Problem 1
A silicon wafer is uniformly doped with donors with a concentration of $N_D=10^{15}$ cm-3. The left half of the wafer is then doped with acceptors to a concentration of $N_A=10^{16}$ cm-3 while the right half is doped with a concentration of acceptors to a concentration of $N_A=10^{14}$ cm-3.
(a) Draw the band diagram of a pn junction at zero bias voltage bias showing the conduction band edge, the valence band edge and the Fermi energy.
(b) Is the depetion layer wider on the left half or the right half? Why?
(c) What is the concentration of holes on the left half outside the depletion region? What is the concentration of holes on the right half outside the depletion region?
(d) Light falls on this semiconductor. Will the current flow left or right? Why?
For silicon: $E_g = 1.12$ eV, $N_c = 2.78 \times 10^{19}$ cm-3, $N_v = 9.84 \times 10^{18}$ cm-3, and $n_i= 7\times 10^{9}$ cm-3.
Problem 2
(a) Draw a cross section of an n-channel MESFET.
(b) Draw the band diagram for the for this MESFET along a line that goes from the gate metal to the channel for zero applied gate voltage. Label the Schottky barrier.
(c) How does the channel resistance change as the MESFET is heated up?
(d) What can be done to optimize the speed of a MESFET?
Problem 3
(a) Draw a cross section of an p-channel MOSFET showing the source, drain, gate, and body contacts.
(b) Draw the band diagram for the p-channel MOSFET in inversion along a line that goes from the gate metal to the body.
(c) The source and the body contacts are grounded. What voltages need to be applied to the gate and drain to put the p-channel MOSFET in saturation?
(d) How could you experimentally determine the flat-band voltage?
Problem 4
A npn bipolar transistor is made starting with epitaxially grown layers. The lowest layer is the subcolloector, then the collector, the base, and the emitter is the top layer.
(a) Make a drawing of the final transistor including the metal contacts. Be sure there are no parasitic Schottky diodes in your drawing.
(b) Why shouldn't you start with the emitter on the bottom?
(c) Where is the largest mobile charge carrier concentration gradient when the transistor is biased in the forward active regime?
(d) What limits the maximum allowed collector-emitter voltage?
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 |