Transcript video slide - University of Hawaii Physics and Astronomy

Announcements
Added a final homework assignment on
Chapter 44, particle physics and cosmology.
Chap 42 Homework note:
Binding energy is by convention positive (for molecules
and in nuclear physics, next chapter)
Preparing Practice Final Exam
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Why Some Solids Conduct Current
and Others Don’t
Conductors, semiconductors, and insulators:
Basic idea, Their description is provided in terms
of:
Energy Bands for electrons in solids
The Pauli exclusion principle
In order for a material to conduct electricity, it must
be possible to get the electrons moving (i.e., give
them some energy).
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Band gap from PHET University of Colorado
Felix Bloch in the 1950’s
at Columbia U.
Discovered band gaps in
1928 (thesis work in
Germany). 1952 Nobel
Prize for NMR.
https://phet.colorado.edu/en/simulation/band-structure
On MACs need Java enabled. Please
try it at home too.
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Energy bands (Question: why do these arise ?)
Band gap of 5
eV or more
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Small band gap
e.g. 1.12 eV for
Si, 0.67 for
germanium
Metallic sodium is
an example, gap
is 2.1 eV but even
at T=0, conduction
electrons.
Clicker question on energy bands
How would you expect the electric conductivity of a
semiconductor to vary with increasing temperature?
A. It should increase, because more electrons are
thermally excited from the valence band into the
conduction band.
B. It should increase, because more electrons are
removed from their parent atoms and added to the
valence band.
C. It should decrease, because the added thermal
energy breaks apart correlated electron pairs.
D. It should decrease, because the atoms in the
crystal will vibrate more and thus block the flow of
electrons.
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Clicker question on energy bands
How would you expect the electric conductivity of a
semiconductor to vary with increasing temperature?
A. It should increase, because more electrons are
thermally excited from the valence band into the
conduction band.
B. It should increase, because more electrons are
removed from their parent atoms and added to the
valence band.
C. It should decrease, because the added thermal
energy breaks apart correlated electron pairs.
D. It should decrease, because the atoms in the
crystal will vibrate more and thus block the flow of
electrons.
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Tricky Clicker question on energy bands
If you increase the temperature of a block of copper from
300 K to 600 K, what happens to the average kinetic
energy of the electrons in the conduction band? (Copper
remains a solid at these temperatures.)
A. The average kinetic energy increases by a factor of 4.
B. The average kinetic energy increases by a factor of 2.
C. The average kinetic energy increases by a factor of
.
2
D. The average kinetic energy changes by only a small
factor.
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Tricky Clicker question on enegry bands
If you increase the temperature of a block of copper from
300 K to 600 K, what happens to the average kinetic
energy of the electrons in the conduction band? (Copper
remains a solid at these temperatures.)
A. The average kinetic energy increases by a factor of 4.
B. The average kinetic energy increases by a factor of 2.
C. The average kinetic energy increases by a factor of 2 .
D. The average kinetic energy changes by only a small
factor.
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Semiconductors
• A semiconductor has an electrical resistivity that
is intermediate between those of good conductors
and good insulators.
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Holes
• A hole is a vacancy in a
semiconductor.
• A hole in the valence band
behaves like a positively
charged particle.
• The figure on the right
shows the motions of
electrons in the conduction
band and holes in the
valence band with an
applied electric field.
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Question: What is
the force on a
charged particle in
a uniform E field
Impurities
• Doping is the deliberate addition of impurity
elements.
• In an n-type semiconductor, the conductivity is
due mostly to negative charge (electron) motion.
• In a p-type semiconductor, the conductivity is due
mostly to positive charge (hole) motion.
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n-type and p-type semiconductors
• Figure 42.26 (left) shows an n-type semiconductor, and
Figure 42.27 (right) shows a p-type semiconductor.
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Fermi-Dirac distribution
• The Fermi-Dirac
distribution f(E) is the
probability that a state
with energy E is occupied
by an electron (identical
spin ½ particles)
f (E) =
1
e
(E-E f )/kBT
+1
There is a different distribution
for spin 1 (photons) and spin 0
particles [Bose-Einstein]
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Look at the
change with
temperature
Fermi-Dirac distribution example
At what energy above the Fermi level is the probability
that a particular state is occupied equal to 0.01 ?
f (E) =
1
e
(E-E f )/kBT
(E-E f )/kBT
e
+1
= 0.01
1
=
-1
0.01
(E-E f )/kBT
e
1
+1 =
0.01
Note for numeric problems
kB=1.3821 x 10-23J/K
or 8.61 x 10-5eV/K;
kT at room temp ~ 0.0254 eV
1
1
(E - E f ) / kBT = ln(
-1) ==> E - E f = kBT ln(
-1)
0.01
0.01
E = E f + 4.6kBT
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The probability of
occupying a state of
energy 4.6kBT is 1%
EF calculation with Fermi-Dirac distributions
The density of states dn/dE is given by a function g(E).
f (E) =
1
e
(E-E f )/kBT
The number of electrons dN in the range dE
around E is given by (integrate up to EF0)
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+1
EF calculation with Fermi-Dirac distributions
The variable n is the number of free electrons per unit
volume.
Example: At low temperatures , copper (Cu) has a free–
electron concentration of n=8.45 x 1028/m3, what is EF ?
3 p (1.055 ´10 J · s) (8.45 ´10 m )
EF =
-31
2(9.11 ´10 kg)
2/3
4/3
EF = 1.126 ´10
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-34
-18
2
J = 7.03eV
28
-3 2/3
Photocell
• A photocell is a simple semiconductor device.
• In a photo-cell an electron in the valence band can jump
to the conduction band. The conductivity increases in
proportion to the incident light intensity
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The p-n junction
• A p-n junction is the boundary in a semiconductor
between a region containing p-type impurities and
another region containing n-type impurities.
Very important: Many devices including transistors,
integrated circuits and diodes use p-n junctions
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More on the p-n junction
• A p-n junction is the boundary in a semiconductor
between a region containing p-type impurities and
another region containing n-type impurities.
Reverse biased, big energy
gapno current flows across
the junction except by tunneling.
“Depletion region” forms
Question: What happens
when the p-n junction is
biased as shown ?
-
+
p
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n
More on the p-n junction
• A p-n junction is the boundary in a semiconductor
between a region containing p-type impurities and
another region containing n-type impurities.
Question: What happens
when the p-n junction is
biased as shown ?
+
Electrons or holes now flow easily.
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p
n