# Exciton energy splitting in indirect semiconductor

Let's take an indirect bulk semiconductor and imagine the exciton that build up at the indirect gap. Since we have a bulk semiconductor we should find three p-like orbitals: $p_x,p_y,p_z$. Would their energy levels be degenerate due to the mass anisotropy which we have at the indirect gap? My intuition screams yes. But if I try to bring it on the paper I actually find the opposite. Any suggestions, ideas or helpful tips?

-

Just in case someone was interested, I'll give myself an answer :)

Yes they do split due to mass anisotropy. One can see that when solving the Wannier-equation for an indirect semiconductor. For the special cases that the wave vector lies in the $x$, $y$ or $z$ direction one finds that $x$ and $y$ will give the same integral and $z$ will differ from that. One of course has to define the band structure correspondingly: the masses in $x$ and $y$ are the same and in $z$ is different.

-