Motivated by recent data on high-quality MgB 2 thin films implying that the smaller energy gap has l = 6 (i-wave) symmetry, we consider a simple model for an all-MgB 2 symmetric Josephson Junction (JJ). The model assumes an arbitrary-strength delta-function barrier and one-dimensional current conduction. It is shown that in this context a nodal energy gap with i-wave symmetry acts as an isotropic energy gap (s-wave) with an amplitude modified by the energy-gap misalignment-angle with respect to the crystal principal axes. The corresponding exact Green’s function in momentum space is derived employing a novel approach. The ensuing current-phase relations in the strong and weak barrier-strengths limits are calculated and found to confirm known results, e.g., the Ambegaokar-Baratoff current-phase relation. Inspired by an HTS experiment that established the d-wave energy-gap symmetry, we propose a JJ-related experiment with a MgB 2 bicrystal to confirm our premise that the smaller energy has i-wave symmetry.

Today, microbump-based flip-chip technology is a compelling option for heterogeneous integration in microelectronic packaging. Performance as well as density (smaller form factor) requirements continue to drive smaller, microbump-based, finer pitch interconnections. This paper presents heterogeneous integration based on microbump fabrication, characterization, and integration for fine pitch die-to-die and die-to-wafer flip-chip interconnection. A variety of microbump options including indium, indium-coated gold, gold and gold-on-gold were used for bump bonding of fine pitch flip-chip structures. A series of microbumps (2.5-15 mu m) were fabricated using contact and non-contact photolithography on superconducting multi-chip module (S-MCM) wafers. The integration process includes various microbump combinations to reduce microbump spreading / flow during the fine-pitch assembly process. In another study, gold-ball-based interconnects were developed to convert wire bondable chips to a flip-chip process. The use of microbumps to form 10 mu m-pitch flip-chip interconnects and their initial electrical performance are discussed. As a case study, we have developed indium microbump technology capable of interconnecting an array of 10-to-35-mu m-pitch pads to a superconducting multi-chip module (S-MCM) fabricated on 200mm silicon wafers. The S-parameters of several back-to-back microstrip and grounded coplanar waveguide (GCPW) transitions were measured and simulated in a 2.5d (planar) full-wave electromagnetic software package (Sonnet em). The flip-chip configurations showed excellent impedance matching and low insertion loss to multi-gigahertz frequencies. For example, a microstrip-to-microstrip transition using 20 mu m-diameter bumps with 35 mu m pitch in a coaxial configuration (signal bump surrounded by ground bumps) had a simulated return loss of less than -20 dB from DC to 23 GHz. By adding some compensating inductance to the transitions, this simulated response was extended to 81 GHz. Smaller bump diameter and pitch yields a much better impedance match and less reflected energy, with the 10 pm pitch and 5 pm bump versions giving near-perfect performance to 100 GHz and beyond. Flip-chipped Josephson junctions and niobium lines interrupted by indium microbumps between the superconducting integrated circuits (ICs) and the S-MCM maintained their I-V characteristics. This paper also discusses large superconducting multi-chip module (S-MCM) fabrication and bonding approaches for future technology. Various fabrication options including jumper flip-chip, stitching and laser direct writing are considered for large S-MCM fabrication.

Recent progress in superconductor electronics fabrication has enabled single-flux-quantum (SFQ) digital circuits with close to one million Josephson junctions (JJs) on 1-cm^2 chips. Increasing the integration scale further is challenging because of the large area of SFQ logic cells, mainly determined by the area of resistively shunted Nb/AlO_x-Al/Nb JJs and geometrical inductors utilizing multiple layers of Nb. To overcome these challenges, we are developing a fabrication process with self-shunted high-J_c JJs and compact thin-film MoN_x kinetic inductors instead of geometrical inductors. We present fabrication details and properties of MoN_x films with a wide range of T_c, including residual stress, electrical resistivity, critical current, and magnetic field penetration depth λ_0. As kinetic inductors, we implemented Mo_2N films with T_c about 8 K, λ_0 about 0.51 μm, and inductance adjustable in the range from 2 to 8 pH/sq. We also present data on fabrication and electrical characterization of Nb-based self-shunted JJs with AlO_x tunnel barriers and J_c = 0.6 mA/μm^2, and with 10-nm thick Si_1-xNb_x barriers, with x from 0.03 to 0.15, fabricated on 200-mm wafers by co-sputtering. We demonstrate that the electron transport mechanism in Si_1-xNb_x barriers at x < 0.08 is inelastic resonant tunneling via chains of multiple localized states. At larger x, their Josephson characteristics are strongly dependent on x and residual stress in Nb electrodes, and in general are inferior to AlO_x tunnel barriers.

We report results of measurements of Nb stripline resonators with linewidths ranging from 1.0 to 0.25 mu m, fabricated using an 8-Nb-layer process with planarized SiO2 dielectric developed at MIT Lincoln Laboratory for superconductor single-flux-quantum circuits. The fundamental resonant frequency f(0) was varied from 2.3 to 4.5 GHz. The results show that, at 4 K, the losses for the narrowest lines are dominated by losses in the dielectric. At high power, the nonlinear niobium losses dominate. Spiral inductors have also been used to design and fabricate multipole low-pass filters with three and five poles with cutoff at 1 GHz. The measured and simulated results for the filters agree very well and show almost ideal properties. The precision and high reproducibility of this fabrication process hold the promise of fabricating multipole filters without the need for tuning the individual poles.

We present a phenomenological model that indicates with high probability that the smaller of the two energy gaps in MgB2, the so-called  gap, contains nodal lines with a six-fold symmetry (i-wave). The model also indicates that the larger gap, the so-called  gap, is a conventional s wave. The model is an extension of the BCS theory that accounts for the elastic anisotropy in MgB2 and the Coulomb repulsion. It is based on a phononic pairing mechanism and assumes no coupling between the two energy gaps in MgB2 at zero temperature. All of the parameters of the model, such as the sound velocities, are independently determined material constants. The results agree with a previous ad-hoc hypothesis that the  energy gap has six nodal lines. That hypothesis was motivated by low-temperature measurements of the surface impedance and intermodulation distortion in high-quality thin films. We briefly review experimental evidence in support of our hypothesis and review evidence in the literature that has led to the conclusion that both gaps are s wave. We find that the evidence from the literature for s wave is inconclusive. Our finding is that the  gap has six nodal lines.

A test fixture for full 2-port-calibrated, error-corrected measurements at cryogenic temperatures has been built and tested. Through-reflect-line (TRL) calibrations have been demonstrated at frequencies up to 4.5 GHz and at temperatures as low as 4.2 K. Calibrated measurements of both passive filters and active devices, amplifiers have been demonstrated. The calibration standards are collocated with the device under test. The calibration and device measurement can be accomplished in a single cooldown. Mechanical switches at the cold stage are used to switch in the TRL standards and the device under test. Measurements of the repeatability of the calibration will be discussed. The amplitude accuracy is approximately ± 0.03 dB.

We present a phenomenological model that strongly suggests that the smaller of the two energy gaps in MgB2, the so-called π gap, contains nodal lines with a six-fold symmetry (i-wave). The model also indicates that the larger gap, the so-called σ gap, is conventional s-wave. The model is an extension of the BCS gap equation that accounts for the elastic anisotropy in MgB2 and the Coulomb repulsion. It is based on a phononic pairing mechanism and assumes no coupling between the two energy gaps in MgB2 at zero temperature. All of the parameters of the model, such as sound velocities and masses, are independently determined material constants. The results agree with a previous ad-hoc hypothesis that the π energy gap has six nodal lines. That hypothesis was motivated by low-temperature measurements of the surface impedance and intermodulation distortion in high-quality thin films. We briefly review experimental evidence in the literature that is relevant to the energy-gap symmetry. We find that the evidence from the literature for s-wave is inconclusive. Our finding is that the π gap has six nodal lines.

Calculations of the microwave intermodulation distortion (IMD) and surface resistance of impurity-doped YBCO, MgB2 and Nb are presented. These are qualitatively distinct superconductors due to their energy-gap symmetries, d-wave (ℓ=2), i-wave (ℓ=6) and s-wave (ℓ=0), respectively. The calculations are compared with previously published IMD and surface-resistance measurements of impurity-doped YBCO and Nb. The agreement between the data and fitted calculations is excellent in all cases. In the absence of IMD and surface-resistance measurements for doped MgB2, we present representative predictions. The calculations are based on a Green’s-function approach that yields analytical expressions for the penetration depth and the nonlinear kernel in the constitutive relation. This penetration-depth expression reproduces the measured T2 low-temperature variation for doped superconductors and the surface-resistance reduction over that of the pure material. Regarding the IMD in superconductors with a nodal energy gap, the effect of doping is to enhance its magnitude and suppress its low-temperature 1/T2 divergence predicted by the nonlinear Meissner effect.

Magnetic/piezoelectric multiferroic heterostructures with strong magnetoelectric (ME) coupling have recently attracted considerable interest. Since the ratio of magnetostriction lambda(s) over saturation magnetization M-s is a key factor to achieve strong magnetoelectric coupling in ferrite/piezoelectric multiferroic heterostructures, here we find a solution to tune lambda(s)/M-s by aluminum doping. We report aluminum-substituted NiZn-ferrites with different compositions (Ni0.65Zn0.35Fe2-xAlxO4, x = 0, 0.1, 0.3, 0.4, 0.6, 0.8 and 1) fabricated by a solid-state sintering process. The saturation magnetization of these NiZnAl-ferrites was reduced from 6000 to 900 G with increased Al doping, which was accompanied by a significantly narrowed ferromagnetic resonance linewidth from 1870 to 340 Oe. Meanwhile, saturation magnetostriction of these NiZnAl-ferrites was reduced from 6.67 to 1.40 ppm with increased amount of Al doping. Strong ME coupling was demonstrated in the NiZnAl-ferrites/PZT multiferroic heterostructures. A large piezoelectric deformation induced ferromagnetic resonance field change up to 42 Oe was observed in Ni0.65Zn0.35Fe1.2Al0.8O4/PZT heterostructures, corresponding to a large microwave ME coefficient of 4.2 Oe cm kV(-1). These AlNiZn-ferrites and NiZnAl-ferrites/PZT heterostructures with large ME coupling provide a great opportunity for electrical tuning microwave devices.

Based on our measurements of intermodulation distortion in MgB2, we have previously proposed that the π energy-gap in MgB2 entails six nodal lines [Y.D. Agassi, D.E. Oates, and B.H. Moeckly, Phys. Rev. B 80 (2009) 174522]. Here we report high-precision measurements in MgB2 stripline resonators that show an increase of the penetration depth as the temperature is decreased below 5K. This increase is consistent with the ℓ=6 symmetry of the π energy gap that we have proposed. We interpret the increase as a manifestation of Andreev surface-attached states that are associated with the nodal lines of the π energy gap. Penetration-depth calculations are in good agreement with our data. To reconcile the present interpretation with existing literature, we review other penetration-depth data, magnetic-impurity and tunneling experiments, and data on the paramagnetic Meissner effect. We conclude that these data do not rule out the interpretation of our experimental data based on a nodal π energy gap.

A microwave ferrite microstrip resonator with 15% tunability has been approached by application of mechanical strain alone. The frequency tuning arises from alignment control of the unpolarized pattern of magnetic domains by application of uniaxial stress. A variable stress can be produced by a variable voltage applied to a piezoelectric actuator, without a current-controlled magnetizing circuit. For guidance to performance design, the conditions required for stress-tuning of randomly oriented grains with cubic anisotropy constant K1 are analyzed. To account for magnetoelastic effects, the polycrystalline magnetostriction constant λ is the weighted average over the principal cubic symmetry axes. The analyses produce three results: (1) a relation for the tuning range that reflects a dependence on stress σ instead of magnetic field H, with the key materials parameter becoming λ/K1; (2) the stress dominating condition in the ferrite is σλ/K1 > 2/3 for the magnetic vectors along the axis of σ; and (3) for voltage control, a model for estimating the fraction of electrostatic potential energy from the actuator that is converted to elastic energy in the ferrite substrate of the resonator circuit.

Ni0.27ZnxFe2.73-xO4 (with x = 0.03−0.1) thin films with high real permeability μr′ in the GHz range were fabricated by the spin spray process onto glass substrates in the presence of an external magnetic field of 360 Oe. These films exhibit high permeabilities that exceeded the Snoek limit for bulk NiZn-ferrite films and those previously reported for spin spray deposited ferrites. The NiZn-ferrite film with x = 0.06 is low in magnetic losses, having tanδm (μr″/μr′) ∼ 0.027 from 1 to 1.5 GHz, and a high ferromagnetic resonance (FMR) frequency of 2.7 GHz, while the x = 0.1 film exhibited a high μr′ of ∼50 and μr″ > 50 at 1 GHz. These properties are ideal for microwave applications such as antennas, inductors and electromagnetic interference (EMI) suppression in the GHz range.

We present measurements of the microwave properties of high-quality thin films of MgB2 deposited by reactive evaporation on both dielectric and metallic substrates. The measurements include those of the surface impedance and the intermodulation distortion (IMD), both as a function of microwave power at temperatures from 1.8 to 35 K. A stripline resonator at 2 GHz is used for the measurements on dielectric substrates and a dielectric resonator at 10.7 GHz is used for the films on metallic substrates. The surface resistance of the MgB2 is lower than that of our sputtered niobium films, and no power dependence was observed up to surface radio-frequency magnetic fields of 400 Oe at 5 K. The temperature dependence of the IMD at low circulating power shows an increase at temperatures T < 10 K that cannot be explained on the basis of s-wave symmetry of the order parameter in both energy gaps. Within the gap-symmetry constraints of the hexagonal crystal symmetry of MgB2, the best fit with our IMD and penetration depth measurements is obtained for the pi-gap symmetry given by Delta(phi, T) = Delta(0)(T) sin(6 phi), where phi is the azimuthal angle in the ab plane, and Delta(0)(T) is a weakly temperature dependent amplitude at low temperatures. This symmetry entails there being six nodal lines.

We report intermodulation distortion (IMD) in high-quality epitaxial YBa 2 Cu 3 O 7-delta (YBCO) thick films and multilayers prepared by pulsed-laser deposition (PLD) using multiple targets. Two sets of films were prepared: single-layer and multilayer YBCO films in which a 20-nm-thick CeO 2 inter layer is inserted between every 100-nm-thick YBCO layer. With increasing YBCO thickness from 200 nm to 1200 nm, single-layer films exhibited improvement of IMD, whereas multilayer films showed degradation of IMD. Similarly, YBCO crystalline quality in single-layer films was improved with increasing the thickness, while that in multi-layers films degraded. These results suggest that there is a strong correlation between crystalline quality and IMD for YBCO films. The comparison of experimental data with the theory of IMD suggests that improving crystalline quality is essential for YBCO films with thickness greater than 1 mum to achieve an intrinsic nonlinear behavior. PLD using multiple targets is a very useful method to grow thick YBCO films with high crystalline quality and low IMD.

Evidence for non-s-wave symmetry of the pi gap in MgB2 from intermodulation distortion measurements. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We present low-temperature low-power intermodulation-distortion ͑IMD͒ measurements of high-quality MgB 2 thin films that are inconsistent with presumed s-wave symmetry of the order parameter. The measurements were carried out in a stripline resonator at approximately 2 GHz between 1.8 K and T c. The IMD arises from the nonlinear Meissner effect in which the penetration depth is dependent on the RF magnetic field. Specifically, the observed IMD vs temperature T for T Ӷ T c / 2 varies as T −2 , while for an s-wave gap symmetry in the clean limit, the low-temperature IMD decreases exponentially with decreasing temperature. We calculate the IMD from first principles for different order-parameter symmetries using a Green's function approach and compare the results with the measured data. We propose that the observed upturn in the low-temperature IMD implies an admixture of an order parameter with nodal lines into the energy gaps of MgB 2. Most likely, this admixture is prominent for the ␲ gap. Within the constraints of the hexagonal crystal symmetry of MgB 2 , the best fit with our IMD measurements is obtained with a gap ⌬͑␾ , T͒ = ⌬ 0 ͑T͒sin͑6␾͒, where ␾ is the azimuthal angle in the ab plane, and ⌬ 0 ͑T͒ is the amplitude, weakly temperature dependent at low temperatures. This gap symmetry entails six nodal lines. We also present low-temperature penetration-depth measurements that are consistent with the proposed nodal gap symmetry. To relate our proposition with existing literature, we review other low-temperature probes of the order-parameter symmetry. The literature presents conflicting results, some of which are in direct support of the symmetry proposed here.

A novel method of implementing a tunable resonator using an applied voltage is presented. Stress is used to tune a microstrip resonator fabricated on a polycrystalline ferrite substrate. The stress was applied either mechanically with screws or electronically using piezoelectric actuators. We have demonstrated tunability of 300 MHz using screws and 50 MHz using a piezoelectric actuator at a center frequency of 2.3 GHz. Explanation of the tuning method is given and means to extend the tuning range is discussed. This method opens the possibility of compact low-power tunable filters with wide tuning range at microwave frequencies.

We present low-temperature low-power intermodulation-distortion (IMD) measurements of high-quality MgB2 thin films that are inconsistent with presumed s-wave symmetry of the order parameter. The measurements were carried out in a stripline resonator at approximately 2 GHz between 1.8 K and T-c. The IMD arises from the nonlinear Meissner effect in which the penetration depth is dependent on the RF magnetic field. Specifically, the observed IMD vs temperature T for T < T-c/2 varies as T-2, while for an s-wave gap symmetry in the clean limit, the low-temperature IMD decreases exponentially with decreasing temperature. We calculate the IMD from first principles for different order-parameter symmetries using a Green's function approach and compare the results with the measured data. We propose that the observed upturn in the low-temperature IMD implies an admixture of an order parameter with nodal lines into the energy gaps of MgB2. Most likely, this admixture is prominent for the pi gap. Within the constraints of the hexagonal crystal symmetry of MgB2, the best fit with our IMD measurements is obtained with a gap Delta(phi,T)=Delta(0)(T)sin(6 phi), where phi is the azimuthal angle in the ab (&) over cap plane, and Delta(0)(T) is the amplitude, weakly temperature dependent at low temperatures. This gap symmetry entails six nodal lines. We also present low-temperature penetration-depth measurements that are consistent with the proposed nodal gap symmetry. To relate our proposition with existing literature, we review other low-temperature probes of the order-parameter symmetry. The literature presents conflicting results, some of which are in direct support of the symmetry proposed here.

Measured intermodulation distortion IMD power at 1.5 GHz in a series of YBa2Y3O7� stripline resonators of varying strip widths is compared to the predictions of two qualitatively distinct theories of the nonlinear Meissner effect. The stripline resonators are patterned from a single wafer to ensure uniformity of the material properties. According to the first theory T. Dahm and D. J. Scalapino, Phys. Rev. B 60, 13125 1999, the IMD power is dominated by contributions from the strip edges, while according to the second theory D. Agassi and D. E. Oates, Phys. Rev. B 72, 014538 2005 it is dominated by contributions from the body of the strip. The parameter-free comparison of the measured data with the theoretical predictions clearly favors the latter theory. We conclude that the nonlinear component of the penetration depth must be treated with nonlocal electrodynamics. The origins of this outcome are discussed briefly in the framework of a Green’s-function approach.

The nonlinear surface impedance and intermodulation distortion (IMD) products of MgB2 thin films have been measured as a function of power and temperature from 1.7 K to T-C. Both dielectric and metallic substrates have been employed. The measurements on dielectrics use a stripline-resonator technique at 2 GHz. The measurements on metallic substrates have been carried out using a dielectric-resonator method at 10 GHz. The films were grown using the deposition technique of reactive evaporation onto LaAlO3, sapphire, and buffered copper, and stainless steel substrates. The low-power R-S(T) is comparable to that of sputtered Nb films on sapphire, and lower than that of YBCO at the corresponding reduced temperatures. The rf-magnetic-field dependence at T < 20 K follows a moderate slope without breakdown for H < 500 Oe, the limit of the experiment. The measurements of IMD are compared with a theoretical analysis that assumes uncoupled pi and sigma channels and intrinsic nonlinearity to the lowest nonlinear order in the radiation field. While the temperature dependence of the measured IMD on dielectric substrates reflects the calculations qualitatively, it shows features that are not consistent with pure s-wave behavior.