Bandgap and crystal orientation Some of us are designing an experiment to measure the bandgap of intrinsic semiconductor wafer. For that we need rectangular 2D pieces of the semiconductor material.
I want to know if the bandgap of semiconductor material depends on the crystal orientation in which it was cut.
 A: Disclaimer: The answer requires some knowledge of solid state physics. In particular, I assume that concepts like dispersion relation, reciprocal space and effective mass are familiar to you.
The band gap is a fixed characteristic of the material. It does not depend on the crystal orientation. In the band diagram, it is the minimum vertical separation of the conduction and valence bands. The exact momentum (and correspondingly, the crystal axis) which determine the gap are irrelevant to its definition. For a direct semiconductor (e.g. GaAs, InP, but not Si) the gap is even located at the origin of momentum space!
Now it is indeed the case that for different directions in momentum space, the carrier dispersion may look slightly different. Consequently, the effective mass is different, and also carrier mobility. However, when applying an electric field, you do not exclusively excite electrons and holes traveling parallel to the field. Some also move at an angle to it, but together, their net contribution to the axes perpendicular to the field vanishes.
Let us look at it in a different way.
If conductivity depends on the crystal orientation, it must be a tensor. Ohm's law then reads:
$$ j_k = \sum_{l\in \{x,y,z\}}\sigma_{kl}E_l$$
As is explained on this forum (post #9), for any material with cubic symmetry (e.g. Si, Ge, GaAs), we find that $\sigma_{kl}$ must be constant. In other words, conductivity does not depend on the orientation.
A: 
In the picture attached with the answer you can see how the interatomic distance affects the electron energy. This happens because the energy bandgap is directly affected by the periodic potential. Now consider 2 crystal directions. Then in one direction your atomic periodicity is a and in the other direction(diagonal maybe) it is $\sqrt[]{2a}$. The periodic potential will look different and the bandgap will change accordingly.
In fact, for due to the anisotropy all properties like thermal conductivity, electrical conductivity, RI will be different in different direction.
This is what my reasoning tells me. Lets discuss if there's any problem.
