Chapter 9 - Thermoelectrics Flashcards
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.
What are Joule losses?
Joule losses are energy lost to heat due to electron scattering on phonons.
What is the Seebeck effect?
The development of a voltage in a conductor as a result of a temperature gradient.
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.
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.
How is the thermal voltage defined?
Uth = -alpha * ∆T, where alpha is the Seebeck coefficient.
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.
What is the energy transported proportional to?
(E-E_F) * l(E), where l(E) is the mean free path.
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.
For a metal, draw the different situation of electron and hole-like states for metals with Seebeck-coefficient 0, 0.
See notes.
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.
What can the sign of the thermal voltage tell us?
The type of charge carrier.
What happens when we want to measure the thermal voltage?
We connect metals which also produce a thermal voltage.
Draw a schematic of a thermocouple.
See notes.
What can be said of the Seebeck-coefficients dependence on T?
It is generally a strong function of T.
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.
For a Pelter-element, what is the heat flow given as?
dq/dt = πj, where π is the Peltier coefficient, π = alphaT.
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.
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
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.
Draw a typical layout of a thermoelectric power generator.
See notes.
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.
What are the requirements of the “leg”-materials in a thermoelectric power generator?
- large Seebeck-coefficient, alpha = V/K
- large electrical conductivity, sigma = en/pµ = A/Vm
- small thermal conductivity, kappa = W/Km
What is the figure of merit of a thermoelectric device?
Z*T = (alpha^2 * sigma)/kappa * T
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).
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.
For useful power conversions, what does the figure of merit has to be?
Above 1. World record is about 3.
What is a common factor among good ZT-materials?
That they all have heavy atoms and are complex alloys (to reduce thermal conductivity).
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
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.
Name three strategies that are investigated to increase ZT.
i) Reduction of kappa in materials with complex unit cells (phonon glass - electron crystal, “ratteling” atoms)
ii) Superlattices of two different materials, e.g. Bi2Te3 / Sb2Te3. Here we get acoustic impedance change at each interface, which reflects phonons (like light reflection), while electrons can pass through.
iii) Nanostructures (nanowires, quantum dots)
- decrease kappa due to interface/surface scattering of phonons.
- increase of alpha and sigma due to a change in electronic density of states: quantum confinement => higher electron energy.
