solid state physics (3.23)gmc.scripts.mit.edu/gmc/images/stories/files/mlb/solid... ·...
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Solid State Physics (3.23)
kevin gotrik
may 2, 2011
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The big picture is important
• How are humans able to understand the
matter that we can touch and see?
Sometimes it seems to me that a bond between two atoms has
become so real, so tangible, so friendly, that I can almost see it.
Then I awake with a little shock, for a chemical bond is not a real
thing. It does not exist. No one has ever seen one. No one ever thing. It does not exist. No one has ever seen one. No one ever
will. It is a figment of our own imagination.... Here is a strange
situation. The tangible, the real, the solid, is explained by the
intangible, the unreal, the purely mental. Charles A. Coulson
• One of these mental frameworks is quantum
mechanics.
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Quantum Mechanics
• I think I can safely say that nobody understands
quantum mechanics. -Richard Feynman
• Postulates of Quantum Mechanics:
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• 1) The information about a quantum state can be represented by a ket |Ψ(t0)> which belongs to a Hilbert space and behaves ‘nicely’ (continuous, etc.)
a Hilbert space
Euclidean vector space space
|Ψ(t0)> |Ψ2(t0)>
a Hilbert space
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• 2) Every observable (position, momentum,
energy) can be mathematically represented by a
Hermitian operator, A.
a Hilbert spaceAA|Ψ(t0)> = a|Ψ(t0)>
a
|Ψ(t0)> |Ψ2(t0)>
a Hilbert spaceAa
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a Hilbert spaceAA|Ψ(t0)> = a|Ψ(t0)>
a
• 3) The only possible observation is an eigenvalue of the operator . ‘We can predict all possible outcomes!’
|Ψ(t0)> |Ψ2(t0)>
a Hilbert spaceAa
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• 4) The probability of obtaining a certain
observation is P(an) = |<Ψ|u
n>|2
a|<Ψ|u
n>|2
a
un
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• 5) Measurements disturb the quantum state and
the state will remain fixed immediately after.
aa
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• 6) the Schroedinger eq. is true. This can not be derived, it was the result of ingenious mathematical intuition.
I don't like it, and I'm sorry I ever had anything to do with it.
(Erwin Schrodinger talking about Quantum Physics)
A A-> HHA
A-> HH
H y = i Ñ (∑/∑t)y
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Particle in a box + free -> crystal
What about real materials?
x k
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Where the electrons are determines
electronic / optical properties
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Electronic Properties
• Si technology mostly interested in changing conductivity. With band gap engineering we have >1010 control! We do this by manually adding carriers. Interfaces give us devices.
Optical Properties
• The number, energy level of electrons and how they are able to move in a material also affects their permittivity, ε, which changes index of refraction.
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Optical properties
• More math! Quantum + Maxwell’s equations.
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Optical propertiesMaxwell’s equations give us insight into what a
photon is: a self-sustaining electromagnetic wave (B
and E are coupled)
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When light interacts with materials, electrons
play the deciding role in optical properties.
e-e-
c c<c
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Optical properties
No light no party.
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Magnetic Properties
• Also from electrons in the form of spin and from Maxwell’s equations.
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Thank you!
electrons are important!
electrons don’t stop
The end