Single Junction Model Research Articles

Dynamics of First and Second Switches in Bi$_{2}$ Sr$_{2}$CaCu $_{2}$O$_{8+\delta }$ Intrinsic Josephson Junction Stacks Measured by Specifically Designed Electronics

We measure switching probability distributions for the first and the second switches of stacks of Bi 2 Sr 2 CaCu 2 O 8+δ intrinsic Josephson junctions. To measure switching probability distributions, we design a current source and introduced a microcontroller. The resolution and accuracy are sufficient for measuring switching probability distributions of intrinsic Josephson junctions. For the first switch, crossover temperatures between thermally activated escape and macroscopic quantum tunneling are in the range between 0.8 and 2.2 K. The crossover temperatures of the second switch are approximately 8.0 and 6.8 K for the samples with critical densities of 1.0 and 2.0 kA/cm 2 , respectively. We analyze critical current density dependence of the crossover temperature of the second switch. The crossover temperature decreases with increasing critical current density. This anticorrelation can be explained neither by the single-junction model nor by the heating effect. The anticorrelation is a peculiar phenomenon observed in the second switch. We consider that the anticorrelation is attributed to the capacitive coupling. The strength of the capacitive coupling is weaker in IJJs with higher critical current density because the charge screening length is shorter due to increase of carrier density.

Increase of Phase Retrapping Effects in the Switching Rate from the Finite Voltage State of the Underdamped Intrinsic Josephson Junctions

We report a detailed study of the phase switching rate from the first to the fourth switch for a small stack of Bi2Sr2CaCu2Oy intrinsic Josephson junctions (IJJs). Experimental results were analyzed by using the conventional single-junction model including the thermally-activated phase escape and the multiple phase retrapping. It is shown that the phase retrapping effects are more prominent for higher order switches, even for the underdamped IJJs showing a large hysteresis in the current–voltage characteristics. This clearly suggests that the tilted washboard potential representing the phase switch from the finite voltage state in IJJs can be influenced by a rapid oscillation generated in a phase-switched junction.

Equivalent Single-Junction Model of Superconducting Quantum Interference Devices in the Presence of Time-Varying Fields

The reduced dynamical model of a two-junction quantum interference device is generalized to the case of time-varying externally applied fluxes with a d. c. component and an oscillating addendum whose frequency is comparable with the inverse of the characteristic time for flux dynamics within the superconducting system. From the resulting effective single-junction model for null inductance of the superconducting loop, it can be seen that the critical current of the device shows a dependence on the frequency and amplitude of the oscillating part of the applied flux. It can therefore be argued that the latter quantities can be considered as control parameters in the voltage versus applied flux curves of superconducting quantum interference devices.

Quantum interference in parallel connections ofN × (0–π) overdamped Josephson junctions

A one-dimensional array of N cells of 0- and π-junctions in parallel is considered. By assuming that junction parameters and effective loopareas alternate as one moves along the longitudinal direction of the array, going from 0- toπ-junctions, an effective single-junction model is derived. By this model, interferencepatterns of the critical current as a function of the applied magnetic flux can beanalytically found.

Equivalent single-junction model for two-junction quantum interferometers with small inductance in the presence of noise

We illustrate, in the limit of small values of the parameter β , a method to analyze the stochastic equations governing the time evolution of a two-junction quantum interferometer in the presence of noise. The analysis takes into account the different characteristic times of the two processes involved in the system, in such a way that the appropriate probability density function for each process is derived by means of one-dimensional Fokker–Planck equations. Therefore, the present analysis is equivalent to a generalization of the reduced single-junction model in the case of thermal fluctuations in the junctions. Voltage–current characteristics, transfer functions and circulating currents in 0-SQUIDs and π -SQUIDs are calculated by means of the proposed analytic approach.

Josephson plasma excitation and vortex oscillation mode in Josephson vortex state

The Josephson plasma resonance has been investigated in Bi 2Sr 2CaCu 2O 8+ δ single crystals in parallel magnetic fields to the ab-plane. We found two resonance modes; one appears at higher frequency in high fields above the plasma frequency ω p at zero field and absolute zero, and the other lies below ω p and is observed only in magnetic fields without considerable field dependence. Two resonance lines were also found in numerical simulations in a single junction model with randomness of the critical current. The higher frequency mode is attributed to the Josephson plasma mode modified by the periodic structure of Josephson vortices, while the lower frequency mode is interpreted as oscillations of Josephson vortices.

Modelling of the magnetic behaviour of random granular superconductorsby the single junction model

The magnetic measurements of the Josephson critical field andintergranular critical currents are presented for the Bi2223 compound. Theinvestigations prove that the Josephson critical field value is mainlydependent on the intergranular critical current density. The other factorslike the grain dimensions and shapes, sample porosity and density are lessimportant. The relation between the Josephson critical field and critical currentHcJ(Jc) is well described within the single junction model,Hcj∝JcλJ. The temperaturedependence of HcJ can also be well fitted according to the single junctionmodel with a critical current dependence, Jc∝(1-T/TcJ)α. The critical currentdensity versus temperature is almost linear indicating the presence ofsuperconductor-insulator-superconductor (SIS)type junctions.

Midgap states in a-Si:H and a-SiGe:H p-i-n solar cells and Schottky junctions by capacitance techniques

The midgap density of states (MGDOS) in a-SiGe:H alloys is investigated by capacitance measurements on p-i-n solar cells. Past work on thick a-Si:H Schottky barriers is extended to thin a-SiGe:H p-i-n cells. Four methods of determining the MGDOS from the measured capacitance are described, and each is applied to two p-i-n devices having 0% and 62% Ge in the i layers, respectively. The first method involves fitting an equivalent circuit model to the measured admittance. Close agreement is found over a wide range of temperature and frequency. The single junction model is shown to apply equally well to p-i-n and Schottky diodes, justifying the neglect of the n-i junction and thin doped layers in the p-i-n admittance analysis. A second method determines g0 from the limiting capacitance at high temperature. The third and fourth methods extract g0 from the dependence of capacitance on voltage bias. One of these is novel, presented here for the first time. Thus, a unique feature of this study is the application of several different capacitance methods to standard p-i-n solar cell devices. Agreement within ±25% is found among the values of the MGDOS from the four methods. The MGDOS increases exponentially from (1–2)×1016 to (3–4)×1017/cm3 eV as the Ge increases from 0% to 62%, in general agreement with results of others.

Characterization of a-Si:H and a-SiGe:H p-i-n and Schottky junctions by admittance circuit modeling

The midgap density of states (MGDOS) and junction properties of a-Si:H and a-SiGe:H alloys are investigated by admittance measurements on p-i-n solar cells. An expression for the capacitance is derived from the frequency, temperature, and bias dependence of the deep state response. The measured admittance is analyzed with an equivalent circuit model. The density of states g/sub 0/, attempt-to-escape frequency, and the Fermi energy are adjusted to fit the measured admittance. Close agreement is found with the measured capacitance and conductance over a wide range of temperature and frequency. The single junction model is shown to apply equally well to p-i-n and Schottky diodes, justifying the neglect of the n-i junction and thin doped layers in the p-i-n device analysis. Fitted values of g/sub 0/ are confirmed by values of g/sub 0/ obtained from the limiting capacitance at high temperature.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>