Problem 1
(a) A region of a silicon wafer is doped with donors at a concentration of 3 ×1017 cm-3 and with acceptors at a concentration of 2 ×1016 cm-3. Assuming that all of the dopants are ionized, what is the density of electrons in the conduction band and the density of holes in the valence band at 300 K?
For silicon, $n_i = $ 6.4 ×109 cm-3 at 300 K.
(b) Light falls on this semiconductor. What happens to the concentration of the electrons and the concentration of holes?
(c) Describe what happens to the concentration of electrons and the concentration of holes as the temperature is increased from room temperature.
(d) There is a sudden change in the concentration of electrons at a certain temperature. What is this temperature?
Problem 2
(a) Draw a p-channel JFET.
(a) What voltages should you apply to the gate and drain to bias it in saturation?
(b) What determines how far the drain contact is placed from the gate contact?
(c) Where is the largest electric field in a p-channel JFET biased in saturation and which direction is it pointing?
(d) What is the dominant current mechanism for the source-drain current? (tunneling, drift, diffusion, thermionic emission).
Problem 3
Consider an n-channel MOSFET.
(a) Draw the band diagram (conduction band, valence band, fermi energy) along a line from the gate through the oxide to the body in accumulation.
(b) Draw the electric field along the same line as in (a) for the case of accumulation.
(c) Explain what the subthreshold current is. How does the subthreshold current change with gate voltage?
(d) During the 'Happy days of CMOS scaling', the gate length was 45 times the oxide thickness. Why was it important to maintain this ratio?
Problem 4
Consider an npn bipolar transistor.
(a) How are the two junctions biased in forward active mode?
(b) What happens to the holes that enter the base from the base contact?
(c) Which way is the hole current going across the base-collector junction?
(d) What changes can be made to increase the punchthrough voltage? What other consequences would these changes have?
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 |