Electronic- Thermoelectric Effects Flashcards
Which electrons can change their energy state due to temperature?
Those near the top of the distribution so are close to the Fermi level
Formula for distribution of electrons between available energy states above absolute 0
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
What happens when E
Exponential part of denominator tends to 0 and the probability of an electron having that energy tends to 1
What happens when E=Ef?
Exponential part of denominator is 1 so probability of electron having that energy is 1/2
What happens when E»Ef?
Exponential part of the denominator tends to infinity so the probability of electron having that energy tends to 0
Fermi-Dirac distributions for different temperatures
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.
What is the width of the thermally-driven electron probability distribution?
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
Which electrons in metals can contribute to Cv?
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
What happens when different metals are placed in contact?
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.
What is the work function?
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
What effects is the contact potential the basis of?
Peltier effect, Seebeck effect, Thompson effect
What is the Peltier effect?
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)
Criteria for maximum cooling by Peltier effect
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)
Applications of Peltier effect
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
Thompson effect
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