Modeling Schottky barrier SINIS junctions J. K. Freericks, B. Nikolić, and P. Miller * Department of Physics, Georgetown University, Washington, DC 20057 * Department of Physics, Brandeis University, Waltham, MA freericks@physics.georgetown.edu (202) 687-6159 (voice) (202) 687-2087 (fax) Most recent preprint: cond-mat/0001269
Josephson Tunnel Junctions I S I S A Superconductor-Insulator- Superconductor sandwich can tunnel coherent Cooper pairs (Josephson current) or can tunnel broken pairs (quasiparticles) through the barrier. I V Ic V If the phases of the superconducting wavefunctions differ, then there is a DC Josephson current I=Ic sin θ. The I-V characteristic is highly nonlinear at low voltages, leading to the possibility of important electronics applications (based on latching technologies which are slow and subject to punch-through, because of the hysteretic IV curves).
Josephson Proximity-Effect Junctions I I S N S V Ic V A Superconductor-Normal metal- Superconductor sandwich where the weak link between superconductors occurs through the proximity effect. Andreev reflection at the N-S boundaries leads to sub-gap bound states that carry the pair current. Single-valuedness of the IV characteristic allows for nonlatching technologies like RSFQ logic. Goal is to optimize the switching speed of these junctions by maximizing IcRn, while maintaining nonhysteretic behavior.
Digital Electronics and RSFQ logic Rapid single-flux quantum logic is used for highspeed applications. A loop of superconducting material has one JJ interrupting it. The absence or presence of a flux quantum in the loop is the binary 0 and 1 of the device. (Much faster than latching technologies.) The flux is changed by generating a voltage pulse through the junction, whose time integral is equal to a flux quantum. Since the voltage scale is set by the product IcRn, which is on the order of a few mv in low-tc superconductors, operating speeds of up to 770 GHz have been already demonstrated. High Tc junctions, with IcRn products larger than 20 mv can possibly produce speeds in excess of 1 THz! The goal for fast electronics is to optimize the IcRn product of a junction, while maintaining nonhysteretic IV curves. X Binary 0, no flux X Binary 1, one flux quantum
Navy Interest High precision, high speed, analog-digital converters for the Advanced Multifunction Radio Frequency System for use in radar, electronic warfare, and communications. Long-term specs include 12 bit ADC with 1GHz of bandwidth. Processing speed is more important than resolution. Short-term goal is a 20 bit ADC with 20MHz of bandwidth. Superconducting digital electronics may provide the solution. The theoretical calculation and modeling is a scalable massively parallel solution to a scientific problem. Work would have an impact on the HTMT JJ-based petaflop computer which could be competitive with IBM s blue-gene project. (But the JJ computer may no longer be funded.) J. K. Freericks, Georgetown University, Josephson Junction Talk, 2001
Optimization of the speed of a JJ Current low-tc electronics employ externally shunted tunnel junctions. SC Weak-link region SC Self-shunted junctions can be made by reducing the linewidth to submicron scales, but spreads in junction properties may be severe if the transport is dominated by pinholes. The SINIS concept is to combine the best properties of tunnel junctions and proximity-effect junctions into a device that potentially is more robust. Here we examine a class of SINIS junctions, where the insulating barrier is made via a mismatch of workfunctions between metals which yields Schottky barriers at the superconductor-normal metal interface.
Many-Body Formalism Inhomogeneous system, with planes stacked along the z-direction. H= Σ t c* c + Σ U n n + long range Coulomb ij iσ jσ i i i Hopping, site energy, and the Coulomb interaction can vary from one plane to another. The superconductor is described by the H-F approximation, which is identical to a selfconsistent solution of the BogulubovdeGennes equations for a short-coherence length, s-wave superconductor. Long-range Coulomb interactions allow the charge to be redistributed if the workfunctions of the superconductor and the normal metal differ. This creates a self-consistently determined Schottky barrier, which is spatially extended and reduces the effective transparency of the junction. i i+1 i+2
Conventional Models SC Weak- Link SC Ε F S Barrier S BTK model, interface scattering, no self-consistency, no electronelectron interactions in the barrier, no bandstructure effects. Simple exercise of matching boundary conditions for plane waves. Generalizations to include bandstructure effects (Fermi wavevector mismatch, varying effective mass) are easy to include. Self-consistency and especially correlations have been much more difficult. All of these effects are automatically included in our approach!
Bulk superconducting properties T c =0.11t, =0.198t, 2 /k B T c =3.6--- behaves like a BCS superconductor Bulk coherence length ξ 0 =3.7a= v F /π ---short coherence length superconductor
Proximity effect Thin barrier (N b =1). This acts pretty much as one would expect. As the Schottky barrier increases, due to a larger workfunction mismatch, the anomalous average decreases within the barrier and becomes sharper in the superconductor. Thick barrier (N b =20). The anomalous average is reduced as the Schottky barrier increases, and becomes sharper in the superconductor, but then the effective thickness becomes larger as the barrier height grows further. Hence, a strong Schottky barrier can have an effective thickness larger than its actual thickness.
Proximity effect (thickness) Notice how oscillations in the pair-field amplitude occur when the barrier thickness is intermediate in size (2-10 planes). This is a length scale on the order of the superconducting coherence length (4a) and of the screening length (3a). The proximity effect decreases for thicker barriers, as expected, and the shape of the depletion of the pair-field amplitude at the interface becomes locked in after the barrier is about 10 lattice spacings thick.
Scaling of Schottky barrier Local charge for the 20-plane barrier as a function of the work-function mismatch. Rescaling the data against the maximum charge deviation produces a data collapse! The shape of the Schottky barrier is independent of the size of the mismatch near half filling. We believe this is because the cubic DOS is relatively flat near half filling and will not hold in the general case.
Current-phase relation (thin barrier) When Ic approaches the bulk critical current, little total phase can be put across the junction. As the barrier becomes more insulating, the current phase relation approaches sinusoidal behavior.
Critical current The semilogarithmic plots show the expected decrease in Ic as a function of the barrier thickness. Note how rapidly the current initially drops for the large barrier, which cannot be described by a simple exponential. When the barrier is small, we approach the bulk critical current shown in the dashed line. Fits for the barrier coherence length range from about 15-20 lattice spacings.
Junction resistance The junction resistance does not depend strongly on the barrier thickness (as expected for clean-ballistic junctions). There is an enhancement of the scattering for moderate width junctions, when the width is on the order of the screening length, as the overlap of the charge depletions within the barrier near each SN interface interfere and reduce the total charge density more than in thicker barriers.
Local charge density Note how the charge depletion is largest for the single and double plane barrier. Since a single plane never can scatter much, this explains why the resistance is largest for a two-plane junction.
Characteristic voltage The characteristic voltage is always less than the planar contact limit of the bulk critical current times the Sharvin resistance. Note how the voltage decreases dramatically with thickness.
Characteristic voltage versus Thouless energy Insulator Dirty Metal Kulik- Omelyanchuk Correlated barrier teaser ---barrier tuned through a metal-insulator transition. Quasiclassical theory predicts a universal form for dirty metals, but we see different behavior for the correlated insulator which predicts a greater sensitivity to intrinsic pinholes.
Outstanding Technical Issues Incorporate Schottky physics, correlations, plus long-range spatial ordering, to describe behavior of grain boundaries in high-tc. (Collaborations being developed with Mannhart s group in Augsburg.) Generalize from s-wave to d-wave to examine high-tc systems. Add spin-dependent physics to model hybrid superconductorferromagnetic structures and to understand spin-scattering effects. Generalize the formalism to calculate nonequilibrium effects needed to determine IV characteristics and to calculate subgap structure. Applications possible to other devices (spintronics and hybrids).
Conclusions Examined properties of a SINIS Josephson junction with self-consistently determined Schottky barriers. Saw that interesting phenomena occur when the barrier thickness is on the order of the screening length (oscillations in the pair-field, enhancement of IcRn). Found a scaling behavior of the Schottky barrier with workfunction mismatch over a wide range of parameters. Schottky-based clean SINIS junctions do not appear to perform well in optimizing the characteristic voltage, since the Schottky barrier destroys the supercurrent much more easily than the resistance is increased.