American University of Sharjah
ELE 241 - Fall 2025 -Section 2
Homework 1
Please fill and keep the first three pages. The homework problems are provided
on pages 2 and 3. Please attach a scanned/digital copy of your answers to this
document before submitting through iLearn.
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Questions for Homework 1:
Question 1 (15 marks):
A) Find the end-to-end resistance of a bar 15 μm long, 3 μm wide, and 1 μm thick,
made of the following materials at room temperature:
a. Intrinsic silicon.
b. n-doped silicon with ND = 5 x 1016 /cm3.
c. Aluminum with resistivity of 2.8 μΩ.cm.
Recall that for intrinsic silicon, μp=480 cm2/V.s and μn=1350 cm2/V.s. For doped silicon
assume that μn=3μp=1200 cm2/V.s.
B) Compare the resistance of the 3 materials.
Question 2 (15 marks):
Find the current that flows in a silicon bar of 10 μm length having a 5 μm by 4 μm
cross-section and having free electron and hole densities of 104 /cm3 and 1016 /cm3,
respectively, when 1 V is applied end-to-end. Use μn=1200 cm2/V.s and μp=500 cm2/V.s.
(relate the electrical field to the voltage).
Question 3 (20 marks):
Holes are being steadily injected into a region of n-type silicon. In the steady-state, the
excess hole concentration profile, shown in Figure 1, is established in the n-type silicon
region at room temperature. Excess in this context means over and above the thermal
equilibrium concentration (with no hole injection), denoted here as pn0. If ND = 1016 /cm3,
ni=1.5 x 1010 /cm3, Dp=12 cm2/s, W=50 nm, find the density of the current that will flow in
the x direction.
Figure 1: The concentration profile of injected holes.
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Question 4 (30 marks):
If, for a particular junction, the acceptor concentration is 1017/cm3 and the donor
concentration is 1016/ cm3:
a. find the junction built-in voltage. Assume ni=1.5 x 1010 /cm3.
b. Find the width of the depletion region (W) and its extent in each of
the p and n regions when the junction terminals are left open.
c. Calculate the magnitude of the charge stored on either side of the
junction. Assume that the junction area is 10 μm2.
d. If a reverse-bias voltage of 3V is applied across this junction, what
will be the new values for W and the magnitude of charge stored on
either side.
e. Find Cj0 and Cj at VR values of 1.5 V, 2.5 V and 3 V.
Question 5 (20 marks):
Calculate IS and the current I for V = 780 mV for a pn junction for which NA = 1017
/cm3, ND=1016 /cm3, A=20 μm2, ni=1.5 x 1010 /cm3, Lp=5 μm, Ln=10 μm, Dp= 10
cm2/s, and Dn=18 cm2/s. Also, calculate the components of the current due to
hole injection and due to electron injection.
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