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Further investigation of the planar array of superheated superconductors Lu, Yunfei 1993

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FURTHER INVESTIGATION OF THE PLANAR ARRAY OFSUPERHEATED SUPERCONDUCTORSByYunfei LuB. A. Sc. (Physics) Peking University, ChinaA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCETHE FACULTY OF GRADUATE STUDIESDEPARTMENT OF PHYSICSWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIASept. 1993© Yunfei Lu, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of  PAIS/CSThe University of British ColumbiaVancouver, CanadaDate Dd. /4, / 993(Signature)DE-6 (2/88)AbstractThree sizes of the Planar Array of Superheated Superconductors (PASS) were studied.Several 100 x 100 arrays, 250 x 250 arrays and 100 x 1 line arrays of tin squares werefabricated with the photolithography techniques, and then melted in a vacuum chamber.Phase transition curves were mapped out at the earth's field (t— 0.05 mT), 2 mT,4 mT and 4.7 mT for the 100 x 100 array of tin spheres with radius of 12 tem andcenter-to-center spacing of 70 pm. Radiation tests were also made using a low energy7—source. Time distribution curves for granule flipping were measured and comparedwith the calculated response, and good agreement was obtained.Three layers of 250 x 250 tin arrays with granule radius of 3 ictm and center-to-centerspacing of 40 ,am, as well as a single 250 x 250 array, were compared. The spreadsof transition temperatures were essentially the same. The measured response of thethree—layer arrays to 7-rays also agreed with the calculated result.iiTable of ContentsAbstract^iiTable of Contents^ iiiList of Tables^ vList of Figures^ viAcknowledgement ix1 Introduction 11.1 Superheated Superconducting Granules (SSG) . . .^. ^ 11.2 Historical Perspective ^ 41.3 Present Work^..........^.^0^........^. . ^ 51.4 Thesis Outline 52 Theory 62.1 Energy Deposition ^ 62.2 Energy Absorption . ^ 103 Apparatus and Sample Preparation 123.1 Apparatus ^ 123.1.1^Cryostat^.^. •^.^•^. 123.1.2^Data Acquisition 153.2 Sample Preparation ^ 15iii4 Experiments and Interpretations^ 214.1^100 x 100 Array^. .^. . . . ...... . . . . .^214.1.1^Phase Transition . .^. ...... . ..... . . 214.1.2 Radiation Test . 224.1.3 Theoretical interpretation . .^. ...... .^254.2 250 x 250 Array ^  354.3 Three Layers of 250 x 250 Array .......... .^.  ^384.3.1 Phase Transition  ^384.3.2 Radiation Test  ^384.3.3 Theoretical Interpretation ........... .^ 424.4 Line Array ^  434.5 Discussion  ^434.5.1 Energy Sensitivity. ..... .  ^4354.5.2 Energy Resolution4.5.3 Efficiency  ^455 Conclusions^ 47Appendices^ 49A Radiation Simulation Program^ 49Bibliography^ 54ivList of Tables4.1 Spreads of transition temperatures for different samples.^.^46vList of Figures1.1 Phase diagram for a type I superconductor. Solid Line: superheated tran-sition; dashed line: thermodynamic transition; chain dotted line: super-cooled transition. . .......... ......... . . 22.2 Schematic diagram of interaction between a granule and -y-ray. (a): anincoming photon is absorbed and a photoelectron is produced with theincoming photon energy. Then the electron is stopped inside the granuleand deposits all its energy in the granule. (b): the incoming photon isalso absorbed, but the electron produced escapes from the granule, so thegranule only gets parts of energy Eph.   72.3 Schematic diagram for a photoelectron generation in the outer shell (R >r > IR — Rg I). The center of the granule is 0, and A is the place where thephotoelectron is produced. The shaded volume includes all the directionsin which the photoelectron will be stopped. The -y-ray enters along thez-axis.   93.4 Pumped 'Ile cryostat assembly.   133.5 Schematic process of photolithography. 163.6 Image of a 250 x 250 array of tin granules with radius of 3 pm and center-^to-center spacing 40 pm   20vi4.7 Temperature sweeps for the 100 x 100 array at 2 mT. Note the super-heated phase transition temperature is 3.58 K, ATsh is about 27 mK;while supercooled phase transition temperature is 2.85 K, AT„ is about70 mK. . . . 234.8 Temperature sweeps for the 100 x 100 array at 2 mT, 4 mT and 4.7 mT.The SQUID signal is normalized to the same value. Superheated transitiontemperatures are 3.375 K and 3.435 K at 4.7 mT and 4 mT, respectively. 244.9 Radiation test for the 100 x 100 array at 4 mT. The temperature wasset at 3.4305 K. The "blocked - unblocked" curve gives out the net signalchange due to the radiation. 264.10 Time distribution of the number of granules flipping due to the radiation.After 300 s, all the granules have flipped to the normal state. . . . 274.11 Step size distribution of the number of granules flipping.   284.12 Temperature sweeps of the 100 x 100 array at 4 mT. The fixed temperaturein the radiation test is T0 , T1 and T2 are the maximum and minimumsuperheated transition temperatures, S0 , Si. and S2 are the correspondingSQUID signals. . . . . . . . . ....... . . . 304.13 Schematic graph of a granule. The center of granule is 0, A is the placewhere the photoelectron is produced. / 0 is the minimum distance theelectron has to travel inside the granule to deposit enough energy. Theshaded part of granule indicates the direction in which the electron cantravel a distance longer than /0. .......... . . . . . . . 334.14 Comparison of experiment and theory result for the 100 x 100 array ofgranules with R = 12 gum. Note there is no free parameter in the theory,and it gives a good agreement with experiment.   36vii4.15 Temperature sweeps at 4 mT and 8 mT for the 250 x 250 array of granuleswith R = 3 pm. The SQUID signals are normalized to the same value. . 374.16 Temperature sweeps of three layers of the 250 x 250 arrays of granules withR = 3 pm at 2 mT, 4 mT and 8 mT. The SQUID signals are normalizedto the same value.^. . . . ............ . . . ..... . . . . . .^394.17 Comparison of transition temperature spreads for single layer of the 250x 250 array and three layers of the 250 x 250 arrays of granules withR = 3 pm at 8mT ^  404.18 Radiation test for three layers of the 250 x 250 arrays at 8 mT. The"unblocked - blocked" curve is the response of detector to the radiation.^414.19 Comparison of experiment with theory for the 250 x 250 array of granuleswith R = 3 pm. In this model, we take radius equal to 3 pm. To justifyour model, we also give theoretical curves for R = 2 pm and R = 4 pm.^44viiiAcknowledgementI would like to thank my supervisor, Dr. Brian Turrell, for his helpful suggestions,financial support and extreme patience in reading this thesis.Also, I wish to express my appreciation to Dr. Andrzej Kotlicki for his help, patienceand availability to discuss problems. I would also like to acknowledge his encouragementto write this thesis; without him the thesis would never have been finished.In addition, I would like to thank Gail Aileen Meagher, for her invaluable assistancewith many aspects of work in the laboratory, studying physics and appreciation of lifein Vancouver. My thanks go out to Dr. Xing-Fei He with whom I was always feltcomfortable in discussing problems, and to the technical staff in the physics departmentwho helped me through my ignorance.Finally, I would like to thank my husband for his constant support. Without him Iwould never have felt confident in physics.ixChapter 1Introduction1.1 Superheated Superconducting Granules (SSG)Superheated Superconducting Granules (SSG) are made from type I superconductingspheres of radius in the range 1 --, 100 pm. According to the theory of superconductiv-ity, a type I superconductor has positive interface energy between superconducting andnormal states at Ho ( applied magnetic field) H, (thermodynamical critical field) for<11 [1], where IC is the Ginzburg—Landau parameter. It can exhibit metastablestates — superheating and supercooling — as shown in figure 1.1.Superheating occurs when superconductivity for a given applied field is observed inthe range of temperature T, < T < Tsh, where T, is the thermodynamic transition tem-perature and Tsh is the superheated transition temperature. In the Ginzburg—Landauapproximation (GL) [1], Hsh 2-1141 K -112 Hc . Similarly, supercooling occurs when thenormal phase is maintained in the range T„ < T < Tc , where Ts, is the supercooledtransition temperature. The "X" in figure 1.1 shows the state of granules in the SSGdetector, with the temperature slightly below Tsh, but well above Ts,When an incoming particle or radiation collides with the granule, it deposits enoughenergy to "flip" the granule from the superheating to the normal phase. The granulesare placed in a uniform magnetic field so that the phase transition of the granule willcause a change in magnetic flux due to the Meissner effect. Through a pick-up coil, thischange can be read out by an rf SQUID magnetometer. The Superconducting QUantum1Chapter 1. Introduction^ 2Ca "..J n shwa:a Hew7.1a. ua ii gc<Tsc^Tc^T.,1,TEMPERATUREFigure 1.1: Phase diagram for a type I superconductor. Solid Line: superheated transi-tion; dashed line: thermodynamic transition; chain dotted line: supercooled transition.Chapter 1. Introduction^ 3Interference Device ( SQUID ) is a instrument, based on Josephson tunneling through a"weak link" between two superconductors. The device can be used for measurements ofmagnetic flux with the sensitivity of about 10 -400 , where 00 = 2.07.10 -15 Wb is the fluxquantum. Note that the supercooled phase transition temperature is much lower thanthe operating temperature so that the granule will not flip back.Previous SSG detectors consisted of a "colloid" of many granules randomly suspendedin a dielectric material, such as paraffin, epoxy or varnish. Since each granule acts asa dipole moment in a magnetic field, variations of size and position of granules leadsto an inhomogeneous spread in the local magnetic fields felt by the granules due to theinteractions between the dipole moments. This inhomogeneity resulted in a spread of thetransition temperatures, because the transition temperature for a given granule dependedon the local field on it. On the other hand, measurements on single superconductingSn crystals have shown a considerable anisotropy of the field penetration depth withrespect to the orientation of the crystals in the external magnetic field [2] [3]. Thus thesuperconducting behaviour of a "colloid" of many randomly suspended granules (Hsh andH„) could change according to the orientation of the crystals. It was pointed out thatthis crystalline structure of the granules was probably the dominant factor in spreadingthe transition temperature. This spread was of significance for an SSG detector since itsmeared the energy threshold, and consequently limited the sensitivity and efficiency ofthe detector. A more detailed discussion is given in section 4.5.To solve this problem, our group had developed a new kind of detector—the PlanarArray of Superheated Superconductors (PASS). It consisted of a regularly distributedarray of type I superconducting spheres produced by photolithography on a substrate.The principle of energy detection was the same as for the SSG colloid, but the obtainedspread in transition temperatures was nearly an order of magnitude smaller than "colloid"granules [4]. It was probably because that the regularity in position and size loweredChapter 1. Introduction^ 4the spread of local fields, and the special fabrication process reduced the anisotropy ofthe orientation of the crystallographic axis in the external magnetic field; probably itproduced a different polycrystalline structure.1.2 Historical PerspectiveThe initial idea of using superheated superconducting granules (SSG) for particle detec-tion came from the Orsay group[5]. They performed a very elegant experiment twentyseven years ago, and showed that 2 pm diameter granules doped with radioactive goldchanged state irreversibly when heated by the emitted 0 rays. The first irradiation re-sults with a low energy electron beam were subsequently obtained by J.Blot et al.[6]. Afew years later, the idea of transition radiation detection[7] led to the first attempts tobuild prototypes of photon detectors.More recently, the growing interest in high sensitivity devices and cryogenic detec-tors for astrophysics and particle physics led to new proposals. In 1984, A.K.Drukier andL.Stodolsky suggested the SSG could be used to detect solar neutrinos[8]. Since then, var-ious applications were proposed using SSG, such as detection of magnetic monopoles[9],cold dark matter[10][11] (through nucleus recoil energy) and solar axions[12] (throughaxio electric Primakoff effect), especially the detection of galactic photinos[13] throughinelastic scattering using 119Sn as target.SSG detectors are still at the stage of feasibility study. One major obstacle relatedto the basic properties of the detector is the spread of the superheated superconductingtransition temperatures. This implies a large loss in efficiency for a required energysensitivity. In 1990, the UBC group of Le Gros et al. first reported experimental resultsfor the Planar Array of Superheated Superconductors (PASS)[4] which showed that thespread in transition temperature was an order of magnitude smaller than for the "colloid"Chapter 1. Introduction^ 5devices. The efficiency is much increased, but there is still the obstacle of finding afabrication technique to make a large detector.Since 1990, our group has been studying the feasibility of the PASS detectors fordetection of WIMPs. The idea is that the nuclear recoil energy after the elastic scatteringof the WIMP off nuclei is transformed into heat, which may cause a phase transition in thegranule. Weakly Interacting Massive Particles—WIMPs are one of the most fascinatingpuzzles of the present day. The detection and identification of a WIMP would havetremendous implications for cosmology and particle physics. As such, the need for betterand more sensitive WIMP detectors is extremely important.1.3 Present WorkThe main work of this thesis involved the fabrication and testing of 100 x 100 planararrays, 250 x 250 planar arrays, three layers of 250 x 250 arrays and 100 x 1 line arraysof superconducting granules of various radii. Temperature swept phase transition curveswere measured and radiation tests were performed using an rf SQUID read-out system.The mechanism of the granule flipping was studied for two different cases.In order to test the feasibility of a 3-D detector, we also compared results for amultilayer of planar arrays and single layer planar array.1.4 Thesis OutlineIn chapter two, the mechanism of energy deposition by low energy 7-rays and energyabsorption by granules is discussed in detail. The procedure to fabricate the arrays andthe experimental apparatus are described in chapter three. Chapter four outlines allthe experiments, including experimental results, graphs, theoretical interpretation anddiscussions. Finally, chapter five presents the conclusions drawn from the experiments.Chapter 2TheoryThe sensitivity of the PASS detector depends on the energy deposition by the incomingparticles and the energy absorption by the granules. Next we will discuss these twofeatures.2.1 Energy DepositionIn our experiment, the PASS detector ( array of granules ) was irradiated using a l'Sn7-source which emits 65 keV and 24 keV[14} gamma photons at the rate of 4.44 10 7 8 -1and 8.88 • 106 s -1 respectively.Since the incoming 7-photon energy is low, the interaction between the granule andphoton is dominated by the photoelectric process[15], which means that the incomingphoton is absorbed and then a photoelectron is produced with approximately the in-coming photon energy. (Strictly, the electron only obtains kinetic energy of (Eph — Eb),where Eb is the binding energy, but in this case Eb < Eph. ) The photoelectron may bestopped inside the granule so that all the incoming photon energy is deposited. But ifthe interaction occurs close to the surface of the granule, the photoelectron may escape, so that only part of the incoming photon energy is deposited in the granule. Figure 2.2(a) shows the case for the photoelectron stopping inside the granule so that energy Ephis deposited; while (b) shows that the photoelectron escapes from the granule so thatenergy less than Eph is deposited.Here we assume the photoelectron does not produce secondary electrons, or change6Chapter 2. Theory^ 7(a): E-Ei„,(b): E<E,„,Figure 2.2: Schematic diagram of interaction between a granule and 7-ray. (a): anincoming photon is absorbed and a photoelectron is produced with the incoming photonenergy. Then the electron is stopped inside the granule and deposits all its energy in thegranule. (b): the incoming photon is also absorbed, but the electron produced escapesfrom the granule, so the granule only gets parts of energy Eph.Chapter 2. Theory^ 8its direction along the track, and the energy deposited per unit length along the trackis constant. The maximum distance the photoelectron can travel inside the granule(electron range) before it is stopped is given by[16]:R,[g/crn 2] 0.15E — 0.0028 (2.1)Rg [cm] = 1—(0.15E — 0.0028) (2.2)Here E is the electron energy in MeV and p is the density of the stopping material whichis 7.31 g/cm3 for tin[17]. Thus the range of 24 keV electron and 65 keV are 1.1 pm and9.5 pm respectively.Considering only the inner sphere of the granule with r < (R — R9 ), we note that, nomatter where the photoelectron is produced inside, and no matter in which direction theelectron travels, it must stop inside the granule, because the distance to the surface ofthe granule is always longer than the range. In this case, the granule will always obtainthe entire incoming photon energy Eph.However, if the photoelectron is produced outside the inner sphere (R > r > R— R,),there are two possibilities: in one, the electron stops inside the granule; in the other,the electron escapes from the granule. Of course, in the former case, the entire Eph isdeposited. The second case is more complicated, because energy deposition in the granuledepends on where the photoelectric process occurs and in which direction the electrontravels.Figure 2.3 shows the schematic diagram of the interaction of photon and granulewhich occurs in the outer shell. 0 is the center of the granule, and A is the position ofphotoelectron production. The shaded volume includes all the directions in which thedistance from A to the surface is longer than the range Rg , so that the electron will bestopped inside if it is emitted in this volume, and the entire Eph will be deposited in thegranule.Chapter 2. Theory^ 9Figure 2.3: Schematic diagram for a photoelectron generation in the outer shell(R > r > IR — R9 1). The center of the granule is 0, and A is the place where thephotoelectron is produced. The shaded volume includes all the directions in which thephotoelectron will be stopped. The -y-ray enters along the z-axis.Chapter 2. Theory^ 10We construct two sets of spherical coordinates, one has origin at 0, the z-axis alongthe incident photon direction and the 0 = 0 plane is that containing atom A and z-axis.We use this coordinate set to define the position of photoelectron production; the otherframe has origin at A and z"-axis along OA direction, and the 0" = 0 plane coincideswith the 0 = 0 plane.We assume that the energy deposited in the granule is linearly proportional to thedistance the electron travels inside the granule, which is1E Eph—R^(2.3)g Here / is the length of electron track inside the granule. From figure 2.3, we see that therelation between / and 0"isR2 = r 2^72 2r1 cos 0"so that / is given by(2.4)(2. 5)/^=^r cos 0" + Vr 2 cos2 0" + (R2 _ r2)r cos 0"^VR2 — r 2 sin2 0"When the photoelectric process occurs at A, the energy deposited in the granule isEPhE(r, 0")^ 0") for=^(rcos0" +^— r2 sine^(0" < 00")E(r, 0")^=^Erh for (0" > 0) (2.6)Here 00" defines the critical direction in which the distance from A to the granule surfaceis just Rg . We see that the energy deposited in the granule depends on r, the place wherephotoelectron process occurs, and 0", the direction in which the photoelectron is emitted.2.2 Energy AbsorptionIn the global heating model, it is assumed that the entire grain is uniformly heated beforeit eventually undergoes a phase transition. For a superconductor in thermal equilibrium,Chapter 2. Theory^ 11the amount of heat per volume V needed to raise the temperature from To to T1 is givenby:E^ T1fcdTV Towhere c is the specific heat per unit volume.Strictly, the specific heat should be that for the superconductivity state,c aT3 8.57T, exp(-1.4471c/T) (2.8)Here a, 7 are constants. However, a reasonably good estimate for the energy needed fora given temperature increase can be obtained using the specific heat of the normal state.If a granule's superheated transition temperature is T, and the operating temperatureis T - AT, then it must absorb energy large enough to heat up AT in order to flip tothe normal state. Since AT < T, (AT ti 10 mK, and T 1 K) we may simplify theintegral as:4E(AT)=, -371- R3 p0C,AT (2.9)where po is molar density of tin (6.16.10 -2 mole/cm3)[17] and Cv is its molar specificheat 1.8 • 10 -3 T Jrnole -1K -1 [17].In general, when E(r, 0") is greater than E(AT), the granule will flip. Otherwise,it will remain in the superconducting state. This simple model is further developed insection 4.1.3 to calculate the probability of granule flipping due to low energy gammaradiation.(2.7)Chapter 3Apparatus and Sample Preparation3.1 ApparatusAll the experiments were performed in a dedicated pumped 4He cryostat. The samplewas cooled by a copper plate "oven" ( heated by a thermally anchored resistor) whichwas connected to a pumped 4He pot (T 1 K pot). The connection between sample andthe oven was via a copper cold finger, allowing temperatures ranging from 1.7 K to 5 K tobe obtained. A superconducting solenoid surrounding the sample provided the magneticfield, and an rf SQUID read-out system measured the changes in flux distribution in thesample via a pick-up coil.3.1.1 CryostatThe pumped 4He cryostat assembly is shown in figure 3.4. It is of conventional designwith two pumping lines, one for the 1 K 4He pot, which is shown in the figure, and theother one for the vacuum can, which is not shown.The vacuum can, which enclosed the 1 K pot, was immersed in the liquid heliuminside the outer helium dewar.The temperature of the sample was controlled by the copper plate oven through acopper cold finger. The oven was screwed on the 1 K pot and was heated by a thermallyanchored resistor, fed by an external temperature controller, so that the temperature ofthe sample could be changed and maintained in the range from 1.7 K to 5 K with the12^► pump^► fill line.^ 1 K pot^► ovencalibratedgermanium 4^thermometerChapter 3. Apparatus and Sample Preparation^ 13Figure 3.4: Pumped 'He cryostat assembly.Chapter 3. Apparatus and Sample Preparation^ 14temperature stability of the order less than 1 mK .The magnetic field on the sample was provided by a superconducting solenoid. Thesolenoid leads were shorted by a superconducting niobium wire, which was thermallyconnected to a 1 kf2 resistor. The resistor acted as a heat switch. When the heat switchwas off, the magnetic field was provided by the persistent current in the solenoid. Whenthe heat switch was on, the superconducting wire was driven normal, which allowedthe persistent current in the solenoid to be changed by the external controller. Thisarrangement reduced the noise coming from the external controller. The sample wasplaced inside the solenoid, as shown in the figure, where the magnetic field was relativelyuniform.The SQUID was used to measure the magnetic flux changes when granules in thesample underwent phase transitions. It was encased in a niobium cylinder to shield itfrom external magnetic fields, since niobium goes superconducting at --, 9 K. As shownin the figure, the SQUID was mounted outside the solenoid.The pick-up coil for the SQUID consisted of a differential coil of diameter 1.2 cm,which had two oppositely wound loops, 6 windings each, separated by 2.2 cm, and oneof which was located next to the sample. This arrangement allowed only changes in fluxclose to the coil to be picked up, while changes at long distance were almost cancelledout by the two oppositely wound loops.The radiation source used in the experiments was a 2 mCi l 'Sn 7-source. A leadblock was mounted between the source and the sample. The source could be moved bya pulley arrangement, manipulated at room temperature, so that the -y-rays from thesource either impinged directly on the sample or were attenuated by the block. The twostates of the source — "blocked" and "unblocked"— allowed the response of detector tothe radiation to be determined.Chapter 3. Apparatus and Sample Preparation^ 153.1.2 Data AcquisitionThe data was collected using a resistor bridge and a voltmeter, which through a GPIB buswere connected to an IBM 386 computer employing the LabTech Notebook Program[18].A file with the SQUID signal in millivolts, temperature in Kelvins and time in secondswas created for each run. The SQUID read-out system has upper and lower limits inthe output. When the signal tended to exceed the limits, the SQUID would "reset" thesignal to somewhere within the limits, and then continued to read out the next signalbased on the signal after "reset". A program "Correct", written by Dr. A.Kotlicki, wasused to obtain the net SQUID signal when SQUID "resets" occurred in a run, as wasquite common.3.2 Sample PreparationA photolithographic technique was used to make arrays of tin squares on a kapton sub-strate. Tin film was sputtered on to the substrate and a thin layer of a photosensitivepolymeric material — photoresist   was deposited on the tin surface, and then certainareas of the resist were exposed to ultraviolet light. The pattern of the exposed area wasdefined by a mask. The photolithography process for obtaining an array of tin squareson a kapton substrate is shown schematically in figure 3.5, and the details are as follows.First, a thin film of tin was sputtered on to the kapton substrate by Dr. R. Parson'sgroup at UBC. The sputtering, rather than evaporation, was found to produce betteradhesion of the film to the substrate.Second, a thin uniform layer of photoresist was deposited on the clean surface of thetin film. This was done by spinning the sample for 1 – 2 seconds on the spinner after 2 –3 drops of photoresist were put on the sample. Then the sample was baked on a hot plate(65°C) for three minutes. A small aluminum foil cover was placed over it to prevent thetin filmphotoresistChapter 3. Apparatus and Sample Preparation^ 16kapton substrateFigure 3.5: Schematic process of photolithography.Chapter 3. Apparatus and Sample Preparation^ 17ambient light reacting with the resist and also to protect the sample from atmosphericdust. The photoresist used was negative and consisted of a mixture of 30% of KPR thinfilm resist thinner and 70% of KPR thin film resist [20].Third, the sample was covered with the pattern mask and exposed to UV light [20].The pattern mask was fabricated with chrome on quartz by Align-Rite Corporation. Thechrome, which is opaque to the light, defines the pattern transferred to the resist. Thefirst sample produced was a 100 x 100 array of 40 pm x 40 pm squares with center-to-center spacing of 70 pm. The usual exposure time was four minutes.Fourth, the sample was developed in a KTFR developing solution[20] for 40 , 60seconds. Since a negative resist was used, the resist which had not been exposed to theUV light was loosened and rinsed away while the exposed resist was chemically changedand remained on the surface of the tin. The developing process was accelerated and madeuniform by frequently squeezing a pipette in the solution which stirred it.Finally, the sample was etched in a mild acid made of one part of concentrated HClto ten parts of ethanol. The uncovered tin was removed leaving the array of tin squares(with some kind of oxidation on the surface ) on the kapton. Use of a hot plate speeded upthe etching reaction, which usually lasted 1 — 6 minutes, depending on the temperatureand the age of etch.The next step was to melt the tin squares into spheres. We had melted indiumarrays very successfully before, but melting this array was more difficult because tin hasa melting temperature of 232°C, considerably higher than the melting temperature ofindium 157°C.The main obstacle in melting was associated with the concentration of flux. Thepurpose of the flux, a solution made from yellow abietic acid crystals dissolved in isopropylalcohol with a boiling temperature about 140°C, was to destroy the oxide layer on thesurface of the tin squares to allow them to melt and easily form spheres. However,Chapter 3. Apparatus and Sample Preparation^ 18the concentration of the flux increases with the temperature, so that in melting, if theconcentration of flux was high and the temperature went up above 140°C, the flux wouldseparate into several small drops. This resulted in some of the tin squares having no fluxaround them, and as a result, only some of the tin squares formed spheres. On the otherhand, if the concentration was low, the flux mixture would form bubbles and evaporatewhen temperature went up, so that there was very little flux on the tin squares either.This also impeded the formation of the spheres. Although the whole melting processwas troublesome, we still made some very good samples with extreme patience and hardwork.To avoid heat loss in the air, the melting process was done in a glass vacuum chamberwhich was sealed by a rubber ring. The sample was placed on a rectangular copper boat(2.5 cm x 3.5 cm in size), which was anchored by four screws to an aluminum block,which in turn, was fixed by two long screws to the chamber cover (made of transparentPlexiglas). There were four screws on the copper boat to adjust the boat level, and twocopper clamps on the two diagonal screws which allowed the sample to be pressed downtightly. A Harrison 6203B DC Power Supply, with maximum voltage 7.5 V and maximumcurrent 3 A, was employed to heat up the boat, and a chromel-alumel thermocoupleconnected to the copper boat measured the temperature. All the connection wires andthe pumping line went through the chamber cover, and were sealed with epoxy. Theentire chamber was placed under a microscope for usual observation.To melt the tin squares, the sample was first fixed to the platform of the spinner, 2— 3 drops of flux were placed on it and then it was spun for 1 second. This process wasrepeated 10 — 20 times depending on the concentration of flux. Then the sample wasbaked on the hot plate for at least 30 minutes. This produced a uniform layer of flux onthe top of the tin arrays. Next the sample was placed on the copper boat, and coveredby a glass cover in the middle of which was a square hole big enough for the array ofChapter 3. Apparatus and Sample Preparation^ 19squares to sit right in the hole. The glass cover was pressed down evenly by tighteningthe copper clamps to get a good thermal contact between the sample and the boat. Thepumping was started when the temperature reached close to 140°C to prevent the fluxforming a floppy foam. Usually, the tin arrays would melt at about 200°C — 220°C andwe could see under the microscope that the tin squares first began to shimmer and thenroll into spheres.By this method, we obtained 100 x 100 arrays of tin spheres with R = 12 am andcenter-to-center spacing of 70 pm. Following a similar procedure, we also made several250 x 250 arrays of tin spheres with R = 3 Ain and center-to-center spacing of 40 pm.In this latter case, however, we used pure KTR thin film resist with no thinner, and theexposure time was 5.5 minutes instead of 4 minutes. Figure 3.6 shows the image of oneof the 250 x 250 arrays of tin spheres with radius of 3 pm.The next step was to make 100 x 1 line arrays of 40 um x 40 pm squares with center-to-center spacing of 70pm. However, when we attempted to melt the squares we wereunable to produce a line of spheres consistently. After several attempts two samples weresuccessfully produced.20Chapter 3. Apparatus and Sample Preparation --i100inn50Figure 3.6: Image of a 250 x 250 array of tin granules with radius of 3 fan and cen-ter-to-center spacing 40 pm.Chapter 4Experiments and Interpretations4.1 100 x 100 Array4.1.1 Phase TransitionAs was stated previously, type I superconductors show hysteresis phenomena in theirphase transitions from the superconducting state to the normal state and then back tothe superconducting state when placed in a magnetic field lower than the critical field,which for tin is 30.6 mT at 0 K. Using our pumped 4He cryostat, we obtained hysteresiscurves at the earth's field (— 0.05 mT ), 2 mT, 4 mT and 4.7 mT for a 100 x 100 arrayof tin granules with radius of 12 pm . The following steps were taken to observe thehysteresis cycle:1) The heater was set to zero, allowing the sample to cool down to 1.7 K in zeromagnetic field.2) The current in the solenoid was increased to obtain the desired magnetic field byturning on the heat switch in the solenoid, and then the switch was turned off to allowthe persistent current to run in the solenoid.3) The temperature was raised by applying a slow ramp to the input of the tem-perature controller. The SQUID signal, temperature, and time were recorded for thesuperheated to normal transition.4) Upon reaching a preset temperature where all granules were in the normal phase21Chapter 4. Experiments and Interpretations^ 22and the SQUID signal was constant, the ramp was reversed, slowly lowering the temper-ature of the sample through the normal to supercooling transition.A typical hysteresis curve obtained in a magnetic field of 2 mT is shown in figure4.7. The mid-point superheated transition occurs at T 3.58 K, while the supercooledtransition occurs 730 mK lower at T = 2.85 K.The spread in superheated transition temperature AT sh is about 27 mK, while for thesupercooled transition AT„ is about 70 mK. The superheated transition is steeper thanthe supercooled transition. The "leading edge" in the diagram (from 3.3 K to 3.56 K)perhaps is due to the residual tin between granules and/or paramagnetic effect of copper( due to some iron atoms in copper).Figure 4.8 shows the superheated transitions curves obtained in magnetic fields of2 mT, 4 mT and 4.7 mT. The SQUID signal is normalized to the same value. Themid-point transition temperatures are 3.58 K, 3.43 K and 3.37 K respectively. As canbe observed, the transition temperature decreases as the magnetic field increases. Thespreads of transition curves are approximately 27 mK, 40 mK and 40 mK.4.1.2 Radiation TestThe above measurements allow the magnetic field and temperature to be adjusted to adesired operating point on the transition curve when the response of the sample to y-rayscan be observed.The magnet was first adjusted to give the desired field at a temperature low enoughthat all granules were superconducting. The temperature was then raised to point T o(shown in figure 4.11), which is in the middle of transition curve. This was done with theshutter open so that the granules were directly exposed to the gamma source 1197"Sn. Theindividual flips were detected by the SQUID read-out system and the signals recordedin a file. The observation time was 15 minutes. Then the temperature was loweredChapter 4. Experiments and Interpretations^ 23Figure 4.7: Temperature sweeps for the 100 x 100 array at 2 mT. Note the superheatedphase transition temperature is 3.58 K, ATsh is about 27 mK; while supercooled phasetransition temperature is 2.85 K, AL, is about 70 mK.Chapter 4. Experiments and Interpretations^ 24250020001500Ec. Drz )1000CYcen500O-50033^3.35^3.4^3.45^3.5^3.55^3.6^3.65TEMPERATURE [K]Figure 4.8: Temperature sweeps for the 100 x 100 array at 2 mT, 4 mT and 4.7 mT. TheSQUID signal is normalized to the same value. Superheated transition temperatures are3.375 K and 3.435 K at 4.7 mT and 4 mT, respectively.Chapter 4. Experiments and Interpretations^ 25and the process repeated. All these operations were performed under the control of acomputer. Altogether fifty runs were made with the "unblocked" source. In order toeliminate the effect of background radiation and the residual temperature relaxation,another fifty runs were taken under the same conditions, except that the source wasblocked. By subtracting the "blocked" signals from the "unblocked" ones, the responseof the detector to the radiation from the source was obtained.Figure 4.9 shows "blocked" signals, "unblocked" signals and "blocked-unblocked"signals at 4 mT. Applying a program written by Dr. A. Kotlicki, the SQUID signalscould be analyzed to give the time distribution of granule flips and the step signal sizedistribution. Figure 4.10 and figure 4.11 show the time distribution and the step sizedistribution respectively.The step size distribution curve shows that most signal steps have a size of 25 mV,which corresponds to the first large peak, and there are two smaller peaks at step sizesof 50 mV and 75 mV. The large peak at 25 mV indicates those events in which a singlegranule flips at a given time, while the smaller peaks at 50 mV and 75 mV indicatetwo or three granules respectively flipping simultaneously. This ability to distinguishbetween multi-granule flips and single granule flips could be quite important for detectingneutrinos and dark matter, since these would be single flip events, while backgroundradiation would cause many flips simultaneously.4.1.3 Theoretical interpretationAn array of uniform tin spheres with radius R at temperature To is exposed to a 2 mCi119mSn 7-source, which gives out of 65 keV photons and 24 keV photons at the rate of4.44.10' 3 -1 and 8.88.10 6 s -1 , respectively. The probability of a single granule capturingChapter 4. Experiments and InterpretationsFigure 4.9: Radiation test for the 100 x 100 array at 4 mT. The temperature was setat 3.4305 K. The "blocked - unblocked" curve gives out the net signal change due to theradiation.26Chapter 4. Experiments and Interpretations^ 27Figure 4.10: Time distribution of the number of granules flipping due to the radiation.After 300 s, all the granules have flipped to the normal state.Chapter 4. Experiments^ 28Figure 4.11: Step size distribution of the number of granules flipping.a photon is given by:4 T.,3^/P ---- Vrit-Paa 4R-d2Here pa is the number of atoms per unit volume of tin and(4.10)Pa . --P—Nm A7.31 g/cnt3= ^118.69 glmole x 6.02 • 10 23 atomslmole..,- 3.71 • 1022 atoms/cm3The total cross section o of a single Sn atom is 1.25 • 10 -21 cm2/atom and 4.04 -10 -21 cm2 /atom for 24 keV and 65 keV 'y-rays respectively. The distance d betweenthe -y-source and the tin array is 5.3 cm in our cryostat.Chapter 4. Experiments and Interpretations^ 29If the energy deposited by the electron was always enough to cause the granule toflip, then the number of granules left in the superconducting state after time t is givenbyN = No exp(—Pt) (4.11)where No is the total number of granules in the superconducting state at time t = 0.Equation 4.11 yieldsIn (— dNc—IT ) = ln(NoP) — Pt (4.12)So that ln(—dN/dt) is linearly proportional to the exposure time under our assumption.As can be seen in figure 4.10, this is not the case for the R = 12 pm granules. Thereare two reasons for this. First, the granules are not uniform in structure and size so thatthere is inhomogeneity of local magnetic fields and a spread of transition temperatures.This means that some granules with a higher transition temperature have a higher energybarrier for flipping. Similarly, as explained in chapter two, the energy deposition in thegranule varies with the position of the photoelectron event and the direction in which theelectron is ejected, and the granule does not necessarily flip when absorbing a photon.We have developed a model with which to calculate the flipping probability. Figure4.12 shows a typical phase transition curve, in which T o is the preset temperature in theradiation test, and T1 and T2 are the maximum and minimum transition temperaturesfor the ensemble of granules. Considering only the granules with transition temperatureranging from Tsh to Tsh AT,sh, the number of granules in the superconducting stateafter time t is obtained as above and is justN(Tsh AT,h ) — N(Tsh ) = [No (Tsh ATsh ) — No(Tsh )] exP( —P(Tsh)t)^(4.13)where No(Tsh) and No (Tsh AT,h) is the initial number of granules with the transitiontemperature Tsh and Tsh ATsh respectively. P(Tsh ) is the probability of a granule3.43.38 3.483.463.443.42-5003.36250020001500'-'-0c,1czt10000,c/D500o(T1 , S1)(TO , SO)(T2 , S2)Chapter 4. Experiments and Interpretations^ 30TEMPERATURE [K]Figure 4.12: Temperature sweeps of the 100 x 100 array at 4 mT. The fixed temperature inthe radiation test is To , Ti and T2 are the maximum and minimum superheated transitiontemperatures, So, Si and S2 are the corresponding SQUID signals.Chapter 4. Experiments and Interpretations^ 31flipping after absorbing a photon. Divided by ATsh and taking the limit on both sides,equation 4.13 yields(4.14)exp(—P(Tsh)t)dTsh^dTshAssuming No(Tsh ) oc Tsh in the range T0 to T1 in figure 4.12, we then evaluatedNo (Tsh )  fdTsh , asdN(Tsh) dNo (Tsh )dNo (Tsh )^1^  S1 — Sox 100 x 100^(4.15)dTsh^T1 — To Si S2where Si and S0 is the SQUID signal corresponding to T1 and To . Thus the total numberof granules that remain unflipped in the total temperature interval (T 1 — To ) after timet isN 'T1 dNo(Tsh) ^To^dTshexp(—P(Tsh)OdTshfrom which we obtainIn^f1 dNo(Tsh) T ex ( sLdN) = (^ dTshP( sh )^— P(Th)t)Pk)iToTdt(4.16)(4.17)We see that ln(—dN/dt) is in general no longer simply proportional to the exposure time.The next problem is to calculate P(Tsh ), the probability of a granule ( with transitiontemperature in the range Tsh to Tsh Agish ) flipping at temperature To . The minimumenergy required to flip a granule is given by4E(Tsh) = —3 TR3poüv(Tsh — To) (4.18)This amount of energy corresponds to the electron traveling a distance / 0 before it escapesfrom the granule, where= ER—g E (Tsh )^(4.19)Here _Eel is the initial photoelectron kinetic energy, which is very close to the incidentphoton energy for a photon energy much greater than the binding energy of the electronChapter 4. Experiments and Interpretations^ 32in its atomic orbit. Of course, if the electron travels a distance / greater than / 0 insidethe granule, it will certainly deposit more than enough energy to cause a flip.As discussed in chapter two, we divide a whole granule into two parts, an inner sphereand an outer shell separated at r = R-10 (if R < 10 then the inner sphere disappears). Ifthe photoelectron effect occurs in the inner part of the granule, the electron will alwaysdeposit enough energy to cause a flip, no matter in which direction it travels. Theprobability of such an event occurring per unit time isPi = 4-3 ir(R - /or Pau47d2 (4.20)But when R < 10, = O.In the case that the photoelectron is produced in the outer shell, the granule willabsorb enough energy to flip only when the electron is emitted in the shaded volume, asshown in figure 4.13.The two spherical coordinate frames described in chapter two are constructed in thegranule. Note that the photoelectron is emitted with a sine-squared angular distributionwith respect to the incident photon direction if the radiation is unpolarized[22]. So, athird spherical coordinate is constructed to express the photoelectron angular distribu-tion, with the origin at A and the z'-axis parallel to the z-axis and the 0' = 0 planecoincide with the 0 = 0" = 0 planes. The photoelectron cross section can be written inthe z' coordinate as:a(0 1 , 0') sin O'dO'd0' = f f (a-8-773 sin' 0') sin O'c/O'd0'= 0"^ (4.21)But since the shaded volume is not symmetric about the z' axis, we can rotate the z'coordinate along axis 0' = 7r/2, 0' = 7r/2 which is just the z" coordinate. The relationsChapter 4. Experiments and Interpretations^ 33Figure 4.13: Schematic graph of a granule. The center of granule is 0, A is the placewhere the photoelectron is produced. /0 is the minimum distance the electron has totravel inside the granule to deposit enough energy. The shaded part of granule indicatesthe direction in which the electron can travel a distance longer than /0.Chapter 4. Experiments and Interpretations^ 34between the two coordinates aresin 0" cos 0" cos 0 + sin 0 cos 0" = sin 0' cos 0/sin 0" sin 0" = sin 0' sin .0'- sin g" cos 0" sin g + cos 0" cos 0 = cos 0'^sin 0"d0"d0" = sin O idO'd0/^(4.22)This leads to the relationsin2 0' = sin2 0" cos2 0" cos 2 0 + sin2 0 cos 2 0"+2 sin 0" cos 0" cos 0" sin 0 cos 0 + sin2 0" sin2 0"^(4.23)This allows the angular dependent cross section to be expressed in terms of the z" coor-dinate. Integration over the shaded volume gives the probability of an electron producedin volume r 2 sin 0d0d0 depositing enough energy in the granule to cause it to flip, asp(0,0'', .0)r 2 sin 0d0dq = r2 sin 9d0d0cr-387rir jr 21r (sin 2 0" cos2 0" cos 2 0 + sin2 0 cos2 0"fog o+2 sin 0" cos 0" cos 0" sin 0 cos 0 + sin2 0" sin2 0") sin 0"d0"d0"1^1= r2 sin 0d0d0 cr 2- + 24 1— cos 2 0 cos 00" sin2 0 /,:; + 12— cos 2 0 cos Og1^1 1+ — sin2 0 cos' 0' + — cos 00" sin2 0' + — cos 00"^(4.24)12 24^12Here 00" is the angle that the length from A to the surface is just / 0 . The probability ofthe granule flipping due to the photoelectron produced in the outer shell is thusR r 2irP2^f 0.)r2 sin 6d0d047rd2 Pa fIR—/0 I JO f= 27ro- I^ pa JR (1 + cos Onr2 dr47rd2^IR-to I(4.25)cos 00" =2r10R2 r2 /0Chapter 4. Experiments and Interpretations^ 35Using the trigonometric relation(4.26)and substituting it into equation 4.25 and performing the integration finally yields22d2pao- 3[-1 (R3 — IR — 10 1 3) + R411° (R2 — IR — 10 1 2)0R4 - R — 10 1 48/0The total probability for a granule flipping per unit time isP(Tsh) = Pl + p2^ (4.28)The calculation has to be performed for both the 65 keV and 24 keV photons, andthe grand total probability is theP(Tsh) = P65(Tsh) P24(Tsh)Using P(Tsh) in equation 4.17 yields the number of granules flipping per unit time. Theprogram listed in the appendix A was employed to simulate the granule flipping due tothe radiation using the above model. The results (shown in figure 4.14) are comparedwith the experiment results, and good agreement is obtained. Note that there is no freeparameter in the calculation.4.2 250 x 250 ArrayAfter this encouraging result on the 100 x 100 array, we next fabricated 250 x 250 arraysof tin granules with R ti 3 sum. The superheated phase transition curves for 4 mT and8 mT obtained by sweeping the temperature are shown in figure 4.15.Comparing the results for granules with R = 3µm and R = 12 sum, we notice thatthe mid-point in the spread of superheated phase transition temperatures changes veryP2(4.27)(4.29)2.524.543.531.510.50<> 00 \e e ^Chapter 4. Experiments and Interpretations^ 360^50^100^150^200^250 300^350^400TIME [see]Figure 4.14: Comparison of experiment and theory result for the 100 x 100 array ofgranules with R = 12 Note there is no free parameter in the theory, and it gives agood agreement with experiment.Chapter 4. Experiments and Interpretations^ 37TEMPERATURE [K]Figure 4.15: Temperature sweeps at 4 mT and 8 mT for the 250 x 250 array of granuleswith R = 3 Am. The SQUID signals are normalized to the same value.Chapter 4. Experiments and Interpretations^ 38little with the radius of granule, and for both granules is ti 3.43 K for B = 4 mT. Thespreads of transition temperatures are 60 mK for 4 mT and 120 mK for 8 mT.4.3 Three Layers of 250 x 250 Array4.3.1 Phase TransitionNext we stacked three layers of 250 x 250 array using vacuum grease, and measured thesuperheated phase transition curves at 2 mT, 4 mT and 8 mT respectively. These areshown in figure 4.16.The superheated transition at 2 mT is 3.58 K, the spread of transition temperatureis about 60 mK; at 4 mT, Tsh is 3.44 K and ATsh is about 60 mK; at 8 mT, Tsh is3.1 K and ALI, is about 120 mK. This result is very similar to that obtained for the100 x 100 array and the single layer of 250 x 250 array, except that the 100 x 100 arrayhad a narrower spread in transition temperatures. This evidence that the three layers ofarrays have almost the same spread in transition temperatures as the single layer arrayis very encouraging for a 3-D detector in the future. It is shown in figure 4.17 that thespreads of transition temperatures are about the same for single layer 250 x 250 arrayand three layers of 250 x 250 arrays at 8mT.4.3.2 Radiation TestRadiation tests were also made on the three layers of arrays in fields of 2 mT, 4 mT and8 mT magnetic field. For example, the 8 mT radiation test result is shown in figure 4.18.The preset temperature is 3.1 K.Chapter 4. Experiments and Interpretations^ 39TEMPERATURE [K]Figure 4.16: Temperature sweeps of three layers of the 250 x 250 arrays of granules withR = 3 pm at 2 mT, 4 mT and 8 mT. The SQUID signals are normalized to the samevalue.Chapter 4. Experiments and Interpretations^ 40TEMPERATURE [K]Figure 4.17: Comparison of transition temperature spreads for single layer of the 250 x250 array and three layers of the 250 x 250 arrays of granules with R = 3 pm at 8mT.TIME [sec]Chapter 4. Experiments and Interpretations^ 41100000-10000Figure 4.18: Radiation test for three layers of the 250 x 250 arrays at 8 mT. The"unblocked - blocked" curve is the response of detector to the radiation.Chapter 4. Experiments and Interpretations^ 424.3.3 Theoretical InterpretationAs stated in section 4.1.3, the minimum energy E(T) required to be deposited in thegranule to "flip" it is given in equation 2.9. For R 3 pm, ATmas = 50 mK, T = 3.4 K,E(T) = 13 keV, which is half the lower energy of incident photon. Thus, in this case,the outer shell will have very little contribution to the granule flipping since its volumeis very small compared to the whole granule. Therefore, the probability of a granuleflipping is just the probability of absorbing a photon, which is:P24 = 4^7..,3— 71"-n Pa 0-24 4d23= 4.26 x 10 -4 sec-1 (4.30)= 4^,^I— r 113 P a Cr 6 5P65 3 47rd2= 6.59 x 10 -4 sec-1 (4.31)P = P24 + P651.09 x 10 -3 sec-1 ( 4 . 3 2 )So the number of granules in superconducting state after time t is given by equation 4.11.The SQUID signal is linearly proportional to the number of granules in the supercon-ducting state, which isS=aN-Fb^ (4.33)(4.34)SO S f NO Nfwhere S f is the SQUID signal at time t = 900 s, the end of each run and So is the SQUIDsignal at time t = 0 s. S, is any signal between t 0 and t = 900 s. If our model is true,then we will have relationwhere a and b are two unknown parameters. S is the SQUID signal. SoSo — S, No — NZSo —^No —NZ^1 — e—Pt `So — S f No — Nf - 1 - e -Ptf( 4 . 3 5 )Chapter 4. Experiments and Interpretations^ 43In figure 4.19, we plot (So —Si)/ (So —Sf) vs. time, which gives excellent agreement withtheory. We also show the R = 2 µm and R = 4^theoretical curves for comparison.4.4 Line ArrayWe also tried to fabricate several tin line arrays with limited success. For the line arraysthat were produced the spread of transition temperatures was very broad, about 1 K.Also it was expected that individual granule flips would be observed, but none were seen.But this summer, an indium sample made by Sundiep Tehara was put into the exper-iment and gave good results. The sample consisted of two parallel lines containing 100R = 12 ,am granules. Consecutive granule flips were observed although there was still alarge scattering of the amplitudes.4.5 DiscussionAbove, a number of experimental results for the PASS detector have been described, andhere I would like to discuss some properties of our detector.4.5.1 Energy SensitivityThe PASS detector has excellent energy sensitivity because a small deposition of energycan cause a granule to flip and the resulting flux change is read out by a SQUID. Thechange of magnetic flux due to a single tin granule of radius of R undergoing phasetransition is given by:BR'AO = 7rPo a(4.36)where B is the applied magnetic field and a is the radius of the pick-up coil. In our case,for example, for R = 3 ,am, a = 12 mm and B = 2 mT, the change of magnetic fluxis 6.8 • 10 -3 00 , where 00 = 2.07 • 10 -15 Wb is the flux quantum. The rf SQUID usedChapter 4. Experiments and Interpretations^ 44Figure 4.19: Comparison of experiment with theory for the 250 x 250 array of granuleswith R = 3 ,am. In this model, we take radius equal to 3 pm. To justify our model, wealso give theoretical curves for R = 2 ,am and R = 4 lam.Chapter 4. Experiments and Interpretations^ 45has a sensitivity of 10 -3 00 and a dc SQUID is an order of magnitude better. So a singlegranule flip can be detected in our experiment.4.5.2 Energy ResolutionThe energy needed to cause a phase transition of the granule is determined by the granulesize and material, by the operating temperature, and by the applied magnetic field, asdescribed in equation 2.9.For a given granule size and material, the energy threshold can be chosen by varyingthe operating temperature or the applied magnetic field. The PASS detector measuresphase transitions only above a given energy threshold, but it can not discriminate theenergy band. So the energy resolution is poor for the PASS detectors, as with the colloidSSG detectors. However, it may be possible to utilize the thermal micro-avalanche effectto improve the resolution [23]. When the micro-avalanche occurs, the heat released bythe flip of a single granule spreads to the surrounding granules and causes new flips. Thenumber of the granules affected is proportional to the initial energy absorbed in the firstgranule. So far no experiment on the micro-avalanche effect has been reported.4.5.3 EfficiencyAs seen from the above discussion, theoretically, the PASS has an excellent sensitivitybut poor energy resolution or, at least, the resolution is not readily obtained. Also, dueto the fabrication technique, we cannot make the whole array of granules identical andperfect both in crystal structure, size and regularity in position, and this nonuniformitycauses a spread ATsh in transition temperature curves. The efficiency of the detector ismainly restricted by this spread.For example, consider that the PASS granules have a temperature spread AT sh andare at temperature T. An incoming particle can heat up the granule by a temperatureChapter 4. Experiments and Interpretations^ 46magnetic field 2 mT 4 mT 4.7 mT 8 mT100 x 100 arrayR = 12 pm 27+5mK 40+5 mK 40+5 mK250 x 250 arrayR = 3 pm 60+15 mK 120+25 mKThree layers of250 x 250 arrayR = 3 pm60+10 mK 60+10 mK 120 +20 mKTable 4.1: Spreads of transition temperatures for different samples.T. Then, only granules with transition temperature Tsh satisfied Tsh < T + AT can flipto the normal state. This could largely reduce the efficiency.In table 4.1, we give out ATsh for several arrays investigated in our experiments.These values are a little uncertain because it is difficult to estimate the start of thetransition curve due to the leading edge caused by paramagnetic impurities in the coppersample holder. It is clearly seen that the 100 x 100 arrays with R = 12 pm granuleshave the smallest spreads. Although the spread of three layers of 250 x 250 arrays withR = 3 pm is a little bit broader, we believe it can be reduced once the fabricationtechnique improves.In general, the PASS as an alternative neutrino and WIMP detector has certainadvantages. One is that it operates at 1 K, so that a pumped 4He cryostat is adequate,and this reduces the problems in shielding. The other is that the PASS has a potentiallymuch higher sensitivity than presently used Si or Ge detectors. The future of the PASSdetector is very promising if the manufacture and efficiency problem can be solved.Chapter 5ConclusionsUsing photolithography, a number of samples with three patterns of tin squares werefabricated on the kapton substate. These were 100 x 100 arrays of 40 pm x 40 pmsquares, 250 x 250 arrays of 10 pm x 10 pm squares, and 100 x 1 line arrays of 40 pmx 40 ,um squares. They were then melted in a vacuum chamber to obtain PASS arrays.Although the melting procedure has been a problem for tin, several good samples wereobtained for each size of arrays.Using the pumped 'He cryostat, we have studied 100 x 100 arrays of the granules withradius of 12 pm and center-to-center spacing of 70 pm. Superheated phase transitioncurves were mapped out by sweeping the temperature, in the earth's field ( ,-0.05 mT),2 mT, 4 mT and 4.7 mT. As expected, the spreads in transition temperatures increasedwith the applied field. Radiation tests were also made with a low energy 119m sn 7 _source. Time distributions and step size distributions of the granule flips were obtained.We were able to distinguish between the single granule flips and the simultaneous flips ofseveral granules. This could be very useful for discriminating background events in thedetection of WIMPs and other low energy particles. We have studied the mechanism ofenergy deposition and granule flipping, and have been able to obtain very good agreementbetween the theory and experiment.Both three layers 250 x 250 arrays of tin spheres and a single layer 250 x 250 array,with granule radius of 3 pm and center-to-center spacing of 40 ,um, have been studied.Comparison of the two transition curves obtained by sweeping temperature shows good47Chapter 5. Conclusions^ 48agreement: this is a very encouraging result for building 3-D detectors in the future.Radiation tests were also made on three layers of arrays and again there is excellentagreement between theory and experiment.Line arrays of 100 x 1 tin granules with radius of 12 ,am and center-to-center spacingof 70 pm were also studied. The transition curve was broad, however, consecutive granuleflips were observed.It is harder to manufacture tin arrays than indium arrays because the melting tem-perature is much higher, and there is room for improvement of the fabrication technique.Appendix ARadiation Simulation Programc************************************************************************c^Radiation Simulation Program is a program to calculate the ratec^of granule flips when exposed to low energy gamma source Sn,c^which emits 24 keV and 65 keV photon.c***********************************************************************implicit double precision (a-h,o-z)c^tO is the preset temperature, and tl is the maximum transitionc^temperature.t1=3.4434t0=3.4305c^r is the radius of the sphere in micrometer and d is thec^distance between the sample and the source in centimeterr=9.6d=5.3c^minimum temperature divisiondt=(tl-t0)/50000.49Appendix A. Radiation Simulation Program^ 50c^a24 and a65 are the cross section for 24kev and 65 keyc^(in cm/atom)a24=4.04e-21a65=1.25e-21c^some constantsc24=0.2*(7.31/118.69)*6.02e23*a24*1.2e-3*3.7e10*1.e-12/(d*d)c65=(7.31/118.69)*6.02e23*a65*1.2e-3*3.7e10*1.e-12/(d*d)c^range65 and range24 are the ranges of 65 kev and 24 keyc^electrons (in micrometer)range65=9.5range24=1.1c^specific heat for tin spherecyt=(4./3.)*3.14159*1.e-21*r**3*109.6*t0/1.6e-19c^number of spheres over the temperature range TO to Ti,c^which can be got from transition pictureslope=3.35e5open(unit=3, file='tin4mt.prn')c^The first "for" loop is to do the time integral,Appendix A. Radiation Simulation Program^ 51c^the second integral is to do the integral fron transitionc^temperature TO to Ti.do 20 j=1,30t=t0time=j*10result=0.do 10 i=1, 50000t=t+dtet=cvt*(t-t0)if (et .1e. 65.) thenrc=et/65.*range65if (rc .lt. r) thenr65=r-rcp1=1.13.*c65* r65**3elser65=rc-rp1=0end iff1=8.*rc*(r**3-r65**3)-6.*rc*rc*(r**2-r65**2)f2=3.*(r**4+r65**4)-6.*r65**2*r**2p2=0.5*c65*(fl+f2)/(24.*rc)p65=p1+p2elsep65=0.Appendix A. Radiation Simulation Program^ 52end ifif (et .le. 24.) thenrd=range24*et/24.r24=r-rdb1=c24/3.*r24**3g1=8.*rd*(r**3-r24**3)-6.*rd*rd*(r**2-r24**2)g2=3.*(r**4+r24**4)-6.*r24**2*r**2b2=0.5*c24*(gl+g2)/(24.*rd)p24=b1+b2elsep24 =0end ifp=p65+p24result=result+dt*slope*p*exp(-1.*time*p)10^continuec^print output into a filen=resultif (n .gt.0 ) thenresult=log(result)elseAppendix A. Radiation Simulation Program^ 53result =0,end ifwrite(3,*)time,result20^continueclose(3)endBibliography[1] See, for instance, R.D.Parks Superconductivity, Ed. Dekker N.Y. (1969).[2] M.Frank et al. Nucl. Instr.and Meth. A287 (1990).[3] P.C.L. Tai et al. Phys. Rev. B11/1 (1975)411.[4] M. Le Gros, A. Da Silva, B.G. Turrell, A. Kotlicki, and A.K. Drukier, in Low Tem-perature Detectors for Neutrinos and Dark Matter III, Ed. by L.Gonzales-Mestresand D. Perret- Gallix. Frontieres 1990, Page 91.[5] H.Bernas, J.P. Burger, G.Deutscher, C. Valette and S.J. Williamson, Phys. Lett.24A, 721(1967); C. Valette, Thesis 1971.[6] J.Blot, Y. Pellan, J.C. Pineau, J.Rosenblatt, J. Appl. Phys. 45, 1429 (1974).[7] A.K. Drukier, C. Valette, G. Waysand, L.C.L. Yuan, Nucl. Instrum. Methods 138,213 (1976).[8] A.K. Drukier and L. Stodolsky, Phys. Rev. D30, 2295 (1984).[9] L. Gonzalez-Mestres and D. Perret-Gallix, Nuovo Cimento C9, 573 (1986).[10] M.W. Goodman and E. Witten, Phys. Rev. D30, 2295 (1984).[11] A.K.Drukier, C. Freese and D. Spergel, Phys. Rev. D33, 3495 (1986).[12] S. Dimopoulos, G. Starkman and B.W. Lynn, Phys. Lett. B167, 145 (1986) and Mod.Phys. Lett. Al, 491 (1986).[13] L. Gonzalez-Mestres and D. Perret-Grallix, in Proceedings of the Moriond Meetingon Dark Matter, March 1988, Ed. Frontieres.[14] See, for instance, CRC Handbook of Chemistry and Physics 52 Ed (1971-1972) PageB-330.[15] See, for instance, Alpha-, Betea- and Gamma-Ray Spectroscopy vol.l. Ed by KaiSiegbahn. Pub. North-Holland Publishing Company Amsterdam.[16] E.Fenyves and O. Haiman, The Physical Principles of Nuclear Radiation Measure-ments Ed. Academic Press, N.Y. and London (1969).54Bibliography^ 55[17] See, for instance, CRC Handbook of Chemistry and Physics 52 Ed (1971-1972) PageB-34.[18] ibid. Pages 167,138 and 126.[19] Labtech Notebook Version 4.1, Laboratory technologies Corporation, 255 BallardvaleStreet, Wilmington, MA 01887.[20] KPR thin film resis (catalogue number 705), KPR thin film resis thinner (cataloguenumber 715), and KTFR developer (catalogue number 749) from M.G.Chemicals.[21] Blak-ray Long wavelength ultraviolet lamp from UVP Inc. using a 100W long wave-length mercury spot bulb.[22] See, for instance, Leonard I. Schiff in Quantum Mechanics 3rd Ed. 1968.[23] L.Gonzalez-Mestres and D.Perret-Gallix, Proc. Conf, on Neutrinos and Exotic Phe-nomena, Moriond, January 1988, and Dark Matter, Moriond, March 1988.

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