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An analytical expression for the decay rate of quasi-bound states (QBS) in a triangular quantum well is derived by considering the resonance scattering of particles from the triangular potential profile. Asymptotic properties of the Airy functions that are solutions to the Schrödinger equation for a linear or triangular potential and a perturbative expansion for a small broadening of the QBS are utilized to derive the expression for its location E0 as well as the decay rate Γ that further gives the net tunneling current from the well. The triangular well model is commonly used to represent the band-bending near a heterojunction due to the electrostatic field. This compact expression shows excellent agreement with a full numerical solver and improvement over Wentzel–Kramers–Brillouin based calculations is demonstrated. [ABSTRACT FROM AUTHOR]

The program/erase process in floating gate (FG) flash memory devices is modeled by considering sequential quantum tunneling of electrons and taking into account quantum confinement in the channel and FG. We precisely determine location of quasi-bound or decaying quantum states in the inversion layer and in FG comprising a nanocrystal (NC) layer, and compute their lifetime by finding the complex eigenenergy of the resonance transmission problem. Self-consistent solutions to Poisson and Schrödinger equations are obtained for the quantum states of electrons in the inversion layer of MOS devices, and subsequently, sequential Fowler–Nordheim tunneling current to the spherical NCs is obtained using finite-element method considering open boundary conditions. The method described here is capable of determining the tunneling current accurately for arbitrary potential profiles, and can be applied for composite tunnel dielectric stacks. Our results show good agreement with the experimental data for high- $k$ interpoly dielectric flash memory devices. [ABSTRACT FROM PUBLISHER]

A standard experimental setup for Inelastic Electron Tunneling Spectroscopy (IETS) performs the measurement of the second derivative of the current with respect to the voltage ( d 2 I / d V 2 ) using a small AC signal and a lock-in based second harmonic detection. This avoids noise arising from direct differentiation of the current-voltage characteristics (I–V) by standard numerical methods. Here we demonstrate a noise-filtering algorithm based on Tikhonov Regularization to obtain IET spectra (i.e. d 2 I / d V 2 vs. V) from measured DC I–V curves. This leads to a simple and effective numerical method for IETS extraction. We apply the algorithm to I–V data from a molecular junction and a metal-insulator-semiconductor tunneling device, demonstrating that the computed first/second derivatives have a workable match with those obtained from our lock-in measurements; the computed IET spectral peaks also correlate well with reported experimental ones. Finally, we present a scheme for automated tuning of the algorithm parameters well-suited for the use of this numerical protocol in real applications. [ABSTRACT FROM AUTHOR]