Numerical constraints and non-spatial open boundary conditions for the Wigner equation

We discuss boundary value problems for the characteristic stationary von Neumann equation (stationary sigma equation) and the stationary Wigner equation in a single spatial dimension. The two equations are related by a Fourier transform in the non-spatial coordinate. In general, a solution to the characteristic equation does not produce a corresponding Wigner solution as the Fourier transform will not exist. Solution of the stationary Wigner equation on a shifted k-grid gives unphysical results. Results showing a negative differential resistance in IV-curves of resonant tunneling diodes using Frensley’s method are a numerical artefact from using upwinding on a coarse grid. We introduce the integro-differential sigma equation which avoids distributional parts at $$k=0$$ k = 0 in the Wigner transform. The Wigner equation for $$k=0$$ k = 0 represents an algebraic constraint needed to avoid poles in the solution at $$k=0$$ k = 0 . We impose the inverse Fourier transform of the integrability constraint in the integro-differential sigma equation. After a cutoff, we find that this gives fully homogeneous boundary conditions in the non-spatial coordinate which is overdetermined. Employing an absorbing potential layer double homogeneous boundary conditions are naturally fulfilled. Simulation results for resonant tunneling diodes from solving the constrained sigma equation in the least squares sense with an absorbing potential reproduce results from the quantum transmitting boundary with high accuracy. We discuss the zero bias case where also good agreement is found. In conclusion, we argue that properly formulated open boundary conditions have to be imposed on non-spatial boundaries in the sigma equation both in the stationary and the transient case. When solving the Wigner equation, an absorbing potential layer has to be employed.

Current—voltage characteristics of connecting tunnel diodes at temperature heating up to 80°C

Investigations of the temperature stability of the peak tunneling current density of connecting tunneling diodes, which are necessary for the creation on their basis of multijunction photoconverters of powerful optical radiation, have been carried out. The structures of n++-GaAs/i-GaAs/i-AlGaAs/p++-AlGaAs of connecting TD with an intermediate undoped layer thickness of 7.5 nm and a growth temperature of 500 °C (structure ”A”) and with a thickness of 10 nm and a temperature of 450 °C (structure ”B”) were investigated. When heated to 80 °C, an increase in the peak tunneling current density of the TD structure ”B” by 4% is observed. However, for structure ”A”, a decrease in the peak tunneling current density by 5% with heating is observed. The factors leading to the appearance of a negative or positive temperature coefficient of the peak tunneling current density are determined using mathematical modeling of tunneling diodes based on GaAs/AlGaAs materials. By reducing the epitaxial growth temperature of n++–GaAs/i-GaAs/i-AlGaAs/p++–AlGaAs tunnel diode structure to 450 °C and including an undoped i-layer 10 nm thick between the degenerate layers ensure the temperature stability of peak current density when heated to 80 °C.

Predictor of reliability indicators for nanoelectronic heterostructure devices with transverse current transfer under conditions of limited experimental information based on Bayesian inversion

Predictor of the reliability indicators of resonant tunneling diodes with a generalization of the methodology for nanoelectronic heterostructure devices with quantum confinement and transverse current transfer has been developed. The advantage of the developed software is the possibility of interactive input of additional experimental information for further calculation of point and interval estimates of the reliability indicators of semiconductor devices using Bayesian inversion, which allows predicting these indicators under conditions of limited experimental information.