ECE 874 Physical Electronics Prof Virginia Ayres Electrical

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

Lecture 17, 25 Oct 12 VM Ayres, ECE 874, F 12

VM Ayres, ECE 874, F 12

VM Ayres, ECE 874, F 12

VM Ayres, ECE 874, F 12

VM Ayres, ECE 874, F 12

(From practical to fundamental!) VM Ayres, ECE 874, F 12

In 3 D: VM Ayres, ECE 874, F 12

VM Ayres, ECE 874, F 12

Find [m*ij] Then F = q. E Then a = dv/dt for dvx/dt and dvy/dt Integrate with respect to time, 2 x’s, to get x(t) and y(t). Final answer will depend ontime VM Ayres, ECE 874, F 12

Region of biggest change of tangent = greatest curvature: the parabolas shown. E – EV (e. V) 3 D: <111> + <100> For any of these parabolas: <111> L There’s a major axis but also two minor ones G X <100> VM Ayres, ECE 874, F 12

E – EV (e. V) Same: truncate 1/2 <111> L G X <100> Picture taken from Ge, but same situation in Ga. As in L direction VM Ayres, ECE 874, F 12

VM Ayres, ECE 874, F 12

VM Ayres, ECE 874, F 12

Consider just the lowest energy and nearby: VM Ayres, ECE 874, F 12

Goal: make these plausible: For Ga. AS For Si and Ge VM Ayres, ECE 874, F 12

Consider just the lowest energy and nearby: Ga. As: rectangular <100> directions are symmetric with diagonal <111> directions VM Ayres, ECE 874, F 12

Equation of a sphere VM Ayres, ECE 874, F 12

For Si, E-k is NOT symmetric in X and L: k 1 = kz k 3 = ky k 2 = kx But X is symmetric across a face area VM Ayres, ECE 874, F 12

Equation of an ellipsoid VM Ayres, ECE 874, F 12

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 k 1 direction with k 2 and k 3 defined to be orthogonal (transverse) to it. Equation of an ellipsoid VM Ayres, ECE 874, F 12

For Si and Ge: Equation of an ellipsoid BUT: Ge k 1 points in a diagonal type direction Si k 1 points in a rectangular type direction VM Ayres, ECE 874, F 12

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, ECE 874, F 12

Use this in Chp. 04 too. VM Ayres, ECE 874, F 12

(a) Confirm: http: //en. wikipedia. org/wiki/Spheroid VM Ayres, ECE 874, F 12

(a) VM Ayres, ECE 874, F 12

(b) Conduction band minimum energy “valleys” VM Ayres, ECE 874, F 12

(b) Temp not specified At 4 K Does match ellipsoids as shown: Ge = long and skinny Si = not so long and not so skinny VM Ayres, ECE 874, F 12