ECE 874: Physical Electronics
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ECE 874:Physical Electronics
Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]
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Lecture 17, 25 Oct 12
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(From practical to fundamental!)
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In 3 D:
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Find [m*ij]
Then F = qE
Then a = dv/dt for dvx/dt and dvy/dt
Integrate with respect to time, 2x’s, to get x(t) and y(t). Final answer will depend ontime
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Region of biggest change of tangent = greatest curvature: the parabolas shown.
3D: <111> + <100>
E –
EV (
eV)
L X <100><111>For any of these parabolas:
There’s a major axis but also two minor ones
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E –
EV (
eV)
L X <100><111>
Same: truncate 1/2
Picture taken from Ge, but same situation in GaAs in L direction
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Consider just the lowest energy and nearby:
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Goal: make these plausible:
For GaAS
For Si and Ge
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Consider just the lowest energy and nearby:GaAs: rectangular <100> directions are symmetric with diagonal <111> directions
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Equation of a sphere
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For Si, E-k is NOT symmetric in X and L:
But X is symmetric across a face area
k1 = kz
k3 = ky
k2 = kx
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Equation of an ellipsoid
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For Ge, E-k is also NOT symmetric in X and L, AND L is the minimum energy direction:
Want this direction type to be the k1 direction with k2 and k3 defined to be orthogonal (transverse) to it.
Equation of an ellipsoid
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BUT:Ge k1 points in a diagonal type directionSi k1 points in a rectangular type direction
For Si and Ge:Equation of an ellipsoid
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P. 80:Can get ml* and mt* effective masses experimentally
That means: can get an experimental measure of extent of k-space around the energy minima
Can show:
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Use this in Chp. 04 too.
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Confirm: http://en.wikipedia.org/wiki/Spheroid
(a)
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(a)
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(b)
Conduction band minimum energy “valleys”
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(b)
Does match ellipsoids as shown:Ge = long and skinnySi = not so long and not so skinny
At 4K
Temp not specified