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Theoretical and experimental studies of a superconductive detector of energetic particles May, George Anthony 1975

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THEORETICAL AND EXPERIMENTAL STUDIES OF A SUPERCONDUCTIVE DETECTOR OF ENERGETIC PARTICLES by GEORGE ANTHONY MAY M.A., U n i v e r s i t y of Western Ontario 1964 B.Sc. Hon., U n i v e r s i t y of Toronto 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Physics We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA May, 1975 In presenting th i s thesis in par t i a l fu l f i lment of the requirements for an advanced degree at the Univers i ty of B r i t i s h Columbia, I agree that the L ibrary sha l l make it f ree ly ava i lab le for reference and study. I fur ther agree that permission for extensive copying of th i s thesis for scho lar ly purposes may be granted by the Head of my Department or by his representat ives. It is understood that copying or pub l i ca t ion of this thes is for f i nanc ia l gain shal l not be allowed without my writ ten pe rm i ss i on . Depa rtment The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date -22 I S ' - 1 -T h e o r e t i c a l and Experimental Studies of a Superconductive Detector of  Energetic P a r t i c l e s . ABSTRACT:-In n u c l e a r - p a r t i c l e energy-loss spectrometers, i t i s d e s i r a b l e to have the s i g n a l charge per unit energy loss as large as p o s s i b l e , because the f r a c t i o n a l r e s o l u t i o n due to s t a t i s t i c a l f l u c t u a t i o n s i n the s i g n a l charge i s i n v e r s e l y proportional to the square root o f the number o f charge c a r r i e r s generated. Thus superconductors with an i n h e r e n t l y narrow energy-gap 2A would be of i n t e r e s t i f the q u a s i p a r t i c l e s generated from the energy of the incident p a r t i c l e could be d i s t i n g u i s h e d from the Cooper-pairs. A superconductive t u n n e l l i n g j u n c t i o n (STJ) s a t i s f i e s t h i s condition beo.'-'se the current flow consists e s s e n t i a l l y o f q u a s i p a r t i c l e t u n n e l l i n g current provided that the Josephson-supercurrent i s suppressed by a steady magnetic f i e l d . Thus i f the p a r t i c l e energy i s used to create q u a s i p a r t i c l e s i n a STJ the increase i n q u a s i p a r t i c l e density causes a measurable increase i n the t u n n e l l i n g current, which cons t i t u t e s the s i g n a l . The mechanism proposed f o r the transformation of the p a r t i c l e energy to q u a s i p a r t i c l e s involves the conversion of energy to heat when the p a r t i c l e penetrates the STJ and enters the substrate. The transient increase i n the temperature o f the jun c t i o n films increases the thermally generated q u a s i p a r t i c l e density. This thermal model gave numerical r e s u l t s i n good agreement with e x p e r i -mental r e s u l t s obtained with 5.13 MeV a - p a r t i c l e s i n c i d e n t on t h i n f i l m lead and t i n STJ's deposited on microscope glass s l i d e substrate. The SJT's used f o r the experiments consisted o f crossed 2000 A th i c k metal films, separated by an oxide barrier of approximately 12 A thick produced by glow-discharge anodization. Reproducible fabrication of arrays of STJ's was achieved by this method. Measurements were made on the junctions at different temperatures between 1.2 K and about half the c r i t i c a l temperature, and with different junction bias voltages. A steady magnetic f i e l d of 15 gauss was used to suppress the Josephson supercurrent. 5.13 MeV a-particles were directed at the junctions, and voltage signals caused by the particle impacts were observed across the junction. The signal amplitudes were temperature and bias-voltage dependent. The best signal to noise ratios (peak signal/rms noise) observed were 20 and 40 respectively for lead and t i n junctions, using a transformer-input N-channel metal oxide semiconductor preamplifier operated at liquid helium temperatures. The pulse amplitude distributions were analysed and found to consist of an i n i t i a l l y decreasing pulse-density with increasing pulse amplitude, then a nearly f l a t plateau region followed by a rapid drop off. This type of distribution curve was theoretically predicted using the thermal model mentioned above. The form of the distribution curve i s a consequence of the distribution of the position of the particle impacts on the STJ, and of the angle of the particle impact. Thus superconductive particle detectors with this type of geonetry and with uncollimated particle sources do. not give rise to line spectra. Based on the physical understanding of the nature of signal-pulses from the a-bombarded STJ's on glass substrates, a heat-sink chip type detector i s proposed. This is expected to be a superior and practical particle energy spectrometer. Theoretical investigations were made into the relative merits of superconductor-insulator-superconductor (SS) and normal metal-insulator-superconductor (NS) tunnelling junctions as fast response thermometers. 9 For u < 10 Hz, SS junctions were shown to be theoretically superior in sensitivity and signal to noise ratio. It was also found theoretically that for the SS junctions, there i s a temperature which for a specified bandwidth, junction capacitance, and superconductor type optimises the signal amplitude. Moreover, the inherent junction e l e c t r i c a l noise, essentially shot noise, was shown to be inversely proportional to A. - i v -CONTENTS Page CHAPTER 1 INTRODUCTION 1 CHAPTER 2 THEORY OF OPERATION OF THE SUPERCONDUCTIVE QUASIPARTICLE 9 TUNNELLING JUNCTION PARTICLE DETECTOR. - Introduction 9 - Types of Superconductive P a r t i c l e - D e t e c t o r s . 25 1. Glass-substrate type. 28 2. Phonon-barrier type. 30 - S c a l i n g Theory 31 - Response of a Superconductive Tunnelling Junction S.T.J, to Small Temperature Changes 32 - Superconductor-Superconductor Superconductive Tu n n e l l i n g Junctions 33 - Choice of Superconductive Tunnelling Junctions f o r Use as P a r t i c l e - D e t e c t o r s 37 - Metal-Superconductor (N.S.) Superconductive Tunnelling Junctions 37 - Comparisons of N.S. and S.S. Superconductive Tunnelling Junctions 39 - Perfox-mance Figures f o r S.S. S.T.J.'s 41 - Inherent Noise i n S.T.J.'s 45 - Other Factors A f f e c t i n g the Resolution of Super-conductive P a r t i c l e - D e t e c t o r s 50 - S t a t i s t i c a l f l u c t u a t i o n of t o t a l number N of charge c a r r i e r s generated by p a r t i c l e 50 - B a r r i e r oxide thickness f l u c t u a t i o n s 50 - 'Angle' e f f e c t 5 0 . - F i n i t e j u n c t i o n - s i z e e f f e c t 51 - V -Page CHAPTER 3 NUMERICAL METHODS AND RESULTS. 52 - Introduction 52 - M o d i f i c a t i o n of the Form of the C l a s s i c a l Heat-D i f f u s i o n Equation 52 - Boundary Conditions f o r the Heat-Diffusion Problem, Glass-Substrate Type Superconductive P a r t i c l e - D e t e c t o r 54 - Phonon-Barrier Type Superconductive P a r t i c l e - D e t e c t o r 58 - Numerical Solutions with Radial Symmetry 60 - T r a n s l a t i o n to F i n i t e - D i f f e r e n c e s Equations 61 - I n i t i a l and Boundary Conditions 63 - Thermophysical Data Used f o r Numerical C a l c u l a t i o n s 63 - Temperature and Signal-Current C a l c u l a t i o n s 65 - S t a b i l i t y Considerations 66 - Computer-Program Organisation f o r the One-Dimensional R a d i a l l y Symmetric Approximations 68 - V e r i f i c a t i o n of Numerical Methods 73 - Results: One-Dimensional R a d i a l l y Symmetric Approximations f o r Glass Substrated S.P.D., V a l i d f o r E a r l y Times 73 - Results: One-Dimensional R a d i a l l y Syuz.ietric Approximations f o r the Phonon-Barrier S.P.D. 75 - Spherically-Symmetric Approximations 80 - C a l c u l a t i o n o f Glass-Substrated S.P.D. Response to ot-Particle Impact Assuming F i n i t e . Length, Normal Incident a - P a r t i c l e Track, with a F i n i t e Sized Junction 82 - F i n i t e Junction Size E f f e c t s 85 - Magnitude o f the Angle-Effect ^3 - Conclusion 95 - v i -Page CHAPTER 4 SUPERCONDUCTIVE-TUNNELLING JUNCTION FABRICATION 96 - Introduction 96 - S.T.J. Sample F a b r i c a t i o n 98 - Substrate cleaning 98 - Evaporation mask and p o s i t i o n i n g ; 101 - Deposition of j u n c t i o n f i l m s by evaporation 101 - Plasma cleaning and anodization 103 - T y p i c a l S.T.J. F a b r i c a t i o n Run 104 - V i s u a l Inspection 105 - Sample Passivation 107 - Group Separation 107 - Lead Attachment 107 - Sample S t a b i l i t y 107 - V a r i a t i o n s o f Sample F a b r i c a t i o n Procedures 108 - Vapour depositions of polyethylene 108 - Photo r e s i s t covered substrate 108 - A 1 2 0 3 b a r r i e r 109 CHAPTER 5 EXPERIMENTAL METHODS AND RESULTS 110 - Cryogenics 110 - Junction S e l e c t i o n 113 - Junction D.C. C h a r a c t e r i s t i c s Measurements 115 - Junction-Degradation 123 - 'S' Type Negative-Resistance ( f o l d back) 123 - Pulse Measurements with Room Temperature Preamplifier 125 - Pulse Amplitude Dependence on Bias-Voltage • . . 128 - Pulse Amplitude Dependence on Temperature; Sn Junctions 128 - a - P a r t i c l e Induced Pulse-^Signals and Noise 129 V l l Page CHAPTER 5 Cont'd.. Pulse Measurements with Directly-Coupled Liquid-Helium Temperature Amplifier 131 - Liquid helium amplifier details 131 - Low temperature preamplifier test and calibration at liquid helium temperature and measurement of junction capacitance 134 Measurements with Liquid Helium Temperature Amplifier with Input Voltage Step-Up Pulse-Transformer 137 - Voltage step up pulse-transformer fabrication and tests 137 - Pulse-transformer-input low-temperature preamplifier room-temperature tests 141 - Measurements of Pb junctions with the transformer-input low temperature amplifier 142 - Discriminator-counter readings 144 - Effect of temperature variation on signals 144 - The signal to noise ratio for Pb junction R148S2J2 147 Measurements on Sn Junctions Using the Transformer Input Low-Temperature Preamplifier 149 - Amplifier system calibration 149 - a-Particle induced pulses, direct oscilloscope measurements 149 - Kicksorter measurements 151 Summary 152 CHAPTER 6 REDUCTION OF EXPERIMENTAL RESULTS AND COMPARISON WITH THEORY 153 - Introduction 153 - Junction Quasiparticle Current Dependence on Temperature at Constant Bias Voltage 153 - Variation of R, with Temperature at Constant Bias Voltage 7 X 1 158 - Dependence Upon Ambient (Mean Junction) Temperature of Junction Voltage 161 - Response to Low and High Frequency Temperature Changes - Effect of Junction-Capacitance on Junction Voltage Waveform 162 - v i i i -Page CHAPTER 6 Cont'd... - S c a l i n g of Th e o r e t i c a l Signal Current f o r a Reference Junction * g r e f C O to S p e c i f i e d Junction Parameters 163 - Numerical Calculations of the E f f e c t of Junction Capacitance and Amp l i f i e r Rise-Time on Sign a l Voltage Output Waveform and Comparisons with Experimental Observations. Room-Temperature Pr e a m p l i f i e r Case 168 - Numerical C a l c u l a t i o n of a - P a r t i c l e Induced Output Sign a l Voltage from the Transformer Input A m p l i f i e r System and Comparison with Experiments 170 - Comparison o f T h e o r e t i c a l l y Derived and Observed Output Pulse Amplitude D i s t r i b u t i o n 173 - Summary 174 CHAPTER 7 A PROPOSED SUPERCONDUCTIVE PARTICLE DETECTOR, THE HEAT-SINK CHIP TYPE 175 - Description and Analysis - Limits on Performance of the SPD 182 CHAPTER 8 CONCLUSIONS 185 - P r i n c i p a l Results from the Present Work 185 - Expected Performance of Superconductive P a r t i c l e -Detectors 187 - Future Work 188 - i x -Page APPENDIX 5.1 EXPLANATION OF OBSERVED FALSE-PEAK EFFECT DUE TO SIGNAL PULSE CLIPPING BY A CURRENT-STEP ON THE JUNCTION I.V. CHARACTERISTIC. 189 - X -LIST OF TABLES TABLE Page 3.1 Specific Heat and Thermal Conductivity Data of Glass Used in Numerical Calculations Relating to the Glass-Substrated Superconductive Particle-Detector. 64 5.1 Discriminator Counter Readings on Alpha-Particle 124a Induced Pulses from R67S1J3. 5.2 Record from Discriminator Counter Measurements of R148 S2J2 at 1.2 K. 143 5.3 Temperature Dependence of Alpha-Particle Induced Pulses in Lead Junction R148S2J2. 145 - xi -LIST OF FIGURES FIGURE Page 2.1 Energy-Diagram for a Metal-Insulator-Metal Junction with Applied Potential Difference V, (at f i n i t e temperature). 10 2.2 Energy-Diagram of an NS Junction in the Semiconductor Representation, at Finite Temperature, with Applied Potential Difference V. 10 2.3 Energy-Diagram for a S.S. Junction in the Semiconductor Representation, at Finite Temperature with Applied Potential Difference V. 17 2.4 Alpha-Particle Impinging on Glass-Substrate Type Superconductive Quasiparticle Tunnelling Junction Particle-Detector. 26 2.5 Alpha-Particle Impinging on Phonon-Barrier Type Super-conductive Quasiparticle Tunnelling Junction Particle-Detector. 26 2.6 Equivalent Circuit for a Superconductive Quasiparticle Tunnelling Junction. 34 2.7 Current-Response Sensitivity per Unit Junction Normal Tunnel-Conductance. 42 2.8 Voltage-Response Sensitivity, of SS Junction to Temperature Pulse, Frequency as Parameter. 43 X l l L i s t o f Figures Cont'd... FIGURE Page 2.9 V a r i a t i o n of Signal Due to Angle of Incidence of Impinging P a r t i c l e . 49 2.10 V a r i a t i o n of Signal Due to Impact of Incoming P a r t i c l e at D i f f e r e n t Points o f a F i n i t e Sized Junction. 49 3.1A A l p h a - P a r t i c l e Penetrating a Glass-Substrated Super-conductive Tunnelling Junction. 59 3.IB 1-Dimensional R a d i a l l y Symmetric Approximation of the Thermal S i t u a t i o n of an A l p h a - P a r t i c l e Penetrating a Glass-Substrated Superconductive Tunnelling Junction. 59 3.2 Comparison of Temperature P r o f i l e s Obtained A n a l y t i c a l l y and by F i n i t e - D i f f e r e n c e Method. 70 3.3 Temperature P r o f i l e s , 1-Dimensional R a d i a l l y Symmetric Heat-Diffusion i n Glass-Substrate. 71 3.4 Signal-Current as a Function of Time, 1-Dimensional R a d i a l l y Symmetric Approximation of an A l p h a - P a r t i c l e Impact on a Glass-Substrated Superconductive T u n n e l l i n g Junction. 72 3.5 Normal Radius as a Function of Time, Derived from a 1-Dimensional R a d i a l l y Symmetric Approximation o f an A l p h a - P a r t i c l e Impact on a Glass-Substrated Superconductive Tunnelling Junction. 74 3.6 Temperature P r o f i l e s as a Function of Time f o r a T i n Superconductive Tunnelling Junction on a Phonon-Barrier. 76 - X l l l -List of Figures Cont'd... FIGURE 3.7 Signal Current as a Function of Time for a Tin Phonon-Barrier Type Superconductive Particle-Detector at 1.2°K (theoretical). 3.8 Temperature Profiles as a Function of Time for a Lead Superconductive Tunnelling Junction on a Phonon-Barrier (theoretical). 3.9 Signal Current as a Function of Time for a Lead Phonon-Barrier Type Superconductive Particle-Detector at 2.4°K (theoretical). 3.10A Cross-Section of a Normal-Incidence Alpha-Particle Impact on a Glass-Substrated Superconductive Particle-Detector. 3.10B Geometry of 'Cell' Array Used for Numerical Calculations. 3.11 Temperature Profiles at Different Depths in the Glass Substrate as a Function of Time. 3.12 Junction Signal Current as a Function of Time for an Infinite-Area Junction. 3.13 Alpha-Particle Impact Point Coordinate Map. 3.14 Calculated Signal Currents as a Function of Time for Different Alpha-Particle Impact-Points. 3.15 Calculated Probability Density of Signal-Current Amplitudes. 3.16 Calculated Probability Density of Accumulated Signal Charge to Time = 0.56 us. 3.17 Effects of Angle of Impact and Junction Size on Signal Current. -xiv-List of Figures Cont'd... FIGURE 4.1 Superconductive Tunnelling Junction Samples. 4.2 Superconductive Tunnelling Junction Sample Details. 4.3 Apparatus for Junction Fabrication Inside Vacuum Chamber. 4.4 Evaporation Masks and Mask-Changer Details. 4.5 Diagram of Apparatus for Sample Fabrication Inside Vacuum Chamber. 4.6 Superconductive Tunnelling Junction Structural Details. 4.7 Heated-Wire Sample Separator. 5.1 Sample-Holder for Experiments with Sample Mounted, Alpha-Particle Source and Low-Temperature Preamplifier. 5.2 Slide Switch Details on Sample Holder. 5.3 Sample Mounted on Sample Holder, with Alpha-Particle Source Facing Junctions. 5.4 Sample Mounted on Sample Holder, with Alpha-Particle Source Turned Away from Junctions. 5.5 Junction D.C. Characteristics Measurement Circuit Using a 4-Point Method. 5.6 Current Stream-Lines and Voltage Equipotentials for a Junction Without Oxide Barrier, Giving Rise to "Negative-Resistance" in 4 Point Measurements. 5.7 D.C. Junction Characteristics of Lead Junction R123S6J2 at 4.2°K. 5.8 I.V. Characteristics of Tin Junction R77S1J3 at 1.2°K. - XV -List of Figures Cont'd... FIGURE 5.9 Temperature Dependence of I.V. Characteristics of Tin Junction R67S1J3. 5.10 'S* Type Negative Resistance in Junction I.V. Characteristics of Thermal Origin. 5.11 Amplifier Circuiting for Alpha-Particle Induced Pulse Observations. 5.12 Alpha-Particle Induced Pulses in Tin Junction R67S1J3. 5.13 Pulse Amplitude as a Function of Bias Voltage. 5.14 Pulse-Amplitude as a Function of Junction Temperature. 5.15 Circuit Diagram of Direct-Coupled Low-Temperature Preamplifier, Connected to a Tunnelling Junction and 'Post' Amplifier. 5.16 Junction Capacitance Measurement and Amplifier Calibration Using the I.V. Characteristics. 5.17 Variation of Decay Time Constant of Voltage-Response to Calibration Charge with Junction Bias-Voltage. 5.18 Dust-Iron Pulse-Transformer Core Configurations (1.4 times actual size). 5.19 Pulse-Transformer Test-Circuit and Waveforms. 5.20 Circuit Diagram of Transformer Inp-;t Low-Temperature Preamplifier Connected to Junction and 'Post' Amplifier. 5.21 Alpha-Particle Induced-Pulses from Lead Junction R148S2J2, Using the Transformer Input Low Temperature Preamplifier. 5.22 Pulse-Amplitude Distribution Curve from Discriminator Counter Readings for Lead Junction R148S2J2. X V I -List of Figures Cont'd... FIGURE Page 5.23 Amplifier System/Junction Combination Calibration Curve. 148 5.24 'Kicksorter' Record of Pulse-Amplitude Distribution from Tin Junction R164S1J5, (record made with transformer input low-temperature preamplifier). 150 5.25 Alpha-Particle Induced Pulses in Tin Junction R164S1J5, Using Transformer-Input Low-Temperature Preamplifier. 148 6.1 Ratio of Junction Quasiparticle Tunnelling Current at Constant Bias Voltage to Junction Normal Conductance as a Function of Temperature Parameter BA for Lead Junctions (theory and experiment). 154 6.2 Ratio of Junction Quasiparticle Tunnelling Current at Constant Bias Voltage to Junction Normal Conductance as a Function of Temperature Parameter gA for Tin Junctions (theory and experiment). 155 6.3 Variation of the Ratio of Junction Dynamic Tunnel Conductance to Junction Normal Conductance with Temperatur Parameter BA. 157 6.4 Temperature Dependence of Junction Voltage-Response to Alpha-Particle Caused Temperature-Pulse. 160 6.5 Calculated Reference-Junction Signal-Current. jgg 6.6 Output Signal Voltage from Room Temperature Amplifier System (theory and experiment). 6.7 Alpha-Particle Generated Output Response for Tin Junction R164S1J5. 171 - X V I 1 -L i s t of Figures Cont'd... FIGURE 7.1 A l p h a - P a r t i c l e Impinging on Heat-sink Chip Type Superconductive Q u a s i p a r t i c l e Tunnelling Junction P a r t i c l e - D e t e c t o r . APP. 5.1 1 Current-Step Signal-Voltage C l i p p i n g E f f e c t . 2 Observed False-Peak E f f e c t Due to C l i p p i n g . - x v i i i -ACKNOWLEDGEMENTS Spe c i a l thanks are due to my supervisor Dr. B.L. White f o r h i s generous assistance, understanding, and encouragement, e s p e c i a l l y during the w r i t i n g of t h i s t h e s i s . Valuable discussions with Dr. R.E. Burgess are acknowledged with gratitude. H e l p f u l suggestions and other assistance from other members o f my supervisory committee Drs. G. Jones, A.V. Gold, and P. Matthews are g r a t e f u l l y acknowledged. Thanks are due to Dr. G.H. Wood my predecessor, i n t h i s study, who l e f t me the cryogenic system he b u i l t f o r h i s experiments, and valuable information r e l a t e d to the experiments. Thanks arc due to the Van de Graaff Group f o r p r o v i d i n g assistance and a f r i e n d l y environment. - 1 -CHAPTER ONE INTRODUCTION In experimental studies of energetic charged p a r t i c l e s and photons (energy £ IkeV) the name detector i s often applied to a c l a s s of devices which provide as output an impulsive voltage or current s i g n a l which i s corre l a t e d i n time with the passage of the p a r t i c l e or photon i n t o or through the device, and whose amplitude contains information about the amount of energy l o s t by the p a r t i c l e or photon i n the device; where the energy i s of primary i n t e r e s t , the detector i s c a l l e d a spectrometer. In many detectors, the current s i g n a l i s integ r a t e d on the detector cap-acitance, g i v i n g an output signal proportional to the c o l l e c t e d charge. In t h i s t h e s i s we w i l l use the term "detector" to mean a spectrometer, and w i l l r e f e r only to charged p a r t i c l e s and not s p e c i f i c a l l y to photons. A large v a r i e t y of d i f f e r e n t physical e f f e c t s are used i n detectors, b r i e f l y described below, (see Dearnaley § Northrop (Ref. 1.1) f o r a good de t a i l e d account of de t e c t o r s ) . The i o n i z a t i o n chamber and the proportional counter are based on gas i o n i z a t i o n , combined with proportional avalanche m u l t i p l i c a t i o n i n the case of the l a t t e r . They exhibit a reasonably l i n e a r r e l a t i o n s h i p between the signal charge (number of gaseous ions c o l l e c t e d on the electrodes m u l t i p l i e d by the e l e c t r o n i c charge) and the energy l o s t i n the gas by the primary - 2 -energetic p a r t i c l e . S t a t i s t i c a l f l u c t u a t i o n s i n the number of ions c o l l e c t e d f o r given energy l o s s (which i s r e l a t e d to the average energy loss required to generate an ion p a i r i n the gas, about 30 eV f o r most spectrometer gases) give an energy r e s o l u t i o n which i s t y p i c a l l y of the order of 2.5 keV f o r 100 keV e l e c t r o n s . When an energetic charged p a r t i c l e passes through a s c i n t i l l a t i o n c r y s t a l part of the energy deposited by the p a r t i c l e r e s u l t s i n the emission of fluorescent photons by the c r y s t a l . The photons are c o l l e c t e d (by an o p t i c a l system) and measured by a photo-m u l t i p l i e r . The p h o t o m u l t i p l i e r output (charge) i s p r o p o r t i o n a l to the number of fluorescent photons, which i n turn i s p r o p o r t i o n a l to the charged p a r t i c l e energy l o s s . Thus the photomultiplier output i s p r o p o r t i o n a l to the p a r t i c l e energy l o s s ; t h i s i s the basis of the s c i n t i l l a t o r counter, with t y p i c a l r e s o l u t i o n of 150 keV FWHM f o r a 5 MeV a - p a r t i c l e , f o r example. Semiconductor junction detectors w i l l be discussed i n more d e t a i l because of t h e i r p r a c t i c a l importance i n h i g h - r e s o l u t i o n p a r t i c l e - e n e r g y spectrometry, where they are c u r r e n t l y the highest r e s o l u t i o n energy-loss spectrometers a v a i l a b l e . Thus they c o n s t i t u t e a s u i t a b l e b a s i s f o r the comparison and evaluation of the superconductive t u n n e l l i n g j u n c t i o n detectors to be described i n t h i s t h e s i s . In operation the semiconductor ju n c t i o n detector i s reverse biased such that the high e l e c t r i c f i e l d i n t e n s i t y depletion layer extends as completely as p o s s i b l e throughout the volume of the detector. A charged p a r t i c l e passing through and stopped i n the detector has part of i t s k i n e t i c energy converted to electrons and holes (the r e s t of the energy ends up as phonons and r a d i a t i o n damage i f any) . The electrons and holes are acted on by the d e p l e t i o n - l a y e r f i e l d such that the electrons move towards the 'n' region and holes towards the 'p' r e g i o n . - 3 -The c a r r i e r s are said to be " c o l l e c t e d " , and the c o l l e c t e d charge c o n s t i -tutes the s i g n a l . For a given type of inc i d e n t p a r t i c l e the average number of charge c a r r i e r s generated, *N', i s prop o r t i o n a l to the energy l o s s i n the depletion region, thus the measured signal-charge i s prop o r t i o n a l to the energy of the p a r t i c l e W. For a given j u n c t i o n type and p a r t i c l e we can thus s p e c i f y the energy w required to generate a s i n g l e ion p a i r w = W/N. I f the charge production processes were uncorrelated then the standard d e v i a t i o n of the number of p a r t i c l e s produced, o^, would be equal to ^N. But the processes are i n f a c t c o r r e l a t e d by the requirement thatN-w = W (Ref. 1.2), and = vf¥ where F i s the "Fano-factor", with a value of 0 - F - 1, ( F = l f o r completely independent ch a r g e - c a r r i e r production and F = 0 for complete dependence). The 'energy-resolution' R can then be defined as:-where i s the standard d e v i a t i o n of s i g n a l charge, equal to • e and q i s average s i g n a l charge equal to N • e. This d e f i n i t i o n of r e s o l u t i o n i s r e l a t e d to the 'FWHM' d e f i n i t i o n ( f u l l width at h a l f maximum , often used i n spectrometry a p p l i c a t i o n ) by:-(1.1) ^£ _ FWHM(eV) (1.2) Peak Energy(eV) i f the peak i s gaussian i n shape. Ref. (1.2). - 4 -I f the optimum mean square system noise voltage w i t h i n the bandwidth required to measure the signal i s V q 2 ( t h i s includes shot, j u n c t i o n leakage, J o h n s o n ^ 6 ^ " * , and preamplifier n o i s e ) , the energy output r e s o l u t i o n i n the output i s : -Standard d e v i a t i o n of preamp. output _ /Fw - + w'^o ^ " Signal amplitude from preamp. / W F-W-e2 ' where C = detector capacitance. To improve r e s o l u t i o n the preamplifier noise performance must be improved, the detector leakage current decreased and w decreased. The most important f a c t o r i s the decrease of w; with consequent increase of N, large improvements i n r e s o l u t i o n can r e s u l t . The best semiconductor detectors are made from Ge, with an energy gap of 0.67 eV, and w = 2.94 eV, and a measured Fano f a c t o r of < 0.08 (Ref.1.3). Semiconductors of lower energy gap l i k e indium antimonide of Eg = 0.17 eV have been t r i e d , but were found to be unsui t a b l e because of leakage currents due to impurity band conduction. ^ R e f * The energy gap associated with superconductivity i s s u f f i c i e n t l y small to create i n t e r e s t i n using some s u i t a b l e superconductivity e f f e c t i n p a r t i c l e detection. The quasi p a r t i c l e s excited i n a superconductor can be detected by observing the tunnel-current between two superconductors (or superconductor and normal metal) separated by a t h i n i n s u l a t i n g b a r r i e r . Q u a s i p a r t i c l e superconductive t u n n e l l i n g junctions were f i r s t studied i n fRef 1 41 1960 by Gi a v e r v * ' . In NS (normal-superconductive) tunnel junctions biased below A/e and SS (superconductive-superconductive) tunnel junctions biased below 2A/e, with a magnetic f i e l d to bia s o f f the Josephson fRef 1 5~1 supercurrent ' , the junction current r e s u l t s from the t u n n e l l i n g of - 5 -thermally generated q u a s i p a r t i c l e s . (The Cooper p a i r s do not contribute to the t u n n e l l i n g current s i g n i f i c a n t l y ^ e ^ ' ^ , although small c o n t r i -butions due to subharmonic tu n n e l l i n g and m u l t i - p a r t i c l e t u n n e l l i n g are p o s s i b l e ) . Thus some analogy exists between the charge c o l l e c t i o n process i n a semiconductive t u n n e l l i n g junction. I f the p a r t i c l e energy could be used to produce q u a s i p a r t i c l e s (from the Cooper p a i r s ) i n the super-conductive t u n n e l l i n g j u n c t i o n , and the superconductive t u n n e l l i n g j u n c t i o n were properly biased, then the increase i n q u a s i p a r t i c l e density would cause a momentary increase of t u n n e l l i n g current, providing a s i g n a l charge, analogous to electron and holes i s c o l l e c t e d as a signal i n a semiconductor j u n c t i o n detector. This i s the ba s i s of the super-conductive q u a s i p a r t i c l e t u n n e l l i n g j u n c t i o n p a r t i c l e detector proposed fRef 1 7) by B.L. White ' , (hereafter c a l l e d "superconductive p a r t i c l e detector". Note that the analogy between the PN j u n c t i o n p a r t i c l e detector and the superconductive p a r t i c l e detector i s not exact. As w i l l be shown l a t e r i n t h i s t h e s i s , i n the superconductor, q u a s i p a r t i c l e s are mostly thermally generated and only a small f r a c t i o n are generated by i n t e r a c t i o n of the primary p a r t i c l e and secondary p a r t i c l e s with the Cooper p a i r s . Also, the q u a s i p a r t i c l e s are ' c o l l e c t e d ' by d i f f u s i n g i n a f i e l d f r e e region, whereas i n a semiconductor the electrons and holes d r i f t i n the depletion region f i e l d . Assuming the r a t i o W / E g = 5 (eg. f o r S i = 3.34, fo r Ge = 4.34), then the mean energy loss by a charged p a r t i c l e required to create a quasi p a r t i c l e p a i r i n superconducting $n w i l l be W = 5.6 x 10 eV. Assuming the Fano f a c t o r = 1 (the worst possible case), then compared to a Ge detector the s t a t i s t i c a l s i g n a l f l u c t u a t i o n - 6 -/WGe . F G ^ i s l e s s by / ^ = — ^ 64, i . e . the s t a t i s t i c a l f l u c t u a t i o n i s Sn ' hSn reduced by t h i s f a c t o r . With low-temperature low noise a m p l i f i e r s the t o t a l e l e c t r o n i c noise can conceivably be reduced, g i v i n g p o t e n t i a l l y v a s t l y improved energy r e s o l u t i o n . G.H. Wood ' ' ^ ' ^ " ^ fa b r i c a t e d Sn superconductive t u n n e l l i n g junctions on glass substrates and observed tunnel current pulses caused by a-bombardment from a 5.13 239 MeV a - p a r t i c l e source of Pu . It was d e f i n i t e l y established that superconductive t u n n e l l i n g junctions could detect p a r t i c l e s , but the data obtained by Wood was i n s u f f i c i e n t to determine the mode of operation and the energy r e s o l u t i o n performance. The Author's c o n t r i b u t i o n s described i n t h i s t h e s i s are: 1. The experimental work done to achieve a reproducible j u n c t i o n f a b r i c a t i o n process; 2. The experimental work doneon measurements of j u n c t i o n parameters and a - p a r t i c l e induced current pulses with improved instrumentation, obtaining s u f f i c i e n t data to enable comparison with theory; 3. The t h e o r e t i c a l and numerical work done to provide a d e t a i l e d under-standing of the mode of operation of the superconductive p a r t i c l e detector, v e r i f i e d by the experimental data; 4. The design of a t h e o r e t i c a l l y better superconductive p a r t i c l e detector c o n f i g u r a t i o n , the heat-sink chip type, based on the t h e o r e t i c a l understanding of the mode of operation of the gl a s s -substrated superconductive p a r t i c l e detector i n v e s t i g a t e d experimentally i n t h i s work. - 7 -This t h e s i s contains s i x subsequent chapters. Chapter 2 i s the "theory" chapter where the theory.of superconductive tunn e l l i n g i s developed with emphasis on the response of the j u n c t i o n to a temperature change so that the theory i s substrate-independent and thus u n i v e r s a l l y a p p l i c a b l e to d i f f e r e n t substrates. The t h e o r e t i c a l expressions employ BA as a parameter where B = ^/K^T.and A (the energy gap of a superconductor),and are thus a p p l i c a b l e to any type of super-conductors. The p h y s i c a l model of the mode of operation of the g l a s s -substrated superconductive p a r t i c l e detector i s defined. Scaling theory necessary f o r comparison of r e s u l t s from junctions with d i f f e r e n t parameters i s investigated. The temperature response s e n s i t i v i t y and the inherent noise properties of SS and NS junctions are in v e s t i g a t e d and compared, demonstrating the s u p e r i o r i t y of SS junctions as superconductive p a r t i c l e detectors. F i n a l l y p h y s i c a l models of two proposed types of superconductive p a r t i c l e detectors, the phonon-barrier type, and the heat-sink-chip type are discussed, and the t h e o r e t i c a l performance l i m i t s of the heat-sink-chip type ( t h e o r e t i c a l l y the better) operated at conveniently achievable conditions are c a l c u l a t e d . Chapter 3 i s the numerical methods and r e s u l t s chapter. Here the non-linear p a r t i a l d i f f e r e n t i a l equation d e s c r i b i n g the d i f f u s i o n o f the "heat-spike" (generated by the a - p a r t i c l e track i n the glass substrate) i s modified to a form s u i t a b l e f o r and t r a n s l a t e d to a f i n i t e - d i f f e r e n c e s equation. Numerical s t a b i l i t y conditions are i n v e s t i g a t e d , and the computer programs f o r the s o l u t i o n s of the f i n i t e d i f f e r e n c e s equation and the c a l c u l a t i o n of j u n c t i o n current response described. The c a l c u l a t e d r e s u l t s include the numerical s o l u t i o n of a l i n e a r h e a t - d i f f u s i o n problem using one of the computer programs mentioned above, compared ..with the a n a l y t i c a l s o l u t i o n of the same problem to v e r i f y the methods used and the computer program. . Also c a l c u l a t e d are a - p a r t i c l e induced current waveforms, the dependence of current waveform and amplitude on the l o c a t i o n of the a - p a r t i c l e impact with respect to a f i n i t e - s i z e d j u n c t i o n on a glass substrate, the expected pulse-amplitude d i s t r i b u t i o n , and the e f f e c t s of the angle of impact on the current-pulse waveform and amplitude. , Chapter 4 describes the junction f a b r i c a t i o n process d e t a i l s and some v a r i a t i o n s . This Chapter describes a large experimental e f f o r t but may be omitted i n the reading of t h i s t h e s i s i f j u n c t i o n - f a b r i c a t i o n i s of no i n t e r e s t to the reader. Chapter 5 describes the apparatus instrumentation used to measure the ju n c t i o n parameters and pulse response of Pb and Sn junc t i o n s , and the r e s u l t s of those measurements. Chapter 6 compares the t h e o r e t i c a l and numerical r e s u l t s of Chapter 2, and 3, with the experimental r e s u l t s of Chapter 5. The experimental data and the theory appear to agree. Chapter 7 i s the conclusion chapter. I t i s concluded that the mode of operation of the superconductive p a r t i c l e detector should t h e o r e t i c a l l y give b e t t e r energy r e s o l u t i o n than e x i s t i n g semiconductor j u n c t i o n p a r t i c l e detectors. - 9 -CHAPTER TWO THEORY OF OPERATION OF THE SUPERCONDUCTIVE QUASIPARTICLE , TUNNELLING JUNCTION PARTICLE DETECTOR INTRODUCTION: A b r i e f review o f q u a s i p a r t i c l e t u n n e l l i n g i n Superconductive i T u n n e l l i n g Junctions i s i n order. We consider f i r s t t u n n e l l i n g i n normal metal-insulator-metal t u n n e l l i n g j u n c t i o n s . R e f e r r i n g to Figure (2.1), 'the energy vs. density o f states curves f o r the metals are shown on e i t h e r side o f the representation of the b a r r i e r , and occupied states are represented by shaded portions under the curves. The Fermi-energy l e v e l o f side 2 i s used as the reference '0' o f energy measurement. The s i t u a t i o n "in Figure (2,1) represents the a p p l i c a t i o n of -V v o l t s to side 1, referenced to side 2, so that the Fermi l e v e l o f side 1 i s eV above the Fermi l e v e l o f _ s i d e 2. The c o n t r i b u t i o n to the t u n n e l l i n g current density from electrons t u n n e l l i n g from si d e 1 to side 2 at energy E, i n a range dE i s pr o p o r t i o n a l to the product o f the number of electrons i n that energy range on side 1 and the number of unoccupied l e v e l s on side 2 i n the same energy range, thus - d J 1 2 = e . P 1 2 N N 1(E-eV) f(E-eV) • N N 2 ( E ) ( l - f ( E ) ) . d E (2.1) where N^(E) = density o f s t a t e s , normal metal. and P^ 2 i s a p r o p o r t i o n a l i t y constant, having the p h y s i c a l meaning of the number of electrons t u n n e l l i n g from side 1 to side 2, per - 10 F i g . 2.1 Energy-Diagram f o r a Metal-Insulator-Metal Junction with Applied P o t e n t i a l Difference V. E c = 0 F i g . 2.2 Energy-Diagram of an NS Junction i n the Semiconductor Representation, at F i n i t e Temperature with Applied Pot e n t i a l Difference V. u n i t junction area, per u n i t time, per u n i t occupied state density 7on~side 1, per vacant st a t e - d e n s i t y on side 2, per u n i t energy range. f(E) = Fermi functi o n , g i v i n g the p r o b a b i l i t y of occupancy of state at energy E. (note: - ( l - f ( E ) ) then gives the p r o b a b i l i t y o f vacancy of state at E) . e = the e l e c t r o n i c charge S i m i l a r l y considering the electrons t u n n e l l i n g from side 2 to side 1 we get - d J 2 1 = e • P 2 1 N N 2 ( E ) f(E) • N N 1(E-eV) ( l - f ( E - e v ) ) dE (2.2) where P 2 1 i s a p r o p o r t i o n a l i t y constant, corresponding to f ° r t u n n e l l i n g from side 2 to,side 1. • _ • Thus the net t u n n e l l i n g current density from side 1 to side 2 i s given by: JNN d J 1 2 - d J 2 1 = " e P12 N N 1 ( E - V ) N N 2 ( E ) ( f (E-eV)-f(E))dE (2.3) Where we assumed = P.^. At low temperatures^, l e v e l s s l i g h t l y above the Fermi l e v e l are unoccupied, and the l e v e l s s l i g h t l y below become^" f u l l y occupied, thus from equation (2.3) we see that the t u n n e l l i n g current r e s u l t s from states immediately above and below the Fermi l e v e l , and we can approximate N^(E-eV), 'N2 (E) by N N 1 ( 0 ) , NN 2 C ° ) r e s p e c t i v e l y , assuming eV i s small.. Also f(E-eV) - f(E) ".-iiEL . eV f o r small eV. Thus equation (2.3) becomes: JNN = + e 2 p i 2 N N l ^ N N 2 ^ - V MCMI d E 3E Q t V • e2p i 2N N 1(0)N N 2(0) TNN = V'GNN. <2-4> where ' = P 1 2 e 2 N N ^ ( 0 ) N ^ 2 ( 0 ) . A . i s the j u n c t i o n conductance. = .; a • A a = junction conductance per u n i t area A = junction area Thus we get the well known ohmic (l i n e a r ) behavior o f normal-normal tunnel junctions f o r small bias voltages, the negative sign of e a r l i e r equations r e s u l t e d from the choice of -|v| f o r b i a s . We went through the above c a l c u l a t i o n s to get the expression f o r f o r use l a t e r , and to e s t a b l i s h the procedure f o r the c a l c u l a t i o n o f t u n n e l l i n g currents. Following GIAVER (reference 2.1) and using the semiconductor band gap model f o r the superconductor we can derive the t u n n e l l i n g -current c h a r a c t e r i s t i c s of a metal (normal)-insulator-superconductor (NS) t u n n e l l i n g j u n c t i o n . R e f e r r i n g to Figure (2.2) we have a schematic representation of a NS t u n n e l l i n g - j u n c t i o n with si d e '1' the normal metal biased to r a i s e the energy l e v e l eV r e l a t i v e to side 2 the super-conductor. Proceeding as i n the normal-normal t u n n e l l i n g case considered above we get: 13 -NS eA P12 hl^ N S 2 C E ) CfCE-ev) - f(E) ) d E ( 2 T 5 ) where N Q(E) i s the density of states of the superconductor at energy "E" and NN1C0) replaced N N 1(E-eV), v a l i d f o r low applied voltages V. From De Gennes (reference 2.2), we get the expression f o r N g ( E ) N S 2 ^ = N N 2 ^ for- | E | > A = 0 f o r | E | < A energy measured from the Fermi l e v e l , and A h the energy gap o f the Superconductor. Approximating N N 2 ( E ) by.NN2(0) ( v a l i d f o r low temperature) we get: : NS A.e.P 1 2NN 1(0)NN 2(0) / E2_ A2 - ( f ( E - e v ) - f ( E ) ) d E / E^ F " • [ f ( E - e v ) - f ( E ) ] • dE S N [INT 1 + INT 2] INT, [f ( - ( E + eV)) - f ( E ) ] dE E (f(E + eV) - f(E))dE /E z-A z NS °NN J^U, [f(E-eV)-f(E +eV)]dE=5i N_ E+A /EZ+2EA (f(E+A-eV)-f(E+A+eV)) .dE (2.6) - 14 -Expanding the Fermi-function: f'CE) C l * e S E ) - B E r e I , ^m m= Q (-1)"' exp(-mBE) therefore NS 'SIN I C"l) m + 1expC-mBA)sinhCmBeV) e m=p E+A • exp(-mBE)dE v/E^+2EA where B = k -T ' B D , k R = Boltzmann constant and T = temperature. From Laplace transform tables (reference 2.3) , E + A • e ~ C m B E ) dE = . Aexp (mBA) . K (mBA) v/E^+lEA 1 where i s the Bessel function of the second kind, 1st order. We f i n a l l y get (reference 2.1) 2A NS S N I (-l)™4"1 sinh (meVB)K (mBA) m=l (2.7) This i s an a l t e r n a t i n g s e r i e s which converges r a p i d l y , f o r the applied bias voltage of V. = and BA £ 6 thus we can approximate I^g by taking the 1st term, and by the theory of a l t e r n a t i n g s e r i e s , the error i n omitting the fol l o w i n g terms i n smaller than the magnitude of the 2nd term. The r a t i o of term 2/term 1 f o r bias V = ^  (so as to bias near the maximum dynamic r e s i s t a n c e point) at BA = 6 i s 0.034, meaning the erro r of approximation i s smaller than 3.4%. - 1 5 -The approximation i s good over the range of BA values 3 to 8, the range o f , i n t e r e s t i n the operation of the superconductive t u n n e l l i n g j u c t i o n as a p a r t i c l e detector. The approximation can be seen to improve with i n c r e a s i n g BA, thus: 2 A GNN I N S = — sinh (BeV) K^(BA) (2,8) D i f f e r e n t i a t i n g (2.7) with respect to V we obtain an expression f o r the dynamic res i s t a n c e R^^ 1 3 I H C \ 1. - 2G.....BA oo. 2, (-1) m• Cosh (mBeV)K (mBA) 8V /„ R, M C e m=l ' T dyn NS (2.9) Equation (2.9) can be approximated as before by taking the f i r s t term only. The r a t i o s of term 2/term 1 (for bias voltage V = ^ ). BA = 6 i s +3.4%, and improves with i n c r e a s i n g BA, thus: To get the s e n s i t i v i t y of I^g to temperature change we d i f f e r e n t i a t e (2.7) with respect to *T' (temperature) and get: - 16 -•jjY I (-1)™ mBA sinh(m3eV)K (mBA). m=l 00 + I ( - l ) m + * mB2A2k_{sinh(mBeV)[K_(m3A)+K1(mBA)/mBAl m=l B eV Cosh (mBeV)K (mBA)} A 1 (2.11) Equation (2.11) as i t stands is too complicated to allow a simple physical interpretation but some simplifying approximations can be T made since A(T)/A(0) > 0.95 for T< , (from the A(T) vs. T expression of the B.C.S. theory (reference 2.4)). The 14" term may be omitted as a I an approximation (see numerical value given below) . The remaining summation is an alternating series and as before can be approximated by taking only the m=l term, the error then being smaller than the m=2 term. The factor (KQ (mBA) + (mBA)/mBA) in (2.11) came from the differentiation of K^OnBA) and can be approximated by K^mBA). The accuracy of the approximation: 91 NS1 ,9T V 2G. NN '9 k3T ' V 2G. NN B 2A 2k B ( s i n h ( B e V ) C o s h (BeV)^ (BA)) (2.12) •\ . • \ \ • • . • F i g . 2.3 Energy Diagram f o r a SS Junction i n the Semiconductor Representation, at F i n i t e Temperature with Applied P o t e n t i a l D i f f . V. \ - 18 -i s b e t t e r than 14% over the BA range 5-»-7 -, and at bias voltages near A/2e, and improves with increase of BA beyond 7. Proceeding as i n the above d e r i v a t i o n of the t u n n e l l i n g current f o r a NS junction and r e f e r r i n g to Figure (2-3) the schematic representation of a superconductor-insulator-superconductor tunnel junction (SS) we get: SS NN N g l ( E - e V ) # N S 2 ( E ) . [ f rg-eV.)-f (E)]dE " (2.13) e N M 1(E-eV) N^E) where Ng^, ^S2 5 a r e t * i e density o f states i n the superconductors on side 1, 2, r e s p e c t i v e l y . N S(E) Z E ^ A " 2 0 NN ( E ) f o r |E| > 0 f o r |E| < 0 energy measured from the Fermi l e v e l S u b s t i t u t i n g f o r Ng i n (2.13) we get SS NN 00 T E-eV ( ( E - e V ^ - A . ^ (E z-A 2 ) ^ A^+eV E I - [ f ( E - e V ) - f ( B ) ] d E E-eV -rr2 T9"1 9—, 7c2—l—ZTi~ [ f (E-eV)-f (E) ] dE [ ( E - e V ) 2 - A 1 2 ) J S ( E ^ - A 2 Z ) % } K J J S N [INT 1 + INT 2] - 19 -For our^purposes the superconductors on the two sides are the same kind, A 1 = A 2 = A INT, (E + A) (E + A + eV) (EZ+2EL)^ [(E 2+eV) 2+2(E+eV)-A]* 5 INT, [f(E + A) - f ( E + eV + A)]dE (E + eV) . E ((E+eV^-A 2)^ (E 2-A 2) JS r [f[-(E+eV)]-f(-E)]dE (E + eV) ((E+eV) 2=A 2^ ( E 2 - A 2 ) ^ [f(E) -f(E+eV)]dE (E + eV + A) (E + A) 0 [(E+eV) 2+2(E+eV)A]' s (E +2EA)^ - [f(E+A)-f(E+eV+A)]dE = I NT, 2G. Thus I NN SS (E + A) . CE + A + eV) 0 [E +2EA]^ [(E+eV) 2+2(E+eV)A]' 5 r •[f(E+A)-£(E+eV+A)]dE (2.14) Equation (2.14) can be inte g r a t e d only numerically ( r e f . 2.5,2.6) f o r T ^ 0, i . e . the i n t e g r a l cannot be expressed i n tabulated mathematical functions. To obtain a t r a c t a b l e expression approximations must be made. [f(E+A)-f(E+eV+A)] = 1_ 1 + e 3 ( E + A ) " 1 + e 6 ( E + A + e V ) = ( e B e ^ l ) e e C E + A ) . ( l + e B ( E + A ) + e 0 ( E + A + e V ) B(2E+2A+eV)-.-l +er - 20 -= (e 3 eYl) ( e ~ H E + h ) + 1 + e P ^ + e B ( E + A + e > 0 ) " 1 « ( e P e Y l ) e - e C E + A + e V ) = e - 3 A ( l - e - B e V ) . e - B E . The approximation c o n s i s t s o f the omission of the f i r s t three terms of the second f a c t o r . For an operating bias voltage V > ^  , and BA > 3, the error of t h i s approximation i s less than 5% at E = 0, improving with increase of V, BA, and E. The f a c t o r E + A + e V i n t h e integrand of equation (2.14) can be ((E+A+eV) 2-A 2) J2 written as:-n - r—^  ) 2 r % = fi +1 c— ) 2 +1 c—^ i1* +1- (—^ ) 6 + . L lE+A+eVJ J 1 2 LE+A+eVJ 8 LE+A+eVJ 16 lE+A+eVj -- J-the s e r i e s converges r a p i d l y f o r E > 0, V > ^  . At E = 0, and V = ^  , ' I t s ' value i s 1.155. The f r a c t i o n a l e r r o r i n approximating the expression by 1.000 i n the integrand i s -0.134. The e r r o r decreases with the increase o f E, thus the contribution to the e r r o r i n the i n t e g r a l by t h i s f a c t o r i s l e s s than t h i s . Thus the t o t a l e r r o r i n the Fermi f a c t o r s approximation and the above approximation i n the integrand i s l e s s than -0.177, f o r E = 0, V = ^  , and BA = 3. As the e r r o r i s less f o r l a r g e r values of E encountered i n the i n t e g r a t i o n , the e r r o r o f the approximate i n t e g r a l i s less than -17.7%. For BA > 6 the e r r o r i s less than -13.5%. Thus equation (2.14) approximates to: 7C-r _ NN -BeV I s s - (1 - e ) 2G — — (1 - e' B e V)A.K (BA) (2.15) - 21 -where K (8A).A came from the i n t e g r a l as i n the d e r i v a t i o n of equation (2.7) By p a r t i a l d i f f e r e n t i a t i o n of equation (2.15) we get:-\ 9V / ± = 2G N N3Ae" 3 e V.K 1(gA) (2.16) dyn SS where the errors r e s u l t i n g from the approximations i n equation (2.15) and from assuming p r o p o r t i o n a l s c a l i n g of the d e r i v a t i v e the e r r o r s are of the same order. Also by p a r t i a l d i f f e r e n t i a t i o n of equation (2.15) we get:-\ 9T / V 2G NN BA [ ( l+BeV)e" e e Y l]K 1(BA) + BA ( l-e" B e V)K 0(BA) 1 _ . .IA (Le-BeVj K R 8T u (2.17) where the approximation signs r e s u l t from the approximation of I c c i n equation (2.15). Equation (2.17) can be f u r t h e r approximated by dropping 9A the — term, f e a s i b l e because A i s nearly a constant o f temperature f o r o 1 T / T c < 1/2, thus:-2G NN V BA [ ( l+BeV)e" B e Y l]K 1(BA) + BA ( l-e" 3 e V)K Q(BA) (2.18) 3A The f r a c t i o n a l e r r o r i n dropping the — term, and the t o t a l e r r o r r e s u l t i n g a 1 from the approximation of I o c and dropping the ^  term, are tabulated i n Table (2-3). The form of equation (2.18) i s s t i l l too complicated f o r discussions, and can be approximated by r e p l a c i n g _l-± + K (BA) by -K (BA). The r e s u l t i n g expression i s : \ BA / 9K 2(BA) 9(BA) - 22 -V 2G e NN K D.B 2A [A - (eV+A)e" p e V] . K.(BA) (2.19) The error of approximation (2.19) i s l e s s than -30% at BA = 4, decreasing to less than -14% at BA = 7, f o r bias voltage V = A/e a p p l i e d across the junction. In the approximations above we ignored the 3A/3T term; that i s equi-valent to regarding A as a constant (for T/T c < 0.5). Thus f o r the range of v a l i d approximation (pA > 3.5) we can approximate BA by BA(0). - 23 -A large e f f o r t was made i n t h i s section to obtain approximations with simple f u n c t i o n a l forms and to c a l c u l a t e the errors involved i n the approximations. This i s done so that r e l a t i v e l y simple algebraic d e r i v a t i o n s can be used i n l a t e r sections to obtain r e s u l t s on noise, s i g n a l and other performance parameters of NS and SS tunnel junctions used as p a r t i c l e detectors with the re s u l t s q u a n t i t a t i v e l y s i g n i f i c a n t , with errors or e r r o r bounds known. It i s p o s s i b l e to c a l c u l a t e a l l the jun c t i o n parameters using the exact expressions numerically but the consequent l o s s of comprehensibility i s not j u s t i f i e d by the gain i n numerical accuracy. When an a - p a r t i c l e impacts a superconductive t u n n e l l i n g junction deposited on a substrate the p a r t i c l e depending on i t s energy either penetrates part of the ju n c t i o n f i l m s and stops or penetrates a l l of the j u n c t i o n - f i l m s and part o f the substrate and stops. The k i n e t i c energy of the p a r t i c l e i s deposited along the p a r t i c l e track by i n t e r a c t i o n s with the electrons of the atoms of the j u n c t i o n - f i l m s and substrate material and the conduction electrons i n the metal, creating ions, and electrons with kinetic-energy mostly smaller than the energy of i o n i z a t i o n , a maximum energy of ~ 4m E^/M. (reference 2.7) where m = e l e c t r o n mass, Ep = p a r t i c l e energy and M = p a r t i c l e mass. The electrons with k i n e t i c energy greater than the i o n i z a t i o n energy can cause more i o n i z a t i o n . In the ju n c t i o n superconductive f i l m s some 'Cooper-pairs' are broken up to q u a s i p a r t i c l e s by i n t e r -actions with the primary p a r t i c l e and electrons and phonons with energy greater than the superconductor energy gap. This - 24 -r e s u l t s i n an abrupt increase of q u a s i p a r t i c l e s density and consequent increase of junction current. Thus f a r the analogy to the semiconductor-junction detector i s good, the q u a s i p a r t i c l e s t u n n e l l i n g corresponding to the charge c o l l e c t i o n i n the semi-conductor junctions. The Cooper p a i r s recombine with a time constant of the order of <10 8 sec. (reference 2.8). The p a r t i c l e energy i s thus 'thermalized'; i . e . may be considered to produce a l o c a l increase i n temperature. The r e s u l t a n t increase i n thermally generated q u a s i p a r t i c l e causes a corresponding increase i n the j u n c t i o n t u n n e l l i n g current. The p a r t i c l e energy deposited i n the substrate also thermalizes and warms up the substrate and the j u n c t i o n f i l m s near the p a r t i c l e track. This f u r t h e r contributes to the thermal generation of q u a s i p a r t i c l e s and t u n n e l l i n g current. Because of the small recombination and t h e r m a l i z a t i o n time-constant f o r the q u a s i p a r t i c l e s generated by the primary and secondary p a r t i c l e s as compared to the thermal time constants (of the order of microseconds), the signal-charge (which i s the time i n t e g r a l of the s i g n a l current) i s mostly derived from the thermal c o n t r i b u t i o n . This i s where the analogy to semiconductor-detectors i s no longer v a l i d . At 1.2 K f o r Sn, E gap/K RT = 12.08.Thus, f o r example, an increase of temperature of the junction ( r e s u l t i n g from the p a r t i c l e k i n e t i c energy) of 0.2 K to 1.4 K causes an increase i n the j u n c t i o n current of 464%, whereas f o r a S i j u n c t i o n detector at room temperature of 293 K, Egap/k RT = 42.78 the same increase i n temperature would cause increase i n thermally generated current o f only 3%. Further, the heat required to produce the change of temperature i s greater f o r the - 25 -room temperature S i case because of the g e n e r a l l y lower s p e c i f i c heats at cryogenic temperatures. Thus the thermally generated j u n c t i o n current r e s u l t i n g from the p a r t i c l e energy t h e r m a l i z i n g i s even l e s s f o r the semiconductor-junction detector. In contrast f o r the superconductive p a r t i c l e detector the j u n c t i o n s i g n a l -current i s p r a c t i c a l l y a l l due to the thermal c o n t r i b u t i o n , and i n the f o l l o w i n g chapter, the numerical c a l c u l a t i o n s of j u n c t i o n s i g n a l -current w i l l be based on t h i s thermal model. The following sections of t h i s chapter w i l l consider:-Physical models of 2 types of superconductive p a r t i c l e detectors, the glass substrate type, and the phonon b a r r i e r type. The f i r s t nodel applies d i r e c t l y to the experiments discussed, while the second i s a h y p o t h e t i c a l model, examined to see where ei t h e r experimental or t h e o r e t i c a l methods may be improved i n future. - S c a l i n g theory, which allows junctions with d i f f e r e n t parameters to be compared. - The response o f SS and NS junctions to steady and f l u c t u a t i n g temperature changes at d i f f e r e n t operating temperatures. - Noise inherent i n SS and NS superconductive q u a s i p a r t i c l e t u n n e l l i n g -j u n c t i o n s , i . e . Shot noise. - Oxide-barrier thickness f l u c t u a t i o n s and the e f f e c t on the s i g n a l ( i . e . p a r t i c l e s impacting a region with thinner o x i d e - b a r r i e r s than average would give a l a r g e r signal-charge because of the l a r g e r j u n c t i o n conductance per u n i t area i n the r e g i o n ) . - Angle of impact e f f e c t on the s i g n a l current waveform: (The - 26 -F i g . 2.4 A l p h a - P a r t i c l e Impinging on Glass Substrate Type Superconductive Q u a s i p a r t i c l e Tunnelling J un ct io n P a r t i c l e Detector. temperature contours in the STJ at an instant. F i g . 2.5 A l p h a - P a r t i c l e Impinging on Phonon-Barrier Type Superconductive Q u a s i p a r t i c l e T u n n e l l i n g Ju nc ti on P a r t i c l e Detector. - 27 -evolution of the thermal p r o f i l e s at the j u n c t i o n f i l m depends on the angle of impact of the p a r t i c l e ; the j u n c t i o n current waveform i s thus dependent on the angle o f impact). - Junction s i z e e f f e c t on the s i g n a l current waveform: - (The j u n c t i o n deposited on a glass substrate or a phonon-barrier has a f i n i t e area. As the j u n c t i o n current i s dependent on the temperature at each point of the j u n c t i o n , impacts at d i f f e r e n t points i n s i d e the j u n c t i o n area ( and outside, f o r the case of the g l a s s -substrate type) produce d i f f e r e n t thermal p r o f i l e s at the j u n c t i o n f i l m s and thus d i f f e r e n t j u n c t i o n current waveforms). - 28 -TYPES OF SUPERCONDUCTIVE PARTICLE DETECTORS 1. Glass Substrate Type This type of Superconductive P a r t i c l e detector c o n s i s t s of a superconductive t u n n e l l i n g j u n c t i o n deposited on and i n good thermal contact with a substrate which was a soda-glass micro-scope s l i d e . Referring to Figure (2.4), the p a r t i c l e deposits most of i t s energy i n the substrate which r e s u l t s i n a high temperature track, (the "heat-spike"). The heat then d i f f u s e s as described by c l a s s i c a l heat d i f f u s i o n equations. The tunnel-current density of the S.T.J, on the substrate at each point depends on the temperature at that p o i n t . The t o t a l increased tunnel-current i s the output s i g n a l current response. To s i m p l i f y the heat d i f f u s i o n problem the S.T.J, i s regarded as a thermometer s i t t i n g on the glass substrate, not s i g n i f i c a n t l y a f f e c t i n g heat-d i f f u s i o n i n the substrate. This assumption i s v a l i d i f the heat deposited i n the S.T.J, i s a n e g l i g i b l e f r a c t i o n of the t o t a l , and i f the heat capacity of the j u n c t i o n f i l m i s a small f r a c t i o n of that of the thermally a c t i v e p o r t i o n of the glass substrate, i . e . that part of the substrate down to the f u l l depth of the "heat-spike",) and i f heat conduction along the plane of the o junctions f i l m s i s small. The heat deposited i n 4000A of Sn i s 1.47 x lo 1 L f j o u l e s } n e g l i g i b l e compared to the t o t a l of 0.82 x 10~ 1 2 joules f o r the 5.13 MeV a - p a r t i c l e s used i n the experiments. The heat capacity o f a 0 . 2 m m x 0 . 2 m m x 4000A STJ i s 4.03 x 10~ 1 2 J/°K, the heat ca p a c i t y of the a c t i v e p o r t i o n of the glass substrate: 0.2 mm x 0.2 mm x 32 um i s = 14.84 x 1 0 ~ 1 2 - 29 -joules/deg.K, much la r g e r than that of the j u n c t i o n f i l m . F i n a l l y because of the small heat c o n d u c t i v i t y of bulk Sn (Superconducting) and further reduction of he a t - c o n d u c t i v i t y along the plane of the f i l m due to d i f f u s e d s c a t t e r i n g of q u a s i p a r t i c l e s and phonons at the f i l m boundary with o mean free path determined by the 2000A thickness of the STJ f i l m s , the heat c o n d u c t i v i t y along the plane of the f i l m i s a small f r a c t i o n of that of the glass substrate. The numerical d e t a i l s are given i n Chapter 3. Thus the s i m p l i f y i n g assumption i n the heat d i f f u s i o n problem i s j u s t i f i a b l e . Depending on the geometry of the s i t u a t i o n a 1, 2, or 3 dimensional non-linear p a r t i a l . - d i f f e r e n t i a l equation needs to be solved, the non-l i n e a r i t y coming from the temperature dependence of s p e c i f i c -heat and thermal con d u c t i v i t y . The s o l u t i o n of these heat-d i f f u s i o n problems i s po s s i b l e only by numerical methods described i n the next Chapter. This type of superconductive p a r t i c l e detector has inherently the worst r e s o l u t i o n o f the three types, the f a c t o r s degrading r e s o l u t i o n w i l l be described l a t e r i n t h i s chapter. This type of Superconductive p a r t i c l e detector (S.P.D.) i s the easiest to f a b r i c a t e , and once the d e t a i l s of the operation of t h i s type are understood, the operation of the other types can be predicted t h e o r e t i c a l l y with reasonable confidence. This type of Superconductive P a r t i c l e detector together with the phonon-b a r r i e r type are probably subject to r a d i a t i o n damage. The high-temperature p a r t i c l e track i n the j u n c t i o n f i l m s probably causes break-down of the b a r r i e r oxide (at the t r a c k ) , r e s u l t i n g - 30 -i n microshorts, and gradual degradation of the S.T.J. (The junctions appear to keep i n d e f i n i t e l y i f stored at 77°K, however some degradation i s noticable i f the j u n c t i o n i s exposed to the a - p a r t i c l e source during storage f o r a few weeks) . 2. Phonon-barrier type This type of Superconductive P a r t i c l e detector c o n s i s t s o f a S.T.J, deposited on a "phonon-barrier", a polymer of poor acoustical-match to the junction f i l m , f o r example polymerized photo-resist deposited on a glass substrate. The phonon-b a r r i e r i n h i b i t s heat flow between the j u n c t i o n f i l m and the substrate, and thus when a p a r t i c l e i s stopped i n the j u n c t i o n f i l m s the heat deposited e s s e n t i a l l y d i f f u s e s 2 -dimensionally (Figure 2.5) Because of the temperature dependence of s p e c i f i c heat and thermal conductivity, the h e a t - d i f f u s i o n problem can be solved only numerically, by methods described i n the next chapter. This type of S.P.Dean operate as a spectrometer only i f the p a r t i c l e i s stopped i n the junction f i l m s . Because of p r a c t i c a l d i f f i c u l t i e s i n f a b r i c a t i n g S.T.J.s 1 with t h i c k j u n c t i o n f i l m s , t h i s type of S.P.D. i s s u i t a b l e only f o r low energy p a r t i c l e s or X-rays. This type of S.P.D. should give b e t t e r r e s o l u t i o n of p a r t i c l e energy than the glass-substrate type. The phonon-b a r r i e r type, has yet to be f a b r i c a t e d and tested. - 31 -Scaling Theory From equations (2.8), (2.15) we see that I c , I are both d i r e c t l y p r o p o r t i o n a l to the normal tunnel conductance "G". Thus r for a given type of superconductor, the family of I, V, c h a r a c t e r i s t i c s with temperature as a parameter f o r any jun c t i o n can be obtained from a reference set by adju s t i n g the current-scale by m u l t i p l y i n g i t by a factor p r o p o r t i o n a l to the r a t i o of the normal tunnel conductances G / G r e £ . . Thus the c a l c u l a t e d signal-current response f o r a j u n c t i o n with a given normal t u n n e l l i n g conductance can be scaled to provide the s i g n a l - c u r r e n t response of a j u n c t i o n of the same ma t e r i a l having a d i f f e r e n t normal t u n n e l l i n g conductance exposed to the same temperature-profile as a function of time by simply changing the current-scale i n the r a t i o of normal tunnel conductances. From equations (2.10), and (2.16) we see that: 1 = G . F (T,V). (2.20) R d y n 1 This means f o r a given b i a s voltage V and temperature T, the junction dynamic conductance i s proportional to the normal t u n n e l l i n g conductance. This r e l a t i o n i s useful f o r checking the q u a l i t y of the j u n c t i o n : Because of the presence of leakage r e s i s t a n c e s across the j u n c t i o n 1 - £Fi (TiV) "dyn.G - 32 -Thus the r a t i o of measured maximum R^^ at a f i x e d temperature (for example 1.2 K) to the normal tunnel-resistance i s a measure of q u a l i t y (or lack of leakage) of the j u n c t i o n , independent of the act u a l junction parameters.' From equations (2.12), (2.19) we see that: ( f r 3 = GNN"F2 ( T I V ) ( 2 - 2 1 ) V That i s , f o r a given operating temperature and bias-voltage the current response to a given temperature change i s pr o p o r t i o n a l to the normal junction-tunnel conductance. From equations (2.16) and (2.17) we get: # > ' R dyn = F 2 / F l (2.22) v 1 which states the voltage-response to a given temperature change i s the same for a l l junctions with the same superconducting f i l m m a t e r i a l s , but course the measured voltage response depends on the c h a r a c t e r i s t i c s of the pr e a m p l i f i e r as well as the j u n c t i o n . Response of a S.T.J, to Small Temperature Changes In t h i s s e c t i o n we concentrate on the responses of a S.T.J, to a small temperature change 6T, because that i s a ba s i c property of the S.T.J, and i s not substrate dependent. In S.P.D. a p p l i c a t i o n s the substrate thermal p r o p e r t i e s , (of the junction f i l m thermal p r o p e r t i e s i n the case of the phonon-barrier type S.P.D.), determine the temperatur - 33 -Vs. time at each point of the S.T.J, (due to a p a r t i c l e impact) and the response of the S.P.D. r e s u l t s from the temperature increase at each point of the S.T.J. The responses of the S.T.J, to temperature change are expressed as functions of BA, i . e . using BA as a temperature parameter. Thi s i s accomplished by chosing the applied voltage V such that Ve i s some mu l t i p l e y of A (half the energy gap), where y i s determined by the desired bias point, constrained by the r e s t r i c t i o n s on V introduced i n de r i v i n g equations (2.8), (2.15). Using BA as a temperature parameter the response equations (and curves) are then a p p l i c a b l e to S.T.J.'s with any A. Superconductor - Superconductor (S.S) S.T.J. We choose V such that Ve = A, as that i s near the maximum R d y n p o i 1 1 * * a n ^ i s within the range f o r v a l i d i t y of equation (2.15). From equation (2.19) s u b s t i t u t i n g A for Ve and rearranging terms we get:-61 = 2 GNN a KB (BA) 2 e _ B A (1 - 2 e " B A ) . 6T (2.23) B A where we have set K l ^ A) = a (BA) e" For BA >, 3.5 (2.23) can be approximately represented by: ol = 2 GNN K KB (BA e " e A . 6T Thus we see that the current-response to 6T i s a monotonically decreasing function of BA, f o r BA^ 3.5. - 34 -Fig.2.6 Equivalent C i r c u i t f o r a Superconductive Q u a s i p a r t i c l e Tunnelling Junction. - 35 -In the following we work with the maximum frequency F o u r i e r component of a gaussian pulse, (angular frequency u>) to obtain a p e s s i m i s t i c approximate voltage response f o r the temperature pulse. Referring to Figure (2.6) the S.T.J, equivalent c i r c u i t , we see that the voltage response 6V to 6T i s : 6V = 61/ (jo)c T + -rJ— + — ^ (2-24) J Rdyn R l e a k For to -f o and R, , = °° (no leakage and slow temperature changes) 1 eak equation (2.24) becomes: 6 V = 6 1 Rdyn Substituting the expressive f o r R^yn equation (2.16) and r e p l a c i n g Ve by A, and 61 from (2.23) we get: 6V = ^ BA ( e S A -2) . 6T (2.25) The voltage response i s thus independent o f G, and increases monotonically with BA. This increase i s due to the r a p i d increase of R dyn w i t n BA, overcoming the decrease of 61. For p r a c t i c a l cases R leak i s f i n i t e . Thus the voltage response r i s e s i n i t i a l l y with increasing BA u n t i l R^^ becomes comparable with R leak, t h e r e a f t e r 6V/ST f a l l s with i n c r e a s i n g BA. For co 4 0 under conditions where (jto Cj) i s comparable to 1/Rdyn., the capacitance reactance acts as a shunting impedance across Rdyn. Thus the voltage response increases i n i t i a l l y 36 -with increasing 3A. i t i s conceivable that R may be eliminated with leak improved technology but j u n c t i o n capacitance Cj cannot be avoided. For the general case considering the e f f e c t of C. and R , s u b s t i t u t i n g J 1 eak the expression f o r 61 from equation (2.23) and from Equation (2.16) into equation (2.24) we get: 6V = 2 S ^ B ( B A 2 ) e " 3 A 6T / ( j ^ C , + * (2G B A e ^ K ^ B A ) e J K l e a k (2.26) The power-response 6W to 6T i s : 6W = 61.6V = 6 I 2 |Zj| (of t h i s a maximum of h i s a v a i l a b l e to a matched l o a d ) . For u + o and Rieak = °° using equations (2. 23), (2. 25) we get: 6 W = 2 GNN"K B 2 ( g A ) 3 ( 1 _ 2 e _ B A ) 2 6T 2 (2.27) e 2 For BA > 3.5 equation (2.36) can be approximated by 2G....aK 2 o W = — - — — (BA) 3 . 6T 2 (2.28) e 2 Thus the signal power increases as (BA) 3 and i s pr o p o r t i o n a l to G. This monotonic increase i n signal-power i s due to the r a p i d increase i n R^^, overcoming the decrease o f ( 6 1 ) 2 . When Rj_ e a^ i s f i n i t e , or the frequency =f 0 such that (jwCj) i s a s i g n i f i c a n t p o r t i o n of 1 / % y n - 37 -the increase i n \Zj\ i s l i m i t e d , and with increase of BA, 6W increases i n i t i a l l y , then decreases. Choice of S.T.J. f o r use as P a r t i c l e - d e t e c t o r s By using BA as the temperature parameter f o r expressing 61, 6V, 6W, the r e s u l t i n g equations apply to any S.S. S.T.J.'s. Thus the optimum BA operating values f o r maximum response to 6T are the same f o r a l l values of A. Total mean square noise voltage (for a l l frequencies) to be shown i n the "inherent-noise" s e c t i o n to be p r o p o r t i o n a l to A, thus f o r a given G, and C , (and bandwidth) we use the smallest A such that at the lowest operating temperature BA i s the value f o r maximum ( V response to thermal input /Vn T o t a l ) • Another f a c t o r favouring small A and low operating temperatures f o r S.T.J, used as p a r t i c l e detectors i s the decrease of s p e c i f i c heat of the substrate and the j u n c t i o n f i l m s with decrease of temperature. Summing up the choice of A: use the lowest a v a i l a b l e A the value consistent with being able to operate at the optimum BA value. Metal-Superconductor (N.S.) S.T.J. From equation (2.12) and choosing the bias voltage V such that eV = A/2, close to the maximum dynamic impedance point, we get: 61 = (BA) 2 e - BA 1 [1 - 3 e " p u ] . 6T. (2.29) 38 We have BA as the only temperature dependent parameter, thus B A t h i s equation describes a l l N.S. junctions biased at V = /2e. As i n the S.S. case the approximations leading to t h i s equation i s v a l i d f o r BA > 3.5. _BA From (2.29) we can see that f o r large BA,61 i s p r o p o r t i o n a l to (BA) 2e "Z-, and decreases monotonically with BA. From Figure (2. D) we a r r i v e at the same equation f o r 6V as i n the S.S. S.T.J, case (given by equation (2.24)). 6 V = 6 1 7 ( j ^ J ^dyn + ^leak 3 For ai + o and R leak = °° i . e . no leakage and low frequency temperature changes, we have: SV = 6 L R d y n s u b s t i t u t i n g f o r R. from equation (2.2) and j f o r Ve, and 61 from (2.29) we get: 6V = ^ A I1 ~ Q A 1 fiT. (2.30) 2 e l + e " e A - KR ^ BA . 6T f o r (large) BA > 3.5 2e Thus the voltage response as i n the S.S. S.T.J, case i s independent of junction normal tunnel-conductance G N N, and 6V increases l i n e a r l y with BA increase. With the presence of R j g ^ , SV increases i n i t i a l l y with BA u n t i l the increase i n R d y n m a k e s R l e a k s i g n i f i c a n t , then 6V decreases as the decrease i n 61. For ID =[ o as i n the S.S. S.T.J, case the reactance o f Cj acts as a shunting impedance, causing a decrease i n 6V with i n c r e a s i n g BA when Rdyn* i s comparable to | Xc | . - 39 -The power response'6W to 6T i s : 6W = 61. 6V = 6 I 2 | Z J | for u -»• o.and R l e a k = °S using equations (2.29), (2.30) we get: G K 2 6_A_ „ -BA 5 2 ,~ NN B , « A . 3 - 2 1 - 3e °T (2.31) 6W = - ( S A r e z : pTT-4e 1 + e G M MaK 2 BA z M - ^ - (BA)3 e" "Z- 6T 2 Thus the s i g n a l power i n i t i a l l y increases as i n the S.S. S.T.J, case _£A as (BA) 3 then decreases, damped by the e 2 f a c t o r from the current response, even f o r an i d e a l j u n c t i o n . . The maximum occurs at BA ~ 6. Comparisons of N.S. and S.S. S.T.J.'s From equations (2.23) and (2.29) we get f o r N.S., and S.S. S.T.J, with the same and biased r e s p e c t i v e l y at V = , and V = | <5I " -BA — = 4 6 I" ^ ( 2 ' 3 2 ) 6 INS 1 ~ 3 e BA = 4 e~ " 2 _ Thus f o r BA > 2.8 the r a t i o i s < 1, and decreases f o r increasing BA. This r e s u l t o r i g i n a t e s from the f a c t that f o r a q u a s i - p a r t i c l e to tunnel i n the N.S. j u n c t i o n at zero b i a s the energy needed i s A, whereas 2A i s needed i n the case o f S.S. j u n c t i o n s . - 40 -From equations ( 2 . 2 4 ) and ( 2 . 3 0 ) f o r N.S. and S.S. S.T.J.<s with the same A , „ A r c-nA Viiacprl r e s n e c t i v e l v at V = NN ' L J J G ^ , C T, a d b sed p y ^ and V = ^ - , we get: \ 6 V •61 _ / (VPy 03 . • R R . ^ d y n S S * V R l e a k + Jw C j) "NS- 7 ( 1 / R d y n N S + 1 / R l e a k + S u b s t i t u t i n g f o r 6Iss/6Ins from equation (2.32) and using the expressions f o r R d y n s s , RdyriNS> w e § e t : ( 5 V s s \ 2e BA ( e - 3 / 2 g A - 1) ( l 7 R l e a k + ^ C^RdynSS + J w C j + l 7 R l e a k ) (2.33) For co ->- o and Rieak = °° \ NS/ BA (2.34) OJ ~ 2e Thus f o r low frequencies the S.S. S.T.J, gives b e t t e r voltage response, the d i f f e r e n c e increasing with BA. " For toCj R d y n » 1. / ! ! § s \ BA (0 -* do = 4e (2.35) - 41 This"-results, from the j u n c t i o n capacitance swamping the R^yn* of the junctions, making the junctions e s s e n t i a l l y equal i n impedance leaving the voltage r a t i o s equal to the current r a t i o s . This does not occur u n t i l u _10 9 -*10 1 0 f o r the ju n c t i o n s of i n t e r e s t . For p a r t i c l e detector a p p l i c a t i o n s u) _ 10 6 and equation (2.34) s t i l l a p p l i e s . From the equation f o r 6 >v (2.27) and (2.31), f o r ui o, R leak -> °° and b i a s i n g at V = ^ — , and V = — f o r N.S. and S.S. junctions r e s p e c t i v e l y , we get: (1 - 2e- B A) 2 . ( 1 '* e- B A) = 2 e B A / 2 (2.36) = „ ..-BA, 2 . _6A (1 - - 3 e : p u ) We see that f o r low frequencies f o r which |XCj| » R d y n s s t h e S ' S ' junctions give b e t t e r signal-power. The r a t i o (2.36) i s s i g n i f i c a n t when amplifier-noise i s the dominating f a c t o r . Performance f i g u r e s f o r S.S. S.T.J.'s . A useful performance parameter r e l a t i n g to current response of a S.T.J, i s the current-response per degree change i n temperature, per u n i t junction normal tunnel conductance. From equation (2.23) we get: (9_I_) 2 K : 8 T = K i (BA) 2 (BA) 2 ( 1 - 2 e _ B A ) (2.37) GNN F i g . 2.7 Current Response S e n s i t i v i t y Per Unit Junction Normal Tunnel Conductance. - 43 -F i g . 2.8 Voltage Response S e n s i t i v i t y , Frequency as Parameter. - 44 -where Kx (BA) i s the modified 1st order Bessel function of the second kind. The function of equation (2.37) i s p l o t t e d i n Figure (2.7) and i t shows c l e a r l y the decrease of the normalized current response with increase of BA. With the voltage-response i t i s not p o s s i b l e to get such u n i v e r s a l l y a p p l i c a b l e r e l a t i o n as (2.37) because of j u n c t i o n capacitance which i s a d i f f e r e n t function of area and b a r r i e r thickness than G, and R j g ^ can be any value, except f o r the s p e c i a l case of -t o and R q e ak = 0 0. For t h i s s p e c i a l case representing low-frequency temperature changes and no leak i n the juncti o n , from equation (2.25) (-|f) = -T 3A (e B A - 2) (2.38) For usCj 5 1 where the e f f e c t of Cj i s s i g n i f i c a n t i t becomes necessary to use examples. We take f o r t h i s example the parameters of a junction we used i n an experiment, as shown below:-"V = 72-5 c ter * oiar'"1 10 dyn Cj = 1500 pF A = 0.8905 x 1 0 " 2 2 J at 1.2°K corresponding to BA = 5.375, The voltage response curves are shown i n Figure (2.8). They were calculated using 3V SS 8T 81 —SS. . r i w c + _1 r l dyn - 45 -The curves c l e a r l y show the increase of W with increase of £A 0 i and f o r the co = 10 6 curve the decrease of -^ p- (OJ) beyond BA = 5.8. The other curves (w = 10 2 , IO 4 ) would also show such a d e c l i n e i n — for s u f f i c i e n t l y high BA. Inherent E l e c t r i c a l Noise i n S.T.J.'s Because of the low temperature of operation of the S.T.J.'s the only e l e c t r i c a l noise of s i g n i f i c a n c e , i s shot-noise from the j u n c t i o n bias-current. The equivalent c i r c u i t of Figure (2.6) i s used f o r the following c a l c u l a t i o n s . Shot-noise:-^ s h o t = 2 1 e A f (2.39) where I_ = bias current Qp Af = frequency i n t e r v a l of i n t e r e s t . Rd 2 U 2 = f T 2 A-F N shot J AN shot * ? n * o 1 + < D Z C / R , Z J a JUL Rd tan ("o (2.4.0) 46 -where: UQ = the high frequency l i m i t o f the frequency band of i n t e r e s t , here we go from to = 0 to to = to R d (/R + / R ) 1 > the e f f e c t i v e dynamic resistance, dyn leak *"Rdyn i s t h e i n h e r e n t j u n c t i o n dynamic re s i s t a n c e ) . from (2.40) the noise power c o n t r i b u t i o n o f shot noise i s : ^ = V N 2/R = !SE^ t a n " 1 ( a > o C j V shot i : . C T For the s p e c i a l case of to = °° o I/A • e. R , QP d 2 <li> a N , = - ~ (2-46) shot 2C I N .e PN = (2.43) shot 2C T - 47 -The noise powers are u s e f u l i n determining the a m p l i f i e r noise l e v e l to aim f o r to take advantage of the f u l l c a p a b i l i t y o f the superconductive p a r t i c l e detector. For t y p i c a l operating frequency bandwidth of 10 6 Hz , Cj - 2000 pF and R d y n ~ 100 t a n " 1 (woCj R ) * 51.5°, that i s , the noise i s about 0.57 of the a l l frequency case. Note that the above equations (2.40) to (2.43) a p p l i e s to both N.S. and S.S. S.X.J.' s. For S.S. junctions we get from equations (2.15), (2.16) I c c and R bo dyn and s u b s t i t u t i n g i n equation (2.42) we get: BA V..2 , + = A zJ± ( 2 W) S h 0 t S S 2 Cj BA . C ^ For N.S. we get from equations (2.8) and (2.10) I and R dyn (N.S.) ns J J and s u b s t i t u t i n g i n equation (2.42) we get :-V 2 - tanh (BA/2) f_ -VN shot X T C " — W ~ C 2 - 4 5 ) NS J In the above equations f o r mean-square noise voltages the j u n c t i o n normal-tunnelling conductance does not appear as a r e s u l t of our assumption of no leakage, thus f o r shot-noise the I (and I M C ) and R SS Nb dynSS (and R ^ y ^ g ) dependences on G ^ cancels. The above equations are written with BA grouped as a parameter. In equations (2.44) and (2.45) we see A m u l t i p l i e d i n t o functions of BA, which because of BA dependence apply to a l l superconductive q u a s i p a r t i c l e t u n n e l l i n g j u n c t i o n s . The - 48 -presence of A thus i n d i c a t e a l i n e a r dependence of mean square noise voltages on A . Since we previous found (equation (2.25))that the voltage response i s independent of A f o r junctions operating at the same B A , the s i g n a l to noise r a t i o i s dependent on V A . For S.S. junctions we get the noise power from equations (2.44) (2.16):-PN t o t a ! = PN shot " ^ p M M > [1 - <2-«>> and f o r N.S. junctions we get the noise power from equations (2.45) (2.10):-N t o t a l s ^ s h o t ' ^ C 1 K l « « C o s h ( 6 4 / 2 ) (2.47) The noise power and mean-square noise voltages a l s o depend l i n e a r l y on A . The noise powers are also proportional to G, (as f o r signal-power). From equations (2.46) (2.47) we get the r a t i o of noise powers f o r S.S, 'NN' and N.S. junctions (with the same G , C T and biased at V = A/e and V = A / 2 e r e s p e c t i v e l y , W Q = 0 0 a n d R i e a ] c = 0 0 ) PNT SS ( 1 - e " } = 2 e " B A / 2 tanh(6A/ 2) (2.48) — Cosh (3A/ 2 NT NS 2 e-£A/2. approximations v a l i d f o r BA > 3.5 - 49 -or -particle F i g . 2.9 V a r i a t i o n of Signal due to Angle o f Incidence of Impinging P a r t i c l e . temperature contours at an instant F i g . 2.10 V a r i a t i o n of Signal due to Impact of Incoming P a r t i c l e at D i f f e r e n t Points of a F i n i t e Sized Junction. - 50 -We see that the noise power i s smaller for S.S. j u n c t i o n s . We can get the power signa l - t o - n o i s e ratios(S.N.R.) from equations (2.36), and (2.48) 6A power " e (2.49) S.N.R. ~ e We see that S.S. junctions are c l e a r l y favoured f o r use as superconductive p a r t i c l e detectors, where the frequency response required i s smaller than 6 9 10 Hz, ( f a r below 10 Hz when N.S. junctions show comparable performance.) Other factors a f f e c t i n g the r e s o l u t i o n o f SPD': S t a t i s t i c a l f l u c t u a t i o n of t o t a l number N o f charge c a r r i e r s generated by  p a r t i c l e . This e f f e c t has been considered i n d e t a i l i n Chapter 1. As the f l u c t u a t i o n s i n the number i s o f the order o f /~N" the loss o f r e s o l u t i o n due to t h i s e f f e c t i s /N = // N . This favours a large s i g n a l current, thus small A. B a r r i e r oxide thickness f l u c t u a t i o n . Due to the f l u c t u a t i o n o f oxide thickness the l o c a l tunnel cond per u n i t area can f l u c t u a t e and thus cause v a r i a t i o n i n output current with impact l o c a t i o n . This f a c t o r was investigated t h e o r e t i c a l l y and was found to be i n s i g n i f i c a n t due to the r e l a t i v e l y large area o f increased temperature as compared to the s i z e of an area i n which the average deviation from the mean thickness i s s i g n i f i c a n t . Angle E f f e c t . The angle of the p a r t i c l e track r e l a t i v e to the substrate surface o f the STJ f o r the glass-substrate type p a r t i c l e d e t e c t o r s , can cause changes i n output s i g n a l waveform. The two extreme cases are normal-incidence and grazing-incidence. The l a t t e r shows a higher s i g n a l waveform amplitude, but decays f a s t e r as compared to the former, as expected from the p h y s i c a l s i t u a t i o n shown i n F i g . (2. 9 ) . C a l c u l a t i o n s to be - 51 -described i n the "numerical c a l c u l a t i o n s " chapter to follow give d e t a i l s on the c a l c u l a t i o n s performed to estimate t h i s e f f e c t . The 'angle-effect' does not e x i s t f o r the heat-sink chip type of p a r t i c l e detector where the heat pulse i s assumed to be spread uniformly i n the chip i n n e g l i g i b l e time i n r e l a t i o n to thermal r e l a x a t i o n and e l e c t r i c a l time-constants o f the STJ; or the phonon-barrier type where the heat-spread i s e s s e n t i a l l y 2-dimensional. F i n i t e Junction-Size E f f e c t . The e f f e c t i s so named because the p a r t i c l e can impact at the edge or outside the j u n c t i o n , a l s o the thermally a f f e c t e d zone of s i g n i f i c a n c e can be greater than the j u n c t i o n - s i z e . The s i g n a l output depends on the point o f impact of the p a r t i c l e , as can be seen from F i g . (2.1 .) , where the temperature contours at an i n s t a n t due to a p a r t i c l e impact are drawn and the STJ o u t l i n e superimposed at 3 d i f f e r e n t r e l a t i v e l o c a t i o n s . I t i s c l e a r that l o c a t i o n (1) gives the greatest s i g n a l , and at (3) the s i g n a l decays more r a p i d l y than at (2). This e f f e c t was so dominant that no energy ' l i n e 1 or 'peak' was v i s i b l e i n the analysis o f the output s i g n a l s by a pulse amplitude analyser. Instead a r e l a t i v e l y sharp high-energy end cut o f f , corresponding to signal-output due to impacts i n the c e n t r a l regions o f the STJ, was observed. This e f f e c t i s c a l c u l a t e d i n d e t a i l i n the "numerical c a l c u l a t i o n s " Chapter 3. This e f f e c t occurs to a l e s s e r extent f o r the phonon-barrier type o f p a r t i c l e detector. Here i t i s properly c a l l e d "Edge e f f e c t " , because the substrate i s absent thermally, impact near the edge does not cause heat to be l o s t to the STJ ( i f the e l e c t r i c a l contacts are such as to minimize heat l o s s ) , but the s i g n a l output i s a f f e c t e d because of the d i f f e r e n t time-development o f temperature contours. CHAPTER THREE NUMERICAL METHODS AND RESULTS INTRODUCTION In the previous Chapter t h e o r e t i c a l expressions fox the c h a r a c t e r i s t i c s of STJ were derived, i n p a r t i c u l a r the response of the STJ to a small temperature change was c a l c u l a t e d . Except f o r the case of the "heat-sink chip" model the temperature of the junction as a fun c t i o n of time and p o s i t i o n on the ju n c t i o n , could not be c a l c u l a t e d a n a l y t i c a l l y because of the ra p i d change of thermal-constant values with temperature at the low temperatures. Consequently numerical solutions of the non-linear heat d i f f u s i o n problems had to be made. In t h i s Chapter the method of f i n i t e d i f f e r e n c e s with v a r i o u s l y 1,2, and 3 dimensional arrays of c e l l s i s ap p l i e d to the ca l c u -l a t i o n of temperatures i n the phonon-barrier and glass-substrated SPDs. (The phonon-barrier superconductive p a r t i c l e detector was not f a b r i c a t e d . C a l c u l a t i o n s were made only to estimate the performance of t h i s p o s s i b l e type of p a r t i c l e d e t e c t o r ) . M o d i f i c a t i o n of the form o f the c l a s s i c a l h e a t - d i f f u s i o n equation The c l a s s i c a l h e a t - d i f f u s i o n equation f o r temperature dependent s p e c i f i c heat Cp(T), thermal c o n d u c t i v i t y K(T) and density p(T) i s : V • (K(T)-VT) = Cp(T)p. |I ( 3 - 53 -In t h i s form the equation i s too complicated f o r e f f e c t i v e numerical s o l u t i o n . The equation can be s i m p l i f i e d using the methods described i n Jaeger and Carslaw (Ref. 3.4). We define a transformed temperature 6(T) by 1 t *• J Ko T K(TjdT' (3 To where To i s a reference temperature equal to or l e s s than the lowest temperature of the system under consideration, and Ko i s an a r b i t r a r y constant. Note that 6(T) i s a monotonically i n c r e a s i n g f u n c t i o n of T by i t s d e f i n i t i o n . Using equation (3.2) we get: v e m - t ^ - t . ) • e m . i f J E L ? d6_ 3T -> dT ' jx. e i Thus equation (3.1) can be written as: V ' (KoVB(T)) = KoV 26(T) = Cp(T)p(T) Since |I = * L m 36 = JCp_ . 36 3t d6 3f K(T) 3t 3T 3t (3, (3«3) becomes: 54 V2fl - CPCT(6))P(T(8J J . 89 K(T(0)) 3t ( 3- 4) Equation (3.4) i s much more s u i t a b l e than (3.1) f o r numerical s o l u t i o n s . Boundary conditions f o r the heat d i f f u s i o n problem g l a s s - s u b s t r a t e type  superconductive p a r t i c l e detector The g l a s s - s u b s t r a t e superconductive p a r t i c l e detector i s shown i n Figure 2.1 of Chapter 2. The top-surfaces of the j u n c t i o n f i l m and that of the glass substrate not under the j u n c t i o n f i l m are considered i n s u l a t i n g boundaries. I f the surfaces were coated with a p r o t e c t i v e l a y e r of r o s i n (see Chapter 4 f o r d e t a i l s of p r o t e c t i v e l a y e r ) , t h i s layer would form a phonon-barrier. A l t e r n a t i v e l y the j u n c t i o n f i l m surface or glass surface and the s u p e r - f l u i d f i l m which i s assumed to cover the j u n c t i o n f i l m at the operating temperature of 1.2 K, constitutes an i n s u l a t i n g boundary because of the a c o u s t i c a l mismatch R e f * ( 3 . 1 ) y^e g i a s s _ m e t a l ( j unction f i l m ) i n t e r f a c e i s considered to be thermally well coupled to the g l a s s substrate at the glass metal i n t e r f a c e . For the present experiment 98% of the a - p a r t i c l e energy (5.13 MeV) was deposited i n the glass substrate. Thus to s i m p l i f y the computational problem the p a r t i c l e energy was assumed to be a l l deposited i n the substrate. The superconductive t u n n e l l i n g junction i s assumed to be a thermometer, the thermal-presence of which was ignored i n the c a l c u l a t i o n s . T h i s approximation i s v a l i d only i f the heat-capacity of the j u n c t i o n f i l m i s a small f r a c t i o n o f that of the heat a f f e c t e d volume of the glass substrate, and i f the thermal conductance from the impact zone along the plane of the junction f i l m i s small compared to that of the heat a f f e c t e d volume of - 55 -glass. The heat ca p a c i t y of the 0.2 mm x 0.2 mm x 4000A Sn j u n c t i o n f i l m s -12 was 1.03 x 10 J / K, as compared to the heat capacity of the heat affected volume of glass O 0 . 2 mm x 0.2 mm x 32u) of 1.484 x 1 0 - 1 1 g i v i n g a r a t i o of 0.07. Thus we can ignore the heat-capacity of the j u n c t i o n films without introducing too much er r o r . Because of the small f i l m thickness of 2000A and the low temperatures and consequently long mean f r e e path, boundary s c a t t e r i n g of electrons and phonons becomes very prominant and d r a s t i c a l l y decrease the thermal conductivity. D e r i v i n g a value f o r the f i l m thermal c o n d u c t i v i t y r e q u i r e s a chain of arguments, i n which the most p e s s i m i s t i c supportable e x t r a p o l a t i o n procedures have been used i n order to a r r i v e at a v a l i d upper l i m i t . From Andrew's (Ref. 3.7) data i n Table 2 of h i s paper we can derive the r e s i s t i v i t y r a t i o p / i (where p p = f o i l r e s i s t i v i t y (for a PB 13.8K 3.34u Sn f o i l i n t h i s case) and p^ = bulk r e s i s t i v i t y (using the value given f o r a 1950y t h i c k f o i l ) ) as follows: P F 3.8K j PB 3.8K = P F 3.8K  P F 291K PB 291K PB 3.8K Here, we have set Pp 291K = P B 291 D e c a u s e °f small e l e c t r o n mean f r e e path at 291K as compared to the f o i l thickness. Thus from Andrew's data fo r h i s specimen E18, f o i l thickness = 3.34u , p„ _ 0 J p „ ~ n-, v = 20.1 x I O - 4 -4 and f o r specimen E7 f o i l thickness = 1950y , p D _ 0 „ / P r , o r i n i , = 1.80 x 10 , we get: - 56 -:PF 3.8K  PB 3.8K = 11.167 Using the Fuchs-Sondheimer formula f o r s i z e e f f e c t on r e s i s t i v i t y r a t i o (Ref.3.9) f o r x = where t . f i l m thickness and 1= electron mean fre e path, f o r diffuse s c a t t e r i n g at f i l m boundarie ies: ~ = 0.75x- (0.423 - Zn x) F i t was p o s s i b l e to solve f o r x given p^/p^. r is Using the above P p / P B | 3 8 K x =109.2. The electron mean free path i s expected to increase with decreasing temperature, thus t h i s r a t i o should be larger at 1.2"K, our operating temperature f o r the j u n c t i o n . To get some idea of the value at 1.2 K, the r e s i s t i v i t y r a t i o p c / p c f o r r B Andrew's specimen E18 were p l o t t e d vs. temperature and extrapolated g r a p h i c a l l y to 1.2 "K. It was found that the r a t i o was most probably greater than 14, corresponding to a c a l c u l a t e d e l e c t r o n mean fr e e path o f > 0.15 mm. Thus f o r normal Sn at 1.2 K the r e s i s t i v i t y r a t i o Pp/Pg c a l c u l a t e d using the Fuchs-Sondheimer formula was > 142, ( f o r f i l m thickness = 2000A). For superconducting Sn, the mean f r e e path of the q u a s i p a r t i c l e s would be of the order of normal Sn conduction e l e c t r o n mean fr e e path value. Some of the conduction electrons condense to form Cooper-pairs, removing them from heat conduction c o n t r i b u t i o n s . When the q u a s i p a r t i c l e s form the major co n t r i b u t i o n to the thermal c o n d u c t i v i t y , then the Wiedemann-Franz Law ^ K 2 (K — J L T . a ) applies and the thermal conductivity r a t i o s of the 3e 2 - 57 -f i l m to bulk value i s the same f o r the corresponding r a t i o s of e l e c t r i c a l c o n d u c t i v i t y . The phonon cont r i b u t i o n to thermal c o n d u c t i v i t y becomes s i g n i f i c a n t at lower temperatures (for To <0.3Tc See Ref. 3.15) with decrease o f q u a s i p a r t i c l e density. Size e f f e c t reduction o f thermal co n d u c t i v i t y c o n t r i b u t i o n of the phonon component due to f i l m boundary (Ref 3 8) s c a t t e r i n g also occurs^ * ; . In general i t i s expected that the phonon mean free path i s not smaller than the e l e c t r o n mean fr e e path. Thus i t i s reasonable to assume the same s i z e e f f e c t reduction f a c t o r f o r the phonon component of thermal c o n d u c t i v i t y as f o r the el e c t r o n component. Therefore: = ^Fph = SQp_ = ^ F e l _ = ^Fel_ KB ] T,t KBph KBQp K B e l a B e l where K = f i l m thermal conductivity, a = e l e c t r i c a l c o n d u c t i v i t y . Subscripts F = f i l m , B = bulk, Ph = phonon, Qp = q u a s i p a r t i c l e , e l = e l e c t r o n . In conclusion, VKB | Sn.1.2 < 1 / 1 4 2 ' and since K B | gn 1 2K = 7 1 w / m K (Ref.3.5) we get K p j S n n 2K ° - 5 0 0 w / m K > i n the plane of the f i l m . Thus the r a t i o of ( r a d i a l ) thermo-conductance of j u n c t i o n f i l m s to that 2tK p o f the heat a f f e c t e d volume of glass = - 0 • 178 - 58 -thermal conductivity of Sn f i l m i n the plane of the f i l m at 1.2K = 0.500 w/mk K, G thermal conductivity of glass = 0.035 w/mk at 1.2K where Z penetration depth of the a p a r t i c l e i n gla s s = 32y t thickness of Sn junction f i l m , f a c t o r 2 because of the two layers of junction f i l m s . We see that the j u n c t i o n f i l m does play a part i n heat transport but can be ignored to a f i r s t approximation. The e f f e c t of the heat transport by the junction f i l m i s to increase the rate of heat d i s s i p a t i o n from the hot central region of the a - p a r t i c l e impact and decrease the s i g n a l current decay time constant. Phonon-barrier type superconductive p a r t i c l e detector The s t r u c t u r e of the proposed phonon-barrier type superconductive p a r t i c l e detector i s shown i n Figure 2.2 of Chapter 2. The performance of t h i s type of superconductive p a r t i c l e detector i s expected to be b e t t e r than the glass- s u b s t r a t e type, i n p a r t i c u l a r at low p a r t i c l e energies, and i s easier to f a b r i c a t e than the heat-sink chip type superconductive p a r t i c l e detector. Thus the performance figures are of s u f f i c i e n t i n t e r e s t to j u s t i f y the numerical c a l c u l a t i o n s to derive them. The top surface of the junction f i l m s as i n the glass substrate type p a r t i c l e detector i s an i n s u l a t i n g boundary, f o r the same reason. The bottom of the j u n c t i o n f i l m s i n contact with the phonon-barrier l a y e r i s also an i n s u l a t i n g boundary. Thus the heat flow i s e s s e n t i a l l y 2-dimensional, cr - PART ICLE T R A J E C T O R Y GLASS a - P A R T I C L E GENERATED HEATSPIKE TEMP. CONTOURS c r -PART ICLE T R A J E C T O R Y S T J i_ mmn INFINITE LENGTH H E A T TRACK U3 FIG. 3.1A a-PARTICLE PENETRATING A GLASS -SUBSTRATED STJ.. ' FIG. 3.IB 1-DIM. RADIALLY SYMMETRIC APPROX. OF AN a-PARTICLE PENETRATING A GLASS-SUBSTRATED STJ.• 60 in the plane of the junction film between the two insulating boundaries. (Note that as above, because of size effect the thermal conductivity along the direction of the film is reduced and this reduced value must he used in the calculations. Numerical solutions with radial symmetry An a-particle penetrates a glass-substrated STJ at normal incidence, shown in Fig.3.la. Restricting ourselves to early times of the a-particle induced temperature-transient (time shorter than that required for significant heat to diffuse a distance equal to the depth of penetration of the heat spike into the substrate), the temperature profiles at the surface (with insulating boundary condition) can be approximated by a 1-dimensional radially symmetric model shown in Fig.3.lb, with the i n i t i a l deposition of heat per unit length along the symmetry axis given by the average heat deposited per unit length in the a-particle generated heat-track ( R** ?' 3) ("heat spike"). This approximation results in R the radius being the only spatial coordinate for temperature. In Fig.2.2 and in associated discussions in Chapter 2, page 5, we saw that for the phonon-barrier type SPD the heat diffusion essentially occurs 2-dimensionally along the plane of the junction film. Ignoring the edge boundaries of the junction films, a valid approximation for impacts in the central area of the junctions, the heat diffusion problem resulting from an a-particle impact is radially symmetric. It therefore differs from the glass-substrate case only in that the diffusion equation uses the thermal properties of the metal film. Thus the heat diffusion problem can be approximated by the cylindrical symmetry as shown in Fig.3.lb, with the - 6 1 -i n i t i a l deposition of heat per un i t length i n the axis given by the heat deposited i n the f i l m d i v i d e d by the f i l m t h ickness. T r a n s l a t i o n to F i n i t e - D i f f e r e n c e s equations From Equation (3.4) s u b s t i t u t i n g the Laplacian f o r r a d i a l symmetry, we get: V 2 Q = I f ! + I 3£ = Cp(T(6)) -p(T(6)) m 96 9 r 2 r 9r K(T(G)) 3t (Ref 3 4) Trans l a t i n g to f i n i t e d i f f e r e n c e s * ' using r = me , and t = nx we gel 96(r,t) 6m+l, n - 6m-l, n 8m+I, n - 6m,n 9r = 2e °R E where 6m,n = 8(me,mr) = 6 ( r , t ) . Both forms of the f i r s t d e r i v a t i v e are given because the f i r s t i s used as the expression f o r the f i r s t d e r i v a t i v e , and the second i s used to derive the second d e r i v a t i v e expression shown below: — < — > — [6m+l,n - 26m,n +6m-l,n] 9 t 2 e 2 Thus V 2 e 4 - > 2 m e 2 " f C 2 m + 1 ) Q m + l , n - 4m6m,n + (2m - l ) 6m - l , n ] - 62 -further Thus Equation (3.5) written i n f i n i t e d i f f e r e n c e s form i s as fo l l o w s : 1 (6m,n+1 - 6m,n) 2me2 (3.6) Solving (3.6) f o r 8m,n+1 we get: 6m,n+1 = K T [(2m+l) 9m+l,n - 4m8m,n + (2m-l) 6m-l,n] + 6m,n Cpp 2me2 (3.7) The Equation (3.7) gives the transformed temperature at r = me(cell 'm') at time t = (n+l)x i n terms of the transformed temperatures of i t s e l f and i t s neighbours at time t = nx. Using the c o n f i g u r a t i o n shown i n Fig.3.lb f o r ' c e l l s ' , 'm' takes h a l f integer values (%,1%,2%...) m = 0 does not occur, thus avoiding the s i n g u l a r i t y f o r r = 0 (m = 0), ensuring the v a l i d i t y of (3.7) f o r a l l the m values used. For the c a l c u l a t i o n s of 6%,n+1 we need the values of 8-%,n. This value i s provided by the a x i a l "boundary" condition, 8T namely no heat flows into or out of the axis, thus = 0 at r = 0, 38 implying — = 0 at the axis because of the monotonic dependence of 9 on T. This i s equivalent to the f i n i t e d i f f e r e n c e expression f o r an i n s u l a t i n g boundary namely 0-%,n = 8%,n, which i s the required expression f o r 6-%n. - 63 -I n i t i a l and boundary conditions For the present problem the energy of the a - p a r t i c l e was assumed to be deposited as heat i n the a x i a l c e l l (m=%). The r e s u l t i n g temperature and transformed temperature 6 of the a x i a l c e l l was c a l c u l a t e d and the transformed temperature used as the i n i t i a l 8 of the m=h c e l l . The r e s t of the c e l l s s t a r t at the operating bath temperature expressed i n 8. It i s not p o s s i b l e to have boundaries at i n f i n i t y i n a f i n i t e d i f f e r e n c e problem, but the boundary can be placed s u f f i c i e n t l y f a r away such that the e f f e c t of heat-flow or lack of heat-flow through the boundary (corres-ponding to constant temperature and i n s u l a t i n g boundary co n d i t i o n s respect-i v e l y ) i s n e g l i g i b l e f o r the duration of p h y s i c a l i n t e r e s t . For the s o l u t i o discussed i n t h i s Chapter, the boundary c e l l s were f i x e d i n temperature at the "bath-temperature", i . e . a constant temperature outer boundary condition was used. Thermophysical data used f o r numerical c a l c u l a t i o n s Since the p r o p e r t i e s of the glass substrates used (Corning "Process Clean" #2947 microscope s l i d e s ) were not a v a i l a b l e i n the l i t e r a t u r e or from Corning, values of s p e c i f i c heat Cp(T) and thermal c o n d u c t i v i t y K(T) were taken from References (3.10), (3.11) r e s p e c t i v e l y . The Cp(T) values From Reference (3.10) are f o r "pyrex" glass and the values were provided for IK to 20K. The thermal condu c t i v i t y values given i n Reference (3.11) were 'averages' o f quartz, pyrex and b o r o s i l i c a t e g lasses, and values were given down to 4K. Values of K(T), f o r IK to 4K were obtained by extra-polating a 6(T) (thermal boundary p o t e n t i a l ) vs. T curve f o r pyrex gla s s , Ref. (3.12), then c a l c u l a t i n g K(T) by the r e l a t i o n K(T) = . The K(T) - 64 -TEMP.K CpCT)J/Kg.K KCnW/m°K TEMP.K Cp(T)J/Kg.K K(T)W/m-K 1.0 0.109xl0 _ 1 0.305xl0 _ 1 5.5 0.590 0.110 1.2 0.126 II 0.350 II 6.0 0.770 0.113 1.4 0.142 it 0.400 II 6.5 0.100x10 0.115 1.6 0.163 ti 0.460 II 7.0 0.130 II 0.117 1.8 0.197 II 0.520 II 8.0 0.200 II 0.119 2.0 0.238 I I 0.570 II 9.0 0.300 II 0.120 2.2 0.289 II 0.600 II 10.0 0.410 II 0.120 2.4 0.360 II 0.650 II 11.0 0.570 II 0.121 2.6 0.448 it 0.700 II 12.0 0.720 ii 0.123 2.8 0.552 I I 0.750 II 14.0 0.110x10 0.129 3.0 0.686 ti 0.790 II 16.0 0.160 II 0.133 3.2 0.850 II 0.820 I I 18.0 0.210 II 0.140 3.4 0.104 it 0.840 it 20.0 0.270 II 0.146 3.6 0.127 I I 0.900 II 22.0 0.320 ii 0.152 3.8 0.154 II 0.920 it 24.0 0.380 ti 0.162 4.2 0,223 it 0.100 II 26.0 0.430 II 0.170 4.6 0.330 n 0.102 II 30.0 0.550 II 0.190 5.0 0.420 I I 0.107 it 35.0 0.710 II 0.210 Density p = 0.223 x 10 Kg/m n e g l i g i b l e v a r i a t i o n s over temperature range of i n t e r e s t . TABLE: 3.1 S p e c i f i c Heat and Thermal Conductivity Data of Glass Used i n Numerical C a l c u l a t i o n s Relating to the Glass-Substrated Super-Conductive P a r t i c l e Detector - 65 -curve between IK and 4K so obtained was matched to the K(T) curve given by Ref.(3.11) at 4K to obtain a smooth t r a n s i t i o n . The values of Cp(T), K(T) used f o r the numerical c a l c u l a t i o n s on the glass substrated S-P'D are tabulated i n Table (3.1 ). Because of the uncertainty i n the values of Cp(T), K(T) used, the c a l c u l a t e d r e s u l t s are expected to be uncertain to the same degree, but should have s i m i l a r c h a r a c t e r i s t i c shapes as observed r e s u l t s . However, being a glass substrate, the thermal constants are probably not too d i f f e r e n t from the values used, p o s s i b l y within a factor of 2. Thus the numerical r e s u l t s are q u a n t i t a t i v e l y s i g n i f i c a n t to t h i s degree. ( I f the actual thermal constants f o r the glass substrate could be determined and used, the numerical r e s u l t s would be q u a n t i t a t i v e l y v a l i d . ) Thermal constants f o r Sn and Pb used f o r the phonon-barrier type S-P.D c a l c u l a t i o n s were obtained from data given i n Ref.(3.13), (3.14) r e s p e c t i v e l y . For t h i n j u n c t i o n f i l m s the data on K(T) was modified to account f o r the s i z e - e f f e c t reduction of thermal c o n d u c t i v i t y i n the plane of the junction f i l m . The reduction of the K(T) value i s dependent on the junction f i l m thickness and also dependent on the temperature, since the mean f r e e path of the conduction e l e c t r o n i s temperature dependent. However, the change i n temperature over the major p o r t i o n of the signal-current pulse duration i s small, thus the reduction f a c t o r i s e s s e n t i a l l y that at the operating temperature. Temperature and signal-current c a l c u l a t i o n s With the i n i t i a l and boundary conditions described i n the previous section the Equation (3.7) was then used to c a l c u l a t e the transformed temperature f o r a l l the c e l l s f o r a time ' T ' l a t e r . This process was repeated - 66 -f o r as long as desired, g i v i n g the temperature-profiles at i n t e r v a l s of T . The c a l c u l a t e d surface temperatures at each c e l l was used to c a l c u l a t e the-excess junction current flowing through the area of that c e l l . The t o t a l excess-current from a l l areas of the j u n c t i o n covering ' c e l l s ' was summed to give the j u n c t i o n s i g n a l - c u r r e n t . S t a b i l i t y Considerations In f i n i t e d i f f e r e n c e c a l c u l a t i o n s eand T cannot be chosen independently, fRef 3 91 since the round-off errors must not propagate and diverge . 6m,n+1 = M(l + 4- ) 6m+l,n + (1.-2M) 6m,n + M(l - ^-) 6m-l,n ( 3 . 8 ) Representing errors i n 6 by 60 we can derive from (3.8): 60m,n+1 = M(l + i-) 66m+l,n + (1-2M) 6m,n + M(l - j-) 66m-l,n (3.9) ]66m,n+ll ^ JM(1 + ~ ) \ | 60m+l,n] + | (1-2M) | | 60m,n| + |M(1 - i - ) 60m-l,m ( 3 . 1 0 ) I f n i s the la r g e s t of j 69 j then |60m,n+l| < |M(1 + i - ) | + | (1 - 2M) | + |M(1 ~ i r ) ! ) n (3.11) Since M i s greater than zero (by the d e f i n i t i o n of M) and m > % the r i g h t hand - 67 -side of Equation (3.11) = (2M + ](1 - 2m)|)n. For errors not to propagate |66m,n+11 must be ,< n f o r a l l m,n+l. Now (2M + | l - 2M|) = 1 f o r M < h; > 1 f o r M > h (3.12) For errors not to propagate, (2M + | l - 2M |) must not be greater than 1, thus r e q u i r i n g M < h. This condition i s s u f f i c i e n t f o r convergence but not necessary i n a l l cases, since i n Equation (3.10) we have used the worst case errors by taking the absolute values. In p r a c t i c e , M = % i s a b o r d e r l i n e case, and may r e s u l t i n o s c i l l a t o r y but f i n i t e s o l u t i o n s , hence f o r the present s o l u t i o n s an a d d i t i o n a l f a c t o r of 2 f o r sa f e t y was used by chosing M to be smaller than h, i . e . * -r < h Cpp o r T < (3.13) This meant that f o r numerical s t a b i l i t y once E 2 was chosen, then the maximum value f o r T was f i x e d . In the present problem ( — w a s a fun c t i o n of temperature, since (3.13) must be s a t i s f i e d at a l l times and l o c a t i o n s , thus the minimum value of expected to be encountered i n the s o l u t i o n had to be used i n determining the maximum value of T . 68 Computer program org a n i z a t i o n f o r the 1-dimensional r a d i a l l y symmetric  approximations The value o f Cp, p, K obtained from Refs.(3.10), (3.11), (3.12), (3.13) and (3.14) f o r Sn and Pb were supplied i n t a b l e form at d i s c r e t e tempera-tures, from which values f o r inbetween temperatures were obtained by i n t e r p o l a t i o n . From K and the Equation (3.2), chosing Ko = 1 we get the corresponding scale of transformed temperature. The transformed temperature of the bath ("UBTH") i s f i r s t c a l c u l a t e d and was used as the s t a r t i n g temperature f o r a l l but the a x i a l c e l l (m = % ) , and as the boundary constant temperature. The i n t i a l temperature of the a x i a l c e l l f o r a quantity of heat Q deposited by the p a r t i c l e (Q = equivalent heat/unit length of a - p a r t i c l e track, f o r the present approximation. In c a l c u l a t i n g Q, the energy dependence o f dE/dx o f the p a r t i c l e t r a v e r s i n g the substrate was ignored, and i t was assumed that dE/dx = constant so that Q = Ea/£ where Ea was the t o t a l a p a r t i c l e energy los s i n the substrate and Jt was the track length. This assumption was necessary to provide the uniform heat energy per u n i t length along the ce n t r a l c e l l required f o r the 1-dimensional approximation to be v a l i d . Q was c a l c u l a t e d by the i n t e g r a l r e l a t i o n T i n i t i a l Q = CppdT(ire 2) (3.14) T b a t h The i n i t i a l temperature was then t r a n s l a t e d to transformed-temperature, completing the i n i t i a l and boundary c o n d i t i o n s p e c i f i c a t i o n s . U(N, 1) was used to lab e l the transformed temperature of the ( N - l ) ^ c e l l . The transformed temperature of the a x i a l c e l l was thus U(2,l) and - 69 -U(1,1) =~U(2,1) provided the a x i a l boundary co n d i t i o n . The U corresponding to the outer boundary c e l l was set at "UBTH" to provide the constant temperature outer boundary condition. The second l a b e l '1' of U(N,1) was used to in d i c a t e the known temperature at the current value of time, while i n U(N,2) the l a b e l '2' ind i c a t e s the transformed temperatures f o r the subsequent time, c a l c u l a t e d using Equation (3.7). Because of the s t a b i l i t y condition, the time i n t e r v a l T was too short f o r the data to be of in t e r e s t at each step, thus the program repeated the c a l c u l a t i o n s a s p e c i f i e d number of times before t r a n s l a t i n g the U values to temperature ( K) values f o r p r i n t o u t . Using these temperature values and a ta b l e of excess current-density as a function of temperature and bi a s values (for a reference function) the excess-junction current c o n t r i b u t i o n of each element of junction area was summed up to give the t o t a l excess j u n c t i o n current, i . e . the signal-current I g . (The j u n c t i o n b i a s-voltage value used f o r the c a l c u l a t i o n s was the s p e c i f i e d a pplied voltage l e s s the l i n e a r l y extrapolated I times the s p e c i f i e d ' l o a d - l i n e ' equivalent resistance) . In t h i s program when the r a t i o of the transformed-temperature of the c e l l adjacent to the a x i a l c e l l , and that of the a x i a l c e l l f a l l s below a s p e c i f i e d value, the c e l l s i z e s were doubled by averaging the heat between p a i r s of a d j a c e n t . c e l l s , and adding c e l l s (of the new s i z e and at bath temperature) to make up the numbers. The time step T was quadrupled as permitted by the s t a b i l i t y - c o n d i t i o n Equation (3.13), and c a l c u l a t i o n s were continued with the r e s u l t s of the previous c a l c u l a t i o n s as new i n i t i a l conditions. In t h i s manner, when the thermal gradients were small, needless d e t a i l i n c a l c u l a t i o n s were eliminated, shortening the c a l c u l a t i o n s required to reach a s p e c i f i e d value of the p u l s e - e v o l u t i o n time. - 70 -F I G - 5 - 3 TEMP- PROFILES 1 -DIM. RADIALLY SYMMETRIC HEAT-DI FPUS ION IN GLASS. - 72 -FIG. 3.4 Is Vs TIME, 1-DIM. RADIALLY SYMMETRIC APPROX. of a-PARTICLE IMPACT ON GLASS-SUBSTRATED STJ. . T I M E / i S - 73 -V e r i f i c a t i o n of numerical methods To t e s t f o r errors i n the program or the method of c a l c u l a t i o n , the program was used to c a l c u l a t e the temperatures with non-temperature dependent Cp, p, K and the r e s u l t s compared with an a n a l y t i c s o l u t i o n of the same problem:-x2 AT(r,t) = -5— e " 4 t ( t ^ P ) (3.15) 4irKt where AT i s the r i s e i n temperature, and Q the heat per un i t lengths of axis. Some of the r e s u l t i n g temperature p r o f i l e s from both methods were p l o t t e d f o r comparison i n F i g . (3.2). I t i s c l e a r that the agreement i s very good, i n d i c a t i n g the v a l i d i t y of the numerical methods and the computer program. Results: 1-Dimensional r a d i a l l y symmetric approximations f o r glass  substrated SPP, v a l i d f o r e a r l y times The c a l c u l a t e d temperature-profile Vs. time i s p l o t t e d i n F i g . (3.3). The r e s u l t s are good approximations of the r e s u l t i n g surface temperature p r o f i l e s o f normal-incidence a - p a r t i c l e impact with a f i n i t e track-length ('v 32 um) up to the time when the e f f e c t s of the f i n i t e length of the heat track begin to show at the surface. Assuming t h i s occurs approximately at times when temperature changes s t a r t to occur at r a d i a l distances equal to the expected track length, (32 um), the time i n t e r v a l o f v a l i d approximation i s at le a s t 40 ns. The c a l c u l a t e d junction-current i s thus expected to be v a l i d during t h i s i n t e r v a l F i g . (3.4). For times greater - 74 -- 75 than t h i s i t i s necessary to use a more complicated geometry to do the hea t - d i f f u s i o n c a l c u l a t i o n , which requires large c e l l s i z e s to accommodate computer l i m i t a t i o n s . For l a r g e times (t>> time f o r s i g n i f i c a n t heat to d i f f u s e over a distance equal to p a r t i c l e track length) a d i f f e r e n t approximation i s v a l i d , the s p h e r i c a l l y symmetric approximation which i s discussed l a t e r i n t h i s Chapter. The r e s u l t s of c a l c u l a t i o n s using the present approximation are us e f u l i n supplying a d e t a i l e d f i n e mesh look (at the early stages) of temperature-profile development, to make sure that the use of the l a r g e r c e l l s i z e l a t e r d i d not obscure any s i g n i f i c a n t phenomenon. From the temperature p r o f i l e p l o t we can see the i n i t i a l increase, then decrease of the normal radius, i . e . the radius i n s i d e which the temperature i s greater than the c r i t i c a l temperature of the super-conductor which f o r t h i s instance was Sn, T^ , = 3.75 K. The time develop-ment of the normal radius i s p l o t t e d i n Fig.(3.5). Results: 1-Dimensional r a d i a l l y symmetric approximation for the phonon-barrier SPP The same computer program as above was used to c a l c u l a t e the response of the phonon-barrier SPD to a - p a r t i c l e impact. The thermal properties Cp, p, K f o r Sn were supplied i n table form f o r d i s c r e t e temperatures, and the excess current d e n s i t i e s f o r a reference Sn junction f o r d i s c r e t e temperatures and bia s voltages were used. Q, the p a r t i c l e energy deposited per u n i t length, i n t h i s case was the value given by E/t where E = p a r t i c l e energy and t = t o t a l f i l m thickness. The temperature p r o f i l e s as a function of time f o r the Sn phonon-b a r r i e r SPD with operating bath temperature of 1.2 K are shown i n 1.30 i r 0 I I I I I I 1 I R JU 200 FIG. 3 . 6 TEMPERATURE PROFILES AS A FUNCTION OF TIME FOR Sn S.T.J. ON A PHONON-BARRIER. TIME nS - 80 -Fig.(3.6) and Ig as a fun c t i o n of time i n Fig . ( 3 . 7 ) . Using the same methods and the thermal pr o p e r t i e s of Pb, and a set of Pb reference junction c h a r a c t e r i s t i c s the temperature p r o f i l e s vs. time, and Ig vs. time were c a l c u l a t e d and p l o t t e d i n Fig.(3.8), Fig.(3.9) r e s p e c t i v e l y . A higher bath temperature of 2.4' K was used f o r the Pb case to get a 31 larger -5=- value f o r the j u n c t i o n , but the r e s u l t a n t increase of Cp and K o 1 r e s u l t e d i n the Ig being much smaller than f o r the Sn case. Note that though we have ignored the f i n i t e area of the jun c t i o n i n the c a l c u l a t i o n s the approximations should provide a d e s c r i p t i o n v a l i d f o r p a r t i c l e impacts near the centre of the j u n c t i o n . Spherically-symmetric approximation For a glass-substrated SPD i f the a - p a r t i c l e energy were considered t be deposited at a point uniformly d i s t r i b u t e d i n a hemispherical volume with i t s planar surface coincident with the tunnel j u n c t i o n , then by the i n s u l a t i n g surface boundary c o n d i t i o n we have s p h e r i c a l symmetry i n the he a t - d i f f u s i o n problem. This model applies i f the length of the p a r t i c l e - t r a c k can be ignored compared with the s i z e of the heat a f f e c t e d zone as i s the case f o r large times (or short track, due to a low energy or heavy p a r t i c l e ) . This approximation was used to give a preliminary i n d i c a t i o n of the response of the glass-substrated SPD to an a - p a r t i c l e impact at large times. The computer program used was d i f f e r e n t from that of the r a d i a l l y symmetric case only i n the Laplacian, and the formula f o r the ' c e l l ' volume which were s p h e r i c a l s h e l l s instead of c y l i n d r i c a l s h e l l The f i n i t e - d i f f e r e n c e expression f o r the new transformed temperature was: I cr - PART ICLE T T R A J E C T O R Y CROSS-SECTION OF A NORMAL-INCIDENCE a-PARTTCLE  IMPACT ON A GLASS-SUBSTRATE SPD FIG. 3.10 AXIS 'CELLS ' FOR CALCULAT IONS i 00 YZ GEOMETRY OF 'CELL' ARRAY USED FOR CALCULATIONS. - 82 -Gm,n+1 = -L. • J L [(m-1) 6m-l, n+ ( m e 2 c P - 2m) 6m,n ' Me 2 Cpp x K + (m+1). em+l,n] (3.16) Because of the s i m i l a r i t y no further d i s c u s s i o n s are necessary. Calculations of glass-substrated SPP response to a - p a r t i c l e impact  assuming f i n i t e - l e n g t h , normal-incidence a - p a r t i c l e track, with a f i n i t e  sized j u n c t i o n . Fig.(3.10) shows the cross section of the normal incidence a - p a r t i c l e impact, with a f i n i t e p a r t i c l e track i n the glass substrate. The heat d i f f u s i o n problem s t i l l had a r o t a t i o n a l symmetry, but now a 2-dimensional array of c e l l s (each ring-shaped) was needed f o r the f i n i t e d i f f e r e n c e numerical s o l u t i o n . This meant a d i f f e r e n t Laplacian compared to the 1-dimensional r a d i a l l y symmetric problem. With the new Laplacian the transformed temperatures for the next time step were given by: 9£,m,n+l = ^L- [(6£,m+l,n - 2e£,m,n + e£,m-l,n)/e 2 + ((l+%£) • 6£+l,m,n - 26£,m,n + (l-%£) • 6£-l,m,n)/e 2) ] + 6£,m,n (3.17) Where 6£,m,n i s the transformed temperature of the c e l l at r = £G, z = mez and t = nx and E , E are the r a d i a l dimension and the z axis dimension of ' z the c e l l s and the value of - — i s that at transformed temperature of Q £ , R|i loon FIG. 3.11 TEMPERATURE PROFILES AT DIFFERENT DEPTHS IN THE GLASS SUBSTRATE AS A FUNCTION.OF TIME. 1 1 1 ! , 1 , , Time ns 500 FIG. 3.12 JUNCTION SIGNAL-CURRENT AS A FUNCTION OF TIME FOR AN INFINITE AREA JUNCTION. - 85 -m,n. The c e l l shape and l o c a t i o n i s shown i n F i g . (3.10). The i n i t i a l condition i s given by c a l c u l a t i n g the depth of penetration of the a - p a r t i c l e (PENZ) at normal incidence and considering the energy of the a - p a r t i c l e uniformly deposited i n the a x i a l c e l l s from the surface to the depth of penetration, i . e . to z = PENZ. As before the boundary c e l l s were kept at bath-temperature. The s i z e of the array of c e l l s used was 20 x 20 or 400 c e l l s , thus the c e l l dimensions had to be l a r g e r than that i n the 1-dimen-sional cases (8u vs. 0.8y ) to prevent the boundary from a f f e c t i n g the heat d i f f u s i o n s i g n i f i c a n t l y . In a d d i t i o n , since the array s i z e had become 4 times l a r g e r , and the c a l c u l a t i n g more complicated, the increase i n c e l l s i z e allowed the use of a larger time step x, reducing the number of steps to reach a s p e c i f i e d p h y s i c a l time. The p o s s i b l e l o s s of s i g n i f i c a n t d e t a i l i n the information about j u n c t i o n response-current as a fu n c t i o n of time through the use of a larger c e l l s i z e was checked by comparison with the 1-dimensional r a d i a l l y symmetric approximation. No l o s s of s i g n i f i c a n t d e t a i l i n the junction current response was evident. However, as expected the temperature p r o f i l e s f o r e a r l i e r times showed a lower peak temperature for the present case, r e s u l t i n g from the i n i t i a l quantity of heat being d i s t r i b u t e d i n a la r g e r volume i n i t i a l l y . The temperature-profiles as a function of time f o r d i f f e r e n t depths and the j u n c t i o n response current as a function of time f o r an i n f i n i t e j u n c t i o n are p l o t t e d and shown i n Fig.(3.11) and F i g . (3.12) r e s p e c t i v e l y . F i n i t e j unction s i z e e f f e c t s The STJ's used i n t h i s experiment were square (0.2x0.2mm2), and f i n i t e 2,01 lime ns FIG. 3.14 CALCULATED SIGNAL-CURRENTS AS A FUNCTION OF TIME FOR DIFFERENT a-PARTICLE IMPACT POINTS. - 88 -and p a r t i c l e impact with the substrate could occur anywhere i n s i d e or outside the j u n c t i o n . The j u n c t i o n current-response to the a - p a r t i c l e impact i s the excess-current density due to the increased temperature integrated over the junction area. F i g . (3.13) shows a coordinate system fo r l o c a t i n g the impact p o i n t . Because of the 8-fold symmetry only impacts i n the shaded t r i a n g u l a r area shown i n the f i g u r e need to be considered, the e f f e c t of impacts i n the other l o c a t i o n s being obtained by symmetry. The surface temperatures centered about the impact point at a given time were c a l c u l a t e d . Thus on s p e c i f y i n g the impact-point l o c a t i o n r e l a t i v e to the j u n c t i o n coordinates the temperature at a l l points of the junction were known. (Cf. F i g . (3.11)). Integrating over the f i n i t e area of the junction we got the f i n i t e j u nction current-response, f o r a - p a r t i c l e impact at a s p e c i f i e d point r e l a t i v e to the j u n c t i o n . F i g . (3.14) shows the junction-current response to normal-incidence 5.13 MeV a - p a r t i c l e impact at four d i f f e r e n t l o c a t i o n s . As expected the impact at j u n c t i o n centre (0,0) r e s u l t e d i n the maximum amplitude and duration of the response. Impact just i n s i d e the corner of the j u n c t i o n at (4,4) produces almost the same amplitude of response as the impact at (0,0) but decayed more r a p i d l y . This i s expected since at f i r s t the temperature r i s e was confined to a small area and was f u l l y covered by the j u n c t i o n f o r e i t h e r impact p o s i t i o n s . The d i f f e r e n c e was more pronounced as the heat d i f f u s e d over a l a r g e r volume, as the impact at (0,0) allowed the j u n c t i o n to cover the area of increased temperature b e t t e r . Impacts outside the j u n c t i o n can a l s o cause junction-current response because of heat d i f f u s i o n , but o f smaller amplitudes because of the smaller temperature increases at the j u n c t i o n . The accumulated signal-charge was also c a l c u l a t e d f o r each time and impact x IO"'2 COULUMBS - 91 -point. The computations were terminated at a pulse e v o l u t i o n time of 0.56 us as the amount of computer-time required was considerable. (3000 sec. Cpu time) and further computations would not have given r e s u l t s to j u s t i f y the cos t . From the computed values of I Q ( t ) f o r each impact l o c a t i o n , I peak, the si g n a l - c u r r e n t amplitude was picked out. From the geometry of the impact-coordinate g r i d (Fig.(3.13) and the set of l g peak values, assuming equal p r o b a b i l i t y of impact at each coordinate point a current-amplitude d i s t r i b u t i o n histogram was c a l c u l a t e d and p l o t t e d i n Fig.(3.15). S i m i l a r l y from the accumulated signal-charge values (accumulated to 0.56 vs) at each impact point an accumulated signal charge amplitude d i s t r i b u t i o n histogram was c a l c u l a t e d by summing o v e r a l l impact coordinates and p l o t t e d i n Fig.(3.16). Both histograms show a sharp r i s e towards the low amplitude end because of the larger area (hence p r o b a b i l i t y ) i n which impact would cause a lower amplitude response. A f a i r l y sharp high energy c u t o f f i s expected because impacts i n the j u n c t i o n c e n t r a l area gives the maximum amplitude response. The a n g l e - e f f e c t " discussed l a t e r would cause some increase i n response amplitude f o r i n c l i n e d impacts over the normal-incidence impacts, thus smearing out of the high energy c u t o f f . These predicted amplitude d i s t r i b u t i o n s are c h a r a c t e r i s t i c o f the "thermometer-model" of the glass-substrated SPD, i n which the STJ i s regarded as a thermometer measuring the temperature increase of the substrate due to an a - p a r t i c l e impact. Whereas a semiconductor junction-detector equivalent model of the SPD with q u a s i p a r t i c l e s regarded as d i r e c t analogs of holes and electrons can only give a ' l i n e ' spectrum from the monoenergetic a - p a r t i c l e source. As w i l l be shown i n Chapter 6, the experimental " K i c k s o r t e r " records agree % - 92 -TIME /iS - 93 -with the thermometer model. Magnitude of the "Angle-Effect" An a - p a r t i c l e with non-normal impacting angle causes a larger signal-current amplitude than an impact at normal incidence because a larger area of the surface i s at a higher temperature f o r the i n c l i n e d impact. The l i m i t i n g case i s the grazing impact, i . e . the a - p a r t i c l e penetrates the surface at a very shallow angle. By the method of images we see that the h e a t - d i f f u s i o n problem i s very s i m i l a r to the normal-incidence f i n i t e length a - p a r t i c l e track problem described above, except that here we regard the temperatures of a plane section through the track as the surface temperatures. The equivalent heat d i s s i p a t e d per u n i t track length i s doubled because of the 'image' track r e s u l t i n g from the i n s u l a t i n g surface boundary condition. With these modifications to the computer program the signal-current due to a grazing impact was c a l c u l a t e d f o r an ' i n f i n i t e ' s i z e d junction and p l o t t e d i n Fig.(3.17). Note the rapid r i s e and f a l l of the signal-current compared to that of normal-incidence, f i n i t e a - p a r t i c l e track length r e s u l t s , and the much higher current amplitudes. For the experimental geometry used the maximum angle of incidence was smaller than 45°. Thus the c a l c u l a t e d s i g n a l - c u r r e n t response to an a - p a r t i c l e impact at t h i s angle represents the l i m i t of current amplitude excursion due to angle e f f e c t f o r the present experimental geometry. For impact at an angle r o t a t i o n a l symmetry was l o s t , the only symmetry l e f t was the r e f l e c t i o n about the plane of incidence, f o r the - 94 -h e a t - d i f f u s i o n problem. Thus a 3-dimensional rectangular array of ' c e l l s ' had to be used f o r the numerical c a l c u l a t i o n s , r e s u l t i n g i n a large number o f c e l l s even f o r a very coarse and l i m i t e d array, consequently a large number of c a l c u l a t i o n s per time step. The computer program f o r t h i s case i s p r a c t i c a l l y the same as the others, except f o r the expression f o r c a l c u l a t i n g the transformed temperature of a c e l l f o r the next time step, r e s u l t i n g from the d i f f e r e n t Laplacian f o r the 3-dimensional rectangular coordinates, and the three space-coordinate indices f o r l a b e l l i n g the transformed-temperature of each c e l l , instead of the one or two f o r previous programs. The c a l c u l a t e d s i g n a l current vs. time i s also p l o t t e d i n F i g . (3.17). The s i g n a l - c u r r e n t peak-amplitude f o r 45° impact angle on an ' i n f i n i t e ' area STJ chosen to have the reference-junction current density c h a r a c t e r i s t i c s was 2.5 ya, as compared to 2.09 ya f o r a normal-incidence a - p a r t i c l e impact. Thus f o r the present experi-mental geometry the 'angle-effect' can account f o r nearly 20% spread i n signal-current amplitude. Comparing accumulated signal-charges Qs, the value f o r 45° impact was 0.864 pc. as compared to 0.913 pc. f o r the normal incidence case. The smaller Qs f o r 45° a - p a r t i c l e impact r e s u l t e d from a computational d e f i c i e n c y ; the a r r a y - s i z e used was too small, thus with the boundaries at a constant temperature the excessive heat l o s s due to the closeness of the boundaries to the point o f impact was not n e g l i g i b l e at larger times. In general the Qs values are l a r g e r f o r impacts at a greater angle, (eg. at t = 0.32 ys Qs = 0.947 pc. f o r the grazing incidence case) but v a r i e s to a smaller extent because though the s i g n a l - c u r r e n t amplitudes were larger f o r greater angles of impact, the Ig(t) r i s e and f a l l time-constants were correspondingly smaller. - 95 -In Fig.(3.17) the current-response f o r an a - p a r t i c l e i m p a c t a t normal incidence, at the centre of a f i n i t e - j u n c t i o n (of the nominal experimental STJ size) was also p l o t t e d f o r comparison with the corresponding current-response f o r an i n f i n i t e - a r e a j u n c t i o n . The current amplitudes were 1.84 ya and 2.09 ya r e s p e c t i v e l y , i n d i c a t i n g that the i n f i n i t e - a r e a junction model was a f a i r approximation f o r impacts at the junction centre of a f i n i t e - s i z e d j u n c t i o n . Conclusion The numerical r e s u l t s of t h i s Chapter enabled the comparisons of theory and experiment and thus the v e r i f i c a t i o n of the t h e o r e t i c a l models used as the b a s i s of the c a l c u l a t i o n s . - 96 -CHAPTER FO'JR SUPERCONDUCTIVE-TUNNELLING JUNCTION FABRICATION INTRODUCTION: My predecessor in this study, G.H. Wood, encountered great difficulties in the fabrication of good superconductive-tunnelling junctions (S.T.J.s). He fabricated six S.T.J.s per evaporation run and because of poor reproducibility, a l l six were tested in liquid helium to check the current-voltage characteristics, and then a good junction selected, separated from the other junctions and mounted on a special sample holder for the measurement of a-particle induced current pulses at 1.2 K. In practice the good junction i f any was nearly always degraded when the subsequent low temperature run was made due to low tolerance of the S.T.J. to thermal cycling. With great patience G.H. Wood got one junction that was good enough to register pulses caused by a-particles, thus proving qualitatively the feasibility of the S.T.J. particle detector. Only Sn-SnO^-Sn junctions were successfully made due to process d i f f i c u l t i e s . The fabrication process used by WOOD was described in APPENDIX 'A' of his thesis, and the difficulties encountered in APPENDIX *B' and r C » / r e f " 4' 9^ For the present thesis a great deal of work was done to derive a process for fabricating Sn and Pb S.T.J.s reproducibly. In the present process 36 S.T.J.s were f a b r i c a t e d each run (F i g . 4.1) i n the form o f 6 j u n c t i o n groups on a microscope glass s l i d e , each group c o n s i s t i n g o f 5 S.T.J.? sharing cr.e common e l e c t r o d e , [the bottom l a y e r of the metal f i l m s forming the junctions (see F i g . 4.2 arid F i g . 4.6)]. The 6 groups made per f a b r i c a t i o n run were . 4.3 APPARATUS FOR SAMPLE FABRICATION INSIDF VACUUM CHAMBER F I G . 4.4 EVAPORATION MASKS AND MASK-CHANGER DETAILS fN'-, -v i s u a l l y inspected and the best group s e l e c t e d for. subsequent tunnel l i n g experiments. The t e s t sample holder included a switching arrangement which (Fig. 5.1, 2, 3, 4 £hapter 5) permitted the selection of any S.T.J, o f the group fo r current-voltage characteristic measurements as well as a-particle induced current pulse measurement while the group i s inside the cryostat. This feature greatly improved the probability of having a good junction for measurements, which was p a r t i c u l a r l y s i g n i f i c a n t i n the earli e r stages o f development of the fabrication process, when the percentage y i e l d of good junctions was low. In Chapter 5 details w i l l be given on how the room temperature and l i q u i d nitrogen temperature junction resistance measurements were used to determine the quality o f the S.T.J.s. I f the junctions were 'bad1 (leaking) the l i q u i d helium stages of measurements were omitted, saving time and expense. S.T.J. SAMPLE FABRICATION The process' steps of junction fabrication are standard: thin f i l m depositions by evaporations from metal and insulator sources, and plasma (ref 4 1 2 3 4) cleaning and anodization " ' ' ' . However details o f the complete process of junction fabrication are not available from any one publication. The author feels that the experience gained may be of some value to others contemplating junction-fabrication. The remainder of this chapter may be omitted i f junction-fabrication i s of no interest to the reader. Substrate Cleaning This step was very c r i t i c a l to the s u c c e s s f u l f a b r i c a t i o n of good S.T.J.s. The substrate, a CORNING 2947 "PROCESS CLEAN'" 2.3 cm x 7.5 cm microscope glass s l i d e was scrubbed thoroughly u s i n g a b r i s t l e brush with a dishwasher detergent and r i n s e d and scrubbed under running tap water. A f t e r t h i s p r e l i m i n a r y scrub a l l the f o l l o w i n g steps were done i n the dust free, a i r f l o w of a c l e a n - a i r hood. The s u b s t r a t e was cleaned u l t r a s o n i c a l l y i n deionized water, then blown dry by c l e a n b o t t l e d n i t r o g e n and p l a c e d i n the substrate holder. The s u b s t r a t e h o l d e r was then t r a n s f e r r e d to the vacuum-evaporator chamber ( F i g . 4.3, 4.4, 4.5} i n the c l e a n - a i r flow, with the substrate surface f a c i n g down (to avoid dust p a r t i c l e s i f any s e t t l i n g on the s u r f a c e ) . The vacuum-chamber was then closed, and pumped down with the roughing pump. A c o n t r o l l e d leak o f oxygen was then introduced to give 50 m i l l i t o r r pressure, and a glow-discharge i n i t i a t e d , an oxygen plasma with discharge c u r r e n t o f 50 ma, w i t h the glow-discharge shutter closed. The glow-discharge s h u t t e r was opened f i v e minutes l a t e r a f t e r any coating on the 'halo' e l e c t r o d e due to previous evaporations had been eliminated, t h i s prevented any contaminating fragments from reaching the substrate surface. The substrate was p l a c e d on each o f the f o u r evaporation masks s u c c e s s i v e l y , f o r f i v e minutes, i n the oxygen plasma. The plasma treatment was intended to remove o r g a n i c contaminants i f any from the substrate and the vacuum-chamber. Then an argon glow-discharge, [pressure = 50 m i l l i t o r r , discharge current = 50 ma, s u b s t r a t e holder (and mask c a r r i e r ) biased-50 V ( r e l a t i v e to vacuum chamber ground)] was used t o i o n - c l e a n ( i o n i c bombardment sputter clean) the s u b s t r a t e surface through each o f the four masks used, f i v e minutes at each l o c a t i o n . That the plasma c l e a n i n g was e f f e c t i v e , could be seen by subsequent examination o f the water vapour condensation p a t t e r n on the s u b s t r a t e , the ion-cleaned area showed up as areas without condensation; t h i s was due to Glow Discharge Shutter sh-Pull f sdthrough r Glow-Dis- ' [ irge S hutter Evaporation Source Shutter evaporation Mask Holes] Alumina Ceramic Bead Ulow D i s c h a r g e j ] ^ 3 ^ I L L A T E D H i § h - V o l t a g e Lead Halo o f AL ff P- . High-Voltage L Feedthrough Heat S h i e l d j Source Separator B a f f l e P l a t e To D i f f . Pump FIG. 4.5 DIAGRAM OF APPARATUS FOR SAMPLE FABRICATION INSIDE VACUUM CHAMBER. Base Film Common Electrode f o r Junctions Sample Glass S l i d e MgF Edge-Guard Over Base Film Base-Film (Sn or Pb) Top-Film Over Edge-Guard and Base-Fi lm mm FIG. 4.0 SUPERCO.\":"CTIVB TI?N*NTLLIN'G JUNCTION- STRUCTURAL ".TAILS - 1 0 1 -Evaporation mask f a b r i c a t i o n and p o s i t i o n i n g The four evaporation masks used were drawn with i n d i a ink, then photographed and reduced to s i z e . Two a c t u a l s i z e d negatives were alig n e d and taped on the edges to form a s l e e v e , which was s l i p p e d over a p h o t o - r e s i s t coated 1-mil berylium bronze sheet. The p h o t o - r e s i s t was exposed and developed, and the berylium bronze sheet etched i n ammonium persulphate s o l u t i o n as i n conventional p r i n t e d c i r c u i t board etching. The f i n i s h e d mask was mounted on the m a s k - c a r r i e r s l i d e with round-head screws (Fig. 4.4). The substrate holder had l o c a t i n g c o n i c a l holes i n p o s i t i o n s corresponding to the four round-head screws h o l d i n g each mask i n p o s i t i o n , t h i s r e s u l t e d i n 'sphere and cone' alignment. The substrate h o l d e r suspended by two hooks may be raised*from and lowered onto the mask ho l d e r through a r o t a r y mechanical feed-through from o u t s i d e the vacuum chamber. The mask-carrier s l i d i n a d o v e - t a i l e d slide-way, ( i n s u l a t e d from the s l i d e way by t e f l o n i n s e r t s i n the s l i d e way). The mask-carrier was p o s i t i o n e d from outside the vacuum chamber v i a a r o t a r y -mechanical feed-through, coupled to a rack and p i n i o n gearing system. The rack was mounted on the mask c a r r i e r edge and driven by the p i n i o n . In operation the s u b s t r a t e holder was r a i s e d , and the mask c a r r i e r p o s i t i o n e d , then the s u b s t r a t e holder was lowered g e n t l y onto the mask c a r r i e r . Due to the s e l f - a l i g n m e n t f e a t u r e , the alignment accuracy, was b e t t e r than 50 microns. Better r e s u l t s could have been achieved with more care, but t h i s accuracy was good enough f o r the set o f masks used. Deposition o f j u n c t i o n f i l m s by evaporation Four masks were used f o r the evaporations ( F i g . 4.4, 4 . 6 ) . Mask "1 defined the contact-pad areas, o where leads were attached to f i n i s h e d S.T.J.s. 2000 As o f metal f i l m was deposited i n t h i s area. Mask # 2 defined the ' ' l o n g i t u d i n a l - s t r i p s " or the o base-films of the S.T.J.s. 2 0 0 0 A of metal was deposited i n t h i s area. o Mask #3 defined the "edge-guard" areas where about 1000 A of MgF was deposited. This l a y e r served to d e f i n e one dimension o f the j u n c t i o n r e g i o n and a l s o served to e l i m i n a t e an area at the edge o f the l o n g i t u d i n a l s t r i p where there i s a high p r o b a b i l i t y o f leakage due to s t r e s s induced c r a c k i n g o f the o x i d e - b a r r i e r a t the edges o f the f i l m . Mask #4 d e f i n e d the 'cross-o s t r i p s ' or the top f i l m s o f the S.T.J.s 2000 A of metal was d e p o s i t e d i n t h i s area. Refering to F i g . 4.5, two evaporation sources were used, one f o r the metal (Sn or Pb) and the other f o r the Mg¥^. The best source f o r evaporating the metal was the Tantalum S-18 10 mil boat p i n - h o l e source, which gave the best r e s u l t s when operated c a r e f u l l y . O u t g a s s i n g was done at slowly i n c r e a s i n g temperatures while monitoring the vacuum ion-gauge o f o r excess pressure r i s e , and an evaporation r a t e o f < 300 A per minute was used, to prevent explosive b o i l i n g during evaporation from causing undesirable s p l a t t e r on the deposited f i l m . Source boat c o r r o s i o n with Sn as evaporant was severe and n e c e s s i t a t e d frequent source changes. A plasma-sprayed oxide coated source was t r i e d without success due to the excessive power r e q u i r e d f o r t h i s source and consequent e x c e s s i v e r a d i a t i v e heating o f the s u b s t r a t e . For the MgF 2 source an inhouse f a b r i c a t e d molydenum source was found to'be most s u i t a b l e . The outgassing problems with a f r e s h charge o f MgF^ i n the source was many times worse than f o r the metal source, and took a few hours to complete, but due to the l a r g e c a p a c i t y of the source and the r>mall amounts o f evaporant used per f a b r i c a t i o n - r u n , t h i s was not much of a problem. The two sources were separated by z host shield/vapour scrarater, tc prevent \r r o u r from one source heating the other. The heat shi e l d also defined the aperture, of the evaporant vapours, c u t t i n g down the r a d i a t i o n h e a t i n g o f the s u b s t r a t e by the source d u r i n g e v a p o r a t i o n , and the d e p o s i t i o n o f m a t e r i a l i n areas other than the substrate mask in the vacuum chamber. An evaporation-shutter operated through a mechanical feed through was used to control the duration of the evaporation and to allow source outgassing before deposition. A quartz-crystal o s c i l l a t o r deposit thickness monitor was used to monitor the evaporation process, details were given in WOOD'S thesis pages 185-187, and w i l l not be repeated here. Plasma cleaning and anodization The oxygen plasma anodization method fref 4 1~) f i r s t proposed by MILES and SMITH^ * " J was chosen to be the process used to form the oxide-barrier for the S.T.J.s because close control possible for this process, essential for reproducibility. With plasma anodization, cleaning, mask change under vacuum, and the two evaporant sources, i t was possible to start with a clean substrate and end up with completed S.T.J.s without opening the vacuum-chamber to the atmosphere, thus eliminating the p o s s i b i l i t y of contamination during the fabrication process. The actual experimental apparatus f o r plasma-anodization and cleaning was designed after reading MILES and SMITH ( r e f' 4 , 1 5 , TIBOL and HULL ( r e f' 4 , 2 \ SCHROEN*-1"6^ and DELL'OCA, PULFREY and YOUNG ( r e f' The plasma for oxidation and ion cleaning was generated by the D.C. discharge between a ring shaped aluminium 'halo' cathode surrounding conductors at ground potential. A high voltage ion-pump power supply with overcurrent cutout protection provided the high voltage f o r the D.C. discharge, (a variac at the A..C. i n p u t t o the power s u p p l y c o n t r o l l e d the D.C. output v o l t a g e ) . The s u b s t r a t e - h o l d e r and the m a s k - c a r r i e r were i n s u l a t e d from ground and could ised a t d i f f e r e n t v o l t a g e s . For i o n c l e a n i n g the b i a s was u s u a l l y 10-1 -50 v o l t s , whereas for anodization the p o t e n t i a l was allowed to ' f l o a t ' , the measured voltage while ' f l o a t i n g ' was about - 4 v o l t s . TYPICAL S.T.J. FABRICATION RUN A typical S.T.J. fabrication run went as follows:- The g l a s s - s l i d e substrate was cleaned and placed i n the vacuum chamber, then plasma cleaned as described i n the "substrate cleaning' section above. The vacuum chamber was pumped down with the o i l - d i f f u s i o n pump to about 2 x 10~ 6 Torr, then the metal, source was outgased u n t i l the vacuum chamber pressure f e l l -6 ° to 3 x 10 Torr. 2000 A of metal (Sn or Pb) was deposited through mask o #1 f o r the contact-pads at approximately 300 A per minute. The source was then turned o f f and the substrate allowed to cool for 10 minutes, t h i s cooling period was found to be necessary to produce a smooth f i l m for the o next evaporation. 2000 A of metal was deposited next with mask #2 for the o longitudinal s t r i p . Next, ^ 1000 A of MgF^ was deposited through mask #3 to produce the "edge-guard", the vacuum pressure for t h i s evaporation was a r e l a t i v e l y high 10 ^ Torr. The diffusion pump was then turned o f f and valved o f f , and Argon gas was introduced through a controlled leak (through a l i q u i d nitrogen cold trap to remove moisture) to raise the vacuum chamber pressure to 50 m i l l i t o r r while being pumped'by the roughing pump. The glow-discharge was turned on with the substrate holder (and the mask carrier) biased at -50 v o l t s , and maintained f o r f i v e minutes. This step ion-cleaned the base fi l m of the S.T.J.s to remove any condensed f i l m (due to vapour leakage of MgF^ evaporation) on the portion of the base - f i l m where the oxide-barrier was to be formed. The Argon gas was valved o f f and substituted 105 respectively. The substrate was allowed to stay in the oxygen for 25 minutes, then with the substrate-holder floating electrically the glow-discharge (with discharge current of 50 ma) was maintained for 40 sec. and 15 sec. respectively for Sn and Pb. This step formed the oxide-barrier for the S.T.J.s. The gas was then valved o f f and the vacuum chamber pumped -6 0 down to a pressure < 10 Torr and 2000 A of metal deposited on the substrate through mask #4. This formed the 'cross-strip 1 or the top f i l m of the S.T.J.s. This step completed the fabrication of the S.T.J.s VISUAL INSPECTION It was possible to predict the quality of the junctions based on microscopic examination of the S.T.J.s. In general i f the base and top films were smooth and few splatters were v i s i b l e , and the edge guard was present, and the oxide-barrier was present, the S.T.J.s were good. The presence of an oxide-barrier could be determined v i s u a l l y . Through the o oxide was only about 10 A thick and much too thin to see, the Sn or Pb vapour that strayed to either side of the cross-strip (top film) as defined by mask #4, tended to form a brownish stain, which did not occur i f the barrier layer was absent (see Fig. 4.6). This effect was probably due to the amorphous or microcrystalline form of the Sn or Pb vapour condensed on the oxide barrier as compared to the epitaxial deposition of the vapours on the bare Sn or Pb films. (I have called this effect "barrier shadow" in my laboratory notes). Generally a l l 36 S.T.J.s on the entire substrate were similar in quality. Sometimes, in the presence of splatter (of Sn or Pb) some junctions could be visually determined to be better because of the Copper S t r i p s Fastened This F.nd To Bake l i t e Base Filament Transformer Varinc Heat Control 6 V o l t s Max. 110 \ f Copper -* Wire on S l i d e C l i p f o r Nichrome Wire Ba k e l i t e S t r i p Attached to Copper S t r i p s . Heated-Nichrome Wire 1 lb Lead Weight Sample Glass S l i d e FIG. 4.7 HP.ATF.D WIRE SAMPLE SEPARATOR 107 -Sample p a s s i v a t i o n Rosin was d i s s o l v e d i n ethyl alchohol and a drop o f the o s o l u t i o n was washed over each sample region on the s l i d e l e a v i n g a <v» 1000 A residue layer of rosin. The rosin layer appeared to be effective in 'passivating' the samples, that i s , to protect the sample from atmospheric originated corrosion. Without this 'passivation' Pb samples degrade rapidly in room ambient, as described by WOOD in his thesis pages 201 to 209, forming clusters of 'blisters' on the Pb film. Group Separation The glass-slide with six groups was divided into six pieces, one group per piece, by breaking the glass substrate. First, the slide was scribed to isolate electrically the areas to be contacted by the 'hot-wire' used for breaking the glass. Then the groups were separated using an electrically heated nichrome 'hot-wire' contacting the region where the break was desired (Fig. 4.7). Even contact of the wire with the glass and correct tensioning was essential for success in this method of glass-breaking. The tension in the wire was provided by a lead weight. This method of group separation prevented physical contact with the S.T.J.s, which could easily be damaged. Lead attachment The selected group was provided with electrical leads by soldering 1 mil gold wires to the contact-pad regions with indium solder. The previously applied rosin-solution in alchohol was a good flux, so no problems were encountered from room temperature to 1.2 K with leads attached in this manner. Sample s t a b i l i t y The S.T.J.s, though st a b l e i f kept at or below l i q u i d nitrogen temperatures f o r i n d e f i n i t e period?, degraded at ro*.a temperature r a p i d l y , and were u s u a l l y unusable i n 24 hours. The degradation mechanism involved was probably r e c r y s t a l i i z a t i o n , which can occur at room temperature f o r t i n and lead. A spectacular example of t h i s r e c r y s t a l l -ization was the growth of -tin or lead whiskers from contaminated films and which were observed to grow up to 1 mm in length in a few hours. This effect i s also observed elsewhere (ref. 4.5). The same process o could cause leaks across the 10 A barrier rendering the S.T.J. useless for our purposes. Thermal stresses resulting from thermal cycling could cause junction failures, but in fact, junctions had been repeatedly cycled between 77 K and 1.2 K without visible degradation. VARIATIONS OF SAMPLE FABRICATION PROCEDURES Vapour deposition of polyethylene (ref. 4.7) Polyethylene was evaporated in place of the MgF^ to form a more flexible edge-guard layer. The deposited polyethylene was cross-linked by the Argon glow-discharge. The procedure was successful but the use of evaporated polyethylene resulted in vacuum chamber contamination, which caused 'whisker' gTowth problems in the metal films. Tne conclusion was that the polyethylene evaporation procedure could be useful, but must be carried out in a separate vacuum chamber. "Photoresist covered substrate The photoresist layer produced a phonon barri between the substrate and the S.T.J. films. This layer must be thin to prevent thermal stresses occurring due to the different coefficients of thermal expansion o f the polymer and the metal f i l m s . I d e a l l y the photoresist f i l m should be on top of a lead c r t i n f o i l stuck on the glass difference i n thermal-expansion of the glass substrate and the metal f i l m . This work was not c a r r i e d cut because the problem did not appear i n t h i s area, there was no thermalrcycling problems between 77 K and 1.2 K, but must be done i f room-temperature stable junctions can be produced. AL 20 3 b a r r i e r To guarantee a strong b a r r i e r layer, < 100 A of Al was evaporated on top of the base-film, followed by the usual anodization, and evaporation procedures. This resulted in a S.T.J. with a P, .AL.AL.O,.P, D 2 5 o structure. The AL^O^ layer was much stronger than a comparable PjO x layer. The AL layer had l i t t l e effect on the superconductive characteristics of f r e f 4 8") the junction due to the 'proximity' effect ' . The problem in this procedure was in the change of evaporant source, that necessitated opening of the vacuum chamber to atmosphere which resulted in the formation of a thick barrier oxide (and contamination of the vacuum chamber). The resulting junctions had normal resistances too high to be of use in this study. If an evaporant-source changer was available this procedure of producing S.T.J.s should be feasible. - 110 -CHAPTER FIVE EXPERIMENTAL METHODS AND RESULTS CRYOGENICS The cryogenic apparatus was the same as that used by G.H. WOOD, my predecessor i n t h i s study. R e f e r r i n g to F i g . 5.1A, i t con s i s t e d o f a liquid-h e l i u m dewar, contained i n a l i q u i d n i t r o g e n dewar. The l i q u i d helium dewar was sealed by a dewar-cap to allow pumping as a means o f lowering the l i q u i d helium temperature. The sample holder assembly entered the l i q u i d helium dewar through a c o l l a r with an 'o' r i n g s e a l , to allow the adjustment of the sample holder height above the l i q u i d helium as the l i q u i d helium l e v e l f e l l . The 'push-rod' used f o r j u n c t i o n s e l e c t i o n and a - p a r t i c l e source s h u t t e r i n g also went through an 'o' r i n g seal to allow movement r e l a t i v e to the sample holder. The helium-dewar "vacuum" jacket was connected to a r o t a r y pump, gauges and b o t t l e d gas through a valve, so that the dewar jacket could be pumped out oc c a s i o n a l l y to eliminate the helium that d i f f u s e d i n t o the space, and b a c k - f i l l e d with 1 to 2 t o r r s of nitrogen gas. The fun c t i o n o f the nitrogen gas was to enable e f f e c t i v e c o o l i n g of the l i q u i d helium dewar by the surrounding l i q u i d nitrogen. On adding l i q u i d helium to the l i q u i d helium dewar the N 2 gas i n the jacket was "frozen-out" l e a v i n g a good vacuum i n s u l a t i n g the l i q u i d helium. The Helmhotz-coils provided the adjustable magnetic f i e l d used to suppress the Joselphson super-current. A l l the e l e c t r i c a l leads to the sample and low-temperature p r e a m p l i f i e r went through the o c t a l feed-through on the sample-holder. The temperature of Figure 5 - 1 A Cryogenic Apparatus (Schematic) (see page following for key). .. . . - 112 -KEY TO FIGURE 5-lC ;Gl Marsh D i a l Gauge, Type 100 0-760 Torr : VG2 Edwards.Dial Gauge, Type C.G.3 0-20 Torr ' G3 Edwards Vacustat, Model 2E, 0-1 Tor r , Lowest Reading S e n s i t i v i t y = 0.001 Torr .:' G4 Marsh D i a l Gauge, (no type No.) .0-760 Torr G5 Ashcroft D i a l Gauge, Type 1850 0-760 Torr (vac), 0-380 Torr (press, gauge) 1. Sample mount. 2. E l e c t r i c a l lead feedthroughs. 3. Sample mount support and c o n t r o l tubes. 4. Dewar cap.. 5. Pyrex Tee (3.x 3 x 2 i n . ) . 6. Helium Dewar Interspace pumpout p o r t . ; 7. Helium Dewar, g l a s s , 76 mm i . d . , 90 mm o'.d., approx. 48 i n . long. 8. Nitrogen Dewar, g l a s s , 116 mm i . d . , 150 mm o.d., approx. 38 i n . long. 9. L i q u i d Nitrogen. JLO. L i q u i d Helium. 11. Sample. 12. Helmholtz c o i l s . 13. He return l i n e . .14. Welch Rotary Pump, Model 1402B, 5 cfm. 15. Stokes Pump, Model 49-10, 80 cfm. 16. Welch Rotary Pump, roughing purposes, Model 1405. 17. Mercury manostat (0-100 T o r r ) . 18. Bottled dry N gas; f l u s h i n g purposes. 19. Transfer siphon port. - 113 -the l i q u i d helium was monitored by the vapour-pressure of the l i q u i d helium using the well known temperature-pressure r e l a t i o n s h i p o f helium ("ref 5 11 gas m e q u i l i b r i u m with l i q u i d helium v * ' 1 . JUNCTION SELECTION A reproducible process 'for j u n c t i o n f a b r i c a t i o n was described i n Chapter 4 of t h i s t h e s i s . The s e l e c t i o n step could be dispensed with, but to obtain the best junctions f o r t e s t s as STJ p a r t i c l e detectors, each sample contained a group of s i x junctions ( i n a small area) and the sample was mounted on a sample-holder with a two-pole, s i x p o s i t i o n s l i d e switch. The switch allowed the s e l e c t i o n of each of the junctions i n turn to be connected f o r e l e c t r i c a l measurements while at l i q u i d helium temperatures. Thus the junctions under t e s t had to be cooled to l i q u i d helium temperature only once, t h i s was important because the superconductive t u n n e l l i n g junctions were found to degrade on thermal c y c l i n g from l i q u i d helium temperature to round temperature and back. My predecessor i n t h i s i n v e s t i g a t i o n G.H. WOOD had d i f f i c u l t y i n obtaining a reproducible process f o r f a b r i c a t i n g S.T.J.s, and so he f i r s t tested the s i x junctions f a b r i c a t e d per run, at l i q u i d helium temperatures and selected a j u n c t i o n showing the best D.C. c h a r a c t e r i s t i c s , using a D.C. t e s t sample holder. Following the s e l e c t i o n , he warmed the samples to room temperature, mounted the s e l e c t e d j u n c t i o n i n an A.C. 'sample mount' (at room temperature) and tested the j u n c t i o n at l i q u i d helium temperatures again, f o r s e n s i t i v i t y to a - p a r t i c l e bombardment. The junctions were cycled to l i q u i d helium temperatures twice and the j u n c t i o n c h a r a c t e r i s t i c s were always degraded (current leaks developed) rendering the S.T.J.s unsuitable f o r p a r t i c l e d e t e c t i o n . FIG. 5.1 SAMPLE HOLDER WITH SAMPLE MOUNTED, a-PART-_ j ICLE SOURCE § LOW TEMP. PREAMPLIFIER FIG. 5.3 SAMPLE MOUNTED ON SAMPLE HOLDER, WITH a-PARTICLE SOURCE FACING JUNCTIONS FIG. 5.2 SLIDE-SWITCH DETAILS ON SAMPLE-HOLDER FIG. 5.4 SAMPLE MOUNTED ON SAMPLE-HOLDER, a-PARTICLE SOURCE TURNED AWAY FROM SAMPLE - 115 -Referring to F i g . 5.3, 5.4, the sample consisted o f s i x junctions sharing one electrode, the base f i l m ( l o n g i t u d i n a l s t r i p e ) . The two ends of t h i s f i l m were connected to the I and V terminals r e s p e c t i v e l y , i . e . the bias current negative terminal and the voltage sense negative terminal r e s p e c t i v e l y . The ends of the top f i l m s o f the junctions ( c r o s s - s t r i p e s ) were connected to the switch pole p a i r s , which when selected were connected to the I + and V + terminals. F i g . 5.2 shows the d e t a i l s of the s l i d e - s w i t c h . F i g . 5.1 shows the sample-holder with a sample mounted, the ' s l i d e ' of the s l i d e - s w i t c h connected to a push-rod, and the Pu239 5.13 MeV a - p a r t i c l e source i s thus positioned d i r e c t l y over the j u n c t i o n selected by the switch. The a - p a r t i c l e source was 'shuttered' by the r o t a t i o n of the push-rod, causing the source or the s h i e l d to face the j u n c t i o n as shown i n F i g s . 5.3, 5.4, r e s p e c t i v e l y . JUNCTION D.C. CHARACTERISTICS MEASUREMENT The four-terminal I-, V measurement method was used as the large and unknown magnitude of the voltage-drops along the j u n c t i o n - f i l m s leading to the ju n c t i o n and connecting wires r e l a t i v e to the voltage drops across the junctions made two-terminal measurements meaningless. Referring to F i g . 5.5, a four-point I, V measurement was e s s e n t i a l l y as follows: current I flowed through the I + terminal, through R c , R T, and R„ , and J b 2 out I terminal causing a voltage drop of IRj across Rj the ju n c t i o n r e s i s t a n c e ; t h i s voltage was sensed by the V.T.V.M. (vacuum Tube Voltmeter) through the V + and V terminals. Thus I and V were measured accurately. The lKft r e s i s t o r on the I + l i n e and the 1MQ r e s i s t o r s on the V +, V l i n e s served to i s o l a t e the junction from A.C. i n t e r f e r e n c e pickup. The - 116 -K E I T H L E Y MODEL 600 A /A-AMMETER <p $ <P! d) d) (p V IK • W r 0 - 5 0 K 0-50K r - I T I 50/jf 500A] POT 4.5V I M • W V I M -WA/-I H.P. ASSOC MODEL 425 A| V. T. V. M. 7.5 K I W V 1 6 4 'x' INPUT HE CRY0STAT| ROOM 64 M O S L E Y X-Y RECORDER FIG. 5.5 JUNCTION D.C. CHARACTERISTICS MEASUREMENT CIRCUIT USING 4 POINT METHOD V FIG. 5.6 CURRENT STREAM-LINES AND VOLTAGE EQUIPOTENTIALS FOR A JUNCTION  WITHOUT OXIDE-BARRIER, GIVING RISE TO 'NEGATIVE-RESISTANCE' IN D.C. 4-POINT MEASUREMENTS - 117 -a - p a r t i c l e induced pulses were measured across the I + and I~ terminals. The D.C. junction c h a r a c t e r i s t i c s were p l o t t e d using an X-Y recorder, as shown i n F i g . 5.5. D.C. measurements were made at room temperature and 77 K to determine the normal tunnel-conductances at these temperatures. I t was observed that i f the re s i s t a n c e at R.T. (room temperature) was negative, the junction was h e a v i l y shorted, or the barr i e r - o x i d e was exceedingly t h i n or absent. F i g . 5.6 shows the expected current-streamlines and voltage equipotential f o r overlapping metal f i l m s without a b a r r i e r , (by analogy with two-dimensional f l u i d - f l o w ) . I t i s cle a r that the V terminal i n such a case i s more p o s i t i v e than the V + terminal,.causing an apparent negative-resistance reading. Note that the magnitude of t h i s e f f e c t i s d i r e c t l y proportion to the me t a l - f i l m sheet r e s i s t i v i t y . GIAVER has observed t h i s e f f e c t , see page 27, 28 o f r e f . (5.9). Another i n t e r e s t i n g observation was that f o r good junctions the junction resistances increased with decreasing temperature, t h i s was probably due to the decrease of c a r r i e r - d e n s i t y o f the ( b a r r i e r ) semiconducting oxides (SnG^ or PbC^) with temperature. The r a t i o o f the resistances at 77 K and R.T. are.of the order 1.6 f o r j u n c t i o n normal resistances of greater than 1 ohm. For smaller j u n c t i o n - r e s i s t a n c e s , the mechanism described above causing the 'negative-resistance'•readings i s more dominant and because of the la r g e r metal-film r e s i s t i v i t y at room temperature than at 77 K acts to decrease the R.T. reading more than the 77 K reading, thus causing a l a r g e r r a t i o . For Sn junctions which were not superconducting at 4.2 K a fu r t h e r j u n c t i o n normal conductance reading could be made, and the j u n c t i o n resistances showed a f u r t h e r increase of the order of 1.1 -*• 1.2 over the 77 K value. A 'bad' or leaky j u n c t i o n F IG. 5.7 D.C. JUNCTION CHARACTERISTICS OF RI23S6J2 (Pb) AT 4.2K. - 119 -showed a decrease i n junction r e s i s t a n c e s with decrease^of temperature as expected,since the m e t a l l i c bridges causing the shorts decrease i n resi s t a n c e with temperature decrease. Based on the above observations measurements on a sample were stopped at R.T. or at 77"K i f the readings i n d i c a t e d a poor sample, thus saving a l o t of experimental time and expense. At 4.2 K ( l i q u i d helium at atmospheric pressure) lead i s a super-conductor, thus the Pb junctions showed superconductive-tunnelling c h a r a c t e r i s t i c s . The voltage current c h a r a c t e r i s t i c s were p l o t t e d f o r each of the s i x junctions on the sample, and the 'best' junctions (no leaks, high junction-conductance) noted at t h i s stage. Further D.C. measurements at lower temperatures and a - p a r t i c l e induced s i g n a l pulse measurements concentrated on these junctions. F i g . 5.7 shows,the D.C. I, V c h a r a c t e r i s -t i c s of the Pb junction R123S6J2 at 4.2 K with bias-magnetic f i e l d of 10 gauss. The c h a r a c t e r i s t i c was p l o t t e d at three d i f f e r e n t current scales to show d e t a i l s of the curve. As the bias-voltage was increased the current at f i r s t increased r a p i d l y u n t i l a plateau was reached. This s e c t i o n of the c h a r a c t e r i s t i c represented the i n c r e a s i n g t u n n e l l i n g p r o b a b i l i t y of the thermally generated q u a s i p a r t i c l e s , u n t i l the l i m i t imposed by the Q.P. density and the j u n c t i o n t u n n e l l i n g conductance was reached. As the bias-voltage neared the 2A/e value Q.P.'s were created by the breakups of cooper p a i r s and the current rose r a p i d l y but bounded by the normal t u n n e l l i n g c h a r a c t e r i s t i c , which represent the l i m i t i n g case where a l l the charge c a r r i e r s are q u a s i p a r t i c l e s (unpaired electrons) f r e f 5 21 ' " . The junction R12356J2 had a z 45^, two orders of magnitude higher than the junctions used f o r p a r t i c l e detection. This ju n c t i o n was chosen i n order to show the complete t u n n e l l i n g c h a r a c t e r i s t i c , - 122 -since the junctions with low R^ showed a 'foldback' e f f e c t which made p l o t t i n g the true Ii V. c h a r a c t e r i s t i c impossible. With the b i a s i n g magnetic f i e l d ' o f f Josephson super-current was observed. This current was e a s i l y d i s t i n g u i s h e d from shorts, by i t s s e n s i t i v i t y to magnetic f i e l d s . When the j u n c t i o n current exceeded the maximum super-current l i m i t ( f o r the operating temperature and ambient magnetic f i e l d ) or when the b i a s i n g magnetic f i e l d was increased (which cause a decrease of super-current maximum value) the junction switched abruptly to the q u a s i p a r t i c l e t u n n e l l i n g mode. A general decrease of super-current maximum with increase of b i a s i n g f i e l d was observed but the t h e o r e t i c a l | s i n x/x | type of dependence could not be resolved due to the noisy electromagnetic environment. • At 4.2 K Sn i s a normal conductor, (Tc o f Sn i s 3.75 K) thus only the normal-tunnelling c h a r a c t e r i s t i c s was measured at t h i s temperature. The' Helium cryostat was then pumped down to 1.2 K where the superconductive t u n n e l l i n g j u n c t i o n I. V. c h a r a c t e r i s t i c s were measured. A representative set of I.V. c h a r a c t e r i s t i c s f o r a Sn junction i s shown i n F i g . 5.8. Other than a s l i g h t 'bump' i n the c h a r a c t e r i s t i c at A/e, which i s a frequently observed feature f o r Sn junctions the curves are s i m i l a r to that o f Pb junctions traced at the same gA value, i . e . at ^ 2 . 3 K. The 'bump' i s (ref 5 2) theorized as due to two p a r t i c l e t u n n e l l i n g by Adkins " " S c h r i e f f e r ( r e f 5 3) and Wilkins ' ' . F i g . 5.9 shows the v a r i a t i o n of the I. V. c h a r a c t e r i s t i c s with temperature o f the Sn j u n c t i o n R67S1J3. Note the increase of j u n c t i o n current and decrease of with i n c r e a s i n g temperature at the b i a s point of 0.3 mv i n agreement with theory. - 123 -JUNCTION-DEGRADATION Sn and Pb junctions f a b r i c a t e d i n t h i s lab (with SnO^ and PbO^ oxide b a r r i e r s ) d e t e r i o r a t e at room temperature. Most junctions with b a r r i e r s t h i n enough f o r t h e i r use as p a r t i c l e - d e t e c t o r s develop leaks of large enough conductances i n 24 hours at room temperature to r u i n t h e i r usefulness as superconductive p a r t i c l e detectors. Thermal-cycling to room temperature and back to l i q u i d helium temperatures caused i r r e v e r s i b l e degradation of c h a r a c t e r i s t i c s . For example, i n sample R67S1, junctions 1 to 5 showed super-shorts (superconductive short c i r c u i t s ) and the dynamic r e s i s t a n c e of junction 6 decreased from 5.4ft to 0.7ft a f t e r thermal c y c l i n g . The degradation due to c y c l i n g may simply be due to the actual time spent at room temperature rather than the thermal c y c l i n g . Thermal c y c l i n g between 1.2 K and 77 K caused only minor changes i n the junction c h a r a c t e r i s t i c s , and junctions have been kept f o r weeks at 77 K without degradation. The mechanism f o r degradation at room temperature appear to be d i f f u s i o n and r e c r y s t a l l i z a t i o n of the Sn and Pb f i l m s . One dramatic phenomenon confirming t h i s i s the r a p i d growth of Sn and Pb whiskers on the junction f i l m s at room temperature, whiskers grew to m i l l i m e t e r lengths i n a few hours, when the evaporations o f the f i l m s were c a r r i e d out i n a contaminated vacuum chamber. This phenomenon had been observed by others (ref. 5.4) 'S' TYPE NEGATIVE-RESISTANCE (foldback) With junctions of high t u n n e l l i n g conductances s u i t a b l e f o r SPD app l i c a t i o n s the D.C. current at the "current-step" ( i . e . at the r a p i d -current r i s e near 2A/e) caused s u f f i c i e n t heat d i s s i p a t i o n to increase the - 124 -(A ) (B) FIG. 5.10 'S' TYPE NEGATIVE RESISTANCE IN JUNCTION I.V. CHARACTERISTICS OF THERMAL ORIGIN. HORI. = 0.2ys/cm VERT. =50 mV/cm ORTEC INTEGRATOR OUT DIFF. OUT COARSE GAIN 'x 3' FINE GAIN 'x 1' ORTEC VOLT. GAIN = 152 R.T. PREAMP. V.G. = 35.2 JUNCTION BIAS V. = 0.3 mV MAGNETIC BIAS = 13.5 Gauss TEMP. = 1.2°K FIG. 5.12 a-INDUCED PULSES IN Sn JUNCTION R67S1J3. -124a-FIG. 5.11 AMPLIFIER CIRCUITRY FOR a-PARTICLE INDUCED PULSE OBSERVATIONS TIME SHUTTER DISC. SETTING COUNT COMMENTS 7 :57 -»• 8:02 Open 0.088 1619 Usual Transients 8 :03 8:08 Closed i t 45 tt 8 :09 8:14 Closed 91 1 burst "^ 60 pulses 8 :15 -* 8:20 Open . t i - 1980 1 burst 8 :34 5 -»• 8:39. S Open ff 1705 Quiet 8 :43 5 -»- 8:48. 5 Closed tt 25 tt 8 :49 S -> 8:54. 5 Closed i t 11 11 8 :59 9:04 Open i t 1652 tt TABLE 5.1 DISCRIMINATOR COUNTER READINGS ON a-INDUCED PULSES FROM R67S1J3. - 1 2 5 -junction temperature and decrease ^the superconductor energy gap. This e f f e c t i s observed to be more pronounced f o r Pb ju n c t i o n s , probably because of the l a r g e r energy gap. Thus with a ju n c t i o n current of 0.5 ma and 2A = 2.54 ma,- the d i s s i p a t i o n i s 1.27 yW which i s s u f f i c i e n t to produce a l o c a l temperature increase and lower the energy gap because of the low heat-conductivity of the glass at the operating temperatures, F i g . 5.10A shows t h i s e f f e c t . In junctions of l a r g e r tunnel conductance the 'foldback' was observed to occur before the 'current step'. In t h i s case an increase of current through the jun c t i o n increases d i s s i p a t i o n , causing the junction to heat up, thus the voltage i s determined by the I. V. c h a r a c t e r i s t i c of the increased'temperature, which r e s u l t s i n a lower voltage, i . e . , a current c o n t r o l l e d or 'S' type negative r e s i s t a n c e , cf. • F i g . 5.10B. Further the e f f e c t was more pronounced when the jun c t i o n was above the liquid- h e l i u m l e v e l than when the same j u n c t i o n was immersed, confirming the probable thermal o r i g i n of the negative r e s i s t a n c e e f f e c t . PULSE MEASUREMENTS WITH ROOM TEMPERATURE PREAMPLIFIER When D.C. measurements were completed and a 'good' j u n c t i o n selected, the amplifier-system shown i n F i g . 5.11 was used to observe the a - p a r t i c l e induced p u l s e - s i g n a l s from the junct i o n . The a m p l i f i e r system was ca l i b r a t e d using a "dummy-junction" c o n s i s t i n g of a r e s i s t o r and capacitor i n p a r a l l e l , having values 100ft and 2000pF r e s p e c t i v e l y ( i . e . the expected maximum-dynamic re s i s t a n c e , and capacitance of a representative junction) and i n j e c t i n g into i t square-wave pulses or simulated j u n c t i o n s i g n a l current waveforms. The pr e a m p l i f i e r voltage gain was found to be 35.2 ( l i n e a r ) . The equivalent input noise was approximately 3 microvolts R.M.S. - 126 -The Johnson noise from the dummy input accounted f o r 1 yV and the am p l i f i e r and pickup of in t e r f e r e n c e 2 yV. This i s much b e t t e r than the manufacturer's s p e c i f i c a t i o n of 9 yV, probably because of the low supply voltage of ±, 3 v o l t s used, instead of the allowed maximum of ± 8 v o l t s . The ORTEC l i n e a r a m p l i f i e r had a measured voltage gain of 152 at X3 coarse gain and XI f i n e gain s e t t i n g s , the equivalent input noise was approximately 3 yV R.M.S., n e g l i g i b l e compared to the preamp c o n t r i b u t i o n . Sn junctions R67S1 J l -> J6 were found to have d e s i r a b l e c h a r a c t e r i s t i c s f o r operation as STJ p a r t i c l e detectors from the D.C. c h a r a c t e r i s t i c s measurements. In p a r t i c u l a r j u n c t i o n #3 (J3) was the best j u n c t i o n , having a low R^ = 0.22ft (normal t u n n e l l i n g resistance) and the best ^ t j y n / ^ j r a t i o , i n d i c a t i n g l i t t l e leakage, and a = 20.0ft . Pulse-amplified measurements confirmed that J3 gave the best signal-amplitude ( F i g . 5.12). This junction was used f o r f u r t h e r measurements. That the signal-pulses were i n f a c t induced by a - p a r t i c l e bombardment was proved by 'shuttering' the a - p a r t i c l e source, or by stopping the a - p a r t i c l e s by immersing the j u n c t i o n i n l i q u i d helium. A s e r i e s of count-readings using the discriminator-counter i s shown i n ta b l e (5.1). The counting was done with the pulses monitored on the C.R.O., and any unusual i n t e r f e r e n c e was noted. From the readings i n table 5.1, i t i s c l e a r that a - p a r t i c l e induced pulses are d e f i n i t e l y observed, and e l e c t r i c a l i n t erference i s minimal, as low as 2 C.P.M. i n quiet periods and at most 18 C.P.M. i n noisy periods, (these may be compared to G.H. WOOD'S count rates of 1.3 -> 1.8 x 10 4 C.P.M. without noise burst g r a t i n g ) . The int e r f e r e n c e was mostly common-mode, thus by using the F a i r c h i l d yA733 d i f f e r e n t i a l a m p l i f i e r as a prea m p l i f i e r , with the high common mode r e j e c t i o n r a t i o of - 127 -200 f SIGNAL AMPLITUDE mV ' X - R67SIJ3 SN AT 1.2 °K x 100 + 4 U 0 0.2 0.4 0.6 JUNCTION BIAS VOLTAGE mV F I G . 5 .13 P U L S E - A M P L . V s BIAS VOLTAGE 200f SIGNAL AMPLITUDE mV lOOf R67SIJ3 SN BIASED AT 0.3 mV -I 1 1 4 L. .2 1.4 1.6 JUNCTION TEMP. °K F I G . 5.14 PULSE-AMPL. Vs TEMPERATE OF JUNCTION - 128 -70db in t e r f e r e n c e was d r a s t i c a l l y reduced. PULSE-AMPLITUDE DEPENDENCE ON BIAS-VOLTAGE 91 ' The pulse-amplitude which i s dependent upon C g j " )y• was found to vary with the voltage at the operating-point, (the point at which the bia s - r e s i s t o r l o a d - l i n e i n t e r s e c t s the I. V. c h a r a c t e r i s t i c of the junction at the operating temperature). The l a r g e s t maximum-amplitude pulses were observed at 0.3 v o l t b i a s , corresponding to the point of maximum R^^- Fig- (5.13) shows the pulse-amplitude maximum Vs. bias voltage f o r the Sn.junction R67S1J3. From the c a l c u l a t i o n s i n Chapter 2 31 ^ST^V i s expected to be nearly independent of bias-voltage f o r 8A of >5.4 (Sn at 1.2 K) and bias-voltage > 0.5 A/e (/M).3mV) (C.F. Eqn. (2.6), thus 31 the observed decrease of R, = (TTT)„ with increase of bias-voltage dyn 3V^T 6 31 ^ beyond 0.3mV r e s u l t s i n a decrease of (—),..R, . With decrease of J V3T^V dyn 31 31 bias-voltage below 0.3mV, both ( - ^ r ) w and R. decreases, thus (-r=r),r.R, 3T V dyn V3T V dyn also decreases. PULSE-AMPLITUDE DEPENDENCE ON TEMPERATURE; Sn JUNCTIONS 3V From F i g . (2.6) Chapter 2 the voltage-response s e n s i t i v i t y (-^f) T Vs 31 1 BA curve f o r a frequency of 1 MHz frequency peaks at BA=5.8. Assuming t h i s i s representative of the response to the a - p a r t i c l e induced thermal-pulse, an increase of operating temperature o f the Sn j u n c t i o n above 3 V 1.28 K (BA = 5.8) should r e s u l t i n a decrease of .(—) . Further, with o 1 1 increased operating temperature the s p e c i f i c - h e a t of the glass-substrate increases, r e s u l t i n g i n a smaller r i s e i n temperature f o r the same heat-pulse, c o n t r i b u t i n g to the decrease of output pulse amplitude with increased - 129 -temperature. This i s i n fact observed, the v a r i a t i o n of pulse amplitude with temperature i s shown i n F i g . (5.14). i q-PARTICLE INDUCED PULSE-SIGNALS AND NOISE The observed pulse s i g n a l s as shown i n F i g . (5.12) vary between 130 to 160 mV, the lower l i m i t being a C.R.O. t r i g g e r threshold. The density of traces by v i s u a l i n s p e c t i o n appear to be uniform to 160 mV. The pulse-amplitudes corresponded to signal-voltage amplitudes of 24.3 to 29.9 mV at the preamp input, and as the R^^ f o r the ju n c t i o n was 209, , t h i s corresponded to signal-current amplitudes of 1.2 to 1.5 ya, disregarding the j u n c t i o n capacitance (the e f f e c t of which i s to increase the r i s e - t i m e , decrease the peak voltage, and increase the f a l l time). The 'noise' voltage v i s i b l e on the C.R.O. trace appeared to be approximately 60 mV peak to peak, corresponding to approximately 3.3 yV Rms at the input to the preamp. The s l i g h t increase i n 'noise' could only be accounted f o r by the increased pickup of i n t e r f e r e n c e when the sample was connected to the preamp. The shot-noise, the only s i g n i f i c a n t source of inherent j u n c t i o n noise, generated i n the j u n c t i o n by the bias- c u r r e n t of 0.025 ma was only 0.056 yV Rms. Thus the noise o r i g i n a t i n g i n the jun c t i o n was n e g l i g i b l e compared with i n t e r f e r e n c e pickup and p r e a m p l i f i e r noise, and to improve the si g n a l to noise r a t i o , a low-temperature p r e a m p l i f i e r p h y s i c a l l y close to the junc t i o n i s necessary. Pb junctions were not tested with the room temperature p r e a m p l i f i e r because Pb j u n c t i o n f a b r i c a t i o n technology was not developed at the time. The Pb junctions were t e s t e d l a t e r when a low temperature p r e a m p l i f i e r had been developed. - 130 -• R -VW-6 . 8 K : O.luf A o 2 ^ I00K >I00K lOpf IM> >|M 0 . 1 ^ IM AW I V G 9 —> CALIB. VOLT. —=*- V -L. He TEMR R. TEMR F i g . 5.15 DIRECT-COUPLED LOW. TEMP.. PREAMPLIFIER, CONNECTED TO JUNCTION AND •POST1 AMPLIFIER. ~ ~ : : — ^ (A) OUTPUT J J CALIB. VOLT. (B) FIG."5.16 JUNCTION CAPACITANCE MEASUREMENT AND AMPLIFIER CALIBRATION USING THE IV CHARACTERISTICS^ '. ~~ - 131 -PULSE MEASUREMENTS WITH DIRECTLY-COUPLED LIQUID HELIUM TEMPERATURE  AMPLIFIER LIQUID HELIUM TEMPERATURE AMPLIFIER DETAILS A v a i l a b l e l i t e r a t u r e ( r e f . 5.5 -* 5.11) and p r i v a t e communications i n d i c a t e d that at l i q u i d helium temperatures only superconductive a m p l i f i e r s , some M.O.S.F.E.T.'s (Metal Oxide Semiconductor F i e l d E f f e c t T r a n s i s t o r s ) , and some GeJF.E.T.'s (Germanium Junction F i e l d E f f e c t T r a n s i s t o r s ) were usable as a m p l i f i e r s . Superconductive a m p l i f i e r s such as the Cryotron type required too much research and development to be f e a s i b l e f o r t h i s p r o j e c t , though t h i s i s probably the most s u i t a b l e type f o r eventual ap p l i c a t i o n s using the S.T.J. Such GeJ.F.E.T.'s as the TIM301 (Texas Instruments) had good performance f i g u r e s at 4.2 K according to 0. PARRISH, (private communications). The charge c a r r i e r s i n Ge are frozen out at 4.2 K and the J.F.E.T. works only because of impact i o n i z a t i o n of the impurity. The problem with using the GeJ.F.E.T. i s that T.I. no longer manufacture these devices, t h e r e f o r e they are not e a s i l y a v a i l a b l e . M.O.S.F.E.T.'s work at 4.2 K (and below) by i n j e c t i o n of charge c a r r i e r s from the 'source' contact, and these devices are e a s i l y a v a i l a b l e and inexpensive. The N-channel d e p l e t i o n mode M.O.S.F.E.T. 3N140 manufactured by R.C.A. was recommended f o r l i q u i d helium temperature operation by Fred Witteborn (of Stanford Research I n s t i t u t e i n a p r i v a t e communication to Professor GUSH of the Physics Department, U.B.C.); t h i s i s the device used f o r the present low temperature p r e a m p l i f i e r . R e f e r r i n g to F i g . (5.15) the low temperature p r e a m p l i f i e r had a 'cascode' type input, followed by a 'source-follower' to d r i v e the 50Q - 132 -impedance of the microcoaxial cable connecting the p r e a m p l i f i e r to the post a m p l i f i e r . In Q-^.Q^ of the cascode stage the gates 1, and 2 of the F.E.T.'s were connected together and used as a s i n g l e gate. This reduced the operating drain-current i n the cascode stage to reduce power d i s s i p a t i o n . In gate 2 o f the F.E.T. was t i e d to the p o s i t i v e supply voltage to increase the transconductance and thus lower the source impedance. This increased the current through the device but the d i s s i p a t i o n i n the device was kept low by keeping the drain-source voltage low by the c i r c u i t shown. The D.C. bias of was adjusted e x t e r n a l l y , t h i s was e s s e n t i a l as the optimum operating b i a s v a r i e s with temperature. I t was found that f o r the set o f t r a n s i s t o r s used the room temperature optimum bias was ^-2.8 v o l t s and the l i q u i d helium temperature optimum bias was ^+0.8 v o l t s . For b e t t e r performance the bias of Q^, should also have been e x t e r n a l l y adjustable, but t h i s would have required two more pins on the feed-through i n t o the sample-holder and two more e l e c t r i c a l leads down to the l i q u i d helium p o r t i o n of the l i q u i d helium cryostat, i n c r e a s i n g the heat-leak. Thus f o r convenience and to decrease l i q u i d helium usage rate Q^, were not e x t e r n a l l y biased. The output of the p r e a m p l i f i e r drives the microcoaxial l i n e terminated by a 50ft r e s i s t o r to match the coaxial line-impedance. In s e r i e s with the 50ft r e s i s t o r i s a c a p a c i t i v e l y by-passed lKft r e s i s t o r . This r e s i s t o r was used to decrease the drain-source voltage o f Q^. The s i g n a l across the 50ft r e s i s t o r fed the inputs of the p o s t - a m p l i f i e r (a F a i r c h i l d uA733, pre v i o u s l y used as a room temperature p r e a m p l i f i e r ) . The p o s t - a m p l i f i e r then drove the ORTEC l i n e a r a m p l i f i e r , which i n turn drove the other devices as before. The p r e a m p l i f i e r gate-bias c o n t r o l and battery, the - 133 -preamplifier-supply c o n t r o l s and b a t t e r i e s , the p o s t - a m p l i f i e r supply voltage regulator and b a t t e r i e s , the junction-bias c o n t r o l s and b a t t e r i e s , and a ua meter used f o r monitoring j u n c t i o n b i a s - c u r r e n t , were housed i n a metal box c a l l e d the ' c o n t r o l ' box p h y s i c a l l y mounted on the sample-holder o c t a l e l e c t r i c a l feed-through during operation. This was to minimize interference pickup. Another microcoaxial cable was used to feed a c a l i b r a t i o n pulse to a lOpf capacitor connected to the input of the preamplifier. A step voltage V applied to the lOpF capaci t o r dumped a -11 V x 10 coul. charge i n t o the j u n c t i o n capacitance, causing an 'instantaneous' r i s e of voltage across the j u n c t i o n and approximately exponential decay, dependent on j u n c t i o n c h a r a c t e r i s t i c s . This voltage was amplified by the p r e a m p l i f i e r , and the output from the p r e a m p l i f i e r (v i a the p o s t a m p l i f i e r ) used to c a l i b r a t e the gain of a m p l i f i e r system. The p r e a m p l i f i e r was checked at room temperature together with the post-amplifier, as shown i n F i g . (5.15). The p r e a m p l i f i e r voltage-gain was found to be 25. The p o s t - a m p l i f i e r - g a i n was 35.2. Output wideband , noise was approximately 0.01 v o l t s Pons at the p o s t - a m p l i f i e r . Since the post-amplifier alone contributes only < 105 uV Rms at the output most of the noise came from the p r e a m p l i f i e r , corresponding to 11.3 uV Rms equivalent input noise at the p r e a m p l i f i e r . This could i n future be improved by t r a n s i s t o r s e l e c t i o n , and/or adjusting the gate b i a s of Q 2, e x t e r n a l l y . Such a procedure may r e s u l t i n an expected equivalent input noise of approximately 5 y v o l t s ^ e ^ * *>.9, 10) ^ ^ w a s decided that the improvement was not worth the e f f o r t s at the time. Despite the apparently higher equivalent input noise f o r the low temperature a m p l i f i e r , the actual noise-performance when used i n conjunction with an input step-up pulse - 1 3 4 -transformer i s much be t t e r than the room temperature p r e a m p l i f i e r , as w i l l be shown i n the following s e c t i o n s . LOW TEMPERATURE PREAMPLIFIER TEST AND CALIBRATION AT LIQUID HELIUM  TEMPERATURE AND MEASUREMENT OF JUNCTION CAPACITANCE Referring to F i g . (5.16A) we see that as the ju n c t i o n bias-voltage increases the R^^ increases from a small value at (1) to a maximum value at point (2), and with f u r t h e r increase i n bias-voltage R^^ decreases and becomes very small at (3) the "current-step", and with f u r t h e r increase takes a value approaching R^ (normal tunnel resistance) at (4). With a small c a l i b r a t i o n voltage step V c, smaller than 2A/10.e say, applied to the c a l i b r a t i o n capacitance C^ ,, the voltage across the ju n c t i o n r i s e s abruptly by an amount CC VSo = VC • " C 5 - X ) C +C +0 where Cj i s the junction capacitance, and i s the p r e a m p l i f i e r input capacitance with a l l the associated s t r a y capacitances. The voltage increment then decays as:-V S ( t ) = VSo • " ' r , „ = VSo e " t / T  e ( C c + C J + G N ) . R d y n Since R^y.n at any bias-voltage can be measured from the ju n c t i o n D.C. c h a r a c t e r i s t i c s the C j can be found by measuring x, knowing C^ ,, and ^dyn' Note that t h i s procedure i s v a l i d only f o r small voltage-steps as ^dyn c a n n o t ^ e regarded as a constant over large ranges of voltages. - 135 -R137SlJlPb JUNCTION BIAS VOLT. = OV HORI. = 0.5ys/Div VERT. = l.OOmv/Div BOTH TRACES, BOTH PICTURES R136SlJlPb JUNCTION BIAS VOLT, at max. R D y N POINT. 0.7 n FIG. 5.17 VARIATION OF DECAY TIME-CONSTANT OF VOLTAGE-RESPONSE TO CALIBRATIOh CHARGE WITH JUNCTION BIAS VOLTAGE. - 136 -Having found C j , Vg Q i s known from eqn. (5.1), thus knowing the output voltage from the p r e a m p l i f i e r , the voltage-gain can be c a l c u l a t e d . The v a r i a t i o n of the decay time constant with b i a s - v o l t a g e i s c l e a r l y shown i n F i g . (5.17). For R136SlJ4Pb, a lead-junction used i n the above described measurement procedure, the R j ^ maximum bias point was located by adjusting the b i a s -voltage f o r maximum time-constant. The time-constant T measured from the output waveform was 1.2 vs, R^^ maximum was found to be 935ft and ~ 10pF, thus using eqn. (5.2) Cj was found to be 1270pF. This j u n c t i o n had o r r e f 5 12") a R^ of l i f t , corresponding to a b a r r i e r oxide thickness of ^ 12A For a j u n c t i o n with ~ 0.5ft, more s u i t a b l e f o r S.P.D. use, the o corresponding b a r r i e r thickness i s ^10A, and thus the junction capacitance has a value of 1520pF, (since the j u n c t i o n capacitance i s i n v e r s e l y p r o p o r t i o n a l to oxide b a r r i e r t h i c kness). The C values f o r the junctions used i n the a - p a r t i c l e induced pulse measurements were estimated i n t h i s manner. Following the above described procedure the p r e a m p l i f i e r voltage gain was found to be 25.8 at 1.2 K as compared to 25.0 at room temperature. The equivalent Rms noise input voltage was found to be 9.9 uV as compared with 11.3 uV at room temperature. The p r e a m p l i f i e r equivalent input noise was too-high f o r observation of a-induced s i g n a l - p u l s e s with d i r e c t coupling of the junction to the p r e a m p l i f i e r input. Since the p r e a m p l i f i e r input impedance i s high compared with the j u n c t i o n impedance, c o n s i s t i n g at the frequencies of i n t e r e s t , <1 MHz, of approximately 5pF, and s t r a y capacitances of another 5pF, a step-up pulse-transformer could be used to improve the voltage gain of the input a m p l i f i e r and reduce the equivalent input noise voltage. For example a step-up r a t i o of 15:1 could - 137 -reduce the equivalent input noise voltage to 0.66 uV,(the transformer i t s e l f was not expected to contribute s i g n i f i c a n t n o i s e ) . The advantage, of the present low-temperature p r e a m p l i f i e r over the room temperature a m p l i f i e r i s intrinsically.-;the r e l a t i v e l y higher input impedance of the low-temperature p r e a m p l i f i e r , and the p o s s i b i l i t y o f p l a c i n g i t close to the superconductive p a r t i c l e detector and the step-up transformer. The high impedance input of the p r e a m p l i f i e r enables the use o f the step-up transformer, and the high impedance of the secondary of the step-up trans-former ne c e s s i t a t e s short leads to the p r e a m p l i f i e r . The p r e a m p l i f i e r can then drive a 50ft c o a x i a l l i n e feeding the room temperature a m p l i f i e r system with an amplified s i g n a l , c u t t i n g down the e f f e c t of i n t e r f e r e n c e pickup. I t might be suggested that the superconductive p a r t i c l e detector a low impedance device,would drive a t r a n s m i s s i o n - l i n e which then would feed the step-up transformer/preamplifier combination at room temperature which would give an equivalent input noise of only 0.75 uV Rms, but t h i s c o n f i guration would have the disadvantage of the long transmission l i n e c arrying an unamplijFied-signal and subjected to i n t e r f e r e n c e pickup, and the thermal-noise c o n t r i b u t i o n of the transmission l i n e . MEASUREMENTS WITH LIQUID HELIUM TEMPERATURE AMPLIFIER WITH INPUT VOLTAGE  STEP-UP PULSE-TRANSFORMER Voltage step-up pulse-transformer f a b r i c a t i o n and t e s t s Commonly a v a i l a b l e commercial pulse-transformers were e i t h e r f e r r i t e core or tape wound core types. The f e r r i t e core type could not be used because the f e r r i t e material loses permeability at low temperatures. The - 138 -POT-CORE (A) TOROID (B) TOROID (C) F I G - s - 1 8 DUST-IRON PULSE-TRANSFORMER CORE CONFIGURATIONS 1 4 TIMES : ACTUAL SIZE. • . • : PULSE KTTN GEN. R 2 - 3 K f C R O PROBE >50A i • 470 • K J - 5 ! J - IO pf £10 M 100 (A) TRANSFORMER TEST CKT. TIME 2 0 10 (B) TEST WAVEFORM SUPPLIED BY ATTENUATOR RISE TIME I ~ 0.6 ps (C) TRANSFORMER OUTPUT TO CURRENT WAVEFORM ' B ' FED INTO JUNCTION I--5.19 • PULSE-TRANSFORMER TESTS CIRCUIT AND WAVEFORMS - 139 -tape wound core type could not be used f o r the-frequencies of i n t e r e s t because of eddy-current l o s s e s . 'Dust-iron' cores are s a t i s f a c t o r y because of good permeability even at l i q u i d helium temperatures and low losses, but dust-iron cores are now n e a r l y obsolete, not a v a i l a b l e commercial on short n o t i c e . Three d u s t - i r o n cores were obtained non-commercially. F i g . (5.18A) shows a 'pot-core' machined from a TV I.F. tuning component. F i g . (5.18B) shows a dust-iron t o r o i d machined from a tuning-slug. F i g . (5.18C) shows a miniature t o r o i d obtained from F a r i n o n - E l e c t r i c of Santa Clara, C a l i f o r n i a , p r i v a t e l y . Because of the d e s i r a b l e small s i z e of 'C 3 2 eight attempts were made to wind approximately 10 turns secondary and 10 turns primary f o r the required impedance l e v e l s without success, each time the secondary was found to be open c i r c u i t e d , probably because of the accumulated s t r a i n on the f i n e wire used f o r the windings. 'A' and 'B' cores were wound s u c c e s s f u l l y , and on measurements 'A' performed b e t t e r and was chosen despite the l a r g e r s i z e . The pulse-transformer was wound such that f o r the expected waveforms of the a - p a r t i c l e induced pulses the primary had an input impedance o f approximately 100ft to match the desi r e d ^dyn v a-*- u e °^ a j u n c t i o n , and the secondary was wound with as many turns as p h y s i c a l l y p r a c t i c a l , about 1500 times. The impedance o f the primary f o r the waveforms o f the expected s i g n a l s (Fig. 5.19B), was measured using the c i r c u i t of F i g . (5.19A). Knowing the input-voltage at (A) and the voltage at the dummy-junction load at (B) , with and without the transformer, the primary impedance - 97ft, (assuming the primary z i s r e a l ) , close to the planned 100ft. The value was determined by measuring the amplitude of the voltage pulse at point (A) ( F i g . 5.9A) with, and without the connection to the primary of the transformer. - 140 -• •.. .,... — V -• . ; - , V . . — • ^ v + FIG. 5.20 TRANSFORMER INPUT LOW-TEMP. PREAMP. CONNECTED TO JUNCTION and 'POST'-AMPLIFIER. R148S2J2Pb a t 1.43°K, Mag. Bias = 28 Gauss Ho r i z o n t a l = O.Sys/div V e r t i c a l = 0.2ys/div Ortec Coarse Gain x~3 " Fine Gain x-1 " V.G. = x 152 Post Amp Gain = x 35,2 FIG. 5.21 a-PARTICLE INDUCED PULSES FROM Pb JUNCTION R148S2J2, USING .. THE TRANSFORMER INPUT LOW. TEMP. AMPLIFIER. '—-. . - 141 -Knowing R^, a n < ^ t h i s allowed the c a l c u l a t i o n of the impedance at the input o f the transformer. With the input current-waveform of F i g . (5.19B), the waveform F i g . (5.19C) was observed at the secondary, with a rise-ti m e of 0.6 usee. Note that the output-pulse i s much slower than the input pulse, and the r a t i o of input pulse-amplitude to the output pulse-amplitude i s 1:8.2, and the r a t i o of input peak to peak and output peak to peak voltage r a t i o i s 1:12.6, smaller than the turns r a t i o of 1:15. The pulse-transformer acts as an 'integrator' f o r pulses shorter than 0.6us, i thus although the output-pulse amplitude i s lower than i n d i c a t e d by the turns r a t i o f o r short input pulses, the duration of the output-pulse i s longer. In response to a current-step input, the input voltage pulse-amplitude: output pulse-amplitude was 1:14.9, close to the expected value of 1:15. During the tes t s on the transformer i t was found that the secondary lead corresponding to the outside windings must be used as the hot-lead otherwise the response r i s e - t i m e i s much longer and the amplitude less.. This e f f e c t r e s u l t e d from the c a p a c i t i v e coupling between the primary and the secondary inner winding laye r s , the primary windings provid i n g a low-impedance path to ground, thus e f f e c t i v e l y i n c r e a s i n g the winding s t r a y capacitance of the secondary. The transformer was then wrapped i n l e a d - f o i l providing a superconducting transformer s h i e l d . Pulse-transformer input low-temperature p r e a m p l i f i e r room temperature t e s t s The low temperature p r e a m p l i f i e r and STJ b i a s i n g c i r c u i t was modified to include the pulse transformer, to the c o n f i g u r a t i o n shown i n F i g . (5.20). A dummy-junction was used i n place of the STJ f o r room temperature t e s t s . It was found that f o r Vpp output: /V z M r >^ c p of 1:1 the input voltage - 142 -required at the transformer input was ^ 0.5 uV. For a voltage-step applied to the c a l i b r a t i o n lead, a 10 mV step r e s u l t e d i n Vpp out: /V^ ., . r r r Noise out of 1:1. Since the c a l i b r a t i o n capacitor was now 5pf, the corresponding c a l i b r a t i o n s i g n a l charge was 0.05 picocoulomb f o r a SNR of 1. Measurements of Pb junctions with the transformer input low temperature  a m p l i f i e r A large e f f o r t was^made to obtain a reproducible process f o r Pb STJ's, because o f the promise of junctions stable at room temperature and f r e f 5 13) immune to thermal c y c l i n g ' ' . However the Pb junctions f a b r i c a t e d i n t h i s laboratory degraded at room temperature. Pb junctions were required also to check the present theory f o r the STJ's f o r high BA values. Sn (junctions) at 1.2 K corresponded to (SA '= 5.4, while Pb at \ 1.2 K corresponded to BA = 12.3, thus Pb j u n c t i o n measurements provided the data f o r STJ's at BA between 5.4 to 12.3. The Pb j u n c t i o n R148S2J2 was used f o r the f o l l o w i n g measurements. On c o o l i n g to l i q u i d helium temperature the a m p l i f i e r system was c a l i b r a t e d . A 20 mV voltage step was applied to the c a l i b r a t i o n capacitor, r e s u l t i n g i n a t e s t charge o f 0.1 picocoulombs i n C j . This charge gave an output s i g n a l peak to peak voltage of 80 mV. The observed noise voltage at the output was 25 mV Rms. Thus a s i g n a l charge of 0.03 pc would be observable, using v P P / ^ N o ^ s e = 1 as the o b s e r v a b i l i t y c r i t e r i o n . Here we have switched to d e s c r i b i n g the s i g n a l by "signal-charge" instead of " s i g n a l - v o l t a g e " . "Charge" i s a more s i g n i f i c a n t parameter i n view of the " b a l l i s t i c " or i n t e g r a t i n g nature of the step up pulse transformer i n the input c i r c u i t of the low-temperature p r e a m p l i f i e r f o r s i g n a l pulse durations much smaller than the - 143 -COUNTS PER DISC. SETTING INTERVAL DISC. SETTING COUNT DURATION COUNT. 'MIN. COUNTS PER DISC. SET. INTERV. 010 19015 1 min. 19015 •+ 17649 012 1366 1366 -*• 1103.. 014 263 !t 263 •-»• 100 1 016 163 II 163 62 018 101 II 101 ->- 69.5 020 63 2 min. 31.5 17.5 022 28 II 14.0 TABLE 5.2 RECORD FROM DISCRIMINATOR COUNTER MEASUREMENTS OF R148S2J2 AT 1.2UK. OIO 012 014 016 018 020 022 024 DISC. SETTING FIG. 5.22 PULSE-AMPLITUDE DISTRIBUTION USING DISCRIMINATOR-COUNT. FOR Pb JUNCTION R148S2J2. - 144 -resonant period of the transformer output c i r c u i t . Discriminator-counter readings a - p a r t i c l e induced pulses were c l e a r l y observed with the Pb junction R148S2J2, of the expected waveform and with good s i g n a l to noise r a t i o , as shown i n the C.R.O. record F i g . (5.21). No k i c k s o r t e r was av a i l a b l e at the time o f the experiment but the discriminator-counter was used to obtain the data shown i n ta b l e (5.2) and the histogram i n F i g . (5.22). At d i s c r i m i n a t o r s e t t i n g 020 a sharp drop o f f i n count-rate occurs, preceded by a s l i g h t r i s e at s e t t i n g 018. This agrees with the t h e o r e t i c a l p r e d i c t i o n o f a s l i g h t r i s e followed by a sharp cut o f f at the high energy end ( C F . F i g . 3.15, 3.16). I f a ' l i n e ' was present i t could l i e between 018 and 020 and be o f low amplitude, since i n the histogram F i g . 5.22 at that p o i n t such a l i n e could conceivably be obscured by the low r e s o l u t i o n . E f f e c t o f temperature v a r i a t i o n on s i g n a l s we wished to make measurements at temperatures i n the range 1.2 K to 4.2 K. At 4.2 K the helium gas i n the liquid-helium cryostat was at atmospheric pressure. Assuming the helium gas was also at 4.2 K, then the range of the 5.13 MeV a - p a r t i c l e was only 0.3 cm. Since the spacing between the source and the detector was 0.5 cm, the p a r t i c l e would be stopped before reaching the detector. To t r y to obtain higher j u n c t i o n temperatures while maintaining low helium gas pressure i n the cryo s t a t , measurements were made by r a i s i n g the col d -f i n g e r o f the sample holder above the l i q u i d helium surface, and monitoring the junction temperature by the junction-current at a voltage b i a s - p o i n t having been previously measured at d i f f e r e n t temperatures. This scheme Temp. 3A Pulse Ampl. Sig . Charge Q Therm. Cond. Normalized Sig. Charge Q* . Q* Corrected f o r a-Attn. 1.19°K 12.38 .540 mV .675 pc 0.34 x 10w/mk 0.675 pc 0.675 pc 1.34°K 11.00 660 mV .825 pc 0.39 t! 0.946 pc 0.946 pc 1.45°K 10.17 560 mV .825 pc 0.41 II 0.994 pc 0.990 pc 1.93°K 7.64 520 mV .650 pc 0.55 II 1.051 pc 1.077 pc 2.16°K 6.82 470 mV .588 pc 0.60 II 1.037 pc 1.092 pc Table 5.3. Temperature Dependence of a - P a r t i c l e Induced Pulses i n Pb Junction R148S2J2. - 146 -was found to be i m p r a c t i c a l because the temperature changed too r a p i d l y . The output pulse amplitude was therefore measured at f i v e d i f f e r e n t temperatures up to 2.16 K (gA = 6.82) where the helium vapour pressure was 36 t o r r , and d i d n o t . s i g n i f i c a n t l y attenuate the a - p a r t i c l e energy (AE/E ^ .047) and the r e s u l t s are l i s t e d i n table (5.3). The pulse amplitude i n i t i a l l y increased with i n c r e a s i n g temperature, even though the increased temperature decreased the R ^ ^ J t h i s was due to the increase of 91 ^3T^V w^ t^ 1 temperature. With f u r t h e r increase i n temperature R^y^ decreased f u r t h e r and the impedance becomes smaller.than the j u n c t i o n -capacitance impedance (X - 106ft at lO^Hz) and leakage r e s i s t a n c e i n p a r a l l e l , i f any, and because s i g n i f i c a n t i n the reduction o f s i g n a l 81 amplitude, overcoming the increase i n (g^Oy with increased temperature. Further, the increase i n temperature increased the s p e c i f i c heat o f the glass substrate, thus the same heat-pulse r e s u l t e d i n a smaller temperature r i s e with increased substrate temperature, consequently a smaller s i g n a l current amplitude. The signal-charge depended on the duration and the current-amplitude. Since the duration was i n v e r s e l y p r o p o r t i o n a l to the K d i f f u s i v i t y (—p—) , the signal-charge was i n v e r s e l y p r o p o r t i o n a l to K K Cp.(—TT—) = /p . Since the density p i s ne a r l y constant over the pLp temperature range o f i n t e r e s t , the signal-charge v a r i e s as K, the thermoconductivity. . Thus by m u l t i p l y i n g the observed signal-charge at temperature T by (ICp/K^ ^ - > (where K^, ^ ^ a r e r e s p e c t i v e l y the thermoconductivities of the glass substrate at temperature T, and 1.2 K) * * we get a 'normalized' signal-charge Q T . Q T i s the signal-charge from a superconductive-tunnelling junction at temperature T subjected to the same small temperature excursion as that at 1.2 K due to a 5.13 MeV - 147 -* a - p a r t i c l e impact. Thus the Q^ , 's i n d i c a t e the S.T.J. c h a r a c t e r i s t i c s independent of substrate p r o p e r t i e s . The above discussion i s v a l i d q u a l i t a t i v e l y only because o f the assumption of a small and uniform excursion of temperature i n the S.T.J. whereas f o r an a - p a r t i c l e impact the temperature excursion i s l o c a l i z e d near the a-impact s i t e and not small ( i . e . thermal properties change values s i g n i f i c a n t l y during the temperature pulse) c o r r e c t i n g f u r t h e r f o r a - p a r t i c l e energy attenuation o f ~ .0.047 f o r the 2.16 K (36 Torr) and * 0.025 f o r the 1.93 K (19 Torr) * cases, the largest signal-charge Q^ , occurs at PA = 6.8. R e f e r r i n g to Fi g . 2.6, Chapter 2 the voltage-response s e n s i t i v i t y to temperature 3V i change of a S.T.J. curve (-=- , n6 Vs BA), has a maximum at gA = 5.8, thus despite the q u a l i t a t i v e nature of the above discussion the t h e o r e t i c a l , and experimental values of peak gA are close. The above d i s c u s s i o n attempts to explain the p h y s i c a l nature o f the change of signal-charge amplitude with temperature. The exact treatment requires numerical s o l u t i o n o f a non-linear problem which i s o f l i t t l e help i n understanding the physics, and was not done. The S.N.R. f o r Pb junction R148S2J2 From F i g . (5.21) we can see that the peak to peak noise voltage at the output i s approximately 80 mV, V^ Rms = 32 mV ( f o r gaussian n o i s e ) . . The maximum signal-amplitude peak to peak i s approximately 660 mV, thus Vpp/Zv2^" = 20.6. Sn junctions are expected to give b e t t e r s i g n a l to noise r a t i o s as explained i n the theory chapter. - 148 -FIG. 5.23 AMPLIFIER SYS./JUNCTION COMBINATION CALIBRATION CURVE R164SlJ5Sn at 1.2 'K, V Bias = 0.3 mV. FIG. 5.25 KICKSORTER RECORD OF PULSE-AMPLITUDE DISTRIBUTION FROM Sn JUNCTION R164S1J5 (MADE WITH LOW-TEMPERATURE TRANSFORMER INPUT PREAMPLIFIER) - 149 -MEASUREMENTS ON Sri JUNCTIONS USING THE TRANSFORMER INPUT LOW-TEMPERATURE  PREAMPLIFIER Sn STJ's are expected by theory to give b e t t e r signal-amplitude because the optimum STJ response to a temperature i s at a lower temperature (than Pb), where the thermal conductance and s p e c i f i c - h e a t of the substrate i s lower. The inherent SNR i s also expected to be be t t e r f o r the Sn STJ, because of the /K dependence o f the Rms shot noise ( c f . Eqn. 2.48, Chapter 2). For the present measurements, a m p l i f i e r noise dominated so the improvement of SNR r e s u l t s from the increased signal amplitude f o r Sn junctions. A m p l i f i e r system c a l i b r a t i o n F i g . (5.23) shows the response of the am p l i f i e r system to an approximately 5-function c a l i b r a t i o n charge of 0.2pc. (This response-curve was used i n Chapter 6 to c a l c u l a t e the expected output waveforms from a - p a r t i c l e induced s i g n a l - c u r r e n t s i n the STJ.) R164S1J5 was biased at maximum R, f o r t h i s c a l i b r a t i o n curve. dyn The charge s e n s i t i v i t y f o r the Ortec l i n e a r a m p l i f i e r s e t t i n g of V.G. = 304 was 3.2 volts/picocoulomb. The peak to peak noise voltage was ^ 200 mV at the output corresponding to V Rms of ^  79.9 mV, (equivalent to a noise-charge of 0.0221 p c ) . a - p a r t i c l e induced pulses, d i r e c t o s c i l l o s c o p e measurements A f t e r the junction plus a m p l i f i e r system was c a l i b r a t e d , the a - p a r t i c l e source was direct e d towards the junctions and output-waveforms r e s u l t i n g from the a - p a r t i c l e bombardment were monitored us i n g a Tekronix 465 portable O s c i l l o s c o p e . The waveforms were monitored continuously during the - 150 -.2 (A) R164SlJ5Sn at 1.2 K V„. - 0.3 mV Bias HORI. = lus/Div VERT. = 1 V/Div Ortec Coarse Gain x 3 " Fine Gain x 3 (Ortec V.G. = x 456) Post-Amp. V.G. = x 35.2 CRO TRIGGERING THRESHOLD SET LOW TO SHOW LOW-AMP. PULSES FIG. 5.24 a-PARTICLE INDUCED PULSES IN Sn JUNCTION R164S1J5, USING TRANSFORME INPUT LOW-TEMP. PREAMP. - 151 -" k i c k s o r t e r " (pulse amplitude d i s t r i b u t i o n analyser) accumulation runs as a precautionary measure against unforseen noise sources ( i f any) and • equipment f a i l u r e . Two o f the a - p a r t i c l e induced output o s c i l l o s c o p e records are shown i n F i g . (5.24A, 5.24B). *A' shows the output s i g n a l before the k i c k s o r t e r run Acc. 9 and 1B' shows the output-signal from the same junction before k i c k s o r t e r run Acc. 20, with the o s c i l l o s c o p e t r i g g e r i n g threshold set low to show lower-amplitude pulses. The maximum signal-output peak to peak voltage f o r 'A' was 3.2 v o l t s f o r the same amplif i e r s e t t i n g as the c a l i b r a t i o n curve. This s i g n a l output corresponded to a s i g n a l charge o f 1.0 picocoulomb. The maximum peak to peak signal-output voltage f o r 'B' was 4.85 v o l t s at a m p l i f i e r voltage gain gain = 304). Thus the maximum .a-particle induced s i g n a l charge i s also 1 pC f o r 'B1. Note the good s i g n a l to noise r a t i o i n 'A' and *B' C.R.O. records and the wide range o f s i g n a l amplitudes v i s i b l e i n 'B'. ' The s i g n a l to noise r a t i o Vpp/VV 7^ i s 40.0 f o r R164S1J5SN compared to 20.6 f o r Pb j u n c t i o n R148S2J2 pc. The Pb junction had = 0.12ft, ^dyn > ^ ' ^ ^ a t compared to the Sn normal junction t u n n e l l i n g resistance R^ o f 0.30ft and R^ ^ = 72.5ft, c l e a r l y v e r i f y i n g the t h e o r e t i c a l p r e d i c t i o n s , as the Sn j u n c t i o n was d e f i n i t e l y b e t t e r even with a smaller junction normal conductance (G = VR.,) • a m p l i f i e r combination was s u f f i c i e n t l y high that the k i c k s o r t e r output would d e f i n i t e l y show a ' l i n e ' or peak i f the pulse amplitude d i s t r i b u t i o n had such a peak. 20 k i c k s o r t e r records were made Acc 1 to Acc 20 = 456, t h i s corresponded to a Vpp o f 3.2 at the s e t t i n g s f o r 'A' (voltage KicksOrter measurements The s i g n a l to noise r a t i o of t h i s j u n c t i o n -- 1 5 2 -(Acc = Accumulation). Acc 1 to Acc 3 showed a f a l s e peak due to ' c l i p p i n g ' r e s u l t i n g from inadvertent b i a s i n g o f the junction close to a current-step i n the I.V. c h a r a c t e r i s t i c s the o r i g i n of t h i s e f f e c t w i l l be described i n d e t a i l i n Appendix 5.1. Acc 7, 8 were records o f runs made with junction R164S1J1. The remaining f i f t e e n records were o f k i c k s o r t e r runs with R164S1J5. The large number o f runs were made to be sure that no peak was missed. A good representative record was Acc 16 shown i n F i g . (5.25). No peak was v i s i b l e , the record was of the form p r e d i c t e d by the present theory. To f u r t h e r ensure that noise did not smear out any "peaks' the record Acc 6 was made, and then with i d e n t i c a l s e t t i n g and accumulation time record Acc 6 was made with the p a r t i c l e source shuttered. Acc 6 recorded no pulses i n any o f the channels displayed, i . e . a l l the pulses accumulated i n Acc 6 were s i g n a l pulses. Summary of Measurements Chapter a - p a r t i c l e induced pulses were d e f i n i t e l y observed v e r i f y i n g GHW's r e s u l t s . temperature dependence of pulse-amplitudes i n Pb and Sn junctions were measured, the r e s u l t s agree with theory. - the S.T.J. capacitance was measured d i r e c t l y and voltage gain of the low temperature p r e a m p l i f i e r simultaneously measured, a low-temperature p r e a m p l i f i e r was developed to improve the SNR. ju n c t i o n / a m p l i f i e r combined response to charge deposited i n the junction was measured, ( t h i s was req u i r e d f o r t h e o r e t i c a l d e r i v a t i o n o f the output waveform f o r comparison with the experimentally measured waveform) . - 153 -CHAPTER SIX Reduction o f Experimental Results and Comparison with Theory  Introduction T h i s chapter i s organised i n t o three p a r t s . The f i r s t part compares the t h e o r e t i c a l expressions f o r Igg/G and l / ^ y i / G a s f u n c t i o n s o f 8A at constant voltage bias (derived i n Chapter 2) with experimental data, to e s t a b l i s h the v a l i d i t y of these expressions and other expressions and conclusions derived from these. The t h e o r e t i c a l j u n c t i o n voltage response f o r a high frequency temperature change as a function o f 3A i s q u a l i t a t i v e l y compared with the experimental data (from Chapter 5). The second part of t h i s chapter uses the j u n c t i o n current I c ( t ) -c a l c u l a t e d i n Chapter 3, as a basis to c a l c u l a t e the expected s i g n a l voltage output from the room temperature a m p l i f i e r system and the low temperature a m p l i f i e r system (with transformer input) f o r comparison with the respective experimental waveforms. The t h i r d part of t h i s chapter compares the t h e o r e t i c a l peak s i g n a l current and t o t a l s i g n a l charge amplitude d i s t r i b u t i o n curves (derived i n Chapter 3) with the experimental s i g n a l output amplitude d i s t r i b u t i o n curves from Chapter 5. Junction q u a s i p a r t i c l e t u n n e l l i n g current dependence on temperature at  constant bias voltage. From eqn. (2.15) of Chapter 2 we get f o r bias voltage V = A/e:-- 154- -• C 6 - 1 ) a s a function of SA. -.155 -• (6.2) I /G as a function of BA. - 156 -I s s / G = — K^BA) [ l - e " 3 A ] (6.1) e where as explained i n Chapter 2, we approximate A by A = A(o) f o r BA > 3.5. The equation i s shown i n graphical form ' i n F i g . (6.1) f o r lead, and F i g . (6.2) f o r t i n j u n c t i o n s . The experimental values o f Igg/ G a s a function o f BA obtained from one lead S.T.J. and two t i n S.T.J.s are p l o t t e d i n F i g . (6.1) and F i g . (6.2) r e s p e c t i v e l y , u s i n g constant energy gap values o f 1.12 mV and 2.54 mV f o r t i n and lead r e s p e c t i v e l y to c a l c u l a t e ;he BA values o f the experimental p o i n t s . R e f e r r i n g t o F i g . (6.1) the experimental points f a l l c l o s e to the t h e o r e t i c a l curve. T h e o r e t i c a l l y the experimental points are expected to f a l l s l i g h t l y above the curve, due to the approximations leading to eqn. (2.15) ( C f . Chapter 2). This deviation may be accounted f o r i f we assume that A f o r the lead j u n c t i o n f i l m s i s s l i g h t l y l a r g e r than the value used (^  17% l a r g e r ) . R e f e r r i n g to F i g . (6.2) we see that the experimental p o i n t s f o r t i n S.T.J.s f a l l close to but above the t h e o r e t i c a l curve, as required by theory f o r BA < 4.5. For BA > 4.5 the d e v i a t i o n increases, probably due to the i n c r e a s i n g s i g n i f i c a n c e o f leakage currents with i n c r e a s i n g BA. Thus i t appears that the lead S.T.J. we used f o r F i g . (6.1) data i s a b e t t e r (lower leakage) j u n c t i o n than the t i n S.T.J.s we used f o r F i g . (6.2) data. From the above disc u s s i o n we can conclude that (6.1) i s j u s t i f i e d experimentally to the degree o f accuracy required f o r the t h e o r e t i c a l discussions i n Chapter 2. 9 I S S The 9 T /G Vs. BA curve was p l o t t e d i n F i g . (2.7) Chapter 2. Since 81 the -^Y / G e x P r e s s i o n was derived from eqn. (2.15) by p a r t i a l d i f f e r e n t i a t i o n , the v e r i f i c a t i o n of the Igg expression also j u s t i f i e s the expression f o r - 157 -FIG. (6-3) Variation of 1/R .G with BA - 158 -(3Igg/3T)/G at constant bias voltage. V a r i a t i o n of R^^ with temperature at constant bias voltage. From the I.V. c h a r a c t e r i s t i c f o r j u n c t i o n R67S1J3 shown on F i g . (5.9) we see that the dynamic r e s i s t a n c e R^^ o f the j u n c t i o n does decrease with increased temperature (decreased BA) as required by the f o l l o w i n g t h e o r e t i c a l expression derived from eqn. (2.5) of Chapter 2: 1 / ( R d y n - G ) = 2BAK 1(BA)e" 0 e V (6.3) The maximum R^^ f o r experimental Sn junctions occurred at j u n c t i o n b i a s voltage o f 0.3 mV, corresponding to eV = 0.536A instead o f eV = A because i t was found experimentally that m u l t i p a r t i c l e t u n n e l l i n g e f f e c t s caused a 'bump'in the I.V curve at eV = A thus lowering the R^^ around t h i s p o i n t . Thus the eqn. (6.3) becomes f o r Sn junctions at t h i s bias value: 1 / i R d y n - G ) = 2 B A K 1 ( 8 A ) e " ° - 5 3 6 A $ (6.4) This equation i s shown g r a p h i c a l l y i n F i g . (6.3). Experimental r e s u l t s f o r t i n junctions R67S1J3, R77S1J4, R47S1J1,3,6 were used to c a l c u l a t e ^/(R^^.G) and p l o t t e d Vs BA i n the same f i g u r e . The p o i n t corresponding to BA = 3.85 f o r R67S1J3 f a l l s close to the t h e o r e t i c a l curve but the r e s t of the data points f o r large BA are above the t h e o r e t i c a l curve. For R77S1J4 the data points corresponding to BA ~ 3.3 t o 4.0 f a l l c l o s e l y on the t h e o r e t i c a l curve, and f o r l a r g e r BA, the data points are above the curve but to a l e s s e r extent. The data points f o r R47S1J1, R47S1J3, R47S1J6 at BA ~ 5.46 (T ~ 1.19 K) were p r o g r e s s i v e l y c l o s e r to the t h e o r e t i c a l curve - 159 -than the corresponding points f o r R67S1J3, R71S1J4. The above described deviations from theory are i n t e r p r e t e d as the presence o f leakage r e s i s t a n c e . R67S1J3 had = 0.22 Si, while R77S1J4 had Rj^ = 7.33 SI. R77S1J4 having the l a r g e r j u n c t i o n normal t u n n e l l i n g r e s i s t a n c e probably had r e l a t i v e l y l e s s leakage than R67S1J3. Thus as $A increased, R^y^. increased and the specimen with the smaller leakage r e s i s t a n c e e x h i b i t e d a smaller d e v i a t i o n from the t h e o r e t i c a l curve. Note that f o r smaller BA values, i s s u f f i c i e n t l y small t o swamp out the e f f e c t s o f the leakage, and the experimental p o i n t s f a l l c l o s e to the t h e o r e t i c a l curve. To f u r t h e r v e r i f y t h i s hypothesis, data (at 1.19 K) from R47S1J1,3,6 junctions with s t i l l higher R^ than R77S1J4 were p l o t t e d . As described above these points f a l l c l o s e r to the t h e o r e t i c a l curve. (RXI = r v N R47S1J6 620 SI). On removing the e f f e c t o f the leakage r e s i s t a n c e component from the data points f o r R67S1J3 at 6 5.45, such that t h i s point f a l l s on the t h e o r e t i c a l curve, the next two data points ( f o r higher temperature) f a l l on the t h e o r e t i c a l curve but the points corresponding to BA = 3.84 and 4.25 now f a l l below the curve. This i n d i c a t e d temperature dependence o f the leakage: the leakage conductance decreases with increased temperature. The experimental R^y^ value was obtained by measuring the slope o f a tangent at the point o f i n t e r e s t on the I.V. c h a r a c t e r i s t i c curve, thus the accuracy o f the R^y^ value depended on the accuracy i n drawing the tangent l i n e to the curve at the i n d i c a t e d point, which i s u n l i k e l y to be b e t t e r than 10% i n most cases. Within t h i s accuracy and the approximations i n the d e r i v a t i o n s of the t h e o r e t i c a l expression the experimental data agree with the t h e o r e t i c a l expressions f o r R^y^* - 161 Dependence upon ambient (mean junction)temperature of junction voltage  response to low and high frequency temperature changes. Since the junction voltage response for low frequency temperature changes i s given by:-3T 3T d y n and the theoretical expressions for the two factors on the RHS were shown to be supported by experiment the theoretical expression for the low frequency voltage response: SL- - .» (2.25) 3T 2e 1+e B A can be considered as verified. For the response to high frequency temperature changes we can use the experimental data on the dependence on mean junction temperature of the amplitude of a-particle induced signals for R148S2J2, shown in Table (5.3), Chapter 5. Since we are interested here in the response of the junction to a standard temperature pulse as a function of BA, i t i s necessary to correct the measured junction signals to allow for the temperature dependence of the substrate thermal characteristics. If uncorrected, the temperature pulse produced by a given a-particle energy loss w i l l depend on the mean temperature and thus on BA. In Table (5.3) the normalized signal charge response i s the calculated equivalent signal-charge value produced at a normalizing standard temperature of 1.2 K, based on a small signal (small uniform temperature change) model. This procedure therefore removes the substrate properties as a factor affecting the S.T.J. response, - 162 -leaving the S.T.J, response to a 'fi x e d ' temperature pulse. The observed values of the normalized s i g n a l charge response does decrease with inc r e a s i n g 3A beyond SA y 6, confirming the expected voltage response behavior described i n Chapter 2. It must be emphasized that the procedure used i n Chapter 5 to get the 'normalized? s i g n a l charge was an approximation accurate only f o r temperature charges which are small and uniform over the j u n c t i o n . The actual a - p a r t i c l e heat spike induced temperature changes were of the order of 1 K near the impact area at the time o f s i g n a l current 2 peak (^10 ns a f t e r a - p a r t i c l e impact) and were not uniform over the j u n c t i o n . Thus the above di s c u s s i o n i s v a l i d only q u a l i t a t i v e l y . I t i s p o s s i b l e to c a l c u l a t e numerically the current, voltage and charge response o f a glass substrated S.T.J, to a - p a r t i c l e impact at d i f f e r e n t bath (and therefore average junction) temperatures as described i n Chapter 3 by simply s e t t i n g the bath temperature input to the computer program to d i f f e r e n t d e s i r e values and run the program, but t h i s was not done because i t was f e l t that the gain i n understanding, i f any, does not j u s t i f y the large amounts o f computation. Other than the above crude q u a l i t a t i v e argument and th*; numerical approach, very l i t t l e can be s a i d because of the complex non-l i n e a r nature of the problem. E f f e c t of Junction-Capacitance on j u n c t i o n voltage waveform. F i g . (2.7) shows the equivalent c i r c u i t of S.T.J. The current source IgCt) i - s t n e s i g n a l - c u r r e n t , that i s , the thermally-generated excess j u n c t i o n current. R. , i s the twin-lead cable terminating r e s i s t a n c e at Lo a Ci the room temperature p r e a m p l i f i e r input. The s i g n a l current Ig(t) can be considered as a sequence of charges Q^, deposited i n the j u n c t i o n . A single-charge deposited i n the j u n c t i o n causes the f o l l o w i n g voltage - 163 -across the junction: V q (t) = — e~ / t where x = C-.^/R. + 1/R1 v + 1/R, J - 1 ' bT r J dyn leak ' load (6.5) Thus by linear-superposition the junction voltage i s given by: K QM - ( t ^ - t M ) b K i i N=0 Cj K I (t ) -(K-N)6t = I - ^ - S t e ( 6 . 6 ) N=0 C j where <5t i s the length of the discrete time interval between the arrival of successive charges. Q N is the charge deposited at t N = N.6t., and Q N = J I s ( t ) dt =• 6 t . I s ( t N ) . t N - 1 Going over to the integral gives ft V q(t) = i -J o dt (6.7) (6.7) i s derived i n this manner because i t gives a better physical picture and the equation (6.6) i s used later in this chapter for numerical calculations of the junction signal voltage based on the signal current Ig(t) calculated numerically in Chapter 3. Scaling of theoretical signal current for a reference junction I„ ,.(t) _ Sref to specified junction parameters. In Chapter 3 we calculated the signal current by integrating the thermally caused excess current over the junction expressed methematically: - 164 -IsCtO = ( J „ ( T ) - J C Q'(T n))dA S S t l J - J S S U B J J d A (6.8) A J where Jgg(T) = current per u n i t area o f the ju n c t i o n at temperature T. T = T(x,y,t) i . e . , temperature i s a f u n c t i o n o f l o c a t i o n and time. Tg = bath or ambient temperature. A j = j u n c t i o n area, we can thus write f o r the reference j u n c t i o n : -= I ( J SS re fm " J S S r e f ( V ) d A ^ A J r e f 6 I S S m ' 5 I S S r e f m Since J S S ( T ) - and J g S r e f ( T ) = S ^ f SA 6A where 6A i s a small area element of the jun c t i o n and 61 (T), the current flowing i n t h i s element at temperature T; the same s i z e o f area <SA i s chosen both i n the actual j u n c t i o n and i n the reference j u n c t i o n . Thus Jgg(T) 6 I S S ( T ) J S S r e f ( T ) 6 I S S r e f ™ Confining our at t e n t i o n to t h i s j u n c t i o n element f o r the moment and r e f e r r i n g to the f i r s t paragraph of the s c a l i n g theory s e c t i o n where Igg Q 5^SS SG showed that j— = r ~ » w e S e t T T ^ ~ = 7 7 ^ > where SG, 6G ^SSref G r e f 6 I S S r e f 6 G r e f are the conductances f o r the area elements 6A. Assuming that the junctions are uniform, such that we 6G G / A j 6 G r e f G r e f / A J r e f - 165 where G, G r e f are r e s p e c t i v e l y the j u n c t i o n conductances f o r the ju n c t i o n under consideration and the reference j u n c t i o n r e s p e c t i v e l y . We get:-Jss C T) _ JSSref< T> G r e f / A J r e f and C6.8) becomes: G / A J f I s C t ) = 7~/A J C J S S r e f m " JSSrefCV)dA G r e f / A J r e f fl  A J Thus: I , ( t ) ' G/A JtJSSrafm " JsSraftV"" = 1 Aj G__JA r e f J r e f J ( J S S r e £ ( T ) -A J r e f (6.10) I f A j = A j r e £ then the r a t i o o f the i n t e g r a l s c l e a r l y equals u n i t y . For the case o f an 5.13 MeV a - p a r t i c l e impact at the j u n c t i o n centre even -4 2 when Aj IS i n f i n i t e , and A J r e f = 4 x 10 cm . the r a t i o i s only <1.13. As c a l c u l a t e d i n Chapter 3 and shown i n F i g . (3.17), an a - p a r t i c l e impact on an ' i n f i n i t e ' area j u n c t i o n gave a peak current o f 2.09 ya and an impact -4 2 i n the centre of a f i n i t e j u n c t i o n o f area 4 x 10 cm and the same j u n c t i o n conductance per un i t area gave a peak current of 1.84 ya, thus l i m i t i n g the r a t i o of i n t e g r a l s i n (6.10) to l e s s than 1.13. The r a t i o i s c l e a r l y close to u n i t y i f the ju n c t i o n area i s comparable to the reference j u n c t i o n area, thus we can write I (t) G/A (6.11) ^ S r e f ^ G r e f / A J r e f This s c a l i n g r e l a t i o n i s used l a t e r i n t h i s chapter. - 166 -« • o in lg Curve As Calculated with Assumed Glass Properties I g Curve with Time-Scale Factor = 0.75 (Equivalent to Changing Diffusivity Values by Same Factor) 200 400 600  TIME nsec. FIG. (6.5) Calculated Reference Junction Signal Current. - 167 -- 168 -Numerical c a l c u l a t i o n s o f the e f f e c t o f ju n c t i o n capacitance and a m p l i f i e r  r i s e time on signal-voltage output waveform and comparisons with experimental  observations. Room temperature p r e a m p l i f i e r case. We s h a l l consider the observations made with the Sn ju n c t i o n R67S1J3 and the room temperature a m p l i f i e r f i r s t . As the a m p l i f i e r s i n the system were wide-band RC coupled types the output waveform resembles the ju n c t i o n s i g n a l voltage waveform V ( t ) , which i s S l r e l a t e d to the jun c t i o n s i g n a l current I c ( t ) by equation (6.7). The pre-a m p l i f i e r r i s e time of /v>5 ns can be ignored as i t i s much smaller than the minimum r i s e time 80 ns of the fo l l o w i n g Ortsc l i n e a r - a m p l i f i e r . Assuming the l i n e a r - a m p l i f i e r had a RC type r i s e and f a l l c h a r a c t e r i s t i c s (e.g. -t/x -t/x (1-e ) r i s e , e f a l l ) then the 80 ns ri s e - t i m e from 10% to 90% corresponds to an equivalent RC i n t e g r a t i o n time constant o f 38.5 ns. Thus V„ (t) the signal-voltage output waveform was obtained from V c (t) by ^2 ^1 convolution with t h i s RC time constant. -4 2 R67S1J3 had = 0.22 ft and Aj = 0.0586 x 10 m . Using equation (6.11) t h i s gives Ig(t) =1.55 I r e f ( t ) (Fig> 6.5). The estimated j u n c t i o n capacitance C j = 1500 pf combined with the p a r a l l e l sum of R^^* ^leak* and R ^ o a c j (18 ft) gives a j u n c t i o n RC time constant of 27 ns. Using the procedure o u t l i n e d above and the values o f I^fOO f ° r a (0>0) a - p a r t i c l e impact (see F i g . 3.14 f o r coordinates) V (t) was c a l c u l a t e d and p l o t t e d 2 i n F i g . (6.6). The amplitude of the t h e o r e t i c a l V c (t) curve (A) was 2 1.176 times that o f the experimental V c (t) curve (C) and the peaks occurred b2 at 220 ns and 190 ns r e s p e c t i v e l y . Considering the uncertainty i n the low temperature thermal properties of glass, the agreement i s very good. The l a t e r peak time of the t h e o r e t i c a l curve i n d i c a t e d that the glass thermal - 169 - . d i f f u s i v i t y values used were too low. A change i n the glass thermal d i f f u s i v i t y values would r e s u l t i n a s i m i l a r change i n the time sc a l e ; thus to seek a b e t t e r f i t of c a l c u l a t e d curves to experiment, various changes i n the I r efCt) time-scale were t r i e d , each new time-scale g i v i n g a set o f t r i a l I r ef( lO values. For each set o f ^Tef(.t) values a corresponding set o f V„ (t) was c a l c u l a t e d and compared with the experimental curve f o r 2 match i n peak time and match i n the r i s i n g p o r t i o n of the curve. A good match was obtained f o r a time-scale reduction f a c t o r of 0.75 (corresponding to a d i f f u s i v i t y increase of 1.33; t h i s i s shown i n curve (B) F i g . (6.6). The r a t i o of t h e o r e t i c a l to observed amplitude i s now 1.13 and the waveform match i s b e t t e r . In Chapter 3 when we c a l c u l a t e d the T ^ ( t ) curves we ignored the p a r a l l e l r a d i a l thermal-conductance of the junction f i l m s , which was found to be ^0.178 that of the r a d i a l heat conductance of the thermally a f f e c t e d p o r t i o n o f the glass substrate. To account f o r the e f f e c t o f heat t r a n s f e r along the j u n c t i o n - f i l m s exactly we would have to go to a model of the h e a t - d i f f u s i o n problem i n c l u d i n g the thermal presence of the j u n c t i o n f i l m s . The e f f o r t required f o r t h i s i s not p r e s e n t l y j u s t i f i a b l e . We can see that the e f f e c t o f t h i s extra heat path i s to lower the temperatures i n the impact area more r a p i d l y , t h i s being r e f l e c t e d i n a s l i g h t l y lower s i g n a l - c u r r e n t amplitude and a f a s t e r decay r a t e f o r the current waveform. Thus the i n c l u s i o n o f the j u n c t i o n - f i l m heat conductance would br i n g the t h e o r e t i c a l waveform c l o s e r to the experimental waveform. - 170 -Numerical c a l c u l a t i o n o f a - p a r t i c l e induced output s i g n a l voltage from  the transformer input a m p l i f i e r system arid comparison with experiments. The response of the system (junction under t e s t plus the a m p l i f i e r system) to an e x t e r n a l l y a p p l i e d c a l i b r a t i o n t e s t charge was recorded. This gave the jun c t i o n plus a m p l i f i e r system response to a near d e l t a -f u n c t i o n deposition o f charge i n the j u n c t i o n . Thus as i n the d e r i v a t i o n o f eqn. (6.7), the system output response to the s i g n a l current I c ( t ) i s a convolution o f Ig(t) with d e l t a - f u n c t i o n charge response R ( t ) : Y(t) = j l s ( t » ) R ( t ' - t ) d f (6.12) o where Y(t) i s the output response and R(t) i s the system response to u n i t charge, R(t) = 0 f o r negative argument. The experimental output response curve was obtained using Sn j u n c t i o n R164S1J5, with R^ = 0.30 ft area = -4 2 4A2 x 10 m , thus using the si g n a l - c u r r e n t I g W sc a l e d by eqn. (6.11) we derived above f o r the input, we can c a l c u l a t e the expected output using (6.12). Unfortunately Ig(t) values are a v a i l a b l e only to 0.42 ys, (the I r e£(t) curve was c a l c u l a t e d to 0.56 ys, which when contracted by the time-scale f a c t o r 0.75 described above gives an Ig(t) curve from 0<t<0.42 ys, Because o f the complexity o f the problem, with the present U.B.C. computer ^1250 sec CPU time i s required per y sec o f the thermal pulse computation. To compute values o f Ig(t) out to ^  8 ys, needed f o r the convolution (6.12), i s not j u s t i f i a b l e i n terms of r e s u l t s . Thus extrapolated values o f I c ( t ) dig S were used i n the c a l c u l a t i o n s . The values -:— / I 0 were c a l c u l a t e d at a dt o s e r i e s o f points along the f a l l i n g p o r t i o n of the l g curve. It was found that t h i s r a t i o i s n e a r l y constant but decreases slowly beyond 0.30 ys i n d i c a t i n g an exponential type of decay with time . The small decrease JUNCTION R164S1JS ct-PARTICLE GENERATED RESPONSE V.G. X304 Ortec Gain Coarse = X3, Fine • X2 Post-Amp. V.G. = X35.2 Theoretical output signal voltage curves with +• Plain exponential-decay extrapolation of I c & Exponential-decay with increasing time constant extrapolation df I { 3 4 TIME fis i I FIG. (6.7) - 172 i n the r a t i o can be accounted f o r by a progressive decrease o f k with time. Two Y(t) curves were c a l c u l a t e d and p l o t t e d i n F i g . (6.7). One Y(t) curve was c a l c u l a t e d with exponential decay e x t r a p o l a t i o n o f I c ( t ) with a constant time constant. The other used an exponential decay with the time constant i n c r e a s i n g by a f a c t o r o f 1.013 f o r each 6 ns. These two curves bracket that expected from the observed change o f the time constant i n the I g ( t ) curve, estimated at a value o f t near the end o f the computer c a l c u l a t e d s e c t i o n o f the curve. Referring to F i g . (6.7) the d i f f e r e n t extrapolations produced no change i n the f i r s t peak o f the s i g n a l v o l t a g e . The successive peaks are smaller f o r the e x t r a p o l a t i o n with i n c r e a s i n g time constant with time (the i n c r e a s i n g time constant can be thought o f as a decrease i n d i f f u s i v i t y with decrease i n temperature). On the whole the d i f f e r e n c e s between the curves are minor. The t h e o r e t i c a l curves had a smaller f i r s t peak-amplitude than the experimental curve and the peak occurs s l i g h t l y l a t e r . The t i m e - s h i f t o f t h i s peak may be accounted f o r by the uncertainty i n the o s c i l l o s c o p e t r i g g e r i n g delay. But even with t h i s c o r r e c t i o n the f i r s t peak i s narrower than the t h e o r e t i c a l curve, thus suggesting a j u n c t i o n s i g n a l current with a narrower and more pronounced peak. The second peak more c l o s e l y approximates the observed curve. The t h i r d peak i s much lower i n amplitude, suggesting a more gradual decay o f Ig. The maximum peak to peak voltage r a t i o f o r the t h e o r e t i c a l and experimental curves i s 1.24 (using the ' p l a i n ' exponential decay ext r a p o l a t i o n of Ig curve). The agreement of theory and experiment i s reasonable. - 173 -Comparison o f t h e o r e t i c a l l y derived and observed output pulse amplitude  d i s t r i b u t i o n . In Chapter 3 i t was shown how a-impacts at d i f f e r e n t l o c a t i o n s r e l a t i v e to the j u n c t i o n can produce-different s i g n a l - c u r r e n t amplitudes and waveforms. C f . ( F i g . 3.13) and ( F i g . 3.14). The r e s u l t a n t t h e o r e t i c a l s ignal-current peak amplitude and t o t a l signal-charge to 0.56 ys f o r a l l points of the impact coordinate-grid were tabulated and amplitude d i s t r i b u t i o n histograms p l o t t e d i n F i g . 3.15, 3.16. The uneven appearance of the histogram i s due to the coarseness o f the impact coordinate g r i d used f o r the computations; too much computer time i s needed f o r a f i n e r g r i d . F i g . (5.25) Chapter 5 shows a representative experimental " k i c k s o r t e r " record of the a - p a r t i c l e induced output pulses made with the transformer input low temperature p r e a m p l i f i e r a m p l i f i e r system described i n Chapter 5. As the a m p l i f i e r system i s l i n e a r and the output voltage amplitude i s s i g n a l charge dependent due to i n t e g r a t i o n i n the input transformer i t i s reasonable to assume that the expected output amplitude i s d i r e c t l y p r o p o r t i o n a l to the t o t a l s i g n a l charge accumulated up to 0.56 ys. Thus the curve i n F i g . 3.16 should c l o s e l y resemble the output amplitude p r o b a b i l i t y density curve. F i g . 3.15 shows a histogram p l o t o f s i g n a l current amplitude Vs. p r o b a b i l i t y density. I f the waveforms of a l l the pulses were s i m i l a r , then the s i g n a l current amplitude would be pr o p o r t i o n a l to the t o t a l s i g n a l charge and thus proportional to output voltage amplitude. In f a c t the waveforms are only roughly s i m i l a r , so that F i g . 3.15 should only approximately resemble the output amplitude p r o b a b i l i t y density curve. These t h e o r e t i c a l d i s t r i b u t i o n curves ( F i g . 3.15 3.16) are i n f a c t c l e a r l y s i m i l a r to the experimental d i s t r i b u t i o n curve i n F i g . (5.25). The experimental curve contains i n a d d i t i o n to the s i z e e f f e c t , - 174 -the r e s u l t s of the "angle of impact" and o f a m p l i f i e r system noise which a l l tend to smear the d i s t r i b u t i o n , thus the high amplitude cut o f f i s not as sharp as the t h e o r e t i c a l curves. The agreement of theory and experiment here i s very important as only a 'thermometer model' o f the glass substrated SPD can give r i s e to the observed pulse amplitude d i s t r i b u t i o n using a monoenergetic a - p a r t i c l e source. Summary:-1 ST The t h e o r e t i c a l expressions f o r I^/G, /R^^G, and ' Cjjpp) Vs. 8A were 9V i n agreement with experiments thus the t h e o r e t i c a l expression f o r -r^r may oT be c o r r e c t l y used to analyse low frequency s i g n a l s . 'Scaling' o f t h e o r e t i c a l j u n c t i o n currents to obtain t h e o r e t i c a l values f o r comparisons with experiment was discussed. Comparison of observed j u n c t i o n s i g n a l voltage pulses with t h e o r e t i c a l j u n c t i o n s i g n a l voltage pulses was made, and the observed output s i g n a l with the transformer input p r e a m p l i f i e r compared to the t h e o r e t i c a l waveform with good agreement. The experimental pulse amplitude d i s t r i b u t i o n ( k i c k s o r t e r record) was compared to the t h e o r e t i c a l Ig peak and Qg amplitude d i s t r i b u t i o n , again with good agreement. - 175 -CHAPTER SEVEN A PROPOSED SUPERCONDUCTIVE PARTICLE DETECTOR  THE HEAT-SINK CHIP TYPE Referring to Figure (7.1) t h i s hypothetical type of p a r t i c l e detector consists of a S.T.J. deposited on a chip of e l e c t r i c a l l y i n s u l a t i n g material with high heat c o n d u c t i v i t y at low temperature, such as diamond and sapphire, and the chip mounted such that heat l o s s from the chips occurs slowly, mainly by r a d i a t i o n and heat t r a n s f e r to s u p e r f l u i d helium f i l m ; ( i f any). The heat from the p a r t i c l e impact q u i c k l y d i f f u s e s i n the chip r e s u l t i n g i n a quasi uniform increase i n the temperature of the chip and of the.S.T.J. deposited on the chip. In t h i s case the thinner the j u n c t i o n f i l m s the b e t t e r , to reduce the heat-capacity of the c h i p - j u n c t i o n combination, (since the thermal-mass i s decreased). The uniform increase of the S.T.J. temperature r e s u l t s i n increased q u a s i - p a r t i c l e tunnelling-current providing the s i g n a l output. This type of S.P.D. appears p o t e n t i a l l y to be the best of the three described. Because of the more uniform increase i n temperature over the j u n c t i o n area, s i g n a l v a r i a t i o n s from j u n c t i o n non-uniformity, i f any, are reduced. The " a n g l e - e f f e c t " and " f i n i t e j u n c t i o n s i z e e f f e c t s " (described l a t e r i n t h i s chapter) f a c t o r s which severely degrade r e s o l u t i o n i n the previous types do not a f f e c t t h i s type of S.P.D. Because of confinem<. it of the heat to the heat-sink chip, the p a r t i c l e energy u t i l i z a t i o n i s much be t t e r r e s u l t i n g i n an order of magni-tude improvement expected i n si g n a l output. Radiation damage to the S.T.J. i s avoided i n the proposed ve r s i o n of the heat-sink chip S.P.D. i n Figure (7.1) because the p a r t i c l e never reaches the j u n c t i o n f i l m . 176 fa - particle trajectory heat sink chip hSSSSSSVsSSSST glass or other / substrate / /////, STJ phonon barrier chip support F i g . 7.1 A l p h a - P a r t i c l e Impinging on Heat Sink Chip Type Superconductive Q u a s i p a r t i c l e Tunnelling Junction P a r t i c l e Detector. 177 -The heat-sink chip model i s j u s t i f i a b l e i f the time f o r temperature averaging i s much smaller than the temperature decay time. As the range of a 5.13 MeV a l p h a - p a r t i c l e i n diamond i s 19.6 u a 20 u thickness in.the chip i s s u f f i c i e n t to stop the a l p h a - p a r t i c l e s assuming that the chip i s the same area as the j u n c t i o n , the dimensions of the c u r r e n t l y used S.T.J, are 0.2 mm x 0.2 mm., we have the chip dimensions as 0.2 mm x 0.2 mm x 20 um. Thf? mean fr e e path o f phonons i n diamond at <2 K i s much greater than the chip dimensions (Reference 7.1). The a c o u s t i c a l v e l o c i t y i n diamond i s >10lt m/sec. thus the s i n g l e t r a n s i t time <20 n sec. with consequent temperature averaging time a few times t h i s value, much smaller than the expected thermal decay time of > l u sec. Based on the heat-sink chip model we can write the following equations:-M.Cp. 6T = 6Q ( 7 . 1 ) | | = K (T1* - T B* ) ( 7.2) where: M = mass of heat-sink chip* Cp = S p e c i f i c heat of the heat-sink chip. 6T = small change i n temperature of the chip, 6Q = small change i n the quantity of heat i n the chip, T = temperature of the chip, assumed uniform, Tg= 'bath' or surrounding temperature, - 178 -K = constant s t r u c t u r a l l y dependent, (can be selected w i t h i n l i m i t s ) , depends on the area weighted sum o f the r a d i a t i o n heat loss r a t e p r o p o r t i o n a l l y constant and the super f l u i d helium f i l m heat l o s s r a t e p r o p o r t i o n a l i t y constant. Equation (.7,1 ) expresses the d e f i n i t i o n of heat capacity, i . e . |§- = M.C . 3T p Equation ( 7.2) expresses heat-loss rate due to r a d i a t i o n (or l i k e processes). Since • SQ = . 6t . We get from Equations ( 7.1), ( 7.2) Mc p6T = ^ St = - K ( T 4 - T B 4 ) 6 t - C7-3 ) For diamond at low temperatures, C^ = aT 3 where a i s the Debye constant thus we get from (7.3 ) d T _ K (T- - I,-) (7.4) Ma T 3 * dt = -Ma dT K (T 4 - . T 4 ) D or (T1* - T ^ ) A e xPl Ma?l where A i s a constant of i n t e g r a t i o n , equal to (T ^-T 4 ) - 1 7 9 -Thus we get f i n a l l y - 4 K T Tk = ( T o 4 - T BM e Ma" + T ^ - 4 K h -or T(t) = [ ( T ^ - T ^ ) e m * + V ] ^ - 5 ) We next c a l c u l a t e the i n i t i a l temperature T q when a quantity o f heat 6 Q q i s deposited i n the heat-sink chip by the a l p h a - p a r t i c l e : From ( 7 . 3 ) T r 6Q = J Ma T 3 dT = Ma 4 4 (7 . 6 ) 4 1 o B J The i n t e g r a t i o n i s necessary because of the temperature dependence of heat capacity of the chip. Ma and by d i f f e r e n t i a t i o n : -4 6 Q . - 3 / 4 i i = B . ( 7 . 8 ) 6Q_ Ma - 180 -and 61, SS v V 2GAaK Dg 2 e * V r 3 / 4 (ev+A) - A] [• Ma eMa (7.9) From equations ( 7.7) we get the i n i t i a l temperature of the chip chip. S u b s t i t u t i n g T q i n equation ( 7,5) we get the chip (and S.T.J.) temperature as a function of time. S u b s t i t u t i n g t h i s temperature i n equation (2.8) f o r N.S. and equation (2.15) f o r S.S. junctions we get I v r_ or I__ as a fu n c t i o n of time, thus a l l NS SS necessary S.P.D. parameters can be derived a n a l y t i c a l l y . Equation ( 7.9) gives a u s e f u l s e n s i t i v i t y parameter, and can give the signal-current f o r a low-energy p a r t i c l e impact. I t i s po s s i b l e to improve r e s o l u t i o n f u r t h e r at low pa r t i c l e - e n e r g y by reducing the chip thickness and thus the heat capacity. The improvement i s l i m i t e d by the heat capacity of the S.T.J., and heat leakage through e l e c t r i c a l connections to the S.T.J. This type of S.P.D. i s d i f f e r e n t from the glass substrate type mainly i n the e f f e c t i v e thermal s i z e and thermal c o n d u c t i v i t y of the substrate i n contact with the jun c t i o n f i l m s . The heat-sink chip i s chosen such that i t has the smallest p o s s i b l e heat T , when a p a r t i c l e of energy 6Q i s stopped i n the heat sink - 181 -capacity consistent with stopping the impacting p a r t i c l e , and conducting the heat r a p i d l y to a l l parts of the j u n c t i o n f i l m to obtain the maximum r i s e i n temperature at the j u n c t i o n f i l m . None of these features e x i s t f o r the glass substrate type. - 182 -Limits on Performance o f the SPD. The heat-sink chip type SPD o f f e r s the best t h e o r e t i c a l prospects f o r high performance, hence only t h i s type w i l l be dealt with i n t h i s s e c t i o n . One of the l i m i t a t i o n s i s the heat capacity of the STJ f i l m s . For the junctions used i n our experiments, the f i l m thickness was about 4000 A (top and bottom f i l m s ) , o f Sn. The heat capacity of t h i s STJ -12 at 1.2 K (the operating temperature) i s 'v* 2.43 x 10 J / K. Conceivably a STJ can be made with films /10 as t h i c k , with cooled s u b s t r a t e , thus -12 with heat capacity o f 0.243 x 10 J / K. A diamond heat-sink chip with the same heat capacity at 1.2 K must then be 65.7 urn t h i c k , i f i t i s o f the same dimensions as the STJ, e.g. 0.2 mm x 0.2 mm. Assuming = 91 -4 100ft and = 0.526 x 10 amp/ k (these have been experimentally achievable values by the author) we get 0.575 KeV/yV of s i g n a l (or 1.739 yV/ KeV) . From equation (2. ) .BA e -1 V N T = A . and p u t t i n g i n numbers, BA = 5.375 2 C j A = .8905xlO" 2 2J C j = 1.5xl0~ 9 Farad or /Vj^jp = 0.917 yV , t h i s i s an overestimate as we assumed i n f i n i t e bandwidth. Thus f o r a 1:1 SNR c r i t e r i o n of r e s o l u t i o n , i t i s p o s s i b l e to resolve * 0.527 KeV, (assuming a n o i s e l e s s a m p l i f i e r ) . This f i g u r e can b<: improved *' i n f a c t our present low-temperature a m p l i f i e r can give 1:1 SNR f o r 0.5 yV s i g n a l . - 183 -i f STJ's with lower heat capacity can be made. With t h i s s e n s i t i v i t y we come against a l a r g e - s i g n a l l i m i t , a large current-response cause 'saturation*. This s a t u r a t i o n can be avoided by b i a s i n g not at the max. Rdyn P ° i n t » but at a high current low p o i n t , such that f o r the desired s i g n a l s , the device operate at the point of max. R^y^.> thus we have an e l e c t r o n i c a l l y adjustable 'window', o f 2A i n width f o r our -3 example t h i s means a window o f 1.11 x 10 v o l t s or ^  639 KeV width. This l i m i t a t i o n i s inherent, i f S i s the s e n s i t i v i t y of the detector i n v o l t s / KeV and 2A i s expressed i n v o l t s , then the window W i s given by W < 2A/S. 3 Lower operating temperatures are achievable, f o r example using He temperatures o f 0.3 K are r e a d i l y a t t a i n a b l e by simple pumping. With 3 4 He /He d i l u t i o n r e f r i g e r a t o r temperatures of ^  0.015 K can be attained. 3 The He r e f r i g e r a t o r appears to be more p r a c t i c a l . Assuming 0.4 K i s attained at junction films of A l , (corresponding to BA = 5.3, as i n the previous example with Sn). The heat capacity f o r the 0.2 mm x 0.2 mm -14 x 400 A junction films i s 0.896 x 10 J / K. Assuming the same junction parameters as before (since BA i s the same) we get 47.2 yV/KeV f o r the s e n s i t i v i t y o f the detector. Further, since the t o t a l inherent noise i s pro p o r t i o n a l to A (C.F. equation 2.45) the t o t a l inherent junction rms noise-voltage i s <0.522 yV. Thus the inherent r e s o l u t i o n l i m i t f o r SNR (s i g n a l peak v o l t a g e / r m £ . noise voltage) = 1 i s 11.3 eV, assuming a n o i s e l e s s a m p l i f i e r . We next consider the magnitude of s t a t i s t i c a l - f l u c t u a t i o n noise f o r the A l junction at 0.4K. Assuming a p a r t i c l e energy of 20 KeV, we should get 0.943 mV o f s i g n a l voltage or 9.43 ya of si g n a l current. Assuming a current-decay time constant of 5 ys, the s i g n a l charge i s then Q s = 47.15 pC. Corresponding to a number of charge c a r r i e r s N = 0.2943 x 10^. Thus - 184 -i f Faro f a c t o r = 1 the r e s o l u t i o n i s 1.842 x 10 corresponding to 86.6 eV FWHM assuming gaussian l i n e peak I f the Fano f a c t o r i s the same as that f o r Ge, F = 0.08, then — = — = 0.521 x 10" corresponding to 24.5 eV FWHM assuming q N gaussian 1: peak 4 This compares with N =0.6803 x 10 f o r a 20 KeV p a r t i c l e detected by a FWHM. Using the value o f N we had f o r the SPD, above f o r 20 KeV p a r t i c l e energy, we get the energy per charge c a r r i e r w = 0.068 eV as compared to w = 2.94 eV. ' be I f our assumptions and ca l c u l a t i o n s above, based on the h y p o t h e t i c a l 'Heat-sink Chip* type superconductive p a r t i c l e detector are c o r r e c t , then the SPD i s a p r a c t i c a l device, an improvement over the c u r r e n t l y a v a i l a b l e detectors. I t may be o f use i n the spectrometry o f X-rays i n the range 100 eV to 20 KeV say, where the s t a t i s t i c a l noise i s smaller and the inherent noise (11.3 eV) would be dominant. Ge junction-detector, and CTcl/q = 0.343 x 10~ 2, corresponding to 161.2 eV - 185 -CHAPTER EIGHT CONCLUSIONS P r i n c i p a l Results from the Present Work The s i g n a l - c u r r e n t pulse through a superconductive t u n n e l l i n g j u n c t i o n , r e s u l t i n g from the impact o f an a - p a r t i c l e on the ju n c t i o n (deposited on a glass-substrate) was found to be nearly e n t i r e l y due to the subsequent r i s e i n temperature o f the jun c t i o n area near the impact p o i n t , i n c r e a s i n g the q u a s i p a r t i c l e density and thus the t u n n e l l i n g current i n that area. Numerical c a l c u l a t i o n s based upon t h i s mechanism f o r j u n c t i o n signal-current production, and upon c l a s s i c a l h e a t - d i f f u s i o n , gave signal-voltage waveforms resembling observed s i g n a l voltage wave-forms ( C f . Ch. 6 F i g . 6). This approach also p r e d i c t e d that f o r a f i n i t e area j u n c t i o n on a glass substrate an output pulse amplitude d i s t r i b u t i o n ( f o r a monoenergetic source o f a - p a r t i c l e s o f energy 5.13 MeV) would have no l i n e s or peaks. A pulse-amplitude d i s t r i b u t i o n with a r a p i d decrease i n pulse-density (per u n i t energy) with i n c r e a s i n g energy, followed by a plateau region and a sharp high amplitude cut o f f was p r e d i c t e d ( C f . F i g . 3.15, 3.16). A very s i m i l a r amplitude d i s t r i b u t i o n was experimentally observed. Based on the agreement o f theory and experiment we can conclude with reasonable confidence that thermal-model f o r the production o f j u n c t i o n s i g n a l - c u r r e n t i s v a l i d . The parameter 8A was used i n studying superconductive-tunnelling j u n c t i o n c h a r a c t e r i s t i c s . The r e s u l t s were thus app l i c a b l e to super-conductive t u n n e l l i n g junctions made with any superconductor. The - 186 -derived t h e o r e t i c a l expressions f o r j u n c t i o n c h a r a c t e r i s t i c s were v e r i f i e d f o r SS junctions by experimental data, thus the t h e o r e t i c a l p r e d i c t i o n s based on these expressions should be v a l i d . The main t h e o r e t i c a l r e s u l t s are that an optimum BA value e x i s t f o r a s p e c i f i e d junction-capacitance C j and bandwidth of the expected s i g n a l , Af, t h i s value being BA ^ 6 f o r Cj = 1500 p f and Af = 10 6 Hz, and that noise power associated with the junction i s p r o p o r t i o n a l to A. From these r e s u l t s we conclude that f o r the best s i g n a l to noise r a t i o we s e l e c t the lowest A such that at the optimum BA value f o r the j u n c t i o n , the corresponding temperature i s obtainable experimentally. The t h e o r e t i c a l expressions f o r NS junctions were not v e r i f i e d experimentally, but these were based on well accepted t h e o r e t i c a l d e rivations ( f o r example I. GIAVER, r e f . 2.1). The t h e o r e t i c a l comparison between SS and NS junctions showed co n c l u s i v e l y that SS junctions are b e t t e r f o r use as superconductive 9 p a r t i c l e detectors f o r bandwidth < 10 Hz. Experimentally, a - p a r t i c l e induced s i g n a l pulses were observed with Sn and Pb ju n c t i o n s . For the Sn junction R67S1J3 using the room temperature p r e a m p l i f i e r ( C f . Ch. 5), the maximum jun c t i o n s i g n a l voltage amplitude was 29.9 uV, and the measured equivalent input noise was 3.3 uV RMS corresponding to a SNR of 9.06. Using the transformer-input low temperature p r e a m p l i f i e r a s i g n a l t o noise r a t i o o f 20.6 was observed f o r Pb junction R148S2J2 and a SNR o f 40.0 f o r the Sn junction R164S1J5, s u f f i c i e n t to give a r e s o l u t i o n of ^  128 KeV l i n e - . width i f a line-type pulse amplitude d i s t r i b u t i o n were present. With the 5.13 MeV a - p a r t i c l e s used, as mentioned above no l i n e s or peaks were present i n the pulse amplitude spectrum. Based on the agreement between - 187 -theory and observations we can be reasonably confident that the p h y s i c a l phenomena associated with a - p a r t i c l e induced s i g n a l - c u r r e n t i n the superconductive p a r t i c l e - d e t e c t o r are understood. Expected Performance of Superconductive P a r t i c l e Detectors The glass-substrate type S.P.D. because of the f i n i t e j u n c t i o n - s i z e e f f e c t ( d e t a i l e d i n Chapter 3) cannot give a line-type spectrum. In a d d i t i o n , the 'angle-effect' f u r t h e r smears out the expected sharp high-energy cut o f f f o r normally i n c i d e n t p a r t i c l e s i f the p a r t i c l e penetrates deeply i n t o the substrate. Thus the glass-substrate type S.P.D. i s of no p r a c t i c a l value as a p a r t i c l e energy spectrometer. Based on the understanding o f the o r i g i n of the junction s i g n a l - c u r r e n t , a t h e o r e t i c a l l y s uperior type o f S.P.D. i s proposed, the Heat-sink chip type. This type has not yet f a b r i c a t e d , however, based on the geometry of the S.P.D. and our t h e o r e t i c a l understanding we can c a l c u l a t e the s i g n a l -current waveform of t h i s type a n a l y t i c a l l y , the d e t a i l e d d e r i v a t i o n s are included i n Chapter 7. For an Al-Al^O^-Al j u n c t i o n operated at 0.4 K ju n c t i o n 3 temperature (using a He cryogenic system) the inherent noise f o r the S.P.D. was estimated to correspond to <11.3eV, energy r e s o l u t i o n and the energy per charge c a r r i e r (per e l e c t r o n i c charge) w=0.068eV (see Ch. 7). For comparison the best p a r t i c l e energy spectrometers a v a i l a b l e at present are l i t h i u m d r i f t e c f r e f germanium junction detectors which have an inherent noise ^ 115 ev 1 31 and energy per charge-carrier w = 2.94 ev. Thus used with a low noise p r e a m p l i f i e r l i k e the superconductive a m p l i f i e r of Ref. 5.7., the heat-sink chip type S.P.D. promises to be an improvement over e x i s t i n g p a r t i c l e energy spectrometers i n the studies o f low energy (<10 kev) - 188. -p a r t i c l e s and x-rays. Future work As estimated above the heat-sink chip type o f S.P.D. should be a us e f u l device i n the spectrometry of low energy p a r t i c l e s and x-rays. Actual samples o f t h i s proposed S.P.D. must be f a b r i c a t e d t o v e r i f y the estimates. Further improvements are t h e o r e t i c a l l y p o s s i b l e with the use o f lower temperatures and lower energy gap superconductors f o r the tu n n e l l i n g - j u n c t i o n s , (the lower temperatures to be reached with a 3 He d i l u t i o n r e f r i g e r a t o r ) . To f u l l y r e a l i z e the p o t e n t i a l o f the S.P.D., superconductive p r e a m p l i f i e r s mentioned above should be i n v e s t i g a t e d and developed. T e c h n i c a l l y i t should be p o s s i b l e to f a b r i c a t e both devices simultaneously i n the same f a b r i c a t i o n run. A conventional semiconductor low temperature a m p l i f i e r may be used with the superconductive p r e a m p l i f i e stage, i f necessary, before feeding the s i g n a l out o f the c r y o s t a t . I t would be necessary to separate the He gas from the S.P.D. (using, a c o l d finger) toprevent loss of r e s o l u t i o n due to s c a t t e r i n g o f the p a r t i c l e by the gas. As the proposed S.P.D. uses an Al-A^ O ^ - A l tunnel j u n c t i o n , the room temperature degradation and thermal-cycling degradation problems may not e x i s t , as these junctions are known to be durable, however, should there be such problems then t h i s i s another area o f p o s s i b l e improvements. - 189 -APPENDIX 5.1 For low b i a s magnetic f i e l d s current steps can occur i n S.T.J. I.V. c h a r a c t e r i s t i c s due to Josephson e f f e c t . ( F i g . l ) I f the j u n c t i o n i s biased near t h i s current step then the current r i s e produced by a p a r t i c l e impact would cause the voltage across the j u n c t i o n to change l e s s than otherwise, that i s , the voltage change i s 'clipped' by the current step. This c l i p p i n g causes an increase i n the number of pulses with amplitude equal to the d i f f e r e n c e between the b i a s point voltage and the voltage at the current step, thus producing a ' f a l s e ' peak i n the k i c k - s o r t e r record (Fig. 2). T h i s must obviously be prevented i f the STJ i s to be used as a p a r t i c l e energy spectrometer. - 190 -[ * momentary S.T.J. IV char, with p a r t i c l e impact v " S.T.J. IV char. ft v bias point voltage current step voltage FIG. 1. CURRENT-STEP SIGNAL-VOLTAGE CLIPPING EFFECT. I FIG. 2. OBSERVED FALSE-PEAK EFFECT DUE TO CLIPPING FOR JUNCTION R164S1J5. - 191 -BIBLIOGRAPHY  References Chapter 1 s (1.1) Dearnaley, and Northrop, "Semiconductor Counters f o r Nuclear Radiations" 2nd Ed., E. and F.N. Spon Ltd., London, (1966). (1.2) as above, page (89+91) . (1.3) Goulding, Walton and Pehl "Recent Results on Optoelectronic Feedback P r e a m p l i f i e r s " , IEEE Trans, on Nuclear Science (U.S.A.) V o l . 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Mendelsohn, "Cryophysics", p.120, Interscience, (1960). - 195 -References Chapter 4 (4.1) "The formation of metal oxide f i l m s using gaseous and s o l i d e l e c t r o l y t e s " , J.L. Miles and P.H. Smith, J . of the Electrochem. S o c , Vol. 110 p. 1240 Dec. (1963). (4.2) "Plasma anodized aluminium f i l m s " , G.J. T i b o l and R.W. H u l l , J . of the Electrochem. S o c , V o l . I l l p. 1368 Dec. (1964). (4.3) "Physics of Preparation o f Josephson- B a r r i e r " , W. Schroen, J . Appl. Phy., V o l . 39 #6 p. 2671 May (1968). (4.4) "Anodic Oxide Films", C.J. Dell'Oca, D.L. P u l f r e y and L. Young, U.B.C. Department of E l e c t r i c a l Engineering, P r i v a t e Communications. (4.5) " T i n Whiskers" Kehrer and Katdereit, Appl. Phy. L e t t . 1_6 #11 p. 411 June (1970). (4.6) Holland, L., Vacuum Deposition of Thin Films, London, Chapman £ H a l l (19 (4.7) P.P. L u f f and M. White, Vacuum, 18_ #8 p. 437-450, Pergamon Press,(May 19 (4.8) Degennes, Superconductivity o f Metals and A l l o y s , W.A. Benjamin, New York, p. 227-238 (1966). (4.9) G.H. Wood, "The Detection of a - p a r t i c l e s with superconductive t u n n e l l i n g junctions", Ph.D. t h e s i s , Departme.it of Physics, U.B.C. (1969). - 196 -References Chapter 5 (5.1) G.K. Mendelsohn, Cryophysics, Interscience, New York.(i960). (5.2) C.J. Adkins, P h i l . Mag. 8, 105 (1963). Rev. Mod. Phys. 36_, 211 (1964). (5.3) J.R. S c h r i e f f e r , and J.W. Wilkins, Phys. Rev. L e t t s . 20, 581 (1966). J.W. Wilkins, "Tunnelling Phenomina i n S o l i d s " Plenum Press, (E. Burstein and S. Lundquist, Eds.) (1967). (5.4) H.P. Kehrer and H.G. Kadereit "Tracer Experiments on the Growth o f Sn Whiskers", Appl. Phys. L e t t s . 16_, No. 11, p. 411 (1 June 1970). (5.5) R.J. H a r r i s and W.B. Shuler, "500 Vol t Resolution with a S i ( L i ) Detector using a cooled F.E.T. P r e a m p l i f i e r " . Nuclear Insts. and Methods. 51_ 341 (1967). (5.6) E. E l a d and M. Nakamura, "Hypercryogenic Detector-F.E.T. U n i t , Core o f High Resolution Spectrometer". IEEE Trans. Nuclear S c i . (U.S.A.), Vol. NS-15 No. 3 p. 477-85, June 1968. (5.7) K.T. Bumette and V.L. Newhouse, "Observation of Single Fluxon D r i f t through a Superconductor". J.A.P. 42, No. 1 p. 38-146 (January 1971). (5.8) V. Radhakrisnan and V.L. Newhouse "Noise analysis f o r a m p l i f i e r s with superconducting inputs", J.A.P. 42, No. 1 p. 129-139 (Jan 1 (5.9) R.R. Green "Mosfet Operation at 4.2°K" Rev. S c i . Inst. 39_, No. 10 1495-1497, (October 1968). (5.10) 0. P a r r i s h , Report on low temperature a m p l i f i e r s , p r i v a t e communication. (5.11) F. Witteborn, (Stanford Research Inst.) p r i v a t e communicatici to Professor Gush, Physics Department, U.B.C. (5.12) G.H. Wood, Table 3.3, page 76, Ph.D.. Thesis, Department o f Physics, U.B.C (1969). (5.13) W. Schroen, "Physics of Preparation of Josephson-Barriers", J.A.P. 39, No. 6, p. 2671(1968). (5.14) E. Burstein, S. Lundquist, "Tunnelling Phenomena i n S o l i d s " , Plenum Pres (1967). - 197 -References Chapter 7 (7.1) Berman Simon $ Wilks, Nature 168_ 227 (1951) PUBLICATIONS & PATENTS (PARTIAL LIST) "Seismic work with light-weight equipment on arctic glaciers". Axel Heiberg Island Research Reports, McGill University, Prelim, report 61-62 "The Design of a Monolithic Integrated RST-JX Flip-Plop".+ Can. Electronic Eng. Sept, 1966 "Large-Scale Integration by Redundancy Adjustment of Probabilities" Can. Electronic Eng. Nov. 1967 "An Improved Avalanche Injection Transistor" Proc. I.E.E.E., Letters. Jan. 1968. Vol. 56 No. 1 p. 1 0 5 "The Schottky-Barrier-Collector Transistor"+Solid-State Electronics, Pergamon Press, Vol. 11, pp. 613-619. 1968 +Patented, patents assigned to Northern Electric Ltd. Potentiometer" U.S. Pat. 3,284,697 Issued Nov. 1966 Voltage-Scanned Device" U.S. Pat. 3,388,255 Issued Jan. 1970 Voltage-Scanned Device" Can. Pat. 793,399 Issued Aug. 1968 Spot Scanner" U.S. Pat. 3,558,897 Issued II "Electronic Digital Telephone Exchange Spot Scanner" Jan. 1 9 7 1 Can. Pat. 9 0 1 , 6 8 7 May 1 9 7 2 pat. Pending Issued II 

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