Analytic Potential and Charge Model of Semiconductor Quantum Wells


An analytical model is proposed to work out the potential and the electron concentration in 1D-confined quantum-well structures. This model is applicable to any quite asymmetric planar device, such as high-electron-mobility transistors or absolutely depleted semiconductor-on-insulator FETs. It's primarily based on the solution of the Poisson and Schrödinger equations, under the effective mass approximation, for a triangular potential well, and on the primary-order perturbation theory. It's grounded on the physics that governs the device operation and avoids the employment of any fitting parameter. The analytical resolution considers the wave perform penetration into the gate insulator, the effective mass discontinuity at the semiconductor–insulator interfaces, and the Fermi–Dirac statistics. Expressions for the calculation of the subband energies, their corresponding wave functions, still as the potential profile within the structure are provided. It's demonstrated that our analytical model fits very well the numerical ends up in all operating regimes from subthreshold to robust inversion for different device sizes and materials.

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