PHT.301 Physics of Semiconductor Devices
07.03.2025


Problem 1
A silicon wafer is uniformly doped with donors with a concentration of $N_D=10^{15}$ cm-3. Acceptors are then diffused into the wafer from the surface to form a diode.

(a) What measurement can be performed to determine the doping profile of the acceptors $N_A(x)$?

(b) At zero bias voltage, the integral of the electric field across the depletion region is $V_{bi}$. What is the integral of the electric field across the depletion region when a voltage $V$ is applied?

(c) Give a formula for the charge density in the depletion region in terms of $N_A(x)$ and $N_D$.

(d) Give a formula for the electric field in terms of $N_A(x)$ and $N_D$.

(e) What value does the electric field have at the edges of the depletion regions?


Problem 2

(a) Draw an n-channel JFET.

(b) Draw the band diagram (conduction band, Fermi energy, valence band) of the pn-junction of the JFET when it is biased in saturation.

(c) Draw the band diagram (conduction band, Fermi energy, valence band) of the metal-drain contact. Indicate the Schottky barrier in your drawing.

(d) Why is the drain current almost constant in saturation?


Problem 3
A npn bipolar transistor has doping concentrations $N_{De}$, $N_{Ab}$, and $N_{Dc}$ for the emitter, base, and collector, respectively.

(a) What are the equilibrium minority carrier concentrations $p_{ne}$, $n_{pb}$, and $p_{nc}$ in the emitter, base, and collector?

(b) What is the minority carrier concentration at the edge of the depletion region in the base on the emitter side? Your answer should be a function of the voltage emitter-base $V_{eb}$.

(c) The base of a bipolar transistor should be thin. Thin compared to what? Is it possible to make it too thin?

(d) A transistor is biased in forward-active mode. Draw the collector current as a function of collector-emitter voltage. Why is the collector current almost constant for large voltages as the collector-emitter voltage is increased?


Problem 4

(a) A light-emitting diode should produce green light. What properties should the semiconductor have that is used to make this diode?

(b) How do you make metal-semiconductor contacts in a light-emitting diode so that the light gets out?

(c) Explain why sometimes light gets reflected back into the diode at the surface.

(d) What is the difference between a light-emitting diode and 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