Problem 1
(a) Describe some methods that can be used to dope silicon with acceptors.

(b) Silicon is doped with acceptors to a concentration of $10^{17}$ 1/cm³. Plot the hole concentration as a function of temperature indicating the intrinsic, extrinsic and freeze-out regimes. At what temperature does the transition from intrinsic to extrinsic take place?

(c) What is the minority carrier concentration at 300 K?

(d) In the depletion region of a silicon $pn$-junction, the $p$-type semiconductor has an acceptor concentration of $10^{17}$ 1/cm³. What is the maximum value of the derivative of the electric field $\frac{dE}{dx}$?

For silicon: $N_c(300) = 2.78 \times 10^{25}$ m^-3, $N_v(300) = 9.84 \times 10^{24}$ m^-3, $E_g = 1.12$ eV, $\epsilon_r = 11.9$

Problem 2
(a) Draw the band diagram for an unbiased $pn$-junction (conduction band, valence band, Fermi energy).

(b) Draw the band diagram for a forward biased $pn$-junction (conduction band, valence band, Fermi energy). Consider the depletion width, the drift current, and the diffusion current. Do they increase or decrease as a forward bias is applied?

(c) Describe the thermionic emission of electrons and holes in a $pn$-junction (using arguments that are similar to those used for a Schottky diode).

(d) What can be measured with a capacitance-voltage measurement?

Problem 3
(a) Draw an $p$-channel MOSFET showing the source, drain, gate, and body contacts. Draw the electric fields if the MOSFET is biased in saturation.

(b) Draw the band diagram (conduction band, valence band, Fermi energy), and the electric field as a function of position in a MOS capacitor with a $n$-type substrate in accumulation.

(c) In the linear regime, the depletion width does not vary along the channel from source to drain. Why not?

(d) What is the subthreshold current?

Problem 4
In a bipolar transistor,

(a) What determines the emitter efficiency? What determines the base transport factor? How are they related to the current transfer ratio $\alpha =\frac{I_c}{I_e}$?

(b) What is the Early effect. How could you change a transistor to decrease it?

(c) Draw the minority carrier concentration in a pnp ttransistor in the forward active regime.

(d) How can you calculate the collector current?