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10/14/2010
1
LECTURE 2: Energy Bands and
Charge Carriers in Semiconductors
EECS 170A
10/14/2010
1
•
In this part of the lecture we will discuss the band theory of
solids and how they effect the electrical conduction.
•
Topic is cumbersome for a 50minutes lecture and needs review
of basic postulates of quantum mechanics
•
Here we will discuss the basic findings and discuss how they
affect our understanding at microscopic level.
•
The first thing we need to remember from our basic physics
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classes is the blackbody radiation theory which states that
“a
material at a constant temperature absorbs and emits energy
where total rate of radiation generation is equal to rate of
absorption.”
•
The release and absorption of energy is not random and they are
absorbed/radiated at in discrete packets:
,
(Max Planck,
1901) (concept of energy quantization)
–
Hence, energy levels are discrete
En
h
•
Bohr’s model: electrons occupy circular orbits around the nucleus and carry angular
momentum:
•
Combining with Planck’s theory we end up conclusion that says electron occupy
certain orbits with energy state:
•
(how many chocolate bars?)
•
Here L is the angular momentum at n’th orbit, m
0
is the electron mass at rest and r
n
is
the radius of the orbit
•
Results work for Hydrogen atom and fails for others
10/14/2010
3
0
2
nn
h
Ln rn
4
19
0
22
0
13 6
, 1
1.6 10
, 1
0.239
2(4
)
n
mq
E
eV
eV
J
J
calories
•
Next comes the Schrodinger’s wave mechanics that states that electrons in atom can
occupy only certain energy states with fixed principal quantum number, n, azimuthal
quantum number, l, and magnetic orbital quantum number, ±l, and a certain spin.
•
No more than one electron can occupy the same state.
Finding an electron at a
specific state is a statistical value
•
No one can localize the electron and give exact information on their momentum,
energy, etc. (uncertainty principle)
19
11
.
6
1
0(
)
/
()
1
eV
J
in energy
eV
electron
V
eV e or q
V
•
Multi electron atoms:
Finding an electron at a specific state is a
statistical value
•
You can calculate the probability of finding electron at specific
distance, r, from nucleus where a
0
is here is the Bohr radius
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4
2
0
3
0
0
59
21
4
2.
0
n
am
•
You can extend the analysis to find the probability of finding
electrons at certain energy levels and states.
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•
Multi electron atoms:
Si
•
Silicon has 14 electrons: At an isolated state, they occupy 1s, 2s,
2p, 3s, and 3p states. Electrons at the outer shell are valance
electrons that contribute bonding with other atoms
•
Valance has 8 states but only 4 are occupied: 4 more electrons
can also occupy the same energy level
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•
Since exclusion principle says that no more than one electron can occupy the same
energy level at the same state bringing 2 atoms close to each other will cause overlap in
the energy band.
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 Fall '10
 OzdalBoyraz

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