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Analytic Potential and Charge Model of Semiconductor Quantum Wells

An analytical model is proposed to determine the potential and the electron concentration in 1D-confined quantum-well structures. This model is applicable to any kind of asymmetric planar device, such as high-electron-mobility transistors or fully depleted semiconductor-on-insulator FETs. It is based on the solution of the Poisson and Schrödinger equations, under the effective mass approximation, for a triangular potential well, and on the first-order perturbation theory. It is grounded on the physics that governs the device operation and avoids the use of any fitting parameter. The analytical solution considers the wave function 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, as well as the potential profile in the structure are provided. It is demonstrated that our analytical model fits very well the numerical results in all operating regimes from subthreshold to strong inversion for different device sizes and materials.