Characteristics of High-Al-Composed Quantum Structure Under Strain Effects

Abstract

A heterojunction field effect transistor has been studied by a model run self-consistently from the solution of the Schrödinger equation coupled with Poisson equation. The properties of the device drain current, the band structure of device, and the charge distribution have been obtained because of material composition. The efforts have shown that unique reason of having the high carrier concentration in heterostructures is to manage with the piezoelectric and spontaneous polarization. Simulation by means of polarization-related quantities in nitride-based heterostructure systems reveals that the device characterizations of nitride alloys are a linear function of alloy composition. Our simulation results are comparable to other theoretical calculations.

Appendix

Incomplete Gamma functions $I_{r} \left( {a,b} \right)$ and $F_{r} \left( a \right)$ may be written in Mathematica code as follows.

$$I_{rab} \left[ {r,a,b} \right]: = \frac{1}{{{\text{Gamma}}\left[ {r + 1} \right]}}\left( {\frac{{b^{r + 1} }}{r + 1}} \right) + \mathop \sum \limits_{i = 1}^{s} {\text{Binomial}}\left[ { - 1,i} \right]E^{ai} K_{ira} \left[ {i,r,a} \right];$$

$$\begin{aligned} F_{ra} \left[ {r,a} \right]:= \frac{1}{{{\text{Gamma}}\left[ {r + 1} \right]}}\left( {\frac{{a^{r + 1} }}{r + 1}} \right) + \mathop \sum \limits_{i = 1}^{s} \begin{array}{*{20}c} {{\text{Binomial}}\left[ { - 1,i} \right] + K_{ira} \left[ {i,r,a} \right]}\end{array} \\ \quad + \;\mathop \sum \limits_{j = 0}^{s} {\text{Binomial}}\left[ { - 1,i} \right]E^{{a\left( {j + 1} \right)}} \frac{{{\text{Gamma}}\left[ {r + 1, a\left( {j + 1} \right)} \right]}}{{\left( {j + 1} \right)^{r - 1} }}; \\ \end{aligned}$$

$$K_{ira} \left[ {i,r,a} \right]: = E^{ - ai} \mathop \sum \limits_{j = 0}^{s} \frac{{a^{r + j + 1} }}{{\left( {r + j + 1} \right) j!}}i^{j} ;$$

$$n_{z} \left[ z \right]: = A m_{z} \left[ z \right]\mathop \sum \limits_{i = 1}^{s} {\text{Binomial}}\left[ { - 1,i} \right](Abs\left[ {\varphi \left[ z \right]} \right)^{2} {\text{Log}}[1 + E^{B} ];$$