ECE 874: Physical Electronics

ECE 874:Physical Electronics

Prof. Virginia AyresElectrical & Computer EngineeringMichigan State Universityayresv@msu.edu

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