Problem 1
Consider a pn-junction.
(a) Estimate the maximum electric field in a pn-junction. Explain your estimation. Which way does the electric field point?
(b) If the pn-junction is heated up, what happens to the electric field? Why?
(c) State the relationship between the hole concentration on the p-side, the hole concentration on the n-side, and the built-in voltage \(V_{bi}\).
(d) Given the depletion width, \(W\), the donor concentration \(N_d\), the acceptor concentration \(N_a\), and the hole diffusion constant \(D_h\), estimate the hole diffusion current in an unbiased pn-junction.
For silicon at 300 K: $E_g = 1.12$ eV, $N_c = 2.78 \times 10^{19}$ 1/cm³, $N_v = 9.84 \times 10^{18}$ 1/cm³, and $n_i= 1.5\times 10^{10}$ cm-3, $\epsilon_r = 11.9$.
Problem 2
(a) Two JFETs are made with the same dimensions and the same doping concentrations. One is made from silicon and the other is made from GaAs. Silicon is an indirect band gap semiconductor with a band gap of \(E_g = 1.1\) eV while GaAS is a direct band gap semiconductor with a band gap of \(E_g = 1.4\) eV. How will these two JFETs differ in operation?
(b) If light falls on a JFET, where does a current flow?
(c) Explain how the hole mobility in silicon depends on the temperature and on the acceptor concentration.
Problem 3
(a) Draw a cross section of an $n$-channel MOSFET showing the source, drain, gate, and body contacts.
(b) Draw the band diagram (conduction band, valence band, Fermi energy) from the gate to body in accumulation.
(c) Consider a MOSFET in the linear regime (the drain voltage is not so high as to cause pinch-off). Is there a depletion region in the device? If so, where?
(d) Describe how you could calculate the drain current in the linear regime?
Problem 4
(a) The emitter-base junction of a bipolar transistor is a one-sided pn-junction. What experiment could you perform to determine the doping concentration of the base?
(b) Suppose you know the doping concentrations of the emitter, base, and collector. How could you measure the base width with the Early effect or a punch-through measurement?
(c) Plot the minority carrier concentration in an npn bipolar transistor in forward active mode.
(d) Why is a heterojunction bipolar transistor faster than a normal bipolar transistor?
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 |