Download Homework #1 - Dr. John D. Cressler

Homework #3
ECE 3040 “Microelectronic Circuits”
Dr. John D. Cressler
Due Date: Friday, 2/6/15
(in my hands by 5:00 pm)
[1]
Using simple calculations and some reasoning, show that an electron moving
inside a Si crystal should exhibit strongly quantum mechanical behavior. Full
credit requires some numbers and some words.
[2]
Technium has an electron effective mass ratio of 0.93, but Georgium has an
electron effective mass ratio of 1.59. Which of the two materials would be better
suited to building fast switching transistors? For full credit you must carefully
explain your reasoning.
[3]
Pierret, 2.7
[4]
Pierret, 2.12 (both parts)
[5]
Pierret 2.16 (all parts)
[6]
Pierret 2.17 (all parts)
[7]
Consider a sample of Si at 300 K which is doped with 4.0x1017 cm-3 of P, and
3.0x1017 cm-3 of B.
a) which carrier is majority, and which is minority?
b) calculate the majority carrier density (cm-3). Use correct notation for it.
c) calculate the minority carrier density (cm-3). Use correct notation for it.
d) calculate the position of the Fermi level w.r.t. EC (in eV)
e) Sketch the energy band diagram
[8]
Technium has a bandgap of 0.88 eV at 300K. Estimate the maximum useful
operating temperature of a sample of Technium doped with 1x1016 cm-3
acceptors (in K). You may make reasonable assumptions, but MUST carefully
state them. For example, you might assume that its effective masses, etc. are
equal to those of Si, and are weakly T dependent. For full credit you must
carefully describe your reasoning and show your work.
[9]
A Si sample of length 280 µm is doped uniformly with As at 1x1017 cm-3 and
measured at 300K. If we apply a voltage of 8 V across it:
Hint: use Calculus
Hint:
∫ dη(1+eη-ηc)-1 = η - ln (1+ eη-ηc)
a) what is the current density flowing? (in mA/µm2)
b) rework this problem if the sample was 0.8 µm, all else the same (in mA/µm2)
Be careful!
[10]
How long would it take a hole to travel from here to the moon and back, if it were
moving at saturation velocity (in sec)? Assume Si values at 300K. Hint: the mean
distance from the Earth to the Moon is 3.8x105 km.