means to influence the material properties

that enhance the figure of merit z, as well as on the improvement of the tools (equipment) that enable

such level of tweaking.

However, even though the desire for higher performing thermoelectric materials is being

progressively fulfilled, one of the major limiting factors towards application of thermoelectric

technology is upscaling the fabrication process of the improved materials in such a way that they

retain the fundamental changes which lead to the enhancement of their performance. In this chapter

there is an outline of fabrication methods which look promising for the fulfillment of this goal. One

way to differentiate the methods is to split them into two categories: 1) The physical approach “top

down methods” 2) The chemical approach “bottom up methods”

6.1.1. Melt Spinning (MS)

Typically thermoelectric materials are a combination of two or more elements. In the MS

method all of the constituent elements are held in their liquid form above their melting temperatures

before being mixed and rapidly cooled down to room temperature in a quenching process, ideally

resulting in uniform phases of the mixed components. As such, it is crucial for every element involved

that their solid- liquid phase transition diagrams are well studied and understood. Due to the rapid

temperature change, there is limited crystal growth and formation uniformly sized grains.

The melt is spun out of the heated chamber in a ribbon formation and onto a spinning

cylindrical surface where the cooling procedure is carried out. The “quenching disc” which is internally

cooled by appropriate coolant mediums and is maintained in an inert atmosphere (e.g. argon) to avoid

oxidation effects on the end product. The cooling rates is this procedure can reach 106K/s.

Since there is always material in contact with the cooled surface and material that only faces

the inert ambiance the cooling rate varies. Microstructure formation and degree of crystallinity in the

product is dependent of the position of the melt on the disc and in the chamber and the temperature

gradients attributed to this relevant position. Therefore microstructural and crystalline variations are

to be expected even within a single specimen. A densification method like Spark Plasma Sintering (SPS)

typically follows in order reach the final density requirements for the ready-to-use thermoelectric

material.

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6.1.2. Ball Milling

In this method the constituent materials are put in bulk form inside a container, usually made

from cemented carbide material, together with steel crusher-spheres. Depending on the type of

movement that the container and the enclosed parts undergo, there are variations of the milling

process e.g. vibration, rotation, planetary and attrition ball milling. In these processes the bulk

material is mechanically crushed and milled until it reaches a fine powder form. The final size of the

powder particles depends on the duration of the milling and on the size of the spheres. In some cases

the composition of the powder also contains traces of the material that the crushers are made of or

even material from the container walls. If the portion of these traces over the milling time can be

accounted for then the wall-crusher material could be chosen (or coated) in relation to the wanted

end product composition.

The fine powder resulting from such a process usually contains random crystallites originating

from the bulk material, unless it is a single crystal. The powder then is treated with a densification

method e.g. Hot Pressing to form the usable bulk material. The density and the nanograin formation

in the bulk Depend on the pressure, temperature and duration of the Hot Pressing process, as well as

the mean particle size of the milled powder. Thermoelectric materials produced with this method are

usually referred to as “random nanostructured bulks” due to the random crystalline orientation of the

nanograins.

6.1.3. Spark erosion

Spark erosion113,114 is a method of producing nanoparticles with well-defined sizes in the order

of a few tens of nanometers. It involves a charged capacitor attached to electrodes of any conductive

starting material separated by a sufficient predefined distance and contained in dielectric liquid, along

with bulk pieces of material (of identical composition as the electrodes). The dielectric liquid is chosen

in accordance to the materials fabricated to prevent effects such as oxidation. An electric field is

applied across these two electrodes and when it exceeds the dielectric breakdown field, the capacitor

discharges producing a spark (micro-plasma) between the elements involved. The micro-plasma

formed consists of electrons and positive ions and its temperature is in the order of 10000K. The

kinetic energies of the faster electrons and slower ions are deposited on localized regions where the

spark was initiated, superheating them and causing them to boil. When the spark collapses, vaporized

alloy and molten droplets are violently ejected from the boiling regions and propagate through the

plasma region into the dielectric liquid where they are subjected to a fast cooldown. A screening sieve

is placed between the bulk initial materials and the particles collection region in order filter out

particles above a certain size limit.

The production yield and rate, and the size distribution is dependent on the operating

conditions such as the pulse power characteristics, the properties of the dielectric liquid and the

constituent material of the electrodes and charge. Renkun Chen115 has reported production of

thermoelectric magnesium silicide nanoparticles of 20nm at a yield of 5g/hour in a lab scale

apparatus. While P K Nguyen et al.113 reported fabrication of Bi0.5Sb1.5Te3 nanoparticles with a size

range of 20-50nm at a yield of approximately 135g/hour in a similar scale apparatus. The

nanocomposites where later densified into pellets and their thermoelectric performance was found

to be improved.

45

One of the main advantages of this method is that it does not involve mechanical processing

of the materials. This way the contamination ratio can be greatly reduced, the size is more refined and

it allows for processing of more ductile materials i.e. silicides which would otherwise be prone to

issues of plastic deformation.

6.2. Thermal Processing Techniques

These techniques begin with the compounds sealed in ampules where they are thermally

11treated under inert atmosphere. The choice of materials for such processes is based upon the

solubility between the constituent liquid phases. The element with the higher melting point composes

the major phase while the materials with lower melting points create the minor phases also called

precipitates. Rapid cooldown of the liquid phases and often further treatment of annealing steps result

in nanoscale precipitates of the minor phases being embedded in the major bulk phase. The nanoscale

precipitates act both as carrier donors and as phonon scatterers.

Another method that falls under this category is spinodal decomposition. Metastable solid

solutions of two different phases are created via phase segregation while nano-structuring occurs due

to nucleation and growth.

The aforementioned fabrication techniques even though they upscale production while

maintaining nanoscale features in the bulk end product, they do not allow for precise control of their

size or composition. Another disadvantage is that with these methods it is difficult to establish a

standardized set of rules to achieve specific material compositions.

These limitations can be shifted in the “Bottom up” chemical fabrication techniques. These

methods allow for more precise reproducibility, grater scalability and control of the grain sizes and

distributions while simultaneously being more cost effective. Moreover through chemical synthesis a

greater variation of chemical compositions can be studied, thus enabling better control of the carrier

concertation through more accurate doping. In general, chemical synthesis methods achieve

enhanced homogeneity at the nanoscale via manipulation of matter at the molecular level. The

crystals synthesized via these processes are then densified to form the usable TE material.

6.2.1. Solution phase synthesis

Direct chemical precipitation

Commonly in such processes ions of the desired materials which are held in separate solutions

are mixed into an insoluble compound that precipitates from the reaction medium in solid form. The

precipitate is then collected after thorough washing. For the direct precipitation reaction the chemical

components must be soluble in the solvent while the rate and efficiency of the reaction is dependent

on the solubility rules of the reactants. Since such reactions typically occur in water solutions the

reaction temperature can be low and the yields can be very large reducing the production costs. The

size of the crystals synthesized, varies from 5nm to 1μm.

For the fabrication of binary systems only one anion-cation combination is required, while for

doping and for ternary or quaternary systems the reaction becomes more complex. The type of

reactant solution and the pH regulate the reaction product and duration of the synthesis as well as

tune the size of the crystal growth. Thermoelectric materials including oxides, tellurides, selenides and

sulfides can be synthesized this way. No capping molecules are used to limit the growth of the crystals

46

in this method thus purification treatments or annealing processes are redundant, and the product is

ready for densification after collection.

Emulsion process

In such processes, two immiscible liquids are put together forming a continuous and a

dispersed phase since they cannot be mixed. A colloidal solution is formed which can be used as a

nanoreactor. When the solution is left to rest, two constituent phases commonly form like “oil in

water”. Using a surfactant compound, (usually organic molecules containing both hydrophobic and

hydrophilic ligands) the interface between the two phases is stabilized to droplets in the form of

microemulsions consisting of isotropic liquid mix of the immiscible phase, the dispersed phase and the

surfactant.

In microemulsion systems, the surfactant molecules with the hydrophilic tails dissolved in the

oil phase and the hydrophobic heads in the aqueous phase, protect the droplets of the dispersed

phase and thus control the size of the nanocrystals. The system forms self-assembled structures of

variable morphologies from spherical and cylindrical micelles to lamellar phases. The size variation is

a product of water/surfactant ratio.

Solvothermal Synthesis

Solvothermal methods typically involve a sealed reaction vessel held in a temperature above

the boiling point of the solvent used (organic or water). The constituent elements of the target end

product are in the form of precursors in the solvent (commonly in the form of nitrate, chloride, oxide

and hydrate compounds). Due to vaporization of the solvent the pressure in the vessel increases at

high rates. The desired product crystallizes at elevated pressures and temperatures. The relation

between precursors and product depends on the types of the precursors, the type of solvent, the

temperature and pressure conditions, and the volume filling percentage of the solvent with respect

to the volume of the reaction vessel. In order for the reaction to continue until completion all the

precursors need to be soluble in the solvent at elevated temperatures

The advantages of this method is that it allows proper mixing of the reagents, it involves stable

kinetic phases, permits control over the particle size, allows incorporation of dopants and is a single

step procedure. This method has been used for fabrication of nanocrystals of metals, oxides,

tellurides, sulfides, selenides and nitrides with sizes from 5nm to 100nm in large yields.

Polyol Process

An environmentally friendly method occurring at low temperatures. The reactions are taking

place in polyalcohol, or polyol solutions which due to their high boiling points tend to result in products

with higher purity and more monodispersed. The polyols as solvents effectively act as bidentate

chelating agents for the solvated metal cations while simultaneously play their part as limiting and

stabilizing agents once the produced nanoparticles are precipitated. Further control of the size and

shape of the crystals produces can be achieved by the addition of strong reducing agents. Gram scale

synthesis of thermoelectric materials can be achieved this way in a single batch.

47

Organometallic synthesis

Organometallic synthesis is one of the most efficient synthesis methods in terms of controlling

the size of the crystals produced. The production of monodisperse colloid particles is a combination

of coordinated nucleation event followed by slower controlled growth on the created nuclei. By

rapidly adding the reagents to the vessel the precursor concentration is risen above the nucleation

threshold and nanocrystals begin to grow. The size distribution of the crystals is dependent on their

growth rate in combination with the rate of consumption of the reagents. All the nanocrystals grow

at the same rate, therefore the initial size dispersion is mainly determined by the time in which nuclei

are formed and begin to grow. The more homogeneous the initial particles, the more uniform the

nanocrystals will become over the time of growth.

For semiconductor nanocrystals the supersaturation and fast nucleation event can be enacted

by rapid injection of metal-organic precursors into a vial containing the coordinating solvent in the

desired temperature while it is being stirred.

The main drawbacks of this method is that the yields are still limited and single batches are

not enough to proceed to bulk specimen formation, and that the organic ligands remain adhered to

the nanocrystals and are difficult to be removed and are detrimental to the electronic conductivity of

the material. Since however the fine control over the size distribution or the crystals is highly

important in tuning the thermoelectric properties of materials this method can prove to be very

important provided that removal of the organic ligands and sufficient upscale in fabrication is

achieved.

6.3. Powder to Bulk Densification Methods

Fabricating and controlling the micro and nanostructures of the thermoelectric compounds in

the form of fine crystalline powders able to be produced in sufficient yields, is the first step towards

manufacturing bulk thermoelectric materials with nano-features and the benefits that are associated

with that. The second step is to densify the fine powders into polycrystalline specimens without losing

the nanoscale features.

In traditional densification techniques the grain to grain contact is enhanced through use of

static pressure and consecutive sintering of the pressed powders at high temperatures, in order to

obtain dense bulk materials. Small grain powders with high surface to volume ratios usually take

considerable sintering time which in turn promotes grain growth. Grain growth is also promoted at

elevated temperatures. It is therefore important that the right densification method is selected in

accordance to the compounds when preparing TE materials with nanoscale domains. The widely used

densification methods are Cold Pressing (CP) and annealing, Hot Pressing (HP), and Spark Plasma

Sintering (SPS).

Cold Pressing and annealing

One of the simplest and most straight forward methods to densify powdered thermoelectric

materials is to compact them inside a die and punch assembly by applying uniaxial pressure. Since the

pressing takes place at room temperature the pellets formed are not sufficiently dense an annealing

process follows in order to increase the contact area between the grains. A drawback of this method

48

is that the pellets are easily subject to cracking and deformation due to the low temperature during

the pressure application.

Hot Pressing

By applying pressure and at the same time heating the powders up to near the materials

melting temperature more dense polycrystalline pellets can be achieved. The heat in the hot pressing

technique is applied by resistors or inductively, from the outside part of the die inwards, towards the

pressing chamber. HP is widely used for compaction TE materials with nanoscale crystal domains. Care

has to be taken however to avoid plastic deformation when the duration of pressure-heating

application is long and to avoid overgrowth of grains.

Spark Plasma Sintering

The SPS technique is similar to the hot pressing with the variation that the heating of the

powder is applied by running direct electrical current of pulses of current through the compressed

material and through the die. This way, contrary to the resistive, inductive HP method the specimen

is heated form the inside as well as the outside. This added internal heating, reduces the need for long

pressing duration and temperatures near melting point and the risk of large grain formation. Ideally

the temperature gradients formed within the specimen are minimal since current passes

homogeneously between all parts. As current passes through the nano-powders, only their surface

temperature rises rapidly allow for more refined control over grain growth. The enhanced control over

the final micro-nano structure of the densified product results in an increase of the thermoelectric

performance.

49

7. Outlook

This essay gave an overview of the concepts of thermoelectric technology for power generation

applications. Focusing on semiconductor material fundamental aspects, considerations and progress

in their research has been accounted for, and state of the art performance has been reported.

Thermoelectric technology is widely researched and applied in long lasting aerospace missions where

material costs and device implementation complexity are not the priority concerns in favor of the

added benefits that this technology offers such as long term stability and reliability.

Concerning terrestrial applications and especially when efficiency in the priority concern, in

order for this technology to be widely applied, there still has to be significant progress towards

upscaling material fabrication and stabilizing performance as well as overcoming large scale device

implementation problems. This progress is essential in order to reach conversion efficiencies that

would drop the power generation costs to a level comparable with other renewables.

For waste heat recovery applications and other low fuel cost scenarios, small116,117 up to

medium118 scale thermoelectric generators are readily available reaching maximum efficiencies in the

order of 10% in the higher temperature stages. Their applicability is being explored for several

systems including vehicle-exhausts119,120, household furnace devices while micro scale thermoelectric

devices are also explored for harvesting body heat121, i.e. thermoelectric watch application has already

been patented122.

Apart from energy harvesting, thermoelectric technology is widely used in cooling systems i.e.

electronic cooling and small portable refrigerators, exploiting the Peltier cooling effect (reverse

Seebeck effect) as well as sensors and thermal control systems. These application concepts

correspond to what was derived in this work with respect to material research, however a separate

study focused on device level aspects would be needed to fully disclose the potentials of

thermoelectric applications.

In conclusion, the potential benefits of thermoelectric technology are many and could be

utilized in a wide range of fields. It is certainly a field worthwhile of further scientific investigation,

especially with state of the art nanotechnology methods and enabling technologies. Even small

increments in conversion efficiencies could unlock the potential for wider applicability and draw more

attention from potential investors.

50

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