# Effective Masses in Silicon

1. Dec 7, 2008

### mindstream

Hey there.

I have a question concerning the effective masses in silicon. From what I've learned, the effective masses of electrons and holes can be determined from the curvature of the dispersion curve at the extrema. Since the effective mass is inversely proportional to the second derivative of energy, the less curved extrema represent the heavier electrons or holes. The effective mass tables give values of 0,92 (m*/m0) and 0,19 (m*/m0) for the electrons and 0,52 (m*/m0) and 0,16 (m*/m0) for the holes in silicon. Basically, the electron is almost twice as heavy as the heaviest hole. Now the problem I'm facing is that the dispersion curves aren't that diverse from my point of view.
So is there a flaw in my way of thinking and why are the electrons heavier in silicon.

Thanks in regard.

2. Dec 7, 2008

### Dr Transport

The effective mass of silicon electrons is an ellipsoid, you are quoting the longitudinal and transverse masses. They are highly ellipsoidal, so the masses will be quite different.

As for the others, you are quoting the valence bands (heavy hole and light hole), not too much anisotropy there given the approximation. In more exact formulations the band edge effective masses for the holes is much more anisotropic.

There is no reason that the hole masses have to be heavier than the electrons, and I cannot think of any semiconductor where the electron is heavier than the either of the holes. A really good reason escapes me at the present, so I'll have to look at some of my references to better explain it.

3. Dec 7, 2008

### mindstream

My mistake about the transverse/longitudinal masses. I guess I was referring to the density of states effective mass (or whatever the mass that can be determined from the dispersion curves is called).

But according to Wikipedia:

Material Electron effective mass Hole effective mass

Si 1.08 me 0.56 me
Ge 0.55 me 0.37 me

And I still don't see that big of a difference in silicon. It's more distinct in germanium though.

So, I'm guessing there's something wrong with my comprehension of this matter.

4. Dec 7, 2008

### Dr Transport

It's all in the band structure and how it is calculated. Now one thing that needs to be said, what you quoted above is the effective mass, not the density of states effective mass which is different. The density of states effective mass takes into account the band structure in a more general manner and is not constant with respect to direction in the crystal, I worked it out in my dissertation for anisotropic materials and the originator was my advisor, the link is, J. Appl. Phys. 54, 3612 (1983) .