PHT.301 Physics of Semiconductor Devices05.10.2018

Problem 1
A p-type silicon wafer is uniformly doped with boron at a concentration of $10^{15}$ cm-3. N-type doping is then introduced by diffusion. The doping concentration is $N_D= 10^{17}\exp\left(\frac{-x^2}{10^{-12}}\right)$ cm-3. Here $x$ is the distance from the surface of the wafer measured in meters where $x=0$ is the surface of the wafer.

(a) Sketch the concentration of donors, acceptors, electrons, and holes $\left( N_D(x),\, N_A(x),\, n(x),\, p(x)\right)$.

(b) What is the concentration of electrons at $x=20$ μm?

(c) Draw the band diagram (valence band, conduction band, Fermi energy) assuming no voltage bias is applied.

(d) Draw the electric field as a function of $x$.

For silicon: $E_g = 1.12$ eV, $N_c = 2.78 \times 10^{25}$ 1/m³, and $N_v = 9.84 \times 10^{24}$ 1/m³.

Problem 2
(a) Draw an n-channel JFET.

(b) Explain how a JFET works.

(c) Where are there tunnel contacts in this device? What is the purpose of tunnel contacts? Draw the band diagram (valence band, conduction band, Fermi energy) of a tunnel contact.

(d) Why is a JFET slower than a MESFET?

Problem 3
In a silicon $pnp$ bipolar transistor, the emitter is doped to 1019 cm-3, the base is doped to 1014 cm-3, and the collector is doped to 1013 cm-3.

(a) Why is the transistor doped this way?

(b) Plot the minority carrier concentration in forward active mode.

(c) Calculate the equilibrium electron concentration in the collector. (ni = 1.5 × 1010 cm-3)

(d) How can you calculate the collector current?

Problem 4
(a) Describe how a solar cell works.

(b) The depletion region of a solar cell has a certain thickness in the dark. What determines this thickness? What happens to the depletion width when light falls on the solar cell?

(c) If a semiconductor has an indirect bandgap, what consequence does this have for a solar cell?

 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