- 1. How do you increase the carrier concentration in a field effect transistor? (10)
- 2. When I increase the donor dopant concentration in silicon from 1014cm-3 to 1020cm-3, does the electron mobility increase or decrease (5)? Why (5)?
- 3. What are the majority and minority carriers for the silicon sample in problem 2? (5)
- Majority — electrons
- Minority — holes
- 4. Draw a bonding diagram to show why group V elements dope silicon n-type i.e. extra electrons (5)
- 5. Assume a pn diode with p-side doping Na=2×1018cm-3 and n-side doping Nd= 2×1017cm-3. Silicon has a dielectric constant of 12ε0.
- a. Draw the band diagram at equilibrium for the whole pn diode.(5)
- b. Calculate the fermi level positions with respect to the conduction and valence bands on the 2 sides. (5)
- c. Assuming a bandgap of 1.12eV, calculate the built-in voltage. (5)
- d. What is the depletion region width at equilibrium? (10)
- W=√((2*12ϵ_0 Vbi*(1/Na+1/Nd))/q)≈0.08um
- e. How does the depletion region width change in reverse bias? (5)
- f. Assuming a cross sectional area of 1cm2, what is the capacitance of the depletion region at equilibrium? (5)
- g. If I put a series resistance of 1kΩ in series with this depletion capacitance, what is the time constant? (5)

- 6. In a uniformly doped piece of silicon with length 1cm, doping with donors Nd=2x1018cm-3, I apply a constant voltage of 1V. Assuming a carrier electron mobility of 300cm2/Vs:
- a. What is the diffusion constant for electrons? (10)
- b. Calculate the electron carrier velocity? (10)

- 7. Explain why a pn diode conducts in one direction but not the other at equilibrium. (15)