Prof. Sung-Jin Choi
Fall 2014
Midterm Exam:
Semiconductor Engineering (II)
2014.10.23 12:00 ~ 1:30 PM (one and half hour)
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Answer questions and explain your all steps on the exam paper
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Problem
1
2
3
4
5
6
7
8
9
10
Total
Score assigned
20
30
40
20
20
60
10
40
40
20
300
Score earned
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 1 (20 points). A metal, with a workfunction of 4.2 eV, is deposited on an n-type
silicon with an electron affinity of 4.05 eV and energy bandgap Eg = 1.12 eV. Assume full
ionization and room temperature.
(a) Sketch energy band diagram for Nd = 1016 /cm3 at equilibrium state.
(b) Sketch energy band diagram for Nd = 1018 /cm3 at equilibrium state.
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 2 (30 points). A metal, with a workfunction 5 eV, is deposited on a p-type silicon
with an electron affinity of 4.05 eV and Eg = 1.12 eV. Assume full ionization and room
temperature.
(a) Sketch the energy band diagram for zero bias for the case when no space charge region
exists at the metal-semiconductor junction.
(b) Determine Na so that the condition in (a) is satisfied.
(c) What is the potential barrier height (for this case, Schottky barrier height) seen by holes
in the metal moving into the semiconductor?
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 3. (40 points) A metal/n-type silicon Schottky diode has the C-V characteristic given
below. Assume the room temperature and full ionization condition.
1/C2
1.45 × 1015 cm4/F2
Region II
Region I
2.0 × 1014 cm4/F2
Va
-5 V
0.8 V
(a) What is the built-in potential between the region I and the metal?
(b) Explain how the 1/C2 value can be constant in region II (hint: see the hint of prob. (c)).
(c) Find the doping level of each region (Nd,region I and Nd,region II) of the n-type
semiconductor (Hint: For region II, just use a rough approximation, i.e., Nd,region II = ni
exp [(Eg/2)/kT]).
(d) Find the total depletion width at the silicon (Hint: there is no additional depletion for
Va < -5 V).
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 4. (20 points) Assume that the reverse saturation current density for pn-diode and
Schottky barrier diode are 3.66 × 10-11 A/cm2 and 5.98 × 10-5 A/cm2, respectively. Calculate
the forward bias in (a) pn-diode and (b) Schottky barrier diode to obtain the same forward bias
current density of 10 A/cm2. (c) Based on these results, draw the diode current-voltage graphs
of both diodes. (d) The reverse saturation current in Schottky barrier diode is expressed by
 q 
A * T 2 exp   bn  where A* is Richardson constant. What is the Schottky barrier height?
 kT 
Use the A* = 114 A/(K2cm2) and room temperature.
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 5. (20 points) For a metal/silicon Schottky barrier diode where silicon is doped to Nd
= 7 × 1018 /cm3, and Schottky barrier height is 0.67 eV, find out the depletion region width.
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 6. (60 points) A silicon PNP BJT with NE = 5 × 1018 /cm3, NB = 1017 /cm3, NC = 1015
/cm3, and WB (metallurgical junction width of the base) = 3 μm is kept at equilibrium state and
room temperature.
(a) Sketch the energy band diagram for the device, properly positioning the Fermi level in
the three regions.
(b) Sketch (i) the charge density, (ii) the electric field, and (iii) the electrostatic potential
as a function of position inside the BJT.
(c) Calculate the built-in potential between the emitter and the base.
(d) Determine the neutral region width of the base. Bias voltages of VEB = 0.6 V and VCB
= -2 V are now applied to the BJT.
(e) Sketch the energy band diagram for the device (under the applied bias, VEB = 0.6 V and
VCB = -2 V), properly positioning the Fermi level in the three regions.
(f) Based on the sketches completed in part (b), sketch (i) the charge density, (ii) the
electric field, and (iii) the electrostatic potential as a function of position inside the
biased BJT (VEB = 0.6 V and VCB = -2 V).
Semiconductor engineering II
Date: 2014. 10.23
Midterm Exam
(blank for Problem 6)
Prof. S.-J. Choi
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 7. (10 points) Two PNP BJTs are similar, except NB >> NC in transistor A while NB
<< NC in transistor B. Which transistor is expected to have a larger punch-through voltage (i.e.,
breakdown voltage) biasing? Explain briefly.
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 8. (40 points) For a certain PNP BJT, the ratios of carrier concentrations are sketched
as following:
(ΔnE, ΔpB, ΔnC are the excess minority carrier concentration for each region. Moreover, nE0,
pB0, nC0 are the minority carrier concentration at the equilibrium state.)
Emitter
Base
p B
pB 0
collector
10
 nE
nE 0
nC
nC 0
-1
Find out,
(a) The polarity of the emitter-base voltage (VEB). Why?
(b) The polarity of the collector-base voltage (VCB). Why?
(c) The magnitude of collector-base voltage
(d) The bias mode
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
Problem 9. (40 points) Consider the excess minority carrier distribution of a PNP BJT as
shown in the following figure (depletion regions at the junctions are not shown). Assume each
region is uniformly doped. Constant Dn = 30 cm2/sec and Dp = 10 cm2/sec are given. This
device has a cross section area of 10-5 cm2. The doping concentration of the emitter is NE =
1018 /cm3.
ΔnE
1015
ΔpB
8×1014
ΔnC
6×1014
4×1014
2×1014
0
1
Emitter
3 μm
2
Base
Collector
(a) Find the doping concentration in the collector.
(b) What is the bias mode in this BJT?
(c) Find the IEP, IEN, ICP, ICN.
Hint: use below equations:
I EP  qADB
d pB
=
dx x 1 m
I EN  qADE
d nE
=
dx x 1 m
I CP   qADB
d pB
=
dx x  2  m
I CN  qADC
d nC
=
dx x  2  m
(d) Calculate current gain β.
Problem 10. (20 points) Assuming that basic Schottky theory applies, sketch the energy band
Semiconductor engineering II
Date: 2014. 10.23
Prof. S.-J. Choi
Midterm Exam
diagram for (a) ohmic contact between p-type silicon and a metal at equilibrium state and (b)
a rectifying contact between p-type silicon and a metal under 2 V reverse bias.