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6 February 2006, MTLS 3Q3 Materials for Electronic Applications
Assignment 1, Due Feb 13
th
at Class time
(SOLUTION)
In all answers use diagram and concise explanations.
1) Free electron theory and energy distribution electrons in solids.
a) For solid Al, draw a schematic diagram of the energy distributions of valence
electrons indicating the position of the Fermi energy E
F
at a temperature T = 0 K.
b) Draw the same diagram at a finite temperature T>0K and T >> 0 K.
c) What energy distribution would you need to use to calculate the probability of
finding an electron with an energy E>E
F
at T > 0 K.
d) Sketch a density of states diagram for a non freeelectron metal such as Fe.
(5 points)
Answer:
(a)
and (b)
T=0
(c) The probability of finding an electron with an energy E > E
F
at T>0 K is represented
by the FermiDirac distribution:
F
(
E
) = {(exp(
E

E
F
)
/kT
)+1}
1
which is the function of energy,
E
, for a given
kT
.
The occupancy probability of electron at T = 0 K and T > 0 K are shown in figures
below.
E
F
Energy
2p electrons
Bands full 3 s electrons
Parabolic band. Sharp transition at T =
0K but for T>>0 we have electrons at
E > E
F
.
T > 0 K
T >> 0 K
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View Full Document (d) Sketch of density of states diagram for Fe:
2) Band theory and properties of solids.
a)
Using the Ziman model of band theory, explain the origin of the gap in solids.
b) What distinguishes metals and insulators in a simple onedimensional Ziman
model. (Hint, discuss the trends as a function of number of valence electrons).
c) Can this simple one dimensional model explain the metallic state of most
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This homework help was uploaded on 04/17/2008 for the course MATLS Matls 3Q03 taught by Professor Botton during the Fall '05 term at McMaster University.
 Fall '05
 Botton

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