Problem 1
(a) Explain why a Zener diode is heavily doped on both sides.

(b) Draw the band diagram (conduction band, valence band, Fermi energy) of a Zener diode.

(c) Explain why a Schottky diode cannot be heavily doped.

(d) Draw the band diagram of a n-Schottky diode.

Problem 2
Consider a MOS capacitor with a p-type substrate.

(a) Plot the charge density in inversion along a line from the gate, through the oxide, and into the semiconductor.

(b) Indicate which charge is mobile and which charge is fixed in your diagram.

(c) Plot the diffusion current density using the same horizontal axis as for the charge density.

(d) Draw the band diagram (conduction band, valence band, Fermi energy) at the flatband condition.

Problem 3
Consider an n-channel MOSFET.

(a) How does the transconductance $\frac{dI_D}{dV_G}$ depend on the drain voltage in the linear regime and in the saturation regime?

(b) Draw the charge density along a line from the gate, through the oxide, and into the semiconductor when the transistor is biased in the linear regime.

(c) What is the dominant current mechanism in a MOSFET?

(d) What is the subthreshold current and what could be done to decrease the subthreshold current?

Problem 4
a) Describe how a $pnp$ bipolar transistor works and explain the base transport factor and the emitter efficiency.

(b) How would you calculate the electron an hole contributions to the emitter current $I_{En}$ and $I_{Ep}$?

(c) Why does a heterojunction bipolar transistor have more gain than a bipolar transistor?