## PHT.301 Physics of Semiconductor Devices05.02.2018

Problem 1
(a) How is the depletion width of a pn-junction related to the doping?

(b) How can the depletion width be measured experimentally?

(c) What is the built-in voltage $V_{bi}$ of a pn-junction? How can you measure $V_{bi}$?

(d) Describe a Zener diode.

Problem 2
Describe the role of recombination in a:

(a) light emitting diode
(b) bipolar transistor
(c) metal-semiconductor contact
(d) thyristor

Problem 3
(a) Draw an $n$-channel MOSFET showing the source, drain, gate, and body contacts.

(b) Draw the charge distribution, electric field, and band diagram (conduction band, valence band, Fermi energy) in inversion along a line from the gate into the body (like for a MOS capacitor).

(c) Where are the following current mechanisms dominant in a MOSFET?

• Drift
• Diffusion
• Thermionic emission
• Tunneling

Problem 4
Make a drawing of a laser diode and describe how it works. What determines the frequency that is emitted? Why is there a threshold current? How is it different from an ordinary light emitting diode?

 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