Flashcards in Chapter 9 - Thermoelectrics Deck (31):

1

## What is the motivation of using thermoelectric generators?

### There is often a lot of waste heat which theoretically could be extracted using thermoelectric generators. For example in combustion engines, where only 25% of the energy is used to power the vehicle, and the rest goes out the exhaust gas or to cooling the coolant.

2

## What are Joule losses?

### Joule losses are energy lost to heat due to electron scattering on phonons.

3

## What is the Seebeck effect?

### The development of a voltage in a conductor as a result of a temperature gradient.

4

## What is the Peltier effect?

###
The absorption or release of heat at a junction of dissimilar conductors owing to a change in heat capacity of carriers when they leave one medium and enter a different one.

Or: reverse Seebeck effect, apply a voltage and get a temperature gradient.

5

## What is the definition of the Seebeck coefficient?

### alpha = -∆phi/∆T, that is the ratio of the change of potential to the change of temperature.

6

## How is the thermal voltage defined?

### Uth = -alpha * ∆T, where alpha is the Seebeck coefficient.

7

## Explain the Seebeck effect in terms of the temperature dependence of the Fermi-Dirac distribution.

### See slide 5. As the temperature increases, there are more electron-like states and hole-like states. In the case of symmetric carrier transport (holes and electrons have same mobility) there will be no net transport of holes and electrons in a system with two ends held at different temperatures.

8

## What is the energy transported proportional to?

### (E-E_F) * l(E), where l(E) is the mean free path.

9

## How do we achieve a net current flowing between two terminals held at different temperatures?

###
In metals: We need different effective masses for holes andelectrons.

In semiconductors: we dope it.

10

## For a metal, draw the different situation of electron and hole-like states for metals with Seebeck-coefficient 0, 0.

### See notes.

11

## What is the explanation of the Seebeck-effect in semiconductors?

### The side with higher T will have more excited electrons. There will therefore be a concentration gradient in the conduction band, and we have a diffusion of electrons. Since there is a diffusion of electrons from the hot side, there is a net positive charge, which is counteracted by a drift of electrons from cold to hot side. In steady state, these currents cancel each other, but we still have a voltage.

12

## What can the sign of the thermal voltage tell us?

### The type of charge carrier.

13

## What happens when we want to measure the thermal voltage?

### We connect metals which also produce a thermal voltage.

14

## Draw a schematic of a thermocouple.

### See notes.

15

## What can be said of the Seebeck-coefficients dependence on T?

### It is generally a strong function of T.

16

## How would you measure the Seebeck-coefficient?

### You would need a reference material with a known Seebeck-coefficient for contacts. This is usually Pt, which is almost symmetric and has a Seebeck-coefficient of almost 0.

17

## For a Pelter-element, what is the heat flow given as?

### dq/dt = π*j, where π is the Peltier coefficient, π = alpha*T.

18

## When solving the Boltzmann transport equation for the thermoelectrics, what results do we get for i) metals, ii) n-type semiconductors and iii) p-type semiconductors?

###
i) alpha = - π^2 / 2 * k/e * kT/E_F (for e-like)

ii) alpha = -k/e * [(E_C-E_F) / kT + 5/2 + r]

iii) alpha = +k/e * [(E_F - E_V)/kT + 5/2 +r]

where r is the scattering coefficient.

19

## What are the orders of magnitudes of the Seebeck-coefficient for metals, n-type SC and p-type SC?

###
Metals: µV/K

Semiconductors: mV/K

20

## In thermoelectrics, what is the scattering coefficient?

### It denotes the contributions of scattering to the Seebeck-coefficient. It is e.g. -1/2 for phonon scattering, 3/2 for scattering at charged defects. The total contributions usually order of 1 when all is combined.

21

## Draw a typical layout of a thermoelectric power generator.

### See notes.

22

## Why must we have a series of many thermoelectric power generators to get a high voltage?

### Because they are low-impedance devices, which means they have a low voltage and high current. Many are needed in series to create a high voltage.

23

## What are the requirements of the "leg"-materials in a thermoelectric power generator?

###
- large Seebeck-coefficient, alpha = V/K

- large electrical conductivity, sigma = e*n/p*µ = A/Vm

- small thermal conductivity, kappa = W/Km

24

## What is the figure of merit of a thermoelectric device?

### Z*T = (alpha^2 * sigma)/kappa * T

25

## What is the maximum theoretical efficiency of a thermoelectric generator?

###
eta = (T_H - T_C)/T_H * (sqrt(1+ZT_M) - 1) / (sqrt(1+ZT_M) + T_C/T_H),

where the first term is the Carnot efficiency of the system. T_M is the average temperature, that is T_M = 1/2 * (T_H - T_C).

26

## When is the expression of the maximum efficiency of a thermoelectric generator valid?

### When the difference in temperature is way lower than the cold reservoir.

27

## For useful power conversions, what does the figure of merit has to be?

### Above 1. World record is about 3.

28

## What is a common factor among good ZT-materials?

### That they all have heavy atoms and are complex alloys (to reduce thermal conductivity).

29

## How does the figure of merit depend on the carrier concentration? Draw a plot.

###
For metals, the Seebeck-coefficient is proportional to kT/E_F, with E_F being proportional to n^2/3.

For semiconductors it is proportional to E_C-E_F/kT = ln(N_C / n).

This means that it is inversely proportional to the conductivity.

But the figure of merit has conductivity shown up in the numerator.

Thus the Seebeck-coefficient decreases with carrier concentration, and the conductivity increases. This can be shown in a plot (see notes).

When it comes to kappa, there is no real dependence on carrier concentration before it reaches 10^21.

The max is a carrier concentration of around 10^20

30

## How is the figure of merit dependent on temperature?

###
Seebeck-coefficient: for metals directly proportional, for semiconductors inversely proportional.

Conductivity: for metals inversely proportional, for semiconductors directly proportional.

Kappa: Phonons goes as T^3 until the Debye-temperature. After that 1/T (since all phonon modes are excited, and we only loose phonons to scattering when moving to higher T). Electrons goes as T.

31