quantum question

Describe (You may use figures in your answer) the temperature dependence of

a) Electron and hole mobility. (2pt)

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b) Electronic conductivity of metals using σ=Nµq. (3pt)

c) Electronic conductivity of intrinsic and extrinsic semiconductors using σ=Nµq. (4pt)

d) Electronic conductivity of ionic insulators using σ=Nµq. (3pt)

e) Draw and explain the I-V curve for a p-n junction. (4pt)

f) In what materials can you observe the phenomenon below? Briefly explain it. (2pt)

Magnetism
a) Based on χ (or µ), define/classify the magnetic materials into the diamagnetic, paramagnetic, and ferromagnetic materials. (3pt)

b) What contributes to diamagnetism and paramagnetism? Do they have temperature dependence? (4pt)

c) Describe the hallmark of ferroelectricity and ferromagnetism (you may draw figures). (2pt)

d) For the contributions you listed in (b), which should be interpreted with quantum mechanics? And why quantum mechanics has advantages over the classical physics? (3pt)

e) For the material with the electronic band structure shown below, is it diamagnetic or paramagnetic? Provide your justification. (3pt)

Thermal properties
a) Explain why quantum physics should be used to interpret materials’ thermal capacity. What are the main factors that will determine the thermal capacity? (3pt)

b) What is the advantage of Debye Model over Einstein Model in terms of the thermal capacity? (2pt)

c) Why theoretical results from the basic free electron model do not agree with most experimental data for conductors’ thermal capacity? (2pt)

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