Eastern Mediterranean University
Electrical and Electronics Engineering Department
FALL 2001-2002
EE 245 – PHYSICAL ELECTRONICS – MIDTERM EXAM I
Instructors: Erzat Erdil and Huseyin Ozkaramanli
Date: 23 November 2001, Friday
Time Allowed: 100 minutes
Question #
Points
1
25
2
25
3
25
4
25
Total
100
Answer all (4) questions
Name
Number
533572718
Points Earned
1- a) Draw the (2 0 2) and (2 2 2) planes of a cubic lattice structure.
b) Calculate the planar atomic density (surface density of atoms) on the (110)
plane of the -iron BCC lattice in atoms per square millimeter. The lattice
constant of -iron is 0.287 nm. (Reminder:
planar atomic density=equivalent number of atoms whose centers are intersected by the
selected area divided by the selected area.)
c)
Calculate the linear atomic density in the [110] direction in the copper
crystal lattice in atoms per millimeter. Copper is FCC and has a lattice
constant of 0.361 nm. (Reminder:
Linear atomic density=equivalent number of atomic diameters intersected by the selected
length of line in the direction of interest divided by the selected length of line.
Note also that the direction [x0 y0 z0] gives the direction of the vector starting from the
origine (0 0 0) and pointing to the point (x0 y0 z0))
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2- a) The density of states, N(E) is the number of available electronic states per
unit volume per unit energy around an energy E and for a three dimensional
2k 2
system with a parabolic E-k (i.e., E 
) relationship it is given by
2m0
2m03 / 2 1 / 2
E
 23
Derive the above density of states relationship.
N (E) 
f(E)
b) Figure 1 shows the Fermi distribution function for various temperatures.
i)
What are the values of A, B, D? What is the energy level denoted by
C?
ii)
Which temperature is greater: T1 or T2? Explain.
A
T=D K
T1
T2
B
C
Energy, E
Fig. 1 Fermi distribution function for various temperatures
c) Justify the following statement:
“The Fermi Energy is the highest occupied energy state at 0 Kelvin”
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3- Explain in detail (use diagrams if necessary) what is meant by the following:
i) Lattice constant
ii) Miller indices
iii) Fermi energy
iv) Intrinsic semiconductor
v) Compound semiconductor
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vi) Intrinsic concentration
vii) Distribution function
viii)Joyce-Dixon approximation
ix) p-type semiconductor
x) Semiconductor Band-gap
4- Silicon samples with band-gaps 1.1 eV at 300 Kelvin, has properties listed
below.
Case 1:
Case 2:
Case 3:
EC – EF = 0.11 eV
EC – EF = 0.35 eV
EC – EF = 0.55 eV
The three cases above show the position of the Fermi Level EF, relative to the
conduction band edge EC, at different doping levels.
a)
b)
c)
d)
e)
which case shows heavy n-type doping
which case shows nearly intrinsic silicone
for heavy p-type doping, what will be the approximate value of EC – EF .
calculate the density of electrons and holes in case 2 above.
which of these elements, Boron (B), Arsenic (As), Germanium Ge,
Gallium Ga, will act like an acceptor in samples above.
Some useful information:
Effective density of states in the conduction band at 300 K, Nc (cm-3)= 2.82x1019
Boltzman constant , kB=8.62x10-5 eV/K.
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