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Studies of noise in Josephson-effect mixers and their potential for submillimeter heterodyne detection

Robert J. Schoelkopf

Published Nov 7, 2007• 4 citations
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Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis describes both theoretical and experimental investigations into the dynamics and noise processes of Josephson junctions, with the intent of evaluating their potential as mixers in heterodyne instruments for submillimeter-wave (i.e., the frequency range from 300 GHz to 3THz) detection. Superconducting tunnel junctions utilizing the nonlinearity due to photon-assisted tunneling of quasiparticles (SIS mixers) have become the state-of-the-art technology for sensitive heterodyne detection up to frequencies of about 700 [...]. Recent progress in the fabrication of high [...], superconductors has led to Josephson-effect devices with [...] products of up to ten millivolts, which might be suitable for mixing at frequencies of many terahertz. The key question for weighing the prospects for high-frequency Josephson mixers is that of the sensitivity which can be attained. Previous experimental work on Josephson mixing suggests the existence of an "excess" noise, which degrades the sensitivity. Theoretical modeling of mixer performance, based on the resistivelyshunted junction (RSJ) model for the dynamics of the device, also indicates the presence of larger noise than expected. The origin of this noise was not clearly understood, however, nor was its exact magnitude or expected scaling with frequency or junction characteristics known. In addition, previous experiments utilized crude devices of the point-contact type, which were unstable and thus undesirable for real applications. In the first part of this thesis research, extensive numerical simulations were performed with the RSJ model, including calculations of mixer noise and conversion efficiency. These calculations have revealed that the source of excess noise is the AC Josephson oscillations of the device, which can be completely incoherent, with a linewidth comparable to their frequency. Thus they appear as a broadband noise source. While this noise is intrinsic and unavoidable, an optimized mixer is still shown to be capable of interesting sensitivity levels, and the excess noise is expected to become relatively less important as the operating frequency is increased. Secondly, a process has been developed for the fabrication of stable, well-characterized, and reproducible Josephson devices based on resistively-shunted Nb and NbN tunnel junctions. The devices utilize submicron-area, high current-density tunnel junctions and a AuGe shunt resistor to yield completely non-hysteretic I-V curves, normal-state resistances of about [...] products of about half a millivolt. These devices should be nearly optimal for mixing at [...]. Heterodyne measurements using these junctions have been performed in a waveguide mixer mount. Receiver temperatures as low as 190 K (DSB), with -6 dB conversion efficiency, have been obtained at 100 [...], but these results are still a factor of about four higher than those predicted by the RSJ simulations. Accurate measurements of the available noise power of the junctions at the intermediate frequency of 1.5 [...] were made, and confirmed that the receivers were limited by elevated junction output noise. The deviations of the noise from theoretical predictions are shown to be caused by the nonlinear interaction of the junction with the embedding circuit. While this work points out some of the complexity introduced by the strong nonlinearity of Josephson devices, it is still expected that Josephson-effect mixers may be useful for heterodyne detection at very high frequencies.

DOI
10.7907/xezv-q641

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Measurements of noise in Josephson-effect mixers

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We present new heterodyne receiver results obtained at 100 GHz using resistively-shunted Nb and NbN tunnel junctions. In addition, we have carried out accurate measurements of the available noise power of these devices at the L-band (1.5 GHz) IF frequency. Both the heterodyne and the output noise measurements show that the noise of these devices can be a factor of five or more higher than that predicted by the simple current-biased RSJ model. The noise approaches the appropriate thermal or thermal and shot noise limits for bias voltages where the nonlinearity is not strong (i.e., V>I/sub C/R/sub N/), but as expected from the RSJ model, can be significantly higher at the low voltages where the mixers are typically biased. The bias voltage dependence of the noise shows structure which is associated with resonances in the RF embedding circuit. Surprisingly, we find that changes in the high-frequency (100 GHz) impedance presented to the junction can dramatically affect the magnitude and voltage dependence of the low-frequency (1.5 GHz) noise. This emphasizes the necessity of very closely matching the junction to free space over a wide frequency range.>

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Josephson effect mixers have previously been observed to display 'excess' noise both in experiments with point contacts and in numerical simulations using the resistively shunted junction (RSJ) model. This excess noise causes the mixer noise temperature to be a factor of typically 20-100 times the physical temperature of the device. Previously, this excess was ascribed to conversion from unwanted sidebands of the local oscillator and Josephson frequencies and their harmonics. Our numerical modeling of the RSJ equations has led to a new understanding of the excess noise, which is simply due to the intrinsic Josephson oscillations of the device. In addition, we have extended the modeling to include the previously ignored case of finite device capacitance (i.e. RSJ capacitance parameter beta(sub c) does not equal 0, which is more realistic for lithographically defined Josephson such as shunted tunnel junctions or SNS bridges. For some cases, this yields an improvement of a factor of two in noise temperature from the zero capacitance models. We will discuss the device parameters which optimize the mixer performance for frequencies approaching the characteristic frequency of the device, which is given by the Josephson frequency at the I(sub c)R(sub n) voltage (nu = 2eI(sub c)R(sub n)/h). These modeling results predict good conversion efficiency and a noise temperature within a factor of a few of the physical temperature. Experiments are in progress to determine the accuracy of this modeling using a waveguide mixer at 100 GHz with optimized, resistively shunted Nb tunnel junctions. If the modeling results are valid, they are particularly encouraging for mixers in the submillimeter regime, given the possibility of obtaining non-hysteretic Josephson devices with I(sub c)R(sub n) products in excess of a millivolt, using for instance, high-T(sub c) SNS bridges. We discuss the modifications to the classical RSJ model which are necessary in the quantum regime (h nu greater than kT), and conclude the Josephson mixers may attain noise temperatures less than ten times the quantum limit at high frequencies.

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We present test results of a 100 GHz waveguide receiver using resistively-shunted Nb and NbN tunnel junctions. These junctions were fabricated with a process similar to that used previously with Nb junctions [1], which produces non-hysteretic devices with normal-state resistances of 30-50 Ohms, and IcRiz products of 0.5-0.75 mV. The best receiver temperature obtained to date with NbN is 270 K (DSB) with 6-7 dB of conversion loss. A receiver temperature of 390 K (DSB) was previously obtained with Nb junctions; these devices showed qualitative agreement with the predictions of the simple DC and RF current-biased RSJ model. The improvement in receiver performance is probably due to improved RF coupling of the junctions, and due to the higher IcRn products of NbN. However, these NbN devices display different pumped I-V curves and IF power curves than predicted by the RSJ model. We show that these effects can be caused by the strong interaction of the junction with the embedding circuit, and conclude that an accurate model of the impedance presented to the junction will have to be included in the RSJ simulations to compare with the observed performance. Fourth International Symposium on Space Terahertz Technology Page 443 Introduction We are studying the performance of Josephson-effect mixers using resistivelyshunted tunnel junctions in order to develop a better understanding of their behavior, the sources of noise and its limitation, and to determine how to optimize their performance. Also, we wish to compare the observed behavior and performance with the theoretical predictions of the so-called RSJ (resistively shunted junction) model, so that there will be a guide to the expected performance for different frequency regimes and device parameters. This work may be important as high-Tc SNS devices become available [P.A. Rosenthal and E.N. Grossman, these proceedings] with large Ic h?„ products, for they provide the possibility of using Josephson mixers at frequencies in the terahertz range, above the range where SIS mixers are currently available. In contrast, due to the extremely short coherence lengths of the high-Tc materials, junctions suitable for quasiparticle (SIS) mixers may not be feasible with these materials Device Fabrication We have applied the technique used for creating non-hysteretic Nb Josephson devices[1] to NbN/MgO/NbN tunnel junctions. First the junction tfilayer is fabricated, then the junction areas are patterned by electron-beam lithography and subsequently etched using reactive-ion etching (RJE) in the standard method [3]. After planarization of the etched area with evaporated SiO, a AuGe resistor is fabricated on top of the SiO, and the junction and resistor are then contacted with another layer of NbN. A photomicrograph of a completed Nb junction is shown in Figure la. Since the bottom of the etched trilayer lies under the resistor, it acts as a ground plane, and the resistor structure can be analyzed as a lossy transmission line. The impedance of this short microstrip structure is purely real, even up to frequencies comparable to the gap frequency of the superconductor, thus providing the desired broadband shunt. However, the section of Page 444 Fourth International Symposium on Space Terahertz Technology superconductor which contacts the junction and resistor creates a non-negligible parasitic capacitance when compared to the very small area tunnel junctions used, and therefore the area of this contact pad must be kept to a minimum. From a knowledge of the geometry and thickness of the insulator (Si0), we estimate this parasitic capacitance to be 7-8 fF. Shunting of the junction is necessary to reduce the McCumber beta parameter (Pc = 2eIcRN C Ih) of the unshunted tunnel junctions. Junctions with /3, values greater than one have hysteretic I-V curves [4], and their dynamics can be complicated, including the possibility of chaos. Reduction of 13, is accomplished by resistive shunting, which reduces /3 by the square of the ratio of the initial junction resistance to the final resistance of the parallel combination of the junction and the resistive shunt. However, this shunting has the undesirable effect of reducing the 1,Rn product of the junction. For the NbN junctions used, the critical current density was about 331cA/cm 2 , and the specific capacitance is estimated to be about 150/F 1 itm [5], giving an unshunted of about 12. Thus the optimal shunted junction for these parameters would have a shunt resistance of about one-fourth of R,„ and thus an IcR7, reduced from the unshunted value of 3.0 mV to 0.8 mV. 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The Josephson frequency conversion in the millimeter and submillimeter wave region is studied with superconducting Nb-Nb point contact junctions at 4.2 K, using the contact both as the local oscillator and the mixer with intermediate frequencies of 0.1 and 9.2 GHz. Frequency conversion signals are only detected in the latter case with a microwave receiver at 9.2 GHz in a range of Josephson frequencies between 145 and 1 600 GHz. The experiments with intermediate frequency fi of 0.1 GHz indicate for this small value of f i that the observed signals are not related to frequency conversion but noise effects. An analysis of the frequency conversion mechanism in a Josephson junction operated as an oscillator-mixer is proposed which includes the noise effects and also the feedback effects induced in a junction driven by a constant current source. We have then investigated the noise properties up to 450 GHz of superconducting point-contacts using the junction as an oscillator-mixer where the Josephson current is mixed with harmonics of an externally applied signal. The emitted intermediate frequency is detected at 9.2 GHz and its linewidth is measured. In the very high frequency range the dc quasiparticle current dominates in a Josephson weak-link and we compare the corresponding theoretical linewidth calculated by Scalapino with our experimental results.

Revue de Physique Appliquée•Jan 1, 1974•3 citations
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. This thesis describes both theoretical and experimental investigations into the dynamics and noise processes of Josephson junctions, with the intent of evaluating their potential as mixers in heterodyne instruments for submillimeter-wave (i.e., the frequency range from 300 GHz to 3THz) detection. Superconducting tunnel junctions utilizing the nonlinearity due to photon-assisted tunneling of quasiparticles (SIS mixers) have become the state-of-the-art technology for sensitive heterodyne detection up to frequencies of about 700 [...]. Recent progress in the fabrication of high [...], superconductors has led to Josephson-effect devices with [...] products of up to ten millivolts, which might be suitable for mixing at frequencies of many terahertz. The key question for weighing the prospects for high-frequency Josephson mixers is that of the sensitivity which can be attained. Previous experimental work on Josephson mixing suggests the existence of an "excess" noise, which degrades the sensitivity. Theoretical modeling of mixer performance, based on the resistivelyshunted junction (RSJ) model for the dynamics of the device, also indicates the presence of larger noise than expected. The origin of this noise was not clearly understood, however, nor was its exact magnitude or expected scaling with frequency or junction characteristics known. In addition, previous experiments utilized crude devices of the point-contact type, which were unstable and thus undesirable for real applications. In the first part of this thesis research, extensive numerical simulations were performed with the RSJ model, including calculations of mixer noise and conversion efficiency. These calculations have revealed that the source of excess noise is the AC Josephson oscillations of the device, which can be completely incoherent, with a linewidth comparable to their frequency. Thus they appear as a broadband noise source. While this noise is intrinsic and unavoidable, an optimized mixer is still shown to be capable of interesting sensitivity levels, and the excess noise is expected to become relatively less important as the operating frequency is increased. Secondly, a process has been developed for the fabrication of stable, well-characterized, and reproducible Josephson devices based on resistively-shunted Nb and NbN tunnel junctions. The devices utilize submicron-area, high current-density tunnel junctions and a AuGe shunt resistor to yield completely non-hysteretic I-V curves, normal-state resistances of about [...] products of about half a millivolt. These devices should be nearly optimal for mixing at [...]. Heterodyne measurements using these junctions have been performed in a waveguide mixer mount. Receiver temperatures as low as 190 K (DSB), with -6 dB conversion efficiency, have been obtained at 100 [...], but these results are still a factor of about four higher than those predicted by the RSJ simulations. Accurate measurements of the available noise power of the junctions at the intermediate frequency of 1.5 [...] were made, and confirmed that the receivers were limited by elevated junction output noise. The deviations of the noise from theoretical predictions are shown to be caused by the nonlinear interaction of the junction with the embedding circuit. While this work points out some of the complexity introduced by the strong nonlinearity of Josephson devices, it is still expected that Josephson-effect mixers may be useful for heterodyne detection at very high frequencies.
We present new heterodyne receiver results obtained at 100 GHz using resistively-shunted Nb and NbN tunnel junctions. In addition, we have carried out accurate measurements of the available noise power of these devices at the L-band (1.5 GHz) IF frequency. Both the heterodyne and the output noise measurements show that the noise of these devices can be a factor of five or more higher than that predicted by the simple current-biased RSJ model. The noise approaches the appropriate thermal or thermal and shot noise limits for bias voltages where the nonlinearity is not strong (i.e., V>I/sub C/R/sub N/), but as expected from the RSJ model, can be significantly higher at the low voltages where the mixers are typically biased. The bias voltage dependence of the noise shows structure which is associated with resonances in the RF embedding circuit. Surprisingly, we find that changes in the high-frequency (100 GHz) impedance presented to the junction can dramatically affect the magnitude and voltage dependence of the low-frequency (1.5 GHz) noise. This emphasizes the necessity of very closely matching the junction to free space over a wide frequency range.>
Josephson effect mixers have previously been observed to display 'excess' noise both in experiments with point contacts and in numerical simulations using the resistively shunted junction (RSJ) model. This excess noise causes the mixer noise temperature to be a factor of typically 20-100 times the physical temperature of the device. Previously, this excess was ascribed to conversion from unwanted sidebands of the local oscillator and Josephson frequencies and their harmonics. Our numerical modeling of the RSJ equations has led to a new understanding of the excess noise, which is simply due to the intrinsic Josephson oscillations of the device. In addition, we have extended the modeling to include the previously ignored case of finite device capacitance (i.e. RSJ capacitance parameter beta(sub c) does not equal 0, which is more realistic for lithographically defined Josephson such as shunted tunnel junctions or SNS bridges. For some cases, this yields an improvement of a factor of two in noise temperature from the zero capacitance models. We will discuss the device parameters which optimize the mixer performance for frequencies approaching the characteristic frequency of the device, which is given by the Josephson frequency at the I(sub c)R(sub n) voltage (nu = 2eI(sub c)R(sub n)/h). These modeling results predict good conversion efficiency and a noise temperature within a factor of a few of the physical temperature. Experiments are in progress to determine the accuracy of this modeling using a waveguide mixer at 100 GHz with optimized, resistively shunted Nb tunnel junctions. If the modeling results are valid, they are particularly encouraging for mixers in the submillimeter regime, given the possibility of obtaining non-hysteretic Josephson devices with I(sub c)R(sub n) products in excess of a millivolt, using for instance, high-T(sub c) SNS bridges. We discuss the modifications to the classical RSJ model which are necessary in the quantum regime (h nu greater than kT), and conclude the Josephson mixers may attain noise temperatures less than ten times the quantum limit at high frequencies.
Superconducting tunnel diodes (SISs) are investigated for both the generation and detection of submillimeter wavelengths. For detection, heterodyne receivers using SISs are investigated. Josephson currents are found to have a large effect on SIS mixers in the submillimeter, even though their effect is less at lower frequencies. At 492 GHz, fixer conversion gain increased by 4 dB when Josephson currents are not suppressed by a magnetic field. A much higher noise is seen in this gain mode, but further investigation of this recently discovered phenomenon is warranted. For submillimeter generation, a two-dimensional array of SISs is investigated. The ac Josephson effect in the SIS is expected to deliver submillimeter power into a free-space radiation mode traveling perpendicular to the array. No experimental devices have been developed yet, but the authors show computer simulations and microwave scale model measurements of array structures.
We present test results of a 100 GHz waveguide receiver using resistively-shunted Nb and NbN tunnel junctions. These junctions were fabricated with a process similar to that used previously with Nb junctions [1], which produces non-hysteretic devices with normal-state resistances of 30-50 Ohms, and IcRiz products of 0.5-0.75 mV. The best receiver temperature obtained to date with NbN is 270 K (DSB) with 6-7 dB of conversion loss. A receiver temperature of 390 K (DSB) was previously obtained with Nb junctions; these devices showed qualitative agreement with the predictions of the simple DC and RF current-biased RSJ model. The improvement in receiver performance is probably due to improved RF coupling of the junctions, and due to the higher IcRn products of NbN. However, these NbN devices display different pumped I-V curves and IF power curves than predicted by the RSJ model. We show that these effects can be caused by the strong interaction of the junction with the embedding circuit, and conclude that an accurate model of the impedance presented to the junction will have to be included in the RSJ simulations to compare with the observed performance. Fourth International Symposium on Space Terahertz Technology Page 443 Introduction We are studying the performance of Josephson-effect mixers using resistivelyshunted tunnel junctions in order to develop a better understanding of their behavior, the sources of noise and its limitation, and to determine how to optimize their performance. Also, we wish to compare the observed behavior and performance with the theoretical predictions of the so-called RSJ (resistively shunted junction) model, so that there will be a guide to the expected performance for different frequency regimes and device parameters. This work may be important as high-Tc SNS devices become available [P.A. Rosenthal and E.N. Grossman, these proceedings] with large Ic h?„ products, for they provide the possibility of using Josephson mixers at frequencies in the terahertz range, above the range where SIS mixers are currently available. In contrast, due to the extremely short coherence lengths of the high-Tc materials, junctions suitable for quasiparticle (SIS) mixers may not be feasible with these materials Device Fabrication We have applied the technique used for creating non-hysteretic Nb Josephson devices[1] to NbN/MgO/NbN tunnel junctions. First the junction tfilayer is fabricated, then the junction areas are patterned by electron-beam lithography and subsequently etched using reactive-ion etching (RJE) in the standard method [3]. After planarization of the etched area with evaporated SiO, a AuGe resistor is fabricated on top of the SiO, and the junction and resistor are then contacted with another layer of NbN. A photomicrograph of a completed Nb junction is shown in Figure la. Since the bottom of the etched trilayer lies under the resistor, it acts as a ground plane, and the resistor structure can be analyzed as a lossy transmission line. The impedance of this short microstrip structure is purely real, even up to frequencies comparable to the gap frequency of the superconductor, thus providing the desired broadband shunt. However, the section of Page 444 Fourth International Symposium on Space Terahertz Technology superconductor which contacts the junction and resistor creates a non-negligible parasitic capacitance when compared to the very small area tunnel junctions used, and therefore the area of this contact pad must be kept to a minimum. From a knowledge of the geometry and thickness of the insulator (Si0), we estimate this parasitic capacitance to be 7-8 fF. Shunting of the junction is necessary to reduce the McCumber beta parameter (Pc = 2eIcRN C Ih) of the unshunted tunnel junctions. Junctions with /3, values greater than one have hysteretic I-V curves [4], and their dynamics can be complicated, including the possibility of chaos. Reduction of 13, is accomplished by resistive shunting, which reduces /3 by the square of the ratio of the initial junction resistance to the final resistance of the parallel combination of the junction and the resistive shunt. However, this shunting has the undesirable effect of reducing the 1,Rn product of the junction. For the NbN junctions used, the critical current density was about 331cA/cm 2 , and the specific capacitance is estimated to be about 150/F 1 itm [5], giving an unshunted of about 12. Thus the optimal shunted junction for these parameters would have a shunt resistance of about one-fourth of R,„ and thus an IcR7, reduced from the unshunted value of 3.0 mV to 0.8 mV. In order to maintain high enough resistances for the final device, very small (0.3pm on a side) area junctions must be used, and the parasitic capacitance will be comparable to the junction capacitance. This further reduces the final IeR, product attainable. The I-V curve of a typical device is shown in Figure lb. This device had a critical current of 11 microamps and a normal state resistance of 39 Ohms, giving an IcR, product of 430 microvolts. The IV curve is nonhysteretic and follows the RSJ model. Mixer Modelling Mixer performance can be predicted using the RSJ model, in a method similar to that used by Taur[6], but extended to the case of finite junction capacitance. The
This chapter discusses the high sensitivity superconducting mixers, i.e. detectors used in heterodyne receivers. Today, there are essentially two very successful concepts of superconducting mixers, or frequency down-converters, the superconductor-insulator-superconductor tunnel junction SIS mixer and the superconducting hot-electron bolometer mixer. Moving up to higher frequencies in the microwave and millimeter wave electromagnetic spectra makes it more and more difficult to retrieve a good signal-to-noise ratio with ordinary solid-state amplifiers. The driving force for using superconducting mixers is their excellent down-conversion efficiency and capability to down-convert RF signals from microwave frequencies up to the terahertz region. The main purpose of a receiver is to pick up and amplify a weak signal, which can then be accurately determined in amplitude and phase. The mixer noise temperature and conversion gain are the most important parameters for the mixing device. The Josephson junction mixer was one of the first suggested devices based on superconducting point contacts and later tunnel junctions.
The Josephson frequency conversion in the millimeter and submillimeter wave region is studied with superconducting Nb-Nb point contact junctions at 4.2 K, using the contact both as the local oscillator and the mixer with intermediate frequencies of 0.1 and 9.2 GHz. Frequency conversion signals are only detected in the latter case with a microwave receiver at 9.2 GHz in a range of Josephson frequencies between 145 and 1 600 GHz. The experiments with intermediate frequency fi of 0.1 GHz indicate for this small value of f i that the observed signals are not related to frequency conversion but noise effects. An analysis of the frequency conversion mechanism in a Josephson junction operated as an oscillator-mixer is proposed which includes the noise effects and also the feedback effects induced in a junction driven by a constant current source. We have then investigated the noise properties up to 450 GHz of superconducting point-contacts using the junction as an oscillator-mixer where the Josephson current is mixed with harmonics of an externally applied signal. The emitted intermediate frequency is detected at 9.2 GHz and its linewidth is measured. In the very high frequency range the dc quasiparticle current dominates in a Josephson weak-link and we compare the corresponding theoretical linewidth calculated by Scalapino with our experimental results.