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There are 4 problems in this exam.
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Problem 1 (25 points)
Consider a silicon pn junction with a cross-sectional area of 10-4 cm2 and the
following parameters at T = 300K:
N 1017 cm3 , N 5 x1015 cm3, 107 s, 106 s
400 cm / V .s, 1000 cm / V .s
a) (10 points) Sketch the thermal-equilibrium energy-band diagram across the pn
b) (5 points) Determine the ratio of the hole current to total current at the space
charge edge xn for Va=0.5V
c) (5 points) Determine the ratio of the electron current to total current at the space
charge edge -xp for Va=0.5V
d) (5 points) Calculate the total number of excess holes in the n region for
Problem 2 (25 points)
Consider a Si pnp transistor with NE = 2x1017 cm-3, NB = 2x1016 cm-3,
NC = 2x1015 cm-3, a metallurgical base width of 0.5 m. Assume the critical
electric field to be equal to 3x105 V/cm.
n 1.5 1010 cm3 , 11.7 8.854 1014 F / cm
a) (5 points) Draw the energy band diagram under equilibrium.
b) (5 points) Draw the charge density, the electric field, and the potential
across the transistor under equilibrium.
c) (5 points) Draw the excess minority carrier densities across the emitter, base,
and collector bulk regions for VEB = 0.7 V, VEC = 2.7V.
d) (5 points) Determine the common-base breakdown voltage.
e) (5 points) Determine VEC at punch-through (neglect the B-E depletion region).
Problem 3 (25 points)
A MOS capacitor has an aluminum gate and a p-type semiconductor with doping
NA = 1015 cm-3. The silicon dioxide gate has a thickness of 450 A . The oxide
charge density is Qss = 3x1011 cm-2. For the aluminum-silicon dioxide junction,
3.4V and for the silicon-silicon dioxide junction, 3.25V
3.9 , 11.7 , 8.85 10
, E 1.12eV
0.026V , n 1.5 1010 cm 2
Q is the number of electronic charges per unit area in the oxide
(7.5 points) Calculate the flat-band voltage
(7.5 points) Calculate the threshold voltage
(5 points) Is this enhancement or depletion type?
(5 points) Sketch the charge density along the MOS capacitor at the onset of
Problem 4 (25 points)
Consider an n-channel MOSFET biased as shown in the figure below. Assume:
p+ polysilicon gate and:
t 100A, N 2 1017 cm3, Q' 1010 cm2 ,
E 1.12eV ,
Q' is the number of electronic charges per unit area in the oxide
ni 1.5 1010 cm 3 , o 8.854 x1014 F / cm
s 11.7 o , ox 3.9 o
W 10 m, L 2 m, 1000
a) (5 points) Determine the threshold voltage.
b) (10 points) Plot ID versus VDS for VGD = 0
c) (10 points) Plot ID versus VDS for VGD = 2VTN
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