Problem 1
A silicon wafer is uniformly doped with donors with a concentration of $N_D=10^{15}$ cm-3. Acceptors are then diffused into the wafer from the surface to form a diode.
(a) What measurement can be performed to determine the doping profile of the acceptors $N_A(x)$?
(b) At zero bias voltage, the integral of the electric field across the depletion region is $V_{bi}$. What is the integral of the electric field across the depletion region when a voltage $V$ is applied?
(c) Give a formula for the charge density in the depletion region in terms of $N_A(x)$ and $N_D$.
(d) Give a formula for the electric field in terms of $N_A(x)$ and $N_D$.
(e) What value does the electric field have at the edges of the depletion regions?
Problem 2
(a) Draw an n-channel JFET.
(b) Draw the band diagram (conduction band, Fermi energy, valence band) of the pn-junction of the JFET when it is biased in saturation.
(c) Draw the band diagram (conduction band, Fermi energy, valence band) of the metal-drain contact. Indicate the Schottky barrier in your drawing.
(d) Why is the drain current almost constant in saturation?
Problem 3
A npn bipolar transistor has doping concentrations $N_{De}$, $N_{Ab}$, and $N_{Dc}$ for the emitter, base, and collector, respectively.
(a) What are the equilibrium minority carrier concentrations $p_{ne}$, $n_{pb}$, and $p_{nc}$ in the emitter, base, and collector?
(b) What is the minority carrier concentration at the edge of the depletion region in the base on the emitter side? Your answer should be a function of the voltage emitter-base $V_{eb}$.
(c) The base of a bipolar transistor should be thin. Thin compared to what? Is it possible to make it too thin?
(d) A transistor is biased in forward-active mode. Draw the collector current as a function of collector-emitter voltage. Why is the collector current almost constant for large voltages as the collector-emitter voltage is increased?
Problem 4
(a) A light-emitting diode should produce green light. What properties should the semiconductor have that is used to make this diode?
(b) How do you make metal-semiconductor contacts in a light-emitting diode so that the light gets out?
(c) Explain why sometimes light gets reflected back into the diode at the surface.
(d) What is the difference between a light-emitting diode and a laser diode?
Quantity | Symbol | Value | Units | |
| electron charge | e | 1.60217733 × 10-19 | C | |
| speed of light | c | 2.99792458 × 108 | m/s | |
| Planck's constant | h | 6.6260755 × 10-34 | J s | |
| reduced Planck's constant | $\hbar$ | 1.05457266 × 10-34 | J s | |
| Boltzmann's constant | kB | 1.380658 × 10-23 | J/K | |
| electron mass | me | 9.1093897 × 10-31 | kg | |
| Stefan-Boltzmann constant | σ | 5.67051 × 10-8 | W m-2 K-4 | |
| Bohr radius | a0 | 0.529177249 × 10-10 | m | |
| atomic mass constant | mu | 1.6605402 × 10-27 | kg | |
| permeability of vacuum | μ0 | 4π × 10-7 | N A-2 | |
| permittivity of vacuum | ε0 | 8.854187817 × 10-12 | F m-1 | |
| Avogado's constant | NA | 6.0221367 × 1023 | mol-1 |