1. ECE 874: Physical Electronics
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University

2. Lecture 17, 25 Oct 12
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7. (From practical to fundamental!)
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8. In 3 D:
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10. Then a = dv/dt for dvx/dt and dvy/dt
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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11. For any of these parabolas:
Region of biggest change of tangent = greatest curvature: the parabolas shown.
3D: <111> + <100>
E – EV (eV)
<111>
L G X
<100>
For any of these parabolas:
There’s a major axis but also two minor ones
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12. Picture taken from Ge, but same situation in GaAs in L direction
E – EV (eV)
Same: truncate 1/2
<111>
L G X
<100>
Picture taken from Ge, but same situation in GaAs in L direction
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15. Consider just the lowest energy and nearby:
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16. Goal: make these plausible:
For GaAS
For Si and Ge
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17. Consider just the lowest energy and nearby:
GaAs: rectangular <100> directions are symmetric with diagonal <111> directions
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18. Equation of a sphere
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19. For Si, E-k is NOT symmetric in X and L:
k1 = kz
k3 = ky
k2 = kx
But X is symmetric across a face area
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20. Equation of an ellipsoid
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21. Equation of an ellipsoid
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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22. Equation of an ellipsoid For Si and Ge:
BUT:
Ge k1 points in a diagonal type direction
Si k1 points in a rectangular type direction
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23. Can get ml* and mt* effective masses experimentally
Can show:
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
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24. Use this in Chp. 04 too.
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25. Confirm: http://en.wikipedia.org/wiki/Spheroid
(a)
Confirm:
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26. (a)
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27. Conduction band minimum energy “valleys”
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28. Does match ellipsoids as shown: Ge = long and skinny
(b)
Temp not specified
At 4K
Does match ellipsoids as shown:
Ge = long and skinny
Si = not so long and not so skinny
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