Efficient quantum mechanical simulation of band-to-band tunneling

Abstract

In this work, we extend an already existing simulator for tunnel FETs to fully take into account nonparabolicity (NP) of the conduction band in all aspects, namely the wavefunction (WF) and density of states (DOS) corrections for both charge and BTBT current calculation. Comparison against more advanced full-quantum simulators based on TB and k · p Hamiltonians is presented as well and indicates very good matching between models for simple tunnel diodes. An initial parameter study of the Electron Hole Bilayer TFET (EHBTFET) indicates the presence of an optimum channel thickness, determined by the interplay between the subband alignment voltage and ON current level.

The Electron-Hole Bilayer TFET: Dimensionality Effects and Optimization

“…This is due to the use of a direct tunneling matrix element in Agarwal et al that largely differs from the phonon assisted tunneling one [16] that we found to be dominant in Si and Ge devices. Even though direct BTBT is dominant in Ge for bulk 3D-3D tunneling [8], quantization essentially suppresses the direct BTBT in the ON state of the Ge EHBTFET for all the cases considered in this study. Regarding InAs, instead, our results are only 5-10 times lower than the ones in [6] mainly due to the inclusion in our model of the effect of quantization on the matrix element (term C 0 (θ) in Eq.…”

“…The simulator solves the Schrödinger and Poisson equations self-consistently under the effective mass approximation with non-parabolicity corrections [8]. Self-consistency is achieved using the non-linear Schrodinger-Poisson scheme [9].…”

“…The expression for direct BTBT between the valence band and the conduction band minima at the Γ point is given by [8], which sums up the contributions of all aligned electron and hole subband pairs: I BANDGAPS, EFFECTIVE MASSES (ALONG THE QUANTIZATION AND TRANSVERSE DIRECTIONS), VALLEY DEGENERACIES, NONPARABOLICITY COEFFICIENTS ALONG WITH DEFORMATION POTENTIALS AND PHONON ENERGIES (PHONON-ASSISTED BTBT ONLY) USED FOR NUMERICAL SIMULATIONS.…”

“…T em,abs v (E) are the transmission coefficients that are based on the spectral functions, which contain the information about the wavefunctions and the density of states. We refer the reader to [8], [12], [16] for the exact expressions of T em,abs v (E) and of the spectral functions, which are omitted here for brevity. It is worth noting that for both direct and phonon-assisted BTBT, the tunneling current is determined by three components: i) the coupling element M dir(ph) , ii) the density of states (J)DOS and iii) the Fermi occupation term.…”

“…The direct BTBT model has been validated against k • p and tight-binding models elsewhere considering InAs and Ge diodes with different doping levels [8]. Fig.…”