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ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University [email protected]
ECE 874:Physical Electronics
Prof. Virginia AyresElectrical & Computer EngineeringMichigan State [email protected]
VM Ayres, ECE874, F12
Lecture 17, 25 Oct 12
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
(From practical to fundamental!)
VM Ayres, ECE874, F12
In 3 D:
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
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
VM Ayres, ECE874, F12
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
VM Ayres, ECE874, F12
E –
EV (
eV)
L X <100><111>
Same: truncate 1/2
Picture taken from Ge, but same situation in GaAs in L direction
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
VM Ayres, ECE874, F12
Consider just the lowest energy and nearby:
VM Ayres, ECE874, F12
Goal: make these plausible:
For GaAS
For Si and Ge
VM Ayres, ECE874, F12
Consider just the lowest energy and nearby:GaAs: rectangular <100> directions are symmetric with diagonal <111> directions
VM Ayres, ECE874, F12
Equation of a sphere
VM Ayres, ECE874, F12
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
VM Ayres, ECE874, F12
Equation of an ellipsoid
VM Ayres, ECE874, F12
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
VM Ayres, ECE874, F12
BUT:Ge k1 points in a diagonal type directionSi k1 points in a rectangular type direction
For Si and Ge:Equation of an ellipsoid
VM Ayres, ECE874, F12
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:
VM Ayres, ECE874, F12
Use this in Chp. 04 too.
VM Ayres, ECE874, F12
Confirm: http://en.wikipedia.org/wiki/Spheroid
(a)
VM Ayres, ECE874, F12
(a)
VM Ayres, ECE874, F12
(b)
Conduction band minimum energy “valleys”
VM Ayres, ECE874, F12
(b)
Does match ellipsoids as shown:Ge = long and skinnySi = not so long and not so skinny
At 4K
Temp not specified
