Problem 1
A photodiode consists of semiconducting layers $n$+ / $n$ / $p$ / $p$+. No bias voltage is applied.

(a) Draw the band diagram (conduction band, valence band, Fermi energy).

(b) Draw the electric field and the charge density. Which way does current flow when light falls on the photodiode?

(c) Not all photons will generate a current in the photodiode. What conditions should the light satisify to cause a current?

Problem 2
(a) 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 p-type substrate in inversion.

(b) Draw the electric field again for a lower concentration of acceptors in the substrate.

(c) How does the threshold voltage change when the concentration of acceptors is reduced?

Problem 3
Consider a pnp transistor.

(a) Draw the minority carrier concentrations reverse active mode where the emitter-base junction is reverse biased and the base-collector juction is forward biased. Include the positions of the equilibrium minority carrier concentrations in the diagram.

(b) Explain why the gain factor $\alpha = I_C/I_E$ is lower for a reverse active mode than forward active mode.

(c) What can be done to increase the speed of a bipolar transistor?

Problem 4

(a) Draw a cross section of an n-channel JFET showing the source, gate, and insulating substrate. (Make a large drawing that is about as wide as the paper).

(b) The JFET is biased in saturation. Draw the depleted region and put + or - signs in regions where there is positive or negative charge.

(c) Add arrows to the drawing of the JFET to indicate the direction of the electric field at each point.

(d) Where are there tunnel contacts in a JFET?