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

Consider two light emitting diodes that are doped the same. One LED is made of GaAs (band gap = 1.42 eV) and the other is made of GaN band gap (3.4 eV).

(a) Which diode has a higher concentration of minority electrons on the p-side? Why?

(b) How can you determine what color light these diodes will emit?

(c) How can you calculate the diffusion current when the diodes are forward biased?

(d) A current of 30 mA flows through a GaN LED. Estimate how many photons are emitted per second.

Problem 3

(a) Draw an $n$-channel MOSFET including the source, drain, gate, and body contacts.

(b) In the linear regime, the drain current is proportional to the drain voltage. What determines the proportionality constant?

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

(d) What determines the maximum temperature that a MOSFET can operate?

Problem 4
The $\alpha=\frac{I_C}{I_E}$ gain factor of a bipolar transistor is measured in forward active mode and in reverse active mode.

(a) How would $\alpha$ differ in these two measurements?

(b) $\alpha$ is the product of the emitter efficiency and the base transport factor. Explain which of these factors changes the most between the forward active and reverse active measurments.

(c) How can you estimate the ratio of the doping concentrations of the base and the collector from this measurement?