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Assume we have an indirect semiconductor where the effective mass becomes anisotropic in different directions. Usually, one talks about a mass in parallel and perpendicular direction referring to momentum (or k-)space. So if I have a semiconductor sample for which I know the growth direction is lets say the parallel, I know which mass I have to consider when I look along this axes in real space. But what mass acts along the perpendicular direction in real space? Since real and k-space are connected via a Fourier transform, the mass perpendicular to the parallel mass in real space is not the one perpendicular to the parallel mass in k-space. So how can I find the mass acting perpendicular to the growth direction in real space when I know the mass along the growth direction and the mass perpendicular to that but I know it in k-space?

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If you refer to a layered structure along growth direction (e.g. quantum well, superlattice), you can calculate your mass for different states and positions from the 2nd derivative of the wavefunctions.

Perpendicular to it you would have the dispersion (and therefore mass) of a free particle, since you would usually assume that your layer planes are infinite in two dimensions.

If not, you have to solve the Schrödinger equation for more dimensions and again evaluate the mass based on the bending of the wavefunctions.

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