KABARAK
UNIVERSITY
UNIVERSITY EXAMINATIONS
SEMESTER ONE 2020 ACADEMIC YEAR
FOR THE DEGREE OF BACHELOR OF EDUCATION
CODE: PHYS 422 SEMICONDUCTOR PHYSICS SPECIAL/SUPP
TIME: …………
STREAM:Y4S2
EXAMINATION SESSION: DEC 2020
DATE : …………
INSTRUCTIONS TO CANDIDATES
1. Answer Question 1 and any other two questions in the answer booklet provided.
2. Do not write on your question papers. All rough work should be done in your
answer booklet.
3. Clearly indicate which question you are answering.
4. Write neatly and legibly.
5. Edit your work for language and grammar errors.
6. Follow all the instructions in the answer booklet
7. Table 1: Effective Density of States Function and Effective Mass values
Silicon
1.08
0.56
Gallium Arsenide
0.067
0.48
Germanium
0.55
0.37
8. Table 2: Typical Mobility values at T=300 K and low doping concentrations
(
Silicon
1350
(
480
A members of Kabarak University family, we purpose at all times and in all places, to set apart in one’s
heart Jesus as Lord. (1 Peter 3:15)
Gallium Arsenide
8500
400
Germanium
3900
1900
9.
10. Fermi-Dirac integration has a value of
SECTION A: (Compulsory) TOTAL MARKS FOR THIS SECTION IS 30.
1
QUESTION ONE (30 Marks)
a) Explain the conductivity of a semi-conductor at:
i. Absolute temperature
(2 marks)
ii. Above absolute temperature
(2 marks)
b) Electron concentration of an n-type gallium arsenide semiconductor at T=300 K, varies
linearly from
coefficient,
to
over a distance of 0.10 cm. If the electron diffusion
.Calculate the diffusion current density in A/cm2. (3 marks)
c) The Fermi energy level is 0.30 eV below the conduction band energy. Determine the
probability of a state being occupied by an electron at
.
(4 marks)
d) Calculate the probability that a state in the conduction band is occupied by an electron and
calculate the thermal equilibrium electron concentration in silicon at T = 100 K. (given that
Fermi energy is 0.25 eV below the conduction band. The value of
is
for silicon at T =300 K
(5 marks)
e) Calculate the thermal equilibrium hole concentration in silicon at T=400K. Assume that the
Fermi energy is 0.27 eVabove the valence band energy. The value of Nv forsilicon at T =
300 K isNv= 1.04 x 1019cm-3.
(4 marks)
f) Calculate the thermal equilibrium electron and hole concentration in silicon at T = 300 K for
the case when the Fermi energy level is 0.22 eV below the conduction band energy Ec.
(5 marks)
g) Determine the thermal equilibrium electron and hole concentration inGaAs at is
T=300 K for the case when the Fermienergy level is 0.30 eV above the valence
band energy Ev.
(5 marks)
A members of Kabarak University family, we purpose at all times and in all places, to set apart in one’s
heart Jesus as Lord. (1 Peter 3:15)
SECTION B. TOTAL MARKS FOR THIS SECTION IS 40.
ANSWER ANY TWO QUESTIONS FROM THIS SECTION. EACH QUESTION
IN THIS SECTION CARRIES 20 MARKS.
QUESTION TWO (20 Marks)
a) Calculate the position of the intrinsic Fermi level with respect to the center of the band gap
in silicon at T = 300 K. The density of states effective carrier masses in silicon are
and
(4 marks)
b) Determine the position of the intrinsic Fermi level with respect to the center of the band gap
in Gallium Arsenide (GaAs) at T = 300 K.
(4 marks)
c) Explain how a p-type and n-type semiconductor material is formed
(4 marks)
d) Consider phosphorus doping in silicon, for T=300 K, at a concentration of
.
Determine the fraction of total electrons still in the donor states at T = 300 K.
e) Determine the total number of energy states in silicon between
(4 marks)
and
temperature, T=300K.
at
(4 marks)
QUESTION THREE (20 Marks)
a) Silicon semiconductor at T = 300 K is initially doped with donors at a concentration
. Acceptors are to be added to form a compensated p-type material
resistor is to have a resistance of 10
and handle a current density of 50 A/
applied. Calculate the conductivity
when 5V
(6 marks)
b) A given semi-conductor material whose Fermi energy level is 6.25 eV has the electrons
following the Fermi- Dirac distribution function. Calculate the temperature at which there is
a 1% probability that a state 0.30 eV below the Fermi energy level
(6 marks)
c) Calculate the radius (normalized to a Bohr radius) of a donor electron in its lowest
energy state in GaAs.
(4 marks)
d) An n-type silicon semiconductor at T=300 K is doped with donor concentration
and
. If the intrinsic carrier concentration,
(4
marks)
A members of Kabarak University family, we purpose at all times and in all places, to set apart in one’s
heart Jesus as Lord. (1 Peter 3:15)
QUESTION FOUR (20 Marks)
a) Let
so that the Fermi energy is above the conduction hand by approximate 52 meV at
T=300 K. Calculate the electron concentration using the Fermi-Dirac integral.(3 marks)
b) Consider p-type silicon doped with boron at a concentration ofNa= 1016 cm-3. Determine the
temperature at which 90 percent of acceptor atoms are ionized.
(4 marks)
c) Consider a silicon semiconductor at T = 300 K in which Na=1016cm-3 and Nd=
3 x1015 cm-3. Assume ni= 1.5 x 1010 cm-3.
(137/159)
(4 marks)
d) Silicon at T = 300 K contains an acceptor impurity concentration of Na= 1016cm-3. Determine
the concentrationof donor impurity atoms that must be added so that the silicon n type and
the Fermi energy is 0.20 eV below the conduction band edge.
(4 marks)
e) A compensated n-type silicon at T = 300 K, with a conductivity,
=16(Ω-cm)-1 and an
acceptor doping concentration of 1017 cm-3. Determine the donor concentration and the
electron mobility.
(5
marks)
QUESTION FIVE (20 Marks)
a) Consider silicon at T = 300 K so that NC=2.8x1019cm-3 and NV=1.04x1019 cm-3. Assumethat
the Fermi energy is 0.25eV below the conduction hand. If we assume that the band gap
energy of silicon is 1.12 eV, then the Fermi energy will be 0.87 eV above the valence band.
Calculate the thermal equilibrium concentrations of electrons and holes. Hence or otherwise,
explain whether the semiconductor is n-type or p-type
(6
marks)
b) Determine the probability that an energy level 3kT above the Fermi energy is occupied by an
electron given that T=300K.
(4 marks)
c) NC and NV vary as T2/3. Given that the band gap energy of gallium arsenide is 1.42 eV and
does not vary with temperature over 300-450 K, determine the value of kT. Hence or
otherwise, calculate the intrinsic carrier concentration in Gallium arsenide at T = 300 K and
at T = 450 K.
(6 marks)
d) A gallium arsenide sample at T=300 K with doping concentrations of Na=104
and Nd=1016 cm-3.Calculate the drift current density if the applied electric field is E =
A members of Kabarak University family, we purpose at all times and in all places, to set apart in one’s
heart Jesus as Lord. (1 Peter 3:15)
10V/cm
(4
marks)
A members of Kabarak University family, we purpose at all times and in all places, to set apart in one’s
heart Jesus as Lord. (1 Peter 3:15)