ECE 874: Physical Electronics Prof. Virginia Ayres Electrical & Computer Engineering Michigan State University ayresv@msu.edu

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

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 VM Ayres, ECE874, F12

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 VM Ayres, ECE874, F12

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 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: k1 = kz k3 = ky k2 = kx But X is symmetric across a face area VM Ayres, ECE874, F12

Equation of an ellipsoid VM Ayres, ECE874, F12

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 VM Ayres, ECE874, F12

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 VM Ayres, ECE874, F12

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 VM Ayres, ECE874, F12

Use this in Chp. 04 too. VM Ayres, ECE874, F12

Confirm: http://en.wikipedia.org/wiki/Spheroid (a) Confirm: http://en.wikipedia.org/wiki/Spheroid VM Ayres, ECE874, F12

(a) VM Ayres, ECE874, F12

Conduction band minimum energy “valleys” VM Ayres, ECE874, F12

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 VM Ayres, ECE874, F12