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IEEE Transactions on Applied Superconductivity

Direct Measurement of the Josephson Plasma Resonance Frequency From I-V Characteristics

Alan W. Kleinsasser, M.W. Johnson, K. A. Delin

Published Jun 1, 2005• 11 citations
Publisher

Abstract

The speed of Josephson circuits such as those required for rapid single flux quantum logic is limited by the Josephson plasma frequency, /spl omega//sub p/, which (with few exceptions) increases monotonically with increasing critical current density, J/sub c/. Here we describe a new technique for directly measuring /spl omega//sub p/, using the current-voltage characteristics of a simple structure based on externally-shunted, series-connected tunnel junctions. We present both experimental and theoretical demonstrations of the technique and describe its application to the determination of the junction capacitance, a property poorly characterized for high-J/sub c/ junctions.

DOI
10.1109/tasc.2005.849700

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Physical review. B, Condensed matter•Jul 1, 1982•117 citations
The speed of Josephson circuits such as those required for rapid single flux quantum logic is limited by the Josephson plasma frequency, /spl omega//sub p/, which (with few exceptions) increases monotonically with increasing critical current density, J/sub c/. Here we describe a new technique for directly measuring /spl omega//sub p/, using the current-voltage characteristics of a simple structure based on externally-shunted, series-connected tunnel junctions. We present both experimental and theoretical demonstrations of the technique and describe its application to the determination of the junction capacitance, a property poorly characterized for high-J/sub c/ junctions.
We present a technique for linewidth measurement and phase-locking of Josephson oscillators using digital rapid single-flux-quantum (RSFQ) circuits. The oscillator consists of a resistively shunted 6 /spl mu/m/spl times/6 /spl mu/m Nb/AlO/sub x//Nb Josephson tunnel junction that is integrated with RSFQ input and output circuits. A cascade of RSFQ T flip-flops is used to directly monitor the output of the Josephson oscillator. Spectral characteristics have been measured directly for oscillator frequencies ranging from 10-50 GHz. The linewidth can be reduced by over 100 times by phase-locking the oscillator to an RSFQ pulse train generated by an external sinusoidal signal. These Josephson oscillators can be used as on-chip stable high frequency clocks for RSFQ circuits.
We investigated current-voltage characteristics of unshunted and externally shunted Josephson junctions (JJs) with high critical current densities Jcin order to extract their basic parameters and statistical characteristics for JJ modeling in superconducting integrated circuits as well as to assess their potential for future technology nodes. Nb/AlOx-Al/Nb junctions with diameters from 0.5 to 6 μm were fabricated using a fully planarized process with Mo or MoNxthin-film shunt resistors with sheet resistance Rsq= 2 Ω/sq and Rsq= 6 Ω/sq, respectively. We used our current standard MIT Lincoln Laboratory process node SFQ5ee to fabricate JJs with Jc= 0.1 mA/μm2and our new process node SFQ5hs (where “hs” stands for high speed) to make JJs with Jc= 0.2 mA/μm2and higher current densities up to about 1 mA/μm2. Using LRC resonance features on the I-V characteristics of shunted JJs, we extract the inductance associated with Mo shunt resistors of 1.4 pH/sq. The main part of this inductance, about 1.1 pH/sq, is the inductance of the 40-nm Mo resistor film, while the geometrical inductance of superconducting Nb wiring contributes the rest. We attribute this large inductance to “kinetic” inductance arising from the complex conductivity of a thin normal-metal film in an electromagnetic field with angular frequency ω, σ(ω) = σ0/(1 + iωτ), where σ0is the static conductivity and r the electron scattering time. Using a resonance in a large-area unshunted high-Jcjunction excited by a resistively coupled small-area shunted JJ, we extract the Josephson plasma frequency and specific capacitance of high-Jcjunctions in 0.1-1 mA/μm2Jcrange. We also present data on Jctargeting and JJ critical current spreads. We discuss the potential of using 0.2-mA/μm2JJs in very large scale integration single flux quantum circuits and 0.5-mA/μm2JJs in high-density integrated circuits without shunt resistors.
We propose and demonstrate the use of underdamped, one-dimensional parallel arrays of Josephson junctions as a tool for circuit diagnostics. By measuring the Fiske modes and the critical current in a magnetic field, we determined the self and nearest neighbor inductances as well as the capacitances of single junctions. We have used this technique to find the capacitance of Nb-Al/sub 2/O/sub x/-Nb junctions for critical current densities of 0.3-20 kA/cm/sup 2/. We find that the specific capacitance increases by about a factor of 2 over this range. This increase has important consequences for the design of single-flux-quantum circuits and SQUIDs. Measurement of the junction capacitance for critical current densities of 100 kA/cm/sup 2/ is possible, but requires submicron junctions with dimensions of the order of 0.3 /spl mu/m.>
The authors propose a new type of sampler design based on shunted junctions ( beta c =1). The sampler is to be used for the investigation of single flux quantum devices (RSFQ) employing similar junctions (Kaplunenko et al. 1989, Filippenko et al. 1991). They measure the time resolution of the sampler and delay time of the shunted Josephson junction array. The circuit was manufactured on a single chip and was DC powered. They employed Nb-AlO x -Nb tunnel junctions of 300 A m -2 critical current density and observed Josephson oscillations of the output junction at frequencies from 6 to 50 GHz. Despite a long plasma period of 20 ps the time resolution was 5 ps. The transmission line of 27 Josephson junctions (critical current 165 mu A each) demonstrated time delay of 0.5 ps mu A -1 .
The capacitance of a Josephson tunnel junction is an important parameter, which determines its plasma frequency ωp and thus the energy level spacing in the quantum regime. When a microwave signal at the frequency of ω is applied to a current-biased junction in its zero-voltage state, the escape rate from this state is somehow enhanced. The enhancement is expected to go through a pronounced maximum when ωp=ω. Making use of such microwave generated resonant activation in the thermal regime, we have developed a time-resolved measurement scheme for determining the junction capacitance with an uncertainty of less than 2%.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.