Problem 1
An intrinsic silicon sample is doped with donors from one side such that $N_D=N_0\exp (-ax)$.

(a) Draw the band diagram (conduction band, valence band, Fermi energy) as a function of $x$. There is no current flowing so the Fermi energy should be constant.

(b) Draw the electron and hole concentrations ($n$ and $p$) and the electric field as a function of $x$. Explain why these quantities have the form you have drawn.

Problem 2
There are four mechanisms that typically cause currents to flow: thermionic emission, diffusion, drift, and tunneling.

Explain briefly which kind of current mechanisms are important in the following devices. (For some devices more than one type of current flows.)

(a) pn diode
(b) Schottky diode
(c) MOSFET
(d) bipolar transistor
(e) JFET
(f) MESFET

Problem 3

(a) Draw a pnp bipolar transistor showing the emitter, collector, and base contacts.

(b) What are the doping levels of the emitter, the base, and the collector? How does the doping affect the emitter efficiency and the base transport factor?

(c) What is punch-through and what is latch-up?

Problem 4
Describe a light emitting diode. Where do the electrons and holes recombine? How is the bandgap related to the photon frequency? Is the semiconductor direct or indirect? How should the diode be biased? What role does total internal reflection play?