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A Review on Fundamentals, Design and Optimization to High ZT of Thermoelectric Materials for Application to Thermoelectric Technology

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Abstract

Thermoelectricity has been proven as a potential technology for the conversion of waste heat into usable electricity. It involves primarily three parameters, namely the Seebeck coefficient, electrical conductivity, and thermal conductivity. However, there are many other interrelated parameters, such as carrier concentration, mobility, effective mass, multi-valley bands, relaxation time, reduced Fermi energy, phonon modes, scattering parameters, and the number of neighbouring atoms in a given structure. The understanding of these parameters is equally important in order to optimize a high figure of merit (ZT). This article addresses the basics of electronic and thermal transport with the help of Boltzmann transport equation, fundamental concepts for the design of thermoelectric (TE) materials, and implementation of several strategies such as alloying, the phonon-glass electron-crystal (PGEC) approach, band engineering and nanostructuring to optimize the ZT of materials, and finally ends with a discussion of the future prospects of heat extraction through different heat sources.

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Fig. 1
Fig. 2
Fig. 3

reproduced from Ref. 57 with permission from Elsevier, copyright 2009”.

Fig. 4

reproduced from Ref. 8 with permission from John Wiley and Sons, copyright 2009”.

Fig. 5

reproduced from Ref. 8 with permission from John Wiley and Sons, copyright 2009”.

Fig. 6

reproduced from ref.97 with permission from John Wiley and Sons, copyright 2017”.

Fig. 7
Fig. 8

reproduced from Ref. 27 with permission from American Physical Society, copyright 2008”. (b) Seebeck coefficient enhancement on addition of SiC in Yb0.3Co4Sb12, InSb in In0.4Co4Sb12, Si in Bi0.4Sb1.6Te3, and ZnO in SnTe. Data from Refs. 115,116,117,118 (b) Power factor enhancement on addition of W in HH, SiC in Yb0.3Co4Sb12, and Sb203 in Bi0.5Sb1.5Te3 as a function of temperature. Data from Refs. 113, 115, 119

Fig. 9
Fig. 10

reproduced from Ref. 135 with permission from the American Chemical Society, copyright 2020”.

Fig. 11
Fig. 12

reproduced from Ref.162 with permission from John Wiley and Sons, copyright 2007”.

Fig. 13

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Abbreviations

ZT :

Thermoelectric figure of merit

\(\alpha\) :

Seebeck coefficient

\(\sigma\) :

Electrical conductivity

T :

Temperature

k :

Thermal conductivity

f :

Non-equilibrium distribution function

r :

Position vector of electrons

k :

Wave vector of electrons

t :

Time

f o :

Equilibrium distribution function

\(\tau\) :

Relaxation time

E :

Electron energy

E F :

Fermi energy

K B :

Boltzmann constant

E :

External electric field

v :

Carrier velocity

e :

Electron charge

n :

Carrier concentration

g(E) :

Electron Density of states

J :

Charge current density

Q :

Heat current density

m d :

Density of states effective mass

\(\hbar\) :

Reduced Planck's constant

\(\pi\) :

Pi

\(\mu\) :

Mobility of carriers

k e :

Electronic thermal conductivity

L o :

Lorentz number

k bi :

Bipolar thermal conductivity

f p :

Perturbed distribution function

f po :

Equilibrium distribution function

k l :

Lattice thermal conductivity

C l :

Lattice heat capacity

l :

Mean free path of phonons

x :

Reduced energy

\(\eta\) :

Reduced Fermi energy

f 1/2 :

Fermi integral of order ½

\(\gamma\) :

Degeneracy of band extrema

V o :

Average volume of a unit cell

f i :

The fraction of unit cells with mass \({\text{M}}_{{\text{i}}}\)

M i :

The mass of a unit cell

M :

The average mass of all unit cells

E g :

Band gap

\(m_{b}^{*}\) :

Single valley band effective mass

N v :

Band degeneracy

T H :

Hot side temperature of TE module

T C :

Cold side temperature of TE module

ZT avg :

Average ZT

m * :

Effective mass

m c :

Conductivity inertial effective mass

r :

Scattering parameter

\(m_{i}\) :

The effective mass of carriers in ith direction

\(g_{ph}\) :

Phonon density of states

q l :

Heat flux

v :

Group velocity of phonons

\(\overline{E}\) :

Energy of lattice vibrations

\(\eta_{TEG}\) :

Efficiency of TEG

\(\check{r}\) :

Position vector of phonons

\(\check{k}\) :

Wave vector of phonons

f :

Planck Distribution function

\(U_{o}\) :

Total voltage of TEG

\(\alpha_{P - N}\) :

Relative Seebeck Coefficient

\( T\) :

Temperature difference between two sides of TEG

I :

Total current in the circuit

R g :

Internal resistance of TEG

R m :

Load resistance

P :

Power output

\(Q_{in}\) :

Inflow heat at hot side of TEG

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Acknowledgments

This work is dedicated to our late, great mentor Dr. D. K. Misra, who passed away recently and who we continue to recognize as a corresponding author of this work. One of the authors AK highly acknowledges the DST-Inspire Fellowship (Grant No. IF180005) for financial support.

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Authors and Affiliations

  1. CSIR- National Physical Laboratory, Dr. K. S. Krishnan Marg, New Delhi, 110012, India

    Ashish Kumar, Sahiba Bano, Bal Govind, A. Bhardwaj, Komal Bhatt & D. K. Misra

  2. Academy of Scientific and Innovative Research (AcSIR), Ghaziabad, 201002, India

    Ashish Kumar, Sahiba Bano, Bal Govind & Komal Bhatt

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  1. Ashish Kumar
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Kumar, A., Bano, S., Govind, B. et al. A Review on Fundamentals, Design and Optimization to High ZT of Thermoelectric Materials for Application to Thermoelectric Technology. J. Electron. Mater. 50, 6037–6059 (2021). https://doi.org/10.1007/s11664-021-09153-7

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