Analytic Potential and Charge Model of Semiconductor Quantum Wells

Marín, Enrique G.; Tienda-Luna, I. M.; Ruiz, Francisco G.; Gonzalez-Medina, J. M.; Godoy, A.; Gamiz, F.

doi:10.1109/ted.2015.2488362

Cited by 12 publications

(8 citation statements)

References 22 publications

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“…Further, in structures having a spacer layer, we ignore the leakage of the wave functions into the barrier layer, corresponding to the 2 × 2 method in [28]. The wave functions in the channel and spacer layers can then written in terms of Airy functions [31], [32] as…”

Section: Structure and Review Of Analytical Modelmentioning

confidence: 99%

A Closed-Form Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

Menokey¹,

Ajoy²

2023

Preprint

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Section: Structure and Review Of Analytical Modelmentioning

confidence: 99%

A Closed-Form Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

Menokey¹,

Ajoy²

2023

Preprint

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“…Measuring the sub-band levels with respect to the bottom of the potential well, Schrödinger's equation in the channel, spacer and barrier regions can be written as [38]…”

Section: Solution Of Schr öDinger's Equationmentioning

confidence: 99%

“…The double integral in eq. ( 29) can be evaluated analytically using the properties of Airy function integrals [38], [40], for example…”

Section: E Solution Of Poisson's Equationmentioning

confidence: 99%

“…In this work, we develop an analytical model to obtain the charge, charge distribution, wave functions, sub-band energies, surface potential, and band diagram of an N-polar GaN structure. For this, we modify the framework presented by Marin et al [38] to determine the wave function penetration into the gate insulator of a dual gated thin film silicon-on-insulator (SOI) structure. This framework solves the Schrödinger-Poisson problem by first writing the wave function as an appropriate linear combination of Airy functions, followed by perturbative corrections to include the effect of the potential resulting from the charge distribution; this process is repeated iteratively until convergence is reached.…”

Section: Introductionmentioning

confidence: 99%

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Airy Function-Based Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

Menokey

Ajoy

2022

IEEE Trans. Electron Devices

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A systematic, analytical method to obtain the charge density and surface potential in an N-polar GaN/AlGaN heterostructure is presented. This method also provides the wave functions, sub-band energies, and band diagram. The model accounts for the greater leakage of the wave functions into the spacer and barrier layers in the N-polar structure as compared to the Ga-polar structure. The framework is based on the solution of Schr ödinger-Poisson equations for an approximately triangular well potential with finite confinement, achieved using first-order perturbation theory. No fitting parameters are used. Results obtained using our model are in good agreement with numerical results (obtained using the finite difference method) for a wide range of bias conditions (from off to on states) and AlxGa 1−x N spacer mole fractions.

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“…The method described in this work can also be used to compute electron tunneling in sub-band energies and Two Dimensional Electron Gas (2DEG) charge density in a MOSFET [17]. In the GaN/AlN/AlGaN High Electron Mobility transistor (HEMT) and Ultra-thin body (UTB) architecture in [6,18].…”

Section: Introductionmentioning

confidence: 99%

Analytical estimation of lifetime of quasi-bound states in iii-v semiconductors quantum well

Nimje,

Mahajan

2023

Phys. Scr.

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The lifetime of electrons in the Quasi Bound States in a quantum well formed by III-V semiconductors has been calculated numerically by several researchers in the past. In this work, we obtain an analytical expression for the lifetime by finding the poles of the scattering matrix in small-width approximation. Airy functions which are solutions of the Schrödinger equation for triangular potentials are expanded asymptotically for large arguments and in power series for small arguments. A scattering problem for the triangular potential well is solved with the help of mixed boundary conditions to derive the expression for the decay width that further gives the net tunneling current from the quantum well. Heterostructures of III-V materials are modeled with triangular wells whose experimental measurements are in close approximation with the theoretical calculations presented in this paper. The analytically calculated decay width in this work is also compared with the reported values by different numerical methods and found in close agreement with them.

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Analytic Potential and Charge Model of Semiconductor Quantum Wells

Cited by 12 publications

References 22 publications

A Closed-Form Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

A Closed-Form Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

Airy Function-Based Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

Analytical estimation of lifetime of quasi-bound states in iii-v semiconductors quantum well

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