Question:

a) Describe two mechanisms by which electrons can be excited from the valence band to the conduction band?

b) Given that the direct-band gap energy for Gallium Nitride (GaN) is 3.4 eV at room temperature, calculate the phonon energy and phonon momentum that you can expect from such a material with a lattice constant of 3.186 Å and velocity of sound of 5x10³ m/s.

c) Given a P-type semiconductor with NA and ND atom concentrations of 8x1011 cm^-3 and 3x10³ cm^-3 respectively, calculate the electron concentration assuming ni = 1.4x10¹⁰ cm^-3.

d) What do you understand by the Fermi Level of a crystal? According to the Fermi-Dirac function, what is the temperature at which there is 1% probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron?

e) Given a piece of N-type silicon at 0 ºC,

i. Calculate the thermal velocity of an electron with an effective mass of 1.18m₀ and a mobility of 0.25 m²V^-1s^-1.

ii. What is the electric field that needs to be applied to make the electron drift at a velocity of 1000 ms^-1?