Problem 1
(a) A semiconductor is doped along the $x$-axis p then n then p. The n-region is so wide that this acts like two diodes in series. First there is a pn-diode and then a np-diode. A voltage is applied so that the pn-diode is forward biased and the np-diode is reverse biased. The n-region is then made thinner. How thin does it have to be before the current increases significantly? Why does this happen?
(b) In impact ionization, an electron acquires so much energy that it scatters another electron from the valence band to the conduction band. If impact ionization occurs in the pinched off region of an n-channel MOSFET, what happens to the electron that is generated and what happens to the hole that was created in the valence band?
(c) A light emitting diode with a bandgap of 3.2 eV shines directly onto 10 silicon solar cells connected in series. Silicon has a bandgap of 1.12 eV. What is the maximum voltage you can measure across the array of solar cells? Explain your reasoning.
Solution
Problem 2
(a) Draw the band diagram of a p-Schottky diode in reverse bias.
(b) How could you determine the drift current density and the diffusion current density from the band diagram?
(c) How could you determine the thermionic emission current from the band diagram?
(d) In reverse bias, which direction does the drift current, the diffusion current, and the thermionic emission current flow? Metal to semiconductor or semiconductor to metal?
Problem 3
(a) A MOSFET is biased in saturation. Where is the highest electric field in the MOSFET?
(b) You don't know if the MOSFET is n-channel or p-channel. How can you determine this experimentally?
(c) If you decrease the body doping of a MOSFET, what consequence will this have for the threshold voltage? Explain your reasoning.
Problem 4
A bipolar transistor is made from a direct bandgap semiconductor.
(a) What determines how much light is emitted in forward-active mode? Consider the emitter efficiency and the base transport factor.
(b) How should you bias the transistor to maximize the light output?
(c) How could you change the color of the light by changing the bias conditions?
Solution
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 |