high-qual-When the Josephson junction with normal resistance R is incorporated in a high-Tc superconducting ring, Johnson noise generated in R by thermal energy k B T produces a flux flu
Trang 1High-Temperature RF SQUIDS
V I Shnyrkov
Institute for Low Temperature Physics and Engineering, Academy
of Sciences, Kharkov, Ukraine
7.1 INTRODUCTION
Superconducting quantum interference devices (SQUIDs) are extraordinarily sitive detectors of magnetic flux variations These devices have numerous appli-cations as sensors in a wide range of experiments in the fields of physics, geology,medicine, biology, and industry The progress in technology and in understanding
sen-the origin of sen-the noise in low-transition-temperature (Tc) SQUIDs brought a
dra-matic improvement in the resolution of electrical and magnetic measurements.Many rather new and nonstandard applications of SQUIDs have been reviewed indetail; see reviews and contributions in Refs 1 and 2
The discovery of high-Tcoxide superconductors by Bednorz and Muller (3)quickly made apparent that macroscopic quantum phenomena may be very useful
for a number of electronic applications High-Tcmaterials have opened new sibilities by increasing the operating temperature of superconducting instrumentsand sensors
pos-The High-TcSQUID was the first superconducting electronic circuit ploying Josephson junction cooled by liquid nitrogen The development of super-conducting magnetometers operating at 77 K holds promise of expanding the use-ful range of application of these devices to include remote operation in the field
Trang 2em-and space, where the availability of liquid helium as a cryogen may be limited bysome factors (4) In addition, the wider range of operation temperature may per-mit measurement on room-temperature samples such as living tissue (5), nonde-structive material evaluation with Joule–Thomson cryocooler in industry (6), androutine checks of moving samples with greater sensitivity (7), high-TcSQUIDmicroscopy (8), and convenience due to nitrogen cooling.
However, oxide superconductors have introduced some completely newproblems Because of the extremely short coherence length, a conventionalJosephson junction structure is not possible, and various inhomogeneities andstructural defects in these materials lead to the formation of parasitic weak linksbetween regions with well-developed superconductivity, lead to increased fluxcreep, reduce the critical current of the junctions, and creates an excess high noiselevel
In practice, twin boundaries are essentially nonsuperconducting regions in
high-Tcmaterials and SQUIDs due to these can be observed The values of temperature coherence length (0) and lattice parameter c are very much different from the conventional low-Tcsuperconductors Such however, is not the case for
zero-a usuzero-al superconductors:
This difference between a usual and high-TcSQUIDs eliminate the mainphysical and technology problems toward practical application of the new super-conductors: anomalously large critical current anisotropy in single cyrstals andepitaxy sensors at moderate magnetic fields, the existence of intragrain Josephsonjunctions and randomness, frustration effects in presence of a magnetic field, 1/ƒnoise, and so forth
At 77 K, the Josephson coupling energy in high-Tcjunctions may be of theorder of the thermal energy, and under this condition, thermally activated phase-
slippage processes result in an observable reduction of the high-TcSQUIDs’ namic range and sensitivity Except that there are specific for oxide superconduc-tors phenomena, the ultimate sensitivity of both single- and double-junction
dy-SQUIDs is limited by the characteristic frequency R/L of the interferometer The
sensitivity of an optimized dc SQUID is limited primarily by two parameters
de-termined by the high-Tc technology process: loop inductance L and junction
char-acteristics In the case of radio-frequency (RF) SQUIDs, the sensitivity is limited
by pump frequency and preamplifier noise The requirements for fabrication nology are not as strict as for DC SQUIDs However, in external magnetic fieldsboth dc and RF SQUIDs sensitivities are limited by the specific for oxide super-conductors noise sources and make these SQUIDs competitive to each other
tech-Some difficulties in the technology of high-TcSQUIDs have been overcomeand excellent sensitivity is achieved in practical devices with rf sensors (9) with
((0)/c)high T c
(0)/c)usual
Trang 3probably, exact condition on k2Q in quasi-nonhysteretic mode (10) For strument applications, one can make a comparison of different SQUIDs parame-ters: energy sensitivity, magnetic field sensitivity, bandwidth, slew rate, main
real-in-SQUID electronics structure, and so on Deviation in these parameters of high-Tc
RF SQUIDs from the low-TcRF SQUIDs are attributed to specific properties ofoxide superconductors and thermal fluctuations
In this chapter, two different types of high-TcRF SQUID fabricated fromboth bulk ceramic and thin film are briefly reviewed We focus on the most im-portant results and on general problems in the design and fabrication of low-noise
high-Tcmagnetometers based on RF SQUIDs The single-junction interferometer
in the presence of large thermal fluctuations and the RF SQUIDs are discussed
Flux-creep noise in high-Tcmagnetometers and “Josephson fluctuators” are
ana-lyzed Finally, the design and pilot applications of a high-TcSQUID are discussed
7.2 HIGH-Tc SINGLE-JUNCTION INTERFEROMETER IN THE
RSJ MODEL
When connecting two superconducting electrodes by a weak electric contact, themacroscopic coherence of supercoducting state results in the following funda-mental expression:
where Ic is the critical current of a high-TcJosephson junction
Three types of weak-link step-edge junctions (11,12), bicrystal junctions(13,14), and grain-boundary junctions in bulk materials (15) are commonly used
to fabricate high-TcRF SQUIDs A considerable number of articles have beenpublished dealing with these types of weak link (16) and sometimes junctionslooked at as a complicated connection between chaotically located weak linkswith random parameters Perhaps a separate article is needed to review all of theseeffects caused by the magnetic field and current flowing through complicated
junction Regular high-Tcweak-link SQUIDs seem to be more promising both for
RF and dc SQUID applications in low and moderate magnetic fields At present,the bicrystal and step-edge structures seem to be the more promising, which can
2
0
d( dt
Trang 4be made with low intrinsic capacitance (C 10 fF) and a high characterizing
pa-rameter Vc Ic R 0.1–0.5 mV, with the current–phase relation close to RSJ
model (17,18), I Icsin(
1 Step-edge junctions: Step-edge junctions are formed by depositing a thin high-Tcepitaxial film on substrate that has a step etched into thesurface The weak link is then formed as the single-layer film bridgesthe two levels The steps usually are formed by patterning and ionmilling the SrTiO3substrate There are significant advantages to step-edge technology A variety of large-area substrates can be employed inthe step-edge process (bicrystal technology is limited to a 10-mm Sr-TiO3substrate) The step-edge height is highly reproducible However,the junction parameters appear to depend greatly on film thickness, andvariations observed for step-edge technology are probably a result ofthe film thickness and superconducting parameters variations, on the
“bottom” and on the “top” of the step
2 Bicrystal junctions: Bicrystal junctions are fabricated on the substrate
that has a twin boundary formed by two single-crystal domains withdifferent crystal orientations On SrTiO3bicrystal substrates, a misori-entation angle usually is an order 25°–37° They are made by fusing twoseparate single crystals and then dicing substrates from the single piece.This results in a twin boundary down the center of the substrate Whenthe superconductor film is epitaxially grown, a twin boundary forms inthe superconductor film at this interface
More details of the fabrication and characterization of ramp edge andstep edge junction are given in Chapters 3 and 4
3 Josephson’s junctions for bulk HTS SQUIDs are conventionally factured by means of local impact of a pulse laser A sample specimen
manu-is positioned into an optical cryostat, whereas, by nonstop monitoring
of volt–ampere characteristics, the amplitude of pulse irradiation hasbeen increased, up to an emerged required nonlinearity Such sensorsare very inexpensive in manufacture and are relatively low cost (about
$30 each) However, said products are typical for having excessive 1/ƒnoise in low-frequency area A response of said SQUIDs can be im-proved only due to quality of bulk materials and to the creation of superconductive input coils
The investigated step-edge and bicrystal junctions routinely made by manygroups had a width of weak link ranging from 1 to 50 ab(0)] and with
a thickness of 0.1–0.3 m The scaling relation between Ic R and J cfor both edge and bicrystal junctions fabricated from YBaCuO and GdBaCuO and tested
step-at 77K is shown in Figure 7.1 (16) However, there is no technological process for
fabricating high-TcJosephson junctions with reproducible characteristics
Trang 5How-ever, high-quality tunnel junctions can be routinely fabricated for ture superconductors.
low-tempera-In a RSJ model, the total current through the high-TcJosephson junction can
be considered as a sum of the superconducting current, normal current, and biascurrent (19,20):
Here R and C are the normal resistance and junction capacitance, respectively.
When the junction is incorporated in the superconducting ring (Fig 7.2), the stant voltage should occur across it, with only a time variation in the magnetic flux through the ring:
Trang 6Equating Eqs (1) and (5) and integrating with respect to the time results in
an unambiguous relation between the contact-phase difference and total magneticflux through the RF SQUID loop:
Equation (8) is equivalent to a classical equation for the motion of the particle with
the mass M C( 0/2 2in the one-dimensional potential field:
geomet-junction LJ 0/2 c The values and q determine the shape of the curves for
the stationary SQUID characteristic and potential energy and agree upon the sification for the modes of one-contact SQUID operation in a small fluctuationlimit (21)
0
2
0
d dt
d2
dt2
2
0
Trang 77.3 SMALL FLUCTUATION LIMIT FOR HIGH-TcRF SQUIDs
Superconducting rings, coils, and transformers are essential elements of all
high-T csuperconducting magnetometer sensors At 77 K, in a nonshielding ment there are some main sources of noise: Johnson noise generated by thermalenergy in the normal resistance and low-frequency noise generated by magneticflux instability (flux creep noise) and by bistable or multistable Josephson fluctu-
environ-ators in SQUID body The fact is that the excess-noise amplitude of high-Tc
SQUIDs decreases in a low external magnetic field and development of ity epitaxial film system brought a dramatic improvement in resolution The im-portant point about these SQUIDs is that they operate at 77 K in a small thermalfluctuation limit
high-qual-When the Josephson junction with normal resistance R is incorporated in a high-Tc superconducting ring, Johnson noise generated in R by thermal energy
k B T produces a flux fluctuation spectral density in the ring inductance L:
re-practical consideration for high-TcSQUIDs applications is to estimate the tude of fluctuation that will be introduced by a normal-metal enclosure surround-ing the sensor, either outside or inside the dewar
magni-From a practical point of view, it is important to choose different
parame-ters of a high-Tc Josephson junction, such as the critical current Ic, normal tance R, capacitance C, and the geometrical inductance L of a SQUID loop The capacitance is negligible for the high-TcJosephson junction and the McCumberparameter
for these SQUIDs In order to observe the magnetic flux quantization in a SQUID
loop with inductance L, one needs that the uncertainity of the magnetic flux (13)
must be lower than fundamental quantity of the magnetic flux quantum defined by
2 kB TL 2
(15) 0, the transfer function decreases very quickly ( exp(L/2LF) In this mode
( 1, L LF, $ 1), high-TcRF SQUID sensitivity is determined by the noise
temperature of the preamplifier (Tamp) and the pump frequency ):
where%opt L/Ropt, with Ropt,the optimal input impedance of the preamplifier Incontrast with small fluctuations, in this mode one has a higher intrinsic noise of
high-TcRF SQUIDs; if the pump frequency is 30 MHz, 0.5, k 0.1, and L/LF
1, then Tamp 120 K, corresponding to the energy sensitivity "min 2 1027
J/Hz or 5 10-3 0/Hz1/2 These drawbacks explain why inductive ( 1)
High-TcSQUIDs in a high fluctuation limit are rarely used in practice and we needhigh critical current in SQUIDs
The screening current in the RF high-TcSQUID inductance have been
cal-culated recently (31,32) for higher values of l
i cos()t !) exp 2L L
F
gJ1(a) cos (e ƒ2 J1(2a) cos 2(e (48)
where g and ƒ are coefficients that depend on both and $:
Trang 20and suppression of the transfer function of a dc SQUID with L Fis stronger
than in the case of a high-TcRF SQUID
However, taking into account +dc R/L and +RF ()/k)(LT/L)1/2
, the totalvalue of the transfer function and the optimal energy sensitivity can be higher for
dc SQUIDs This formula does not take into account the 1/ƒ noise region It should
be pointed out that for RF SQUIDs, 1/ƒ noise performance can be better due to thenoise parameter $; see, for example, Refs 31, 34, and 35
However, there is no difference between the two types of macroscopicquantum device with dc or RF operation modes because, in practice, the main rea-sons for the sensitivity for both systems are excess noises in high-Tcmaterials inexternal magnetic fields
7.8 EXCESS NOISE IN HIGH-TcMATERIALS AND SQUIDs
A number of materials-related problems have hindered the development of a
tech-nology process for fabrication of high-TcSQUID magnetometers (36) The first 2-3 structure discovered, YBaCuO, is one of the most commonly used materials
1-for high-Tcelectronics device fabrication Depositing high-quality YBaCuO andGdBaCuO thin films (16) forms the development of a reproducible process forstep-edge and bicrystal junctions The critical currents displayed by the bicrystaland step-edge junctions are typically 30–100 A with the Ic R product of
100–200V at 77K for both materials with a current density 5 105
–106A/cm2(Fig.7 1) The noise level of the devices (about 100 fT/Hz1/2) does not appear todiffer significantly between magnetometers fabricated from YBaCuO andGdBaCuO with step-edge and bicrystal Josephson junctions Also, it has beennoted that significant parts of these devices are generally noisier The reason of the
higher noise level of the all types (dc and RF) of high-TcSQUIDs may be discrete
or a large ensemble of Josephson fluctuators (JF) (37,38) and thermally activatedflux motion in oxide superconductors (39,40)
7.8.1 Flux Noise Generated by Josephson Fluctuators
The fluctuation phenomena in high-Tcmaterials result in much more pronounced
features than those observed in traditional low-Tcsuperconductors The
order-pa-rameter depression is essential at temperatures close to Tcand it arises due to theshort coherence length in the oxide superconductors, which may be of the order ofinteratomic distances in the direction transverse to the Cu–O layers Various in-homogeneities and structural and orientation defects in these materials lead to theformation of weak links between regions with a high critical current density Thepower spectral density of the magnetic flux noise in a simple model of a multi-contact weakly coupled system is called the “Josephson fluctuator” (JF), which re-
flects to some extent specific properties of real high-Tcsuperconductors
... significant parts of these devices are generally noisier The reason of thehigher noise level of the all types (dc and RF) of high- TcSQUIDs may be discrete
or a large ensemble of. .. defects of oxide superconductor material SQUID andJosephson junction research has recently made a comeback, because of the im-provement of its characteristics at nitrogen temperature In Section 7 .8, ... SENSITIVITY OF HIGH- T cRF SQUIDs
It would be of significant importance to estimate ultimate noise properties of two
types of high- TcRF SQUID