A computational study of nonparabolic conduction band effect on quantum wire transport (e.g. GaN)

We studied the physics insight the GaN (example) quantum wire FET transistors. The model is based on the four k·p$$\mathbf{k}{\cdot } \mathbf{p}$$ Kane band model. We have introduced closed compact model for the Einstein relation of the diffusivity to mobility ratio (DMR) in quantum wires. The model can be applied for both wide and narrow band gaps of nonparabolic conduction band dispersion. The model is related to the optical matrix elements between conduction and valence bands. We have used 1D electrostatic to model the electron density over the maximum energy point. We have studied the effects of gate-to-source and drain-to-source voltages on the DMR by calculating the electron density using flux theory. We observed that above the threshold the non-parabolic dispersion increases the DMR. Additionally, we have studied the nonparabolic effects on the Fermi level and found that for low doping concentrations, the nonparabolic effect must be considered and an accurate calculation for the optical matrix elements is needed.