Problem 1

A $p$-doped silicon substrate is uniformly doped at $N_A = 10^{17}$ cm^-3 and then an additional doping $N_A=10^{19}\exp (-x/a)$ cm^-3 is added. Here $x$ is measured from the surface of the wafer and $a$ = 1 μ.

(a) Draw the band diagram (conduction band, valence band, Fermi energy). Label the $x$-axis in microns.

(b) Draw the electric field and the charge density. Which way is the electric field pointing? Explain why the field points in this direction.

Problem 2

(a) Draw an $n$-channel MESFET indicating where the depletion layer would be at zero bias. Draw Ohmic contacts at the source and drain.

(b) What determines the depletion width at zero bias? How could you measure the depletion width?

(c) What is pinch-off?

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

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

(f) Why is a MESFET faster than a MOSFET?

Problem 3
(a) Describe how a $pnp$ bipolar transistor works.

(b) How are the emitter efficiency and base transport factor affected if a heterojunction bipolar transistor is made?

(c) What is punchthrough? How can it be avoided?

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 happens to the built-in voltage as the solar cell heats up?

(d) What is the energy that a solar cell delivers per photon? How does it depend on the photon wavelength?