# Effective Mass and Energy Bands

1. May 6, 2007

### WolfOfTheSteps

1. The problem statement, all variables and given/known data

Here is the problem:
http://img413.imageshack.us/img413/748/64my8.th.jpg [Broken]

3. The attempt at a solution

I got the effective mass. That's trivial. My question is, what are these graphs actually of? The horizontal and vertical axes are not labeled.

Is it an energy dispersion? If so, how come some of the curves are negative? All throughout the book, there is not a single energy dispersion curve with negative branches!

It can't be the effective mass vs K, because the second derivative of E with respect to k is not a parabola. And besides, the question "which band has the higher effective mass" would not make much sense. I know that on the dispersion curve, the narrower bands have lower effective mass. But the negative bands are just throwing me off.

Much thanks!

Last edited by a moderator: May 2, 2017
2. May 6, 2007

### leright

It represents energy as a function of wave vector of the electron. The upper and lower graphs are the conduction and valence bands of the material, respectively. The choice of where zero energy is chosen is arbitrary, really.

also, note that the electron momentum is proportional to the wave vector. this is simply because k = 2pi/lambda, but lambda = h/p, where p is momentum. therefore, k = 2pi/(h/p) = 2(pi)p/h. Or, p = (h-bar)k. So, you could have momentum on the x-axis instead of wave vector, if you like.

3. May 6, 2007

### WolfOfTheSteps

Thanks, leright!