Thermoelectric Materials Thermoelectric devices are based on a phenomenon known as the thermoelectric effect which is the direct conversion of a temperature gradient across two dissimilar materials into electricity. The materials used are known as thermoelectric materials. The thermoelectric effect is reversible i.e. it directly converng electricity into a temperature gradient. The thermoelectric effect is based on a combinaon of two different effects, namely, the Seebeck effect and the Peler effect.

Water/Beer Cooler What is thermoelectricity? Thermoelectricity is the conversion of heat differenals into electricity and viceversa. Thermoelectric energy conversion is one of the direct energy conversion technologies that rely on the electronic properes of the material (semiconductor) for its efficiency. It is based on the Seebeck (Power Generaon) and Peler effects (Heat Pumping). Seebeck Effect In 1821, Thomas Seebeck a German Estonian physicist found that an electric current would flow connuously in a closed circuit made up of two dissimilar metals, if the juncons of the metals were maintained at two different temperatures. If the temperature gradient is reversed, the direcon of the current is reversed. Where S is the Seebeck coefficient. It is defined as the voltage generated per degree of temperature difference between the two points. S is posive when the direcon of the current is the same as the direcon of the voltage The basis of the Seebeck effect is electron mobility in conductors and semiconductors, which is a funcon of temperature When two different metals are joined, the relave difference in electron mobility in each of the metals will make that the electrons from the more “mobile” metal jump to the less mobile metal. A potenal difference is created between the two conductors. In the absence of a circuit, this causes charge to accumulate in one conductor, and charge to be depleted in the other conductor. Example: Type K thermocouple

Measure ? The Seebeck Effect The Seebeck effect is the conversion of heat differences directly into electricity. When two dissimilar materials with different carrier densies are connected to each other by an electrical conductor and heat is applied to one side of the connectors, some of the heat input is converted to electrical current, as the higher energy maer releases energy and cools to a lower energy state. The net work is proporonal to the temperature difference and Seebeck coefficient. The simplest thermoelectric generator consists of a thermocouple, comprising a p‐type and n‐type thermo‐element connected electrically in series and thermally in parallel. Heat is pumped into one side of the couple and rejected from the opposite side. An electrical current is produced, proporonal to the temperature gradient between the hot and cold juncons Explanaon of Seebeck Effect In a thermoelectric material there are free carriers which carry both charge and heat. If a material is placed in a temperature gradient, where one side is cold and the other is hot, the carriers at the hot end will move faster than those at the cold end. The faster hot carriers will diffuse further than the cold carriers and so there will be a net build up of carriers (higher density) at the cold end. In the steady state, the effect of the density gradient will exactly counteract the effect of the temperature gradient so there is no net flow of carriers. The buildup of charge at the cold end will also produce a repulsive electrostac force (and therefore electric potenal) to push the charges back to the hot end. The electric potenal produced by a temperature difference is known as the Seebeck effect and the proporonality constant is called the Seebeck coefficient (α or S). If the free charges are posive (the material is p‐type), posive charge will build up on the cold which will have a posive potenal. Similarly, negave free charges (n‐type material) will produce a negave potenal at the cold end. If the hot ends of the n‐type and p‐type material are electrically connected, and a load connected across the cold ends, the voltage produced by the Seebeck effect will cause current to flow through the load, generang electrical power. α2σ is the materials property known as the thermoelectric power factor. For efficient operaon, high power must be produced with a minimum of heat (Q). κ= Thermal conducvity. The thermal conducvity acts as a thermal short and reduces efficiency.

Peler Effect In 1834, a French scienst Jean Peler found that a thermal difference can be obtained at the juncon of two metals, if an electric current is made to flow in them.

Opposite of the Seebeck Effect. The heat current (q) is proporonal to the charge current (I) and the proporonality constant is the Peler Coefficient (Π). When two materials are joined together, there will be an excess or deficiency in the energy at the juncon because the two materials have different Peler coefficients. The excess energy is released to the lace at the juncon, causing heang, and the deficiency in energy is supplied by the lace, creang cooling. The Seebeck and the Peler coefficients are related to each other through the Kelvin relaonship – T is the absolute temperature.

Π >0 ; Posive Peler coefficient. High energy holes move from le to right. Thermal current and electric current flow in same direcon. Π < 0 ; Negave Peler coefficient High energy electrons move from right to le. Thermal current and electric current flow in opposite direcons.

If an electric current is applied to the thermocouple as shown, heat is pumped from the cold juncon to the hot juncon. The cold juncon will rapidly drop below ambient temperature provided heat is removed from the hot side. The temperature gradient will vary according to the magnitude of current applied. The Peler Effect

When two dissimilar materials with different carrier densies are connected to each other by an electrical conductor, electrical current (work input), forces the maer to approach a higher energy state and heat is absorbed (cooling). The energy is released (heang) as the maer approaches a lower energy state. The net cooling effect is proporonal to the electric current and Peler Effect coefficient. Thompson Effect William Thompson (1824‐1907) also known as Lord Kelvin. He observed that when an electric current flows through a conductor, the ends of which are maintained at different temperatures (gradient temperature), heat is evolved at a rate approximately proporonal to the product of the current and the temperature gradient.

is the Thomson coefficient in Volts/Kelvin

Thompson Effect = Seebeck Effect + Peler Effect

The relaonships between the different effects are called the Kelvin relaonships. First Kelvin relaonship:

Second Kelvin relaonship: Thermoelectric Figure of Merit (ZT) Coefficient of Performance

where

Seebeck coefficient

Electrical conductivity TH = 300 K TC = 250 K Freon Temperature Bi2Te 3

Thermal conductivity Requirements for a Good Thermoelectric Material • General consideraons for the selecon of materials for thermoelectric applicaons involve: – High figure of merit – large Seebeck coefficient α (or S) – high electrical conducvity σ

– low thermal conducvity κLace+κelectrons – Possibility of obtaining both n‐type and p‐type thermoelements. – No viable superconducng passive legs developed yet • Good mechanical, metallurgical and thermal characteriscs – Capable of operang over a wide temperature range. Especially true for high temperature applicaons. – To allow their use in praccal thermoelectric devices – Materials cost can be an important issue!

Minimizing thermal conducvity Thermal conducvity consists of two parts: lace conducvity (lace vibraons = phonons), κLace, and thermal conducvity of charges (electrons and holes), κelectrons:

Currently, most of the research efforts are devoted to minimizing the lace conducvity of new phases.

Some ways to reduce the lace conducvity: (1) use of heavy elements, e.g. Bi2Te3, Sb2Te3 and PbTe; (2) a large number N of atoms in the unit cell: the fracon of vibraonal modes (phonons) that carry heat efficiently to 1/N; (3) raling of the atoms, e.g. filled skuerudite CeFe4Sb12; disorder in atomic structure: random atomic distribuon and deficiencies. The last approach is nicely realized in "Zn4Sb3", which can be called an "electron‐crystal and phonon‐glass" according to Slack. This material has electrical conducvity typical for heavily doped semiconductors and thermal conducvity typical for amorphous solids. In fact, its thermal conducvity is the lowest among state‐of‐ the art thermoelectric materials: Minimize thermal conducvity and maximize electrical conducvity has been the biggest dilemma for the last 40 years.! Bismuth telluride is the standard with ZT=1 to match a refrigerator you need ZT= 4 ‐ 5 to recover waste heat from car ZT = 2

Can the conflicng requirements be met by nano‐scale material design? Reduce the lace thermal conducvity by: •Complex crystal structure of high atomic number materials. •Ralers in the structure (Atomic Displacement Parameter – ADP). •Nanostructured Thermoelectrics Complex Crystal Structures Ralers: These are weakly bound atoms that fill cages. They have unusually large values of Atomic Displacement Parameters Properes of many clathrate‐like compounds can be understood by treang “raler” atoms as Einstein oscillators and framework atoms as a Debye solid. Skuerudites, LaB6, Tl2SnTe5 A Characterisc Einstein temperature (or frequency) can be assigned to each raler

Eu8‐eGa16Ge30 Phase With the Ba8Ga16Sn30 Clathrate Structure Type: a = 10.62 Å X8Ga16Ge30 (X= Ba, Sr, Eu)

Ba Nuclear Density Map at Sr Nuclear Density Center of Large Cage ( 6d site of clathrate structure) Map at Center of Large Cage Tunneling States?

Eu Nuclear Density Map at Center of Large Cage Tunneling States ! ADP Data ( ) From 6d Site Advantages of Disadvantages of Thermoelectrics Thermoelectrics •Absence of moving parts •High cost •High reliability •Low efficiency •Quietness •Typically about 3 to 7% •Lack of vibraons •Low maintenance •Simple start up •No polluon •Small •Light weight •No noise •Precise temperature control: within +/‐ 0.1C Applicaons of Thermoelectric

• Consumer Applicaons

• Automobile Applicaons

• Industrial Applicaons

• Military and Space Applicaons Consumer Applicaons

TE Fridge

Beer Cooler

Chocolate Cooler Automobile Applicaons

Can Cooler Seat Cooler/Warmer Industrial Applicaons

Electronic Cooler TE Dehumidifier Military and Space Applicaons

Night Vision Basic Principles • Macroscopic Thermal Transport Theory– Diffusion ‐‐ Fourier’s Law ‐‐ Diffusion Equaon • Microscale Thermal Transport Theory – Parcle Transport ‐‐ Kinec Theory of Gases ‐‐ Electrons in Metals ‐‐ Phonons in Insulators ‐‐ Boltzmann Transport Theory Basic Principles

Heat is a form of energy. The thermal properes describe how a solid responds to changes in its thermal energy. The heat capacity (C) of a solid quanfies the relaonship between the temperature of the body (T) and the energy (Q) supplied to it. The measured value of the heat capacity is found to depend on whether the measurement is made at constant volume (CV) or at constant pressure (CP). Fourier’s Law for Heat Conducon

Q (heat flow)

Hot Cold

Th Tc L

Thermal conducvity Heat Diffusion Equaon 1st law (energy conservaon) Heat conducon = Rate of change of energy storage

Specific heat

•Condions: t >> t ≡ scaering mean free me of energy carriers L >> l ≡ scaering mean free path of energy carriers Breaks down for applicaons involving thermal transport in small length/ me scales, e.g. nanoelectronics, nanostructures, NEMS, ultrafast laser materials processing… 1 km Length Scale Aircra Automobile 1 m Human

Computer

Buerfly 1 mm Fourier’s law Microprocessor Module MEMS

Blood Cells 1 mm Wavelength of Visible Light Parcle MOSFET, NEMS 100 nm l transport Nanotubes, Nanowires Width of DNA 1 nm D D

Total Length Traveled = L

Average Distance between Collisions,  = L/(#of collisions) Total Collision Volume Swept = πD2 L mc Number Density of Molecules = n Mean Free Path Total number of molecules encountered in swept collision volume = nπD2L

σ: collision cross‐seconal area Number Density of kB: Boltzmann constant ‐23 Molecules from Ideal 1.38 x 10 J/K

Gas Law: n = P/kBT

Mean Free Path:

Typical Numbers: Diameter of Molecules, D ≈ 2 Å = 2 x10‐10 m Collision Cross‐secon: σ ≈ 1.3 x 10‐19 m

Mean Free Path at Atmospheric Pressure:

At 1 Torr pressure, mc ≈ 300 mm; at 1 mTorr, mc ≈ 30 cm Wall

b: boundary separaon

Wall

Effecve Mean Free Path: u: energy Net Energy Flux / # of Molecules u(z+z) z + z  qz θ z through Taylor expansion of u u(z- ) z z - z

Integration over all the solid angles  total energy flux

Thermal conductivity:

Specific heat Velocity Mean free path Fermi Energy – highest occupied energy state: Metal

Vacuum F: Work Funcon Level Fermi Velocity: EF Energy

Fermi Temp:

Band Edge Fermi‐Dirac equilibrium distribuon for the probability of electron occupaon of energy level E at temperature T f

k TB 1 T = 0 K Vacuum Level Increasing T

Occupaon Probability, 0 E F Electron Energy, E Work Funcon, F Number density:

Energy density:

Density of States -- Number of electron states available between energy E and E+dE

in 3D Specific Heat in 3D

Mean free me: Thermal Conducvity te = le / vF

e Electron Scaering Mechanisms Bulk Solids • Defect Scaering • Phonon Scaering Increasing • Boundary Scaering (Film Thickness, Defect Concentraon Grain Boundary)

Defect Phonon Scaering Scaering

Temperature, T Mahiessen Rule:

Electrons dominate k in metals Crystalline vs. Glasslike Thermal Conducvity

P. W. Anderson, B. I. Halperin, C. M. Varma, Phil. Mag. 25, 1 (1972). Interatomic Bonding Equaon of moon with nearest neighbor interacon

Soluon

1‐D Array of Spring Mass System Frequency, ω 0 Wave vector, K π /a Group Velocity: Speed of Sound: Lace Constant, a

Opcal Vibraonal y x Modes n‐1 xn yn n+1

LO ω TO

Frequency, TA LA

0 Wave vector, K π/a

Total Energy of a Quantum Oscillator in a Parabolic Potenal

n = 0, 1, 2, 3, 4…; w/2: zero point energy

Phonon: A quantum of vibraonal energy, w, which travels through the lace Phonons follow Bose‐Einstein stascs. Equilibrium distribuon:

In 3D, allowable wave vector K: p: polarizaon(LA,TA, LO, TO) K: wave vector

Dispersion Relaon:

Energy Density:

Density of States: Number of vibraonal states between w and w+dw

in 3D

Lace Specific Heat: In 3D, when Specific Heat in 3D: of States: Debye Density Debye Approximaon: T << θ D , Debye Temperature [K] Frequency, w 0 Wave vector, K p/a

3ηkBT

Diamond Each atom has ‐K)

3 a thermal energy

of 3KBT

C ∝ T3 Classical Regime Specific Heat (J/m

Temperature (K)

In general, when T << qD,

d =1, 2, 3: dimension of the sample Phonon Scaering Mechanisms Kinec Theory • Boundary Scaering • Defect & Dislocaon Scaering Decreasing Boundary • Phonon‐Phonon Scaering Separaon

l

Increasing Defect Concentraon

Phonon Defect Boundary Scaering 0.01 0.1 1.0

Temperature, T/qD • Phonons dominate k in insulators