Problem 1

(a) Draw the band diagram (valence band, conduction band, Fermi energy) of a pn-junction in reverse bias where the donors on the n-side have a concentration ten times higher than the acceptors on the p-side.

(b) What is the built-in voltage $V_{\text{bi}}$ of a pn-junction? How can you measure $V_{\text{bi}}$?

(c) If the acceptors on the p-side of the junction have a concentration of $10^{17}$ 1/cm³, what is the electron minority concentration at the edge of the depletion width on the p-side for $V=-1$ V, $V=0$ V, and $V=1$ V? Here $V$ is the forward bias voltage across the junction.

Problem 2

Describe the role of tunneling and recombination in a:

(a) light emitting diode
(b) bipolar transistor
(c) Zener diode

Problem 3

(a) Draw an $n$-channel MOSFET in saturation indicating the direction of the electric field at the source, drain, and body contacts.

(b) Explain why there is an electric field at the body contact.

(c) What is the primary mechanism that causes the current flow from source to drain? Drift, diffusion, thermionic emission, or tunneling?

(d) The MOSFET is biased in saturation. Explain how you would calculate the voltage across the pinched off region.

Problem 4
A thyristor is built from a semiconductor with a direct band gap.

(a) Starting from zero bias, how does the light emission change as the voltage across the thyristor is increased? Explain your reasoning.

(b) At a critcal voltage, the thyristor enters the conducting state. How can you modify the thyristor to increase this critical voltage?