## PHT.301 Physics of Semiconductor Devices31.01.2020

Problem 1

(a) Draw an p-channel JFET.

(b) Explain how a JFET works. Explain whether the gate voltage should be positive or negative to operate in the saturation regime.

(c) What is the dominant current mechanism for the source-drain current? (tunneling, drift, diffusion, thermionic emission).

(d) Draw the depletion region of a p-channel JFET biased in saturation. Add + and - signs to your drawing to show how the charge is distributed.

Problem 2

The charge density of a MOS capacitor is shown below. Here $n$ is the density of electrons in the conduction band, $p$ is the density of holes in the valence band, and $\rho$ is the charge density.

(a) Is this MOS capacitor biased in accumulation, depletion, or inversion?

(b) Indicate in the drawing where the mobile charge carriers are.

(c) Explain what the threshold voltage is of a MOSFET.

(d) Draw the electric field that would be caused by this charge density.

Problem 3
Consider an npn bipolar transistor.

(a) Explain how a bipolar transistor works.

(b) Explain what a diffusion current is. How is the diffusion constant related to the electron mobility?

(c) In saturation, both pn junctions are forward biased. How could the emitter and collector currents be calculated in this case?

(d) Explain the Early effect.

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