Silicon has its conduction band minima closer to X valley and therefore the electron has a large lattice momentum. When we calculate tunneling probability normal to (100) surface through a barrier (WKB, transmission matrix approach etc), we consider a parabolic band approximation that does not account for this extra source of momentum. The decay of wavefunction amplitude in the barrier does not consider the momentum of the incoming electron rather only considers energy which means this lattice momentum is completely ignored in this calculation. I was wondering if this lattice momentum contributes to tunneling probability or is it not relevant?