Problem 1
A p-type silicon wafer is uniformly doped with boron at a concentration of $10^{15}$ cm^-3. Linear n-type doping is then introduced with a concentration profile $N_D= 10^{17}\left(1-\frac{x}{3\times 10^{-6}}\right)$ cm^-3. Here $x$ is the distance from the surface of the wafer measured in meters where $x=0$ is the surface of the wafer. The donor doping goes to zero at a depth of 3 microns and remains zero for $x > 3\,\mu\text{m}$.

(a) How would you calculate the diffusion currrent density for the electrons and the holes?

(b) Plot the diffusion current density for the electrons and the holes. (positive current flows in the $+x$ direction)

(c) Plot the drift current for the electrons and the holes.

(d) Draw the band diagram (valence band, conduction band, Fermi energy) as a function of $x$ assuming no voltage bias is applied.

For silicon: $E_g = 1.12$ eV, $N_c = 2.78 \times 10^{19}$ 1/cm³, $N_v = 9.84 \times 10^{18}$ 1/cm³, and $n_i= 1.5\times 10^{10}$ cm^-3.

Problem 2
(a) Draw an n-channel JFET.

(b) Should the gate voltage should be positive or negative to operate in the saturation regime? Why?

(c) What is the dominant current mechanism for the source-drain current? (tunneling, drift, diffusion, thermionic emission).

(d) If a JFET is biased in saturation, where is the largest electric field? How would you calculate the value of the electric field at the point where the electric field is largest?

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) Explain how the collector current is calculated.

(d) Why would a bipolar transistor be used in a common base configuration?

Problem 4

(a) What would have a larger reverse saturation current, a light emitting diode or a solar cell? Why?

(b) Can you use an indirect band gap semiconductor to make a solar cell? Explain why or why not.

(c) 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?

(d) One billion ($10^9$) photons each with an energy of 1.8 eV strike a GaAs solar cell with a bandgap of 1.43 eV. What is the maximum energy that could be extracted? Explain your answer.