8a. thermoelectric power and power conversion · 8a. thermoelectric power and power conversion 1lb...

8a. Thermoelectric power and ppower conversion

1 L b O l h d f h l b h i i

Reminder: course requirements

1. Labs: Oral report at the end of each lab; otherwise written report

Andreas will inform more in detail later on

2. Project: Deadline to decide subject has passedj j p

Oral presentation (~15 min): 25/5

Deadline for written report (max 10 pages): 10/5

3. Problems: All must be solved, and solutions handed in before 27/5

Exception: Randomly picked person that solve all their assigned problems on black board (exception only valid for the set of p ( p yproblems assigned that specific time)

4. Lectures Active participation. Maximum two missed

5 Written exam: If #1-4 fulfilled then passing grade acquired without taking5. Written exam: If #1-4 fulfilled, then passing grade acquired without taking written exam

If not, or if higher grade desired, written exam (+# 1-3) a must!


Previous: Temperature gradient along material produces heat

IntroductionPrevious: Temperature gradient along material produces heat flow (carried by phonons and electrons) from hot to cold end

External voltage over conducting material produces electric current (e.g. carried by electrons & holes in semiconductors) from high-Ф end to low-Ф end

But there are also cross effects in electron conductors soBut there are also cross effects in electron conductors, so-called thermoelectric effects, notably:

Seebeck effect. Temperature gradient results in voltage and/or electric current provided there are mobile charge carriers. Heat can be converted into electric power!

P lti r ff t El tri rr nt thr h t nn t dPeltier effect. Electric current through two connected electron conductors will move heat from one junction to the other: Electrically driven solid-state heat pump!


Contact potentialA BContact potential always established at junction between 2

dissimilar materials containing mobile electrons (or other charged particles)

A B

Why?

Difference in chemical potential (μ) of electrons in 2 materials!

(Remember: μ defined as “smallest possible increase in energy when exactly one particle is added to system” ≈ average energy of most energetic particles)of most energetic particles)

Electrons flow (by diffusion) from high μ to low μ

This electron flow produces electric potential difference (Δφ)p p ( φ)(over thin electric double layer) that compensates difference in μ:

Δμ + q*Δφ = Δμ + (-e)*Δφ = 0


Contact potentialΔμ + (-e)*Δφ = 0 → μA - eφA = μB - eφB = ūA = ūB

This corresponds to a situation of electrochemical equilibrium = No net current flows over interface between A and B after initial equilibration!flows over interface between A and B after initial equilibration!

Short-circuiting two metals yields no steady-state electrical current

What would a voltmeter read? ADoes it matter where it is positioned in the loop?

V = 0 V & No!

A

+++ +++ VA voltmeter measures the difference in electro-chemical potential (ECP) between its leads, and the ECP is equilibrated everywhere in the circuit B

- - - - - -

→

Emergence of contact potential between electron conductors A & B → ΔūAB = 0


Thermoelectric potentialIf temperature gradient exists in an electron conductor energy will flow fromIf temperature gradient exists in an electron conductor, energy will flow from high T → low T by diffusion of thermalized electrons (and phonons)In a metal (since phonon heat conductivity is comparatively minor):jq = -κ∇T ≈ -κel∇T

But electrons are charged:

So if more electrons are passing from hot side to cold side than vice versa, then this heat transfer must be accompanied by a netheat transfer must be accompanied by a net charge transfer, i.e. an electronic current!

Q. Is this electronic current a transient or aQ. Is this electronic current a transient or a steady-state current?


Thermoelectric potentialA Depends on ho o meas re

Thot TcoldA. Depends on how you measure

Open-circuit conditions: counteracting voltage develops that Open circuit: Closed circuit:

t = 0

only allows for transient current

Closed-circuit conditions: steady-state current can flow through circuit

+++

---

g

→ Electrochemical potential gradient must exist between hot and cold end: “The thermoelectric potential” Note: (i) Thermoelectric potential depends on

t = tequilibrium

The thermoelectric potential Note: (i) Thermoelectric potential depends on transport properties of electrons; consequently very sensitive to existence of impurities and structural defectsT-gradient in electron

≠defects(ii) All uncompensated charge located at interfaces(iii) Si is the unique Seebeck coefficient of material i

conductor i: Δūi (Th, Tc) ≠ 0

(1/e)*Δūi (Th,Tc)=∫SidT≈Si *ΔT


Seebeck effect (discovered in 1821)T i l h l i d i i 2Typical thermoelectric device contains 2 materials connected at 2 points kept at different T

What is output voltage, i.e. thermoelectric T0p g ,

potential or more generally electrochemical potential difference, between points a & b under open-circuit condition?

0

Δūab = (e*)Vab= ΔūA(T2,T0) + ΔūBA(T2) + ΔūB(T1, T2) + ΔūAB(T1) + ΔūA(T0, T1) =

= [EC contact potentials zero + assume T independent Seebeck coefficients*] →= [EC contact potentials zero + assume T-independent Seebeck coefficients ] →

Vab≈ SA*(T2-T0) + 0 + SB*(T1-T2) + 0 + SA*(T0-T1) = SA*(T2-T1) + SB*(T1-T2) =

= (SA-SB)*(T2-T1) = SAB*ΔT = S*ΔT (at open-circuit, i.e. I = 0)

*: Seebeck coefficients can exhibit sizeable T dependence; also note that Vab independent of T0


What is a typical value of the Seebeck coefficient Si?

No good understandable theory,

but balance between initial electronic diffusion current and counteracting drift current (i.e. the thermo-electric

Si = -(π2/6)(kB/e)(kBT/EF) ~ -10-4 V/K*(10-2 eV/EF) ~ -10-6 V/K for metals (E ~1eV) at RT!

g (effect) gives after approximations and math… :

(EF 1eV) at RT!Examples: SNa = -5 μV/K, SAl = -1.8 μV/K, SPb = -1.8 μV/KBut remember: EF ~ (N/V)2/3 →Semiconductors with low charge densities should have much higher S values?Correct: E.g. Bismuth telluride (Bi2Te3) is a semiconductor with small E ≈ 0.13 eV at RTE.g. Bismuth telluride (Bi2Te3) is a semiconductor with small Eg 0.13 eV at RT Si (n-type Bi2Te3) = -287 μV/K Si (p-type Bi2Te3) = +81 μV/K

Useful with different sign since…


V ≈ S*ΔT = (SA-SB)*(T2 – T1)

d l i k i l i h l diff i S b k ffi i i dFundamental to pick 2 materials with large difference in Seebeck coefficients in order to get significant output voltage!

Using the Seebeck effect for temperature measurements: ThermocouplesUsing the Seebeck effect for temperature measurements: Thermocouples

V = (SA-SB)*(T – Tref) But what about second junction at Tref for T measurements?

Ice water at 0 oC (or 273 K) common choice for reference junctionIce water at 0 C (or 273 K) common choice for reference junction

Cold-junction compensation more convenient alternative that employs built-in electronics to apply a compensating V so that Tref appears to be at 273 K

Chromel-Alumel {(90% Ni & 10% Cr) - (95% Ni & 2% Al 2% Mn & & 1% Si)}: common, economic and stable thermocouple. Also with a relatively small change in Seebeck coefficient with T (S = 40 8 µV/K at RT) → linear sensor function *Seebeck coefficient with T (S = 40.8 µV/K at RT) → linear sensor function

* Problem that Ni magnetic and that Curie temperature located at 354 oC, with an associated marked change in S


Using the Seebeck effect for thermoelectric power generation

If we want to use the Seebeck effect for power generation, we want a device that is efficient in converting heat (T gradients) to electric power →

“Fi f M i ” Z l i“Figure of Merit” or Z-value important parameter:

But first repetition (?) of “maximum power transfer theorem” …

Pout/Ploss ≈ Z*ΔT

Where: Z = S2/(ρ*κ)

High Z = efficient thermoelectric device →


… Z = S2/ρ*κ : High Z = efficient thermoelectric device →

Metals: Poor thermoelectric materials due to low Seebeck

ffi i t d lcoefficients, and large thermal conductivities (κtot = κel + κph; κel > κph)

Semiconductors: Interesting for thermoelectric power applications due to large S values and reasonable low ρand κ values at appropriate pp pdoping levels (1019 cm-3 = 1025

m-3: high) …


Thermoelectric power applications

A th l t i it t i llA thermoelectric power unit typically contains large number of thermocouples in series (a thermopile) to produce (large voltage and) significant powervoltage and) significant power

Many of NASA deep space probes use thermoelectric units as power sources:

E.g. Pioneer 10 is powered by Radioisotope Thermoelectric Generators (RTGs). Heat from decay of plutonium(RTGs). Heat from decay of plutonium 238 isotope used to heat hot side, while the cold of outer space cools cold side.

150 W f d d f th~150 W of power produced for more than 3 decades!

Very stable devices ☺


Thermoelectric power applications

Different scale application: Quartz watch sold by SEIKOpp y

When worn on the wrist, extremely small thermo-electric generator absorbs body heat through the case back and dissipates it at the front

Generator needs to be small enough to fit inside watch and at the same time generate ≥ 1.5 µW at ΔT = 1 - 3 K (Quartz watches

i ll b 1 5 V d 1 A)typically operate at about 1.5 V and 1 µA)

Solution: Serial connection of 10 small! units, each containing 104 elements (80 µm in g (thickness and 600 µm in length), that are attached to 2 mm x 2 mm boards

Thermoelectric generator claimed to be theThermoelectric generator claimed to be the world's smallest by far used on a practical basis!


Current status: Essentially all thermoelectric li i d b d SCpower applications used based on SCs

But for many applications, the currently low Z values (which directly corresponds to lowvalues (which directly corresponds to low power conversion efficiency) needs to be improved upon:

And parameter too improve upon is κ, since even when doping level of conventional SCs selected so low such that:

Z = S2/ρ*κ

conventional SCs selected so low such that:

κ = κel + κph ≈ κph

i ill h hi h i i l SC i lκ is still rather high in conventional SC materials

2 approaches to decrease κ, without affecting S and ρ, currently pursued…


1. Nanoscale structuring of SCs: lattice mismatch at in b nd i k ph n n t n p t diffi lt

Z = S2/ρ*κgrain boundaries make phonon transport very difficult, since phonons typically have very long λ (usually many lattice spacings, while electrons have much shorter λ) →

If lattice divided into pieces of similar size as phonon wavelength phonon propagation is impossible: S (still)

2. Novel materials: Skutterudites (discovered in

wavelength, phonon propagation is impossible: S (still) high, and ρ (still) low, but κ decreases distinctly

(Skutterud, Norway, in 1845) contains SC lattices with guest atoms (so-called clathrate or cage compounds). The SC network gives high S and reasonably small ρThe SC network gives high S and reasonably small ρ, while “rattling” atoms scatter (long-wavelength) phonons efficiently and thus give low κ

Fe/Co: red, Sb: black, Ce: yellow

8b. Thermoelectric power and ppower conversion

Recombination of charge carriers at forward-biased pn junction

p-doped region conducts holes

n-doped region conducts electronsp njunction

+ + -p*n = constant = K = f (Eg, T)

Forward bias: p connected to

+ + - -

positive electrode, n to negative electrode →

Introduction of holes and electrons into junction region, where now p*n > K →

Net recombination of electrons & holes in junction region to restore equilibrium, which produces heat (conduction electrons fall down into open hole states)which produces heat (conduction electrons fall down into open hole states)

Forward biased p-n junction produces heat!


Generation of charge carriers at reverse biased pn junction

p-doped region conducts holes

n-doped region conducts electronsp njunction

+ + -p*n = K = f (Eg, T)

Reverse bias: p connected to

+ + - -

pnegative electrode, n to positive electrode →

Removal of holes and electrons from junction region, where p*n < K →

Net generation of electrons and holes in junction region to restore equilibrium, which requires heat (electrons excited from valence band to conduction band)

Reverse biased p-n junction consumes heat!


Peltier effect (discovered by French physicist Peltier in 1834)Functions by driving DC current throughFunctions by driving DC current through pair of connected p- and n-type materials

1) heat (Q) absorbedabsorbed from surroundings ( h h ) h bi d(the heat source) at the reverse-biased pn-junction

2) same amount of heat dissipateddissipated into surroundings (the heat sink) at the forward-biased pn-junction

∴ A Peltier element functions as a solid-dstate heat pump driven by the applied electric current (I):

dQ/dt = Π*I = S*T*I at small ΔT & IdQ/dt = Π*I = S*T*I at small ΔT & I

Π: Peltier coefficient; S: Seebeck coefficient


Peltier effect: Fully reversible

By changing direction of current: hot side becomes cold side and vice versa!

One of the first demonstrations of Peltier cooling/heating was done by Heinrich Lenz in 1838:

He put a drop of water at a Bi/Sn j nction and ith c rrent in onejunction, and with current in one direction the water drop froze to ice; and with current in the other direction the ice quickly melted ☺


Efficiency of a thermoelectric cooler:

1) Th ( ibl ) h t fl i d i b1) The (reversible) heat flow is driven by the Peltier effect:

P P = -P P = dQ/dt = Π*I = S*T*IPc = -Ph = dQ/dt = Π*I = S*T*I

2) Heat flows from hot to cold side:

P H = P H = K*ΔTPcH = -Ph

H = -K*ΔT

3) The electric current will cause an irreversible Joule heating, which is assumed to be equally split between cold and hot side:assumed to be equally split between cold and hot side:

PcJ = Ph

J = -V*I/2 = -R*I2/2

M ki h ff i li ld id

Coefficient of performance (COP) = PC /Vappl*I < 0.5 at ΔT ~20 K

Making the effective cooling at cold side:

PC = PCP + PC

H + PCJ = S*T*I - K*ΔT - R*I2/2

C appl


Thermoelectric cooler applications

Typical thermoelectric module: Series of p-n junctions (e.g., established in a bismuth-telluride semiconductor) thatbismuth telluride semiconductor) that are connected to a thin ceramic wafer on each side (being the hot and cold end, respectively)respectively)

Ceramic material provides rigidity and necessary electrical insulation & relatively high κ

Electrically in series & thermally in parallelparallel

Number of p-n junctions: 1 - >100


Applications

Russian scientist, Abram Ioffe, was first to demonstrate that doped SCs were much more efficient as thermoelectric devices than metals

His proposal of home refrigeration with SCs was what spurred the initialHis proposal of home refrigeration with SCs was what spurred the initial worldwide interest in SC in 1950s

Then there was microelectronics of course…

The efficiency of thermoelectric coolers is still today only 10 % of that of an ideal refrigerator, while a conventional compression cycle systems reaches 40 %reaches 40 %

Compensating advantages are: Solid-state device with no moving parts and no maintenance

Applications areas are diverse…


Thermoelectric cooler applications

IR sensors

Laser diodes

CCD cameras

Microprocessors

Bl d lBlood analyzers

Heat equilibration on satellites

RefrigeratorsRefrigerators

Etc…


Last time we talked about integrating solar cells into clothing…clothing…

Recently (at the Interactive Telecommunications Program students' final show at the Tisch School of the Arts, a part , pof New York University) it was demonstrated that it is possible to stitch a bikini partially from solar panels and h h biki i d li h h MP3that such a bikini delivers enough power to charge an MP3

player

Also a male version of the Solar bikini named iDrinkAlso, a male version of the Solar bikini named iDrink

With a greater surface area (!) it is able to deliver sufficient power under “summer illumination” to a thermoelectricpower under summer illumination to a thermoelectric cooling module, so that it is capable of cooling a can of beer…

8a. thermoelectric power and power conversion · 8a. thermoelectric power and power conversion 1lb...

Documents