## PHT.301 Physics of Semiconductor Devices17.05.2019

Problem 1

(a) You are given a silicon n-channel JFET. How can you experimentally determine the doping concentration in the channel?

(b) Plot the source-drain resistance of the JFET as a function of temperature. Assume no voltage is applied to the gate.

(c) If you have determined the doping concentration, how could you make a measurement that would estimate the height of the channel $h$?

(d) Where does tunneling occur in a JFET?

Problem 2

The charge density of a MOS capacitor is shown below.

(a) Is the semiconductor n-type or p-type?

(b) Draw the electric field that corresponds to this charge density. The electric field is positive if it points in the positive $x$-direction.

(c) Draw the band diagram that goes with this charge density.

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

Problem 3
(a) Draw a pnp bipolar transistor showing the emitter, collector, and base contacts.

(b) What are the doping levels of the emitter, the base, and the collector? How does the doping affect the emitter efficiency and the base transport factor?

(c) Draw the minority carrier concentration in forward active mode.

(d ) What is punch-through and what is latch-up?

Problem 4

Consider a green light emitting diode.

(a) Draw the electron dispersion relation $E$ vs. $k$. Indicate the value of the bandgap $E_g$.

(b) Draw a cross section of a wafer with an LED. Include the contacts in the drawing.

(c) Describe the problems associated with coupling light out of the diode.

(d) What would you have to do to turn this LED into a laser 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