Problem 1
A silicon wafer is uniformly doped with donors with a concentration of $N_D=10^{15}$ cm^-3. The first micron of the wafer is linearly doped with acceptors $N_A=10^{16}(1-x)$ cm^-3. Here $x$ is measured in microns. No voltage is applied across the junction.

(a) Plot the electron density and the hole density.

(b) Plot the electric field.

(c) Plot the electron and hole diffusion currents.

(d) Plot the electron and hole drift currents.

For silicon: $E_g = 1.12$ eV, $N_c = 2.78 \times 10^{19}$ cm^-3, $N_v = 9.84 \times 10^{18}$ cm^-3, and $n_i= 7\times 10^{9}$ cm^-3.

Problem 2

(a) Draw the band diagram (conduction band, Fermi energy, valence band) of a forward-biased light-emitting diode. Indicate in the diagram the applied forward bias.

(b) Is the electric field in a light-emitting diode larger in forward bias or reverse bias? Explain your reasoning.

(c) What determines the distribution of wavelengths that a light-emitting diode emits?

(d) Name some applications for infrared light-emitting diodes.

Problem 3

(a) Draw a cross section of an n-channel MESFET.

(b) Draw the band diagram for the for this MESFET along a line that goes from the gate metal to the channel for zero applied gate voltage. Label the Schottky barrier.

(c) How does the channel resistance change as the MESFET is heated up?

(d) What can be done to optimize the speed of a MESFET?

Problem 4

This question is about memories.

(a) Explain how DRAM works.

(b) Explain how SRAM works.

(c) Explain how flash memory works