(a) Normalized Gaussian weighting coefficients (black) for , and related (blue), which is the relative contribution of each height to ( is the tunneling probability). (b) The peak of shifts from the peak barrier height by an amount , which can be a significant fraction of the standard deviation of the height distribution. The peak corresponds to the channel dominating the conductance.
Effective barrier height (a) and width (b) determined by fits of vs V for as functions of and (as noted in percent of ). Thin black lines indicate or .
Equivalence of thermal smearing and a barrier height distribution. The smearing of the Fermi distribution in electrodes at finite temperature, as in (a), implies that hot (cold) electrons see a lower (higher) barrier height. Finite temperature can thus be modeled using zero temperature electrodes and a distribution of barrier heights, as in (b), where the distribution is derived from the Fermi function.
Thermal smearing simulations for junctions with and . (a) Bias dependence of tunneling conductance for 0.1 K (blue, solid), 300 K (green, dash), and 600 K (red, dash-dot). (b) The slight insulatorlike temperature dependence of the zero bias conductance (purple), and equivalently the resistance-area product (green), is a signature of tunneling, and is one of Rowell’s tunneling criteria. (c) The best fit barrier thickness (blue) and height (red) change only slightly over a large temperature range, influenced only by thermal smearing. (d) The Fermi–Dirac barrier height distribution (solid) has a less pronounced impact on the effective barrier parameters than the Gaussian distribution (dash) because of its more rapid decay.
Best fit barrier height and width for the two-channel junction as a function of the relative weighting of the secondary channel. Solid: , ; Dashed: , .
Relative impurity density required for primary and secondary tunneling channels to contribute equally to the net current density as a function of the secondary barrier height for the noted primary barrier heights with (left), and the noted thicknesses for a primary height of 2 eV. The thin vertical lines indicate 0.5 eV.
The normalized resistance-area product (RA) at zero bias (red, dashed) decreases as the spin-polarization of tunneling electrons (black, solid) increases when the temperature falls below . The parameters used were , , and . (Inset) Illustration of spin filter tunneling barrier parameters below , according to Eq. (4).
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