ECE 3080: Test #1, Solutions
June 11, 2009
Page 1 of 6
G
EORGIA
I
NSTITUTE OF
T
ECHNOLOGY
S
CHOOL OF
E
LECTRICAL AND
C
OMPUTER
E
NGINEERING
ECE 3080: Semiconductor Devices for Computer Engineering and
Telecommunication Systems
Summer Semester 2009, Test #1
SOLUTIONS
Short Questions (20 questions, 3 points each):
1.
You confine an electron in a (geometrically) smaller and smaller potential well with
infinitely high potential walls. Will the energy difference between neighboring energy states
increase, decrease or stay the same as you decrease the dimensions of the potential well?
Justify your answer.
Once the potential well reaches atomic dimensions, we get discrete energy levels, i.e. the
electron energy becomes quantized. With decreasing lateral dimension (width a) of the
potential well, the energy difference between neighboring energy levels increases, as can be
seen e.g. from the formula for the energy levels
E
n
=
2
2m
n
π
a
⎛
⎝
⎜
⎞
⎠
⎟
2
2.
The solution of the Schrodinger wave equation is the wave function
ψ
; what is the physical
meaning of the product
ψ ψ
∗
dV
, where dV is a volume element?
The integral
ψψ
*dV
∫∫∫
gives the probability to find a particle in a given volume element
dV.
3.
Briefly explain the concept of effective mass of an electron in a crystalline semiconductor.
The concept of effective mass allows us to treat the movement of carriers in the crystalline
semiconductor using classical Newtonian mechanics only by replacing the free electron
mass with the effective mass. The complex interaction of the carriers with the crystal
structure is “hidden” in the effective mass.
4.
What is known as the Pauli exclusion principle?
The Pauli exclusion principle states that no two fermions (e.g. electrons) in a system can
occupy the same state with respect to all of its quantum numbers. In semiconductor physics,
the Pauli principle causes the discrete energy levels of individual atoms to split up when
forming a crystal, finally creating the band structures with allowed and forbidden energy
regimes.
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ECE 3080: Test #1, Solutions
June 11, 2009
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5.
What is described by the density of states function?
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 Spring '08
 Staff
 pn junction, discrete energy levels, minority carrier concentrations

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