## PHT.301 Physics of Semiconductor Devices30.11.2018

Problem 1
A region of a silicon wafer is doped with donors at a concentration of 3 ×1017 cm-3 and with acceptors at a concentration of 2 ×1016 cm-3. Assuming that all of the dopants are ionized, what is the density of electrons in the conduction band and the density of holes in the valence band at 300 K?

For silicon, $n_i =$ 1.5 ×1010 cm-3 at 300 K.

Solution

Problem 2

(a) Draw a cross section of an n-channel JFET showing the source, gate, and insulating substrate. (Make a large drawing that is about as wide as the paper).

(b) The JFET is biased in saturation. Draw the depleted region and put + or - signs in regions where there is positive or negative charge.

(c) Add arrows to the drawing of the JFET to indicate the direction of the electric field at each point.

(d) Where are there tunnel contacts in a JFET?

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) If the transistor is unbiased, which depletion region is wider? Why?

(b) For an unbiased transistor, is the maximum electric field larger in the emitter-base junction or in the base-collector junction? Why?

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

(d) Calculate the equilibrium electron concentration in the collector. (ni = 1.5 × 1010 cm-3)

Problem 4
Describe how a semiconductor laser diode 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