Consider the first two energy levels of a particle in a box

Question

Q1. The lattice constant of Si is 5.43 A^o. It had a modified fcc (face centered cubic) structure, commonly known as a diamond structure See below.

a) How is this structure different from fcc? Be specific about numbers of atmos in each structure and locations of atom in each structure.

b) What does this suggest about the two surfaces?

c) If E_d is 50 meV below E_C, what is the probability of one of the states in the donor levels being occupied? Was the full ionization assumption reasonable or not?

Q2. Consider the first two energy levels of a particle in a box (n = 1 and n = 2). What is the probability of the electron being in the middle 10% of the box?

Q3. Consider the piece of silicon semiconductor.

a) The silicon is doped with arsenic to a concentration of 10¹⁶ cm^-3. Is this going to produce an N of P type semiconductor? Explain why.

b) What are the electron and hole concentrations in the piece of silicon before it is doped at 300K?