Ballistic Metal Research Articles

Modeling of Ballistic Monolayer Black Phosphorus MOSFETs

In this paper, we present two accurate physics-based models of ballistic metal–oxide–semiconductor field-effect transistors (MOSFETs), both using less than ten parameters. These models—the capacitor model and the virtual source model—are based on the Landauer–Buttiker formalism. We show that the nonthermalization of charge carriers in the channels of ballistic MOSFETs leads to two critical effects that need to be considered in the modeling: the ballistic drain-induced barrier lowering (DIBL) effect and the floating source effect. The ballistic DIBL effect is responsible for a drain voltage dependence of the DIBL parameter; the floating source effect intensifies the injection of high-energy carriers from the source as the gate voltage increases. Specifically, the analysis is carried out on devices composed of monolayer black phosphorus, a 2-D semiconductor with unique electronic and mechanical properties, which make it a promising candidate for 2-D digital logic applications.

Josephson current in ballistic superconductor-graphene systems

We calculate the phase, the temperature and the junction length dependence of the supercurrent for ballistic graphene Josephson-junctions. For low temperatures we find non-sinusoidal dependence of the supercurrent on the superconductor phase difference for both short and long junctions. The skewness, which characterizes the deviation of the current-phase relation from a simple sinusoidal one, shows a linear dependence on the critical current for small currents. We discuss the similarities and differences with respect to the classical theory of Josephson junctions, where the weak link is formed by a diffusive or ballistic metal. The relation to other recent theoretical results on graphene Josephson junctions is pointed out and the possible experimental relevance of our work is considered as well.

Erratum: Tuning a Josephson junction through a quantum critical point [Phys. Rev. B64, 054511 (2001)

We have corrected a problem in our computational code that determined the normal-state resistance. In general, we find a reduction of Rn when the correlations are large and there is more than one plane in the barrier. The reduction of Rn affects four figures from the original paper, and affects the conjecture about ‘‘intrinsic pinholes.’’ We discovered that our calculations had not fully converged for the interacting density of states and self energy for small frequencies. This created numerical errors in the calculation of the resistance via the Kubo formula. The error has now been corrected and all resistances recalculated. The error does not affect the superconducting properties at all since they were calculated with a different imaginary-axis code. We show a corrected plot of the Josephson critical current, the normal-state resistance Rn , and the characteristic voltage IcRn for the single plane and two-plane barriers. The plots are on a semilogarithmic scale. The main difference is in the characteristic voltage IcRn in Fig. 4~c!. The optimization now occurs at the ballistic metal limit of U→0, where the IcRn product approaches the product of the bulk critical current times the Sharvin resistance, which is 0.287t/e 51.45D/e . As UFK increases, the characteristic voltage decreases and becomes flat as expected by the AmbegaokarBaratoff limit. The results for the two-plane barrier are modified significantly. The reduction of IcRn is more dramatic for moderate scattering, and as we move into an insulating barrier, we also reproduce the Ambegaokar-Baratoff result, and the unphysical increase with UFK has disappeared. Next we show the corrected figure for the moderately thick barrier ~with Nb55). The critical current, normal-state resistance, and characteristic voltage are plotted in Fig. 9 for Nb55 ~diamond!. The characteristic voltage has interesting behavior. Starting at a value about 20% less than the Ambegaokar-Baratoff limit in the metallic regime, the voltage initially decreases with correlation strength, then has a rapid increase starting at the metal-insulator transition, reaching a maximum near the Ambegaokar-Baratoff result ~up to the values of UFK that we can safely determine the IcRn product!. Junctions in this correlated regime do see an enhancement of the characteristic voltage on the insulating side of the metal-insulator transition, but the enhancement is at most only 20–30 % higher than in the thin tunnel junctions. The thick barrier junction Nb520 has the most significant corrections. We find that the calculations become untrustworthy when UFK becomes too large. We show results up to UFK56, but it is possible the IcRn product is too large there, due to an overestimate of the critical current Ic , as can be inferred by the slight upturn in the Ic data in panel ~a!.

Wave function penetration effects on current–voltage characteristics of ballistic metal–oxide–semiconductor transistors

Effects of wave function penetration into the gate oxide on the drain current in ballistic metal–oxide–semiconductor field-effect transistors (MOSFETs) are studied. MOS electrostatics is treated by self-consistent solution of one-dimensional Schrödinger and Poisson equations. Schrödinger equation is solved with an open boundary condition applied at the silicon–gate-oxide interface. Two-dimensional effects and inelastic scattering of carriers are neglected in the drain current calculation. Numerical results show that wave function penetration has nontrivial effects on modeling of the drain current. These effects are found to depend on the silicon surface orientation. In devices fabricated on (100) silicon, drain current and transconductance decrease when penetration effects are considered although the gate capacitance increases in the presence of penetration. On the other hand, in devices on (111) silicon, penetration effects increase the drain current and transconductance. An explanation for the opposite dependence of the penetration effects on surface orientation is provided. It also appears that the use of only the lowest subband to describe MOS electrostatics, as done in some studies, will lead to significant error in the calculation of drain currents.