Scanning Superconducting QUantum Interference Device (SQUID) microscopy provides valuable information about magnetic properties of materials and devices. The magnetic flux response of the SQUID is often linearized with a flux-locked feedback loop, which limits the response time to microseconds or longer. In this work, we present the design, fabrication, and characterization of a novel scanning SQUID sampler with a 40-ps time resolution and linearized response to periodically triggered signals. Other design features include a micron-scale pickup loop for the detection of local magnetic flux, a field coil to apply a local magnetic field to the sample, and a modulation coil to operate the SQUID sampler in a flux-locked loop to linearize the flux response. The entire sampler device is fabricated on a 2 mm × 2 mm chip and can be scanned over macroscopic planar samples. The flux noise at 4.2 K with 100 kHz repetition rate and 1 s of averaging is of order 1 mΦ0. This SQUID sampler will be useful for imaging dynamics in magnetic and superconducting materials and devices.

A Superconducting QUantum Interference Device (SQUID), a superconducting loop interrupted by Josephson weak links, is a highly sensitive magnetic flux sensor. Scanning SQUID microscopy scans a SQUID over the surface of a sample to image the local magnetic flux.1–4 This technique has the advantage of high flux sensitivity. The spatial resolution has been continuously improved and reached sub-micron level in recent years.5–7 In standard closed-loop scanning SQUID microscopes, however, the bandwidth is still limited to a few MHz by the feedback electronics.8 

Several groups have developed strategies, including open-loop operation and sampling of periodic signals, to extend the bandwidth of scanning SQUIDs.8–11 These techniques can achieve a bandwidth of several hundred MHz (up to a GHz in the case of the sampling method). Pushing the bandwidth even further would be tremendously useful in studies of spintronics and fractional AC Josephson effects, where interesting effects may occur on a sub-nanosecond time scale.12–15 As a part of a joint Stanford/IBM effort, we have designed, fabricated, and characterized a scanning SQUID sampler that uses a Josephson pulse generator16,17 to achieve a 40-ps time resolution with linearized response to periodic signals, effectively extending the bandwidth to 25 GHz.

The layout of the SQUID sampler is shown in Fig. 1. The Josephson junctions on the SQUID are fabricated with the same Nb/Al2O3/Nb tri-layer technology from IBM as our SQUID susceptometers.5 Each sampler is fabricated on a 2 mm × 2 mm silicon chip, which is mounted on a scanning stage and brought close to a sample in a cryostat.

FIG. 1.

Partial chip layout of the SQUID sampler. Different colors indicate different niobium wiring layers. (a) Layout of all functional components of the sampler, located at one corner of a 2 mm × 2 mm silicon chip. (b) Expanded view of the pickup loop and the field coil. The pickup loop shown has 0.2 μm inner width and can be placed as close as a few hundred nm above the sample. (c) Components far away (150 μm) from the pickup loop: modulation coil, pulse generator, and trigger. These components do not affect the local magnetic flux measured by the pickup loop.

FIG. 1.

Partial chip layout of the SQUID sampler. Different colors indicate different niobium wiring layers. (a) Layout of all functional components of the sampler, located at one corner of a 2 mm × 2 mm silicon chip. (b) Expanded view of the pickup loop and the field coil. The pickup loop shown has 0.2 μm inner width and can be placed as close as a few hundred nm above the sample. (c) Components far away (150 μm) from the pickup loop: modulation coil, pulse generator, and trigger. These components do not affect the local magnetic flux measured by the pickup loop.

Close modal

The sampler device is made up of a main flux-sensing SQUID and several other control components/coils. We call the flux-sensing SQUID the “comparator” because we measure flux by comparing the SQUID voltage to a known set-point, explained in more detail in Sec. II B. The shielding layer of the comparator SQUID loop is shaped like a pencil [shown as red mesh in the center of Fig. 1(a)], with the pickup loop and the field coil located at the tip. The modulation coil and the pulse generator are located at the base of the “pencil” and are inductively coupled to the comparator.

Figure 1(b) shows the pickup loop/field coil pair. The pickup loop is a part of the comparator. The leads to the pickup loop (black) are shielded from background magnetic flux by a superconducting layer (red), leaving only a small area to capture the local magnetic flux. The pickup loop is aligned almost parallel to the sample surface with an angle 4°. This allows us to measure at a minimum distance (from the sample) ranging from several hundred nm to a few μm, depending on the size of the pickup loop. For different applications, we have designed four different pickup loop diameters: 0.2 μm, 0.6 μm, 2 μm, 6 μm. The field coil (blue) is used to apply local magnetic fields to the sample for susceptibility measurements.

Figure 1(c) shows the other components of the sampler, which are designed to be 150 μm away from the pickup loop. The modulation coil can be used to apply a magnetic flux to the comparator and modulate its IV characteristics without affecting the sample near the pickup loop. The pulse generator and trigger are a pair of components designed to thread a precisely-timed short flux pulse into the comparator, allowing it to take “snapshot” measurements of flux as a function of delay time with respect to a reference synced to the signal. The pulse generator follows closely the original design by Faris.16 On the arrival of a trigger pulse in L5 in Fig. 1(c), it generates a short current pulse in L4 (as described in the  Appendix), inductively coupling a flux pulse into the comparator.

The bandwidth limitation of a conventional scanning SQUID microscope is determined by the speed of the room temperature readout and feedback electronics. These electronics usually only have a bandwidth of a few MHz or lower. On the other hand, the SQUID itself can operate at the Josephson frequency 2eh V, where V is the voltage across the Josephson junctions. The Josephson frequency is usually hundreds of GHz. Therefore, it would be desirable to overcome the limitations of the room temperature electronics and extend the measurement bandwidth, up to the Josephson frequency. One avenue to achieve this goal is to employ a pulsed-measurement scheme10 similar to an optical pump-probe experiment.

We employ such a technique in the SQUID samplers to achieve a 40-ps time resolution. The circuit diagram is shown in Fig. 2(a) and the current-biasing sequence is shown in Fig. 2(b). The comparator is a hysteretic SQUID whose switching current Iswitch(Φ) is a periodic function of magnetic flux through the SQUID loop. When the comparator is current biased slightly below Iswitch, it can be thermally driven into the normal state with some probability Pswitch. In this regime, Pswitch depends almost linearly on (Iswitch − Ibias). Since Iswitch changes as a function of magnetic flux Φ at fixed Ibias, we obtain a transfer function for PswitchΦ. We measure the switching probability by biasing the comparator with 1000 current pulses and measure the average voltage V. Pswitch = V/Vmax; Vmax = Ibias R, where R is the normal state resistance of the comparator. We can then convert Pswitch to magnetic flux. To obtain the 40-ps time resolution, we use the pulse generator to send a short flux pulse into the comparator (characterization of this pulse in Sec. III C below). In the absence of the pulse, the comparator is biased well-below its switching current and V = 0. The flux pulse from the pulse generator lowers the switching current of the comparator almost down to its bias current [IbiasIswitch(Φpulse)]. The switching probability becomes sensitive to magnetic flux only in the presence of the short pulse; therefore, the switching probability gives a 40-ps “snapshot” measurement of Φsignal. The Josephson junctions in the SQUID have a critical current of Ic = 75 μA and a capacitance of approximately C = 1 pF. Therefore the Josephson plasma frequency is ωJ=2πIcΦ0C = 485 GHz, where Φ0 is the superconducting flux quantum. The plasma frequency is high enough to ensure that the switching probability over 40 ps follows the thermal equilibrium behavior and is thus an accurate measure of the external flux.

FIG. 2.

Schematic and bias sequence of the sampler. (a) The inductive coils labeled L1–5 are shown in Fig. 1. (b) Example of a control pulse sequence to operate the sampler. The bias pulses for the comparator, pulse generator, and trigger are user-defined and remain the same for all measurements. The short pulse in purple is automatically generated by the pulse generator in situ. The red sine wave in the field coil is a specific example for illustration purpose only. The field coil waveform can be arbitrarily defined to fit the goal of the measurement (square pulse, sine wave, ramp, DC, etc.).

FIG. 2.

Schematic and bias sequence of the sampler. (a) The inductive coils labeled L1–5 are shown in Fig. 1. (b) Example of a control pulse sequence to operate the sampler. The bias pulses for the comparator, pulse generator, and trigger are user-defined and remain the same for all measurements. The short pulse in purple is automatically generated by the pulse generator in situ. The red sine wave in the field coil is a specific example for illustration purpose only. The field coil waveform can be arbitrarily defined to fit the goal of the measurement (square pulse, sine wave, ramp, DC, etc.).

Close modal

We measure the DC response of the sampler by applying a DC current into the modulation coil. This allows us to simultaneously measure the DC flux response of the comparator and the mutual inductance between the comparator and the modulation coil, which is important for flux-locked feedback. To determine the switching current, the bias current (Ibias) of the comparator is incrementally changed. At each comparator bias current, the entire biasing sequence is repeated 1000 times and the average voltage across the comparator is measured. The switching current is indicated by a sharp increase in the comparator voltage. This measurement of the switching current is repeated for different DC fluxes applied through the modulation coil. The dependence of the switching probability on the applied DC flux is shown in Fig. 3(a). At Ibias = 135 μA, the switching probability vs. flux is plotted in Fig. 3(b). To linearize the flux response, we use V at Pswitch = 0.5 as a voltage set-point and operate the sampler in a flux-locked feedback loop, in which current is applied to the modulation coil to offset Φsignal and keep V fixed.18 It is important to note that the sampler response can only be well-linearized if Φsignal,maxΦsignal,minΦpulse, due to the possibility of false switches even in the absence of Φpulse (as a reminder, Φsignal varies as a function of time).

FIG. 3.

Response of the sampler to DC magnetic flux. (a) The dependence of comparator switching current on magnetic flux. The horizontal axis is the magnetic flux applied through the modulation coil. The vertical axis is the bias current through the comparator. The color bar shows the superconducting-normal switching probability, measured as V/Vmax over 1000 bias pulses. The blue horizontal line near 150 μA is a glitch in the function generator and not related to the sampler. (b) Switching probability vs. DC magnetic flux (through modulation coil) at comparator Ibias = 135 μA. The feedback set-point is chosen to be V/Vmax = 0.5.

FIG. 3.

Response of the sampler to DC magnetic flux. (a) The dependence of comparator switching current on magnetic flux. The horizontal axis is the magnetic flux applied through the modulation coil. The vertical axis is the bias current through the comparator. The color bar shows the superconducting-normal switching probability, measured as V/Vmax over 1000 bias pulses. The blue horizontal line near 150 μA is a glitch in the function generator and not related to the sampler. (b) Switching probability vs. DC magnetic flux (through modulation coil) at comparator Ibias = 135 μA. The feedback set-point is chosen to be V/Vmax = 0.5.

Close modal

We characterize the AC response of the sampler by applying a sine wave excitation to the field coil using a Tektronix AFG3252 arbitrary function generator. In this configuration, the field coil acts as a microwave antenna and the AC magnetic field produced is measured by the pickup loop. We then fit the measured waveform to a sine function to extract the measured amplitude and frequency and compare them with expected values. Figure 4 shows the sampler’s response to AC flux signals of different frequencies and amplitudes. We measure different amplitudes (0.05, 0.1, 0.2, 0.5, 1.2 Vpkpk) at a constant 10 MHz. We also measure frequencies from 10 MHz up to 240 MHz at a constant 0.5 Vpkpk. The signal amplitude is converted from voltage to flux using the mutual inductance between the field coil and the pickup loop measured at DC (not shown).

FIG. 4.

Sampler response to AC field coil excitation in a flux-locked loop. We apply AC excitations at different frequencies and amplitudes to the field coil to test the AC response of the sampler. The mutual inductance between the field coil and the pickup loop is measured by applying current to the field coil and looking at the periodic modulation of the comparator switching current. (a) Example of data (red dots) and fit (black line). The fit parameters are amplitude, frequency, and phase. (b) Fitted amplitude at constant frequency (blue star) vs. applied amplitude (red dotted line) showing large amplitude distortion. (c) Fitted frequency at constant amplitude (blue star) vs. applied frequency (red dotted line) showing perfect match of the time dependence. (d) Fitted amplitude at different frequencies (blue star) vs. applied amplitude (red dotted line) showing small scatter around the expected mutual inductance value.

FIG. 4.

Sampler response to AC field coil excitation in a flux-locked loop. We apply AC excitations at different frequencies and amplitudes to the field coil to test the AC response of the sampler. The mutual inductance between the field coil and the pickup loop is measured by applying current to the field coil and looking at the periodic modulation of the comparator switching current. (a) Example of data (red dots) and fit (black line). The fit parameters are amplitude, frequency, and phase. (b) Fitted amplitude at constant frequency (blue star) vs. applied amplitude (red dotted line) showing large amplitude distortion. (c) Fitted frequency at constant amplitude (blue star) vs. applied frequency (red dotted line) showing perfect match of the time dependence. (d) Fitted amplitude at different frequencies (blue star) vs. applied amplitude (red dotted line) showing small scatter around the expected mutual inductance value.

Close modal

Figure 4(a) shows an example of the fit at 10 MHz and <0.1 Φpkpk. All of the bootstrapped error bars are smaller than the plot symbols and thus omitted in Figs. 4(b)–4(d). At a constant frequency of 10 MHz, the measured waveform starts to deviate slightly from the expected sine wave at large amplitudes, causing an apparent deviation in the fitted vs. expected amplitudes, shown in Fig. 4(b). This large amplitude distortion is caused by false switches when (Φsignal,maxΦsignal,min) becomes comparable to Φpulse. Figure 4(c) shows that the measured frequencies agree very well with expected frequencies up to 240 MHz. Figure 4(d) shows small scatter in the measured amplitudes at different frequencies, which is possibly due to the frequency response of the fridge wiring being non-uniform. There is no systematic frequency dependence due to parasitic capacitance in the circuit.

The fundamental limit on the time resolution of the sampler is set by the width of the flux pulse from the pulse generator. To characterize the time resolution of the sampler, we measure a “two-pulse interferometer,”16,17 realized by replacing the field coil with a second pulse generator/trigger pair. This allows us to time resolve the pulse from the second pulse generator. The measured waveform of the pulse is shown in Fig. 5. The relative delay time of the two pulses is controlled by a Stanford Research Systems DG645 digital delay generator, which has a 5 ps resolution and <25 ps RMS jitter. The full width at half maximum (FWHM) is 40 ps, which we quote as our time resolution. We have also used a mechanical phase shifter to eliminate the digital jitter and still found the FWHM to be 40 ps. Simulation with the WRspice software shows that the pulse width can be as low as 10 ps if there were no parasitic inductances. The DC flux increase following the pulse is expected from the residual current as explained in the  Appendix. The oscillations following the pulse are not well understood. Our hypothesis is that they are due to the LC components of the pulse generator circuit.

FIG. 5.

Waveform of a short pulse created by a second on-chip pulse generator and measured by the sampler itself. A second pulse generator (identical to the one on the sampler) is fabricated on-chip and inductively couples a short flux pulse into the pickup loop. The resultant signal is found to have a FWHM = 40 ps.

FIG. 5.

Waveform of a short pulse created by a second on-chip pulse generator and measured by the sampler itself. A second pulse generator (identical to the one on the sampler) is fabricated on-chip and inductively couples a short flux pulse into the pickup loop. The resultant signal is found to have a FWHM = 40 ps.

Close modal

The spatial resolution of the sampler is determined by the geometry of the pickup loop and the experimental alignment with respect to the sample. Since the sampler pickup loops are identical to the susceptometer pickup loops, we expect the sampler’s spatial resolution to also be consistent with that of the susceptometers.5 Figure 6 shows an image of a superconducting vortex in a niobium film taken with a 0.6 μm diameter pickup loop. We use superconducting vortices as approximate point sources to characterize the point spread function (PSF) of the sampler in order to obtain images of magnetic field.

FIG. 6.

Characterization of the spatial resolution of a 0.6 μm diameter sampler. (a) Magnetic flux image of a superconducting vortex in a niobium film. The vortex is effectively a point source 1 μm below the pickup loop. The non-circular shape results from the PSF of the sampler’s pickup loop. (b) Horizontal linecut through the maximum of the vortex (red dotted line in the color plot), showing a FWHM of 1 μm.

FIG. 6.

Characterization of the spatial resolution of a 0.6 μm diameter sampler. (a) Magnetic flux image of a superconducting vortex in a niobium film. The vortex is effectively a point source 1 μm below the pickup loop. The non-circular shape results from the PSF of the sampler’s pickup loop. (b) Horizontal linecut through the maximum of the vortex (red dotted line in the color plot), showing a FWHM of 1 μm.

Close modal

We characterize the noise of the samplers by measuring the RMS scatter under zero external magnetic flux. At the base temperature of 4.2 K, the RMS noise is of order 1 mΦ0 for 1 s of averaging per data point at 100 kHz repetition rate. At 100 kHz repetition rate, a single switching event is attempted every 10 μs, so the effective duty cycle is 40 ps/10 μs. The effective noise bandwidth with 1 s of averaging is thus (1s40ps10μs)1 = 250 kHz. Therefore, the measured noise floor of our samplers is 2 ×106Φ0Hz comparable to that reported in previous scanning SQUID devices.2,4,5,11,18 With a fixed pulse width of 40 ps, the measurement duty cycle is directly proportional to the repetition rate. A higher repetition rate would lead to lower RMS noise. The repetition rate is ultimately limited by the duration of the physical process being measured, which can be GHz. We are currently limited by our fridge wiring.

Using our novel SQUID sampler, we have demonstrated an unprecedented 40-ps time resolution and state-of-the-art spatial resolution for a scanning SQUID microscope. The sampler has large dynamic range up to 0.2 Φ0. With a repetition rate of 100 kHz and 1 s of averaging, the sampler has a noise level of 1 mΦ0. The noise level is expected to go down with a higher repetition rate and longer averaging time. We plan to use the sampler to study dynamics in magnetic tunnel junctions, superconducting vortices, and exotic Josephson junctions.

The characterization and analysis in this work were primarily supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract No. DE-AC02-76SF00515. Z. Cui was partially supported by the Gordon and Betty Moore Foundation, Grant No. 3429. The design and fabrication of the samplers were supported in part by the NSF-sponsored Center for Probing the Nanoscale at Stanford, Nos. NSF-NSEC 0830228 and NSF IMR-MIP 0957616 and in part by FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.

This section explains the details of the pulse generator/trigger operation shown in Fig. 2. A finite bias current IPG flows through R1. All Josephson junctions (JJ1,2,3) start in the superconducting state. An external flux pulse in L5 (trigger) is used to instantaneously drive JJ1 and JJ2 normal. The normal state resistance of JJ1,2 causes current to flow in L4. The current through L4 almost immediately drives JJ3 normal, redistributing the current again (i.e., self-reset). After this reset, the current in L4 goes back to almost zero, leaving a small residue. This process triggers an ultrashort current pulse that is inductively coupled into the comparator through L4. The experimentally sampled waveform of the current pulse is shown in Fig. 5. The function of the ultrashort pulse in the sampler operation is explained in Sec. II B.

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