Electronic- Thermoelectric Effects

Question 1

Which electrons can change their energy state due to temperature?

Answer 1

Those near the top of the distribution so are close to the Fermi level

Question 2

Formula for distribution of electrons between available energy states above absolute 0

Answer 2

F(E)=1/(exp(E-Ef/kBT)+1)
F(E) is probability of electron having that energy
E is available energy state
Ef is Fermi level 
kB is Boltzmann constant 
T is temperature

Question 3

What happens when E

Answer 3

Exponential part of denominator tends to 0 and the probability of an electron having that energy tends to 1

Question 4

What happens when E=Ef?

Answer 4

Exponential part of denominator is 1 so probability of electron having that energy is 1/2

Question 5

What happens when E»Ef?

Answer 5

Exponential part of the denominator tends to infinity so the probability of electron having that energy tends to 0

Question 6

Fermi-Dirac distributions for different temperatures

Answer 6

F(E) vs energy. At 0K, horizontal line at 1 until Fermi level where it sharply drops to 0 then continues. At greater temperature, horizontal line at 1 until just before Fermi level where it curves to steep diagonal line down to nearly 0 when it curves to 0 and continues. At even higher temperature, curves begin earlier and diagonal line less steep. All go through 1/2 at Fermi level.

Question 7

What is the width of the thermally-driven electron probability distribution?

Answer 7

Between the levels with probabilities of 0.1 and 0.9 of being occupied.
Upper limit: E=Ef+2.2kBT
Lower limit: E=Ef-2.2kBT

Question 8

Which electrons in metals can contribute to Cv?

Answer 8

Only those approximately in the range Ef+-kT. This is about 2kT/Ef or about 1% of total unbound electrons. Their effect at room temperature is therefore negligible

Question 9

What happens when different metals are placed in contact?

Answer 9

The Fermi levels are different. Electrons flow from the metal with higher Ef until the Fermi levels are equal. A potential step (voltage) builds up between the two different metals equal to the difference in their work functions. This can’t be used directly as the electrons are at equilibrium.

Question 10

What is the work function?

Answer 10

Minimum energy to remove an electron from a solid in a vacuum.
φ=-eV-Ef
Where eV is energy of an electron at rest in the vacuum above the surface.
A metal with a lower Ef has a greater φ

Question 11

What effects is the contact potential the basis of?

Answer 11

Peltier effect, Seebeck effect, Thompson effect

Question 12

What is the Peltier effect?

Answer 12

Electrons flowing across the junction either require heat or give out thermal energy to either cool or heat the bulk material. Heat is absorbed by the metal the electrons flow from (cooling) and is emitted by the metal the electrons flow to (heating)

Question 13

Criteria for maximum cooling by Peltier effect

Answer 13

Need to maximum figure of merit: α^2σ/k
α is coefficient defining size of Peltier effect
σ is electrical conductivity (if low then resistive heating large)
k is thermal conductivity (if high heat conducted along wires to junction, reducing cooling effect)

Question 14

Applications of Peltier effect

Answer 14

Make miniature devices that take DC power and achieve precise temperature control. There are weight and space savings and is in solid state so reliable.
Military: night vision, electronic equipment cooling, cooled garments
Scientific: IR detectors, laser diode coolers, circuit coolers, CCD coolers
Consumer: mobile refrigerators, insulin coolers, drink coolers
Medical: hypothermia blankets, blood analysers, tissue storage

Question 15

Thompson effect

Answer 15

Consider a bar with a thermal gradient. Mobile conduction electrons have a little more kinetic energy (and higher velocity) than at the cold end. A flow from the hot to cold end occurs. A potential difference arises opposing this flow, ΔVT.
ΔVT=sΔT
First T subscript. s is Thompson coefficient. ΔVT typically mVs

Question 16

Set up of the Seebeck effect

Answer 16

There is a circuit of 2 conductors. The temperature at one junction is greater than at the other so there is a temperature gradient in both metals. A Thompson effect present in both and different contact potentials at the junctions. Δφ is modified by the difference in Thompson potentials ΔVT in each material

Question 17

How does the Seebeck effect work?

Answer 17

Thermal excitation at the hot junction drives the electrons over the contact potential. After this the various potentials drive the electrons around the circuit back to the hit junction. Heat is absorbed at the hot junction due to Peltier cooling effect. Heat evolved at cold junction (heating). The heat absorbed is the source of the energy driving the current flow and resistive heating in the wires. Potential is about microvolts per degree temperature difference.

Question 18

Seebeck coefficient

Answer 18

Defined as α such that emf=αΔT

Question 19

How doe thermocouples work?

Answer 19

Use the Seebeck effect and measure the thermally induced potential difference. One temperature is the one you want to find, the other is fixed (e.g 0°C). The junction that would be at the fixed temperature is opened to make 2 reference junctions between which the potential difference, Vout is measured by potentiometer under conditions of 0 current (normally mV)
Vout=f(T1,T2)

Question 20

Considerations for material to use in thermocouples

Answer 20

Maximise Seebeck coefficient. Also consider stability at operating temperature (chemical, mechanical, metallurgical). Low temperatures typically use chromel or alumel (90%+Ni). High temperatures use PtRh alloys for stability but are expensive and have low α.

Question 21

Applications and positives and negatives of thermocouples

Answer 21

High temperature process monitoring under severe conditions where radiation pyrometry is difficult. E.g dusty atmospheres or where radiation pyrometer might be too hot and require excessive maintenance. Some thermocouple types better for vacuum, oxidising conditions, sulfurous conditions, operating temperatures.
Cheap
Not that accurate (<1°C accuracy very unusual)

Question 22

Thermopiles

Answer 22

Several thermocouples placed in series to create larger output voltage. Used in thermoelectric generators to convert heat to energy (heat engine). Useful for portable power generation. Used in IR imaging techniques that detect heating effect of IR (body imaging, ear thermometers)