1. Introduction

IGHLY sensitive microwave detectors are essential for

biomedical research, security control and atmospheric

monitoring. In this field superconducting devices such as

Josephson broadband and selective detectors, mixers, Hilbert

spectrometers offer a viable option. In contrast to conventional

niobium devices high-temperature superconductors (HTSC)

have higher operating temperatures and wider THz frequency

response. Grain-boundary Josephson junctions (JJs) have

already proven their advantages [1]-[3]. Table I shows

parameters of Josephson detectors obtained in different works

for nitrogen temperatures.

The analysis and comparison of the results of Table I is

difficult due to some difference in the working temperature

and the frequency of external influence. Moreover, not all

works contain information about for what type of power,

incident or absorbed, the value of responsivity rV was

obtained. In addition, in paper [4] a frequency selective

responsivity has been measured instead of a broadband one.

Nevertheless, for a numerical analysis as close to reality as

possible we used the sample parameters from these works.

To model the broadband response of a non-hysteretic

junction a resistively shunted junction model is usually

employed [9]-[12]. To simulate such systems quantitatevly we

will use a resistively and capacitively shunted junction (RSCJ)

model even though the junction does not exhibit hysteresis in

its current-voltage characteristics.

The aim of this paper is to study the influence of the

Josephson junction finite capacitance on the characteristics of

the broadband response for different frequencies of external

signal, different ICRN product and optimal IC and RN

parameters at 77 K.

2. Numerical Results

The investigation was performed using the RSCJ model

where the junction phase φ with a critical current IC,

capacitance C, resistance RN is described by the stochastic

differential equation [13]-[14]

BFmwmwC

IItFII

C )2sin(sin



(1)

where voltage V is defined as the derivative dφ/dt∙2πΦ0 with

the magnetic flux quantum Φ0; thermal fluctuations IF are

treated as white Gaussian noise with zero mean and correlation

function < IF(t)IF(t+τ) > = (kBT) / (πRN) δ(τ). A simple

harmonic signal of amplitude Imw and frequency Fmw = ωmw/2π

describes external radiation with power Pmw = Imw2 RN / 2.

Broadband THz detection by YBaCuO Josephson junctions having

finite capacitance

EKATERINA A. MATROZOVA, LEONID S. REVIN,

Institute for Physics of Microstructures of RAS, GSP-105, Nizhny Novgorod, 603950, Russia

Superconducting Nanoelectronics Laboratory, Nizhny Novgorod State Technical University, n.a. R.E.

Alekseev, 603950 Nizhny Novgorod, RUSSIA

Table I. Experimental parameters of YBaCuO bicrystal detectors

obtained in different works. Here rV is the responsivity.

Abstract:—Broadband classical detection of THz radiation by a YBaCuO Josephson junction was studied on

the basis of resistively-capacitively shunted junction model. Numerical simulation was based on the parameters

of the samples experimentally studied in other works at nitrogen temperatures. It is shown that taking into

account the damping of the Josephson junction becomes essential for high frequencies of external signal. The

absolute value of responsivity decreases as junction capacitance increases. Damping parameter also influences

the choice of optimal IC and RN parameters.

Keywords:—YBaCuO Josephson junction, broadband detector, responsivity, RCSJ model.

Received: May 14, 2022. Revised: October 8, 2022. Accepted: November 16, 2022. Published: December 31, 2022.

International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2022.1.2

Ekaterina A. Matrozova, Leonid S. Revin

E-ISSN: 2945-0519

Volume 1, 2022

The receiving characteristics of JJ was analyzed in the bias

current regime to study the responsivity rV in the broadband

detection mode. That is, at the bias current near the critical one

the voltage increment is associated with the change in the

power of the incident signal.

For clarity, Fig. 1a shows current-voltage characteristic and

differential resistance RD for the experimental parameters from

[3]: T = 77 K, IC = 80 μA, RN = 1.5 Ω. Determining the

capacitance of the Josephson junction, and, accordingly, the

damping parameter α = 1/RN ( ћ/(2eICC) )-2 is quite difficult

task. Nevertheless, estimations can be made based on the

fitting of IV curves for different temperatures. For the

experimental current-voltage characteristics from Fig. 3 of [3]

the capacitance value of JJ obtained from the fitting is C ≈ 190

fF (α ≈ 4 for T = 77 K). While for IVs from Fig. 1 of [15] C ≈

2 fF, and it can be assumed that for this case α will be no more

than 3 for nitrogen temperature. Figure 1 was obtained for two

different damping parameters: for the case of overdumped

junction with α = 50 (curve marked with 1) and for α = 3

(curve marked with 2). While the current-voltage

characteristics and RD for the two cases are almost the same,

the response ΔV to a small external signal with Fmw = 614

GHz; Pmw = 10 nW is different (Fig. 1b). This effect will be

described in more detail further.

Choosing an optimal bias IB, we get the maximum voltage

response to the external signal at a given power. Then

responsivity is defined as derivation rV = dV / dPmw. The

voltage amplitude of the response ΔV is a linear function of the

radiation power at low values of this power (the inset of Fig.

2). Thus, the responsivity is constant and has a maximum

value for small external signals, Fig. 2. Note that for the case

of α = 50 the max rV is ~ 2.2 times greater than for the case of

α = 3. At the same time, the responsivity for curve 1 decreases

faster with increasing power than for curve 2. To describe the

rV(Pmw) dependency we will use the upper limit of the power

dynamic range PS defined as the power at which the detector

responsivity decreases by a factor of two.

Let us examine the influence of damping on the value of the

maximum responsivity for different frequency Fmw (Fig. 3). It

is convenient to perform this using the parameters of two

detectors with different ICRN product from Table I. In the

absent of fluctuations and for the normalized frequency Ωmw =

Fmw / FС > 1, where FС is the characteristic frequency, the

analytical formula for the broadband responsivity was obtained

in the framework of the resistively shunted (RSJ) model [9]:

2mw

VRI

r



(2)

where Ωmw = Fmw / (ICRN ∙ 2e/ћ).

Figure 3 shows the data for ICRN = 0.12 mV (curves marked

with 2) and normalized frequencies Ωmw from 3 to 17. The

result for α = 50 is in complete agreement with the analytical

formula. At the same time, a decrease in damping leads to a

stronger rV(Fmw) dependence. A similar dependence on α was

observed in the study of Shapiro steps [16]. In this case, the 0th

Shapiro step, that is, the critical current, can be approximately

considered as the broadband current response of the Josephson

junction in the voltage bias regime. It has been shown that the

IC(P) dependence is slower for lower damping, which means

that the responsivity dIC/dP decreases with decreasing α. This

result can be explained by the increase of the junction

admittance in the simple RC-model. The frequency at which

the influence of α becomes significant is determined by the

condition: Fmw ≥ FP2 / FC, where FP = (2eIC/ћC)-2 is the plasma

frequency. So for curve 2 in Fig. 3 for α = 3 this frequency

Fig. 1 a) Left (solid curve): IV characteristics for IC = 80 μA, RN =

1.5 Ω, T = 77 K without an external signal. Right (dashed

curve): Differential resistance RD. Curves for the two alpha values

α = 3, α = 50 are almost the same. (b) Response ΔV to an external

signal with Fmw = 614 GHz; Pmw = 10 nW depending on the bias

current for two values of α.

Fig. 2 Voltage responsivity versus Pmw. Max rV and PS indicate the

maximum responsivity at low power and the upper limit of the power

dynamic range, respectively. The inset: response amplitude ΔV vs.

external radiation power with a frequency of Fmw = 614 GHz at

temperature of 77 K. Detector parameters are the same as for Fig. 1.

International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2022.1.2

Ekaterina A. Matrozova, Leonid S. Revin

E-ISSN: 2945-0519

Volume 1, 2022

corresponds to 550 GHz. For α = 2 - 230 GHz and for α = 1 -

60 GHz.

For ICRN = 0.9 mV (curves marked with 1) the normalized

frequencies Ωmw are from 0.1 to 2. For Ωmw > 1 the dependence

is similar to the one discussed above. For low frequencies the

responsivity dependence is slower than 1/Ωmw2. In this region,

the difference in rV values for different damping is small and is

associated with a larger value of RD for smaller α.

The dependence of the upper limit of the power dynamic

range on frequency for different α shows an inverse character,

Fig. 4. In the Ωmw > 1 limit PS - value increases with increasing

frequency and decreasing α.

Now let us consider the task of finding the optimal IC and RN

parameters for a given values of ICRN at a temperature of 77 K

to obtain maximum broadband responsivity. Technologically

this task can be solved by adjusting the geometry of the

junction, in particular by the film thickness. IC and RN

parameters can also be changed by low-temperature annealing

of bicrystal junctions in ozone atmosphere [17], annealing in

atomic oxygen [18] and by oxygen aging [19]. In [10] the

results of numerical simulations for the responsivity as well as

the noise-equivalent power (NEP) was obtained in the

framework of RSJ model with thermal noise. There, the rV-

values have their maximum at RN ~ (ћICRN) / (2ekT) for

normalized frequencies Ωmw < 1 and should have them at RN ~

(Ωmw ћICRN) / (2ekT) for large Ωmw ≥ 1. Simulation for α = 50

shows a similar result, Fig. 5. As α decreases, the optimal RN

value shifts to the right, and the responsivity maximum

becomes flatter.

Figure 6 demonstrates optimal RN -value for the greatest

responsivity versus frequency for different α. It can be seen

that the optimal RN is the same for different damping in low

frequency region Fmw < FС while in high frequency region the

RN(Fmw) dependence is almost linear with different slopes.

Fig. 3 Maximum responsivity depending on the frequency Fmw for

ICRN = 0.9 mV (curves marked with 1) and for ICRN = 0.12 mV

(marked with 2) from Table I. Solid curves - α = 50, long dashed

curves - α = 3, short dashed curves - α = 2, dotted curves - α = 1.

Fig. 4 The upper limit of the power dynamic range on the

frequency Fmw for ICRN = 0.12 mV from Table I. Solid curves - α =

50, long dashed curves - α = 3, short dashed curves - α = 2, dotted

curves - α = 1.

Fig. 5 The dependence of max rV on the normal resistance at

constant ICRN = 0.12 mV for different Fmw. Solid curves - α = 50, long

dashed curves - α = 3.

Fig. 6 The dependence of optimal RN on the frequency Fmw for

ICRN = 0.12 mV and different α.

International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2022.1.2

Ekaterina A. Matrozova, Leonid S. Revin

E-ISSN: 2945-0519

Volume 1, 2022

3. Conclusions and Discussion

We have shown that taking into account finite damping can

lead to a change in the rV(Fmw) dependence even for α = 3. In

the high frequency region Fmw ≥ FP2 / FC the absolute value of

responsivity decreases as α decreases. At the same time, the

dependence of the upper limit of the power dynamic range on

damping is inverse. For a more detailed analysis, it is required

to investigate the NEP(α) dependence and, as a consequence,

to investigate the power dynamic range D = PS / NEP (ΔF)-2,

where ΔF is the frequency band in which the output signal is

measured.

Damping parameter also influences the choice of IC and RN

for optimal broadband detection. As α decreases, the

recommendations shift to the region of higher normal

resistances and lower critical currents compared to the

overdamped junction.

Accounting for finite damping is important even when

analyzing the characteristics of HTSC detectors at nitrogen

temperatures. The RCSJ model should be applied for

frequencies Fmw above FP2 / FC.

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Ekaterina A. Matrozova, Leonid S. Revin

E-ISSN: 2945-0519

Volume 1, 2022

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International Journal of Chemical Engineering and Materials

DOI: 10.37394/232031.2022.1.2

Ekaterina A. Matrozova, Leonid S. Revin

E-ISSN: 2945-0519

Volume 1, 2022