## PHT.301 Physics of Semiconductor Devices27.06.2018

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
(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) Draw the band diagram ($E_c$, $E_v$, and $E_F$) along a line from the gate to the substrate for this MOSFET in accumulation.

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

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

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 diode 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