- #1
johng23
- 294
- 1
I need to calculate the density of states for a dispersion relation which is like the free electron dispersion, but with one effective mass in the kx, ky directions, and a different effective mass in kz. So I need to integrate the inverse gradient of E(k) over a surface of constant energy, ie and ellipsoid. I am confused about how to perform this integral.
Looking up some mathematical results on ellipsoids, it seems that you need to define some elliptic integrals which don't have an analytic solution. But I also found a PDF from some other semiconductor course which outlines this exact problem, and then gives a simple result that the density of states is proportional to sqrt(m*1 m*2 m*3) for the case where you have a general ellipsoid. Am I missing some major simplifying trick in the calculation?
Thanks.
Looking up some mathematical results on ellipsoids, it seems that you need to define some elliptic integrals which don't have an analytic solution. But I also found a PDF from some other semiconductor course which outlines this exact problem, and then gives a simple result that the density of states is proportional to sqrt(m*1 m*2 m*3) for the case where you have a general ellipsoid. Am I missing some major simplifying trick in the calculation?
Thanks.