## 513.121 Physics of Semiconductor Devices30.06.2017

Problem 1
(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?

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
(a) Draw an $p$-channel MOSFET showing the source, drain, gate, and body contacts.

(b) How should this MOSFET be biased so that it is in the saturation regime?

(c) A voltage is applied between the source and the body that reverse biases the source-body junction. Explain how this shifts the threshold voltage. Which direction is the threshold voltage shifted and how far can it be shifted?

(d) Explain what latch-up is in CMOS circuits.

Problem 4
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) What is the equilibrium concentration of minority carriers in the collector?

(c) How can you calculate the collector current?

 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