Problem 1
(a) Draw the band diagram for an unbiased $pn$-junction (conduction band, valence band, Fermi energy).

(b) Draw the concentrations of electrons and holes $n$ and $p$ for this unbiased $pn$-junction.

(c) Draw the concentrations of electrons and holes $n$ and $p$ for a reverse biased $pn$-junction.

(d) Explain how the plot drawn in (c) could be used to calculate the diffusion current.

(e) What is the difference between a long diode and an short diode?

(f) What is measured with a capacitance-voltage measurement?

Problem 2
(a) Make a large drawing of a $p$-channel MOSFET showing the source, drain, gate, and body contacts. Draw the distribution of charge if the MOSFET is biased in saturation. Do not forget the charge on the gate or at the body contact. Indicate if the charge is mobile or fixed.

(b) Draw the band diagram (conduction band, valence band, Fermi energy), and the electric field as a function of position in a MOS capacitor with a $n$-type substrate in inversion.

(c) What limits the speed of a MOSFET?

(d) How does the drain current depend on the gate voltage in the saturation regime?

Problem 3
Explain how SRAM, DRAM and flash memories work.

Problem 4
(a) Describe how a solar cell works.

(b) The depletion region of a solar cell has a certain thickness in the dark. What determines this thickness? What happens to the depletion width when light falls on the solar cell?

(c) What limits the efficiency of a solar cell?