Abstract of Study of Vapor-Deposited Au:Er Films and Development of a Metallic

Transcription

1 Abstract of Study of Vapor-Deposited Au:Er Films and Development of a Metallic Magnetic Calorimeter for Future X-ray Astronomy Missions by Hiroshi Eguchi, Ph.D., Brown University, May This thesis describes the development of a metallic metallic calorimeters (MMC) for a soft x-ray detection. A MMC utilize diluted concentration of a paramagnetic material in a non-magnetic metal host as a temperature sensor. The sensor is placed in a weak field and operated typically below 100 mk. The temperature rise on absorption of a particle leads to a change of the magnetization of the sensor material, which is read out by a dc SQUID magnetometer. A field of application for a MMC is x-ray astronomy as a focal plane detector for imaging and high energy resolution spectroscopy. Thin film technology is suitable to fabricate such detector arrays. Thin films of erbium diluted in gold (Au:Er) were dc magnetron sputter-deposited using Au:Er alloy targets under different conditions, and the magnetic properties of the films have been studied. The magnetization of the film agreed with that of the target material from room temperature down to 200 mk, however, the magnetization of the film showed an enhanced exchange interaction among Er ions below 200 mk. The possible origin of the interaction is discussed. Au:Er films were deposited on flux transformer chips of four pixel MMC arrays. Meander pick-up coils for each pixel also provide a magnetic field by applying a superconducting persistent current. The test results of the prototype detector arrays are presented. X-ray signals of 55 Fe source are analyzed.

2 Study of Vapor-Deposited Au:Er Films and Development of a Metallic Magnetic Calorimeter for Future X-ray Astronomy Missions by Hiroshi Eguchi B. A., Washington University in St.Louis, 1999 Submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in the Department of Physics at Brown University Providence, Rhode Island May 2009

3 c Copyright 2009 by Hiroshi Eguchi

4 This dissertation by Hiroshi Eguchi is accepted in its present form by the Department of Physics as satisfying the dissertation requirement for the degree of Doctor of Philosophy. Date Prof. George M. Seidel, Director Recommended to the Graduate Council Date Prof. Ian Dell Antonio, Reader Date Prof. James M. Valles, Jr., Reader Approved by the Graduate Council Date Sheila Bonde Dean of the Graduate School iii

5 Acknowledgements I am thankful to Prof. George Seidel for giving me the opportunity to work with this project, for his continuous guidance and advice from the beginning of the study till the final revision of this thesis. Some of this work depended on the collaboration with other institutions. I am grateful to Dr. Suzanne Romaine for her guidance on thin film fabrications, encouragement, and constant interest. I am grateful to Ric Bruni for his support and helpful discussions. I would like to thank to Dr. Simon Bandler, Dr. Hannes Rotzinger, and members of X-ray Calorimeter group at GSFC for providing me an opportunity of joining the detector test. Some of the important material characterization have been performed using the SQUID magnetometers at the MIT Center for Material Science and Engineering. I would like to thank Dr. Shaoyan Chu and Patrick Boisvert for their advice and support along the years. This work was supported by NASA grants NAG and NNG05WC12G. iv

6 Contents List of Tables ix List of Figures x 1 Introduction 1 2 X-ray Spectroscopy in Astronomy Introduction X-ray Spectroscopy X-ray Processes in Astrophysics X-ray Astronomy with High Resolution Spectrometers X-ray Spectrometers Microcalorimeters Principles of Microcalorimeters Semiconductor Thermistors Transition Edge Sensors Metallic Magnetic Calorimeters Next Generation of Missions in X-ray Astronomy Constellation-X XEUS v

7 3 Metallic Magnetic Calorimeters Introduction Detection Principles Physical Properties of Er in Au Free Er Ion Crystal Field Effect Exchange Interactions Effect of 167 Er isotope Noise and Resolution Limit SQUID Noise Magnetic Johnson Noise Thermodynamnic Energy Fluctuation Deposition of Au:Er Films and Experimental Apparatus Sputtering Deposition Introduction Sputter Yield Energy Distribution of Sputtered Atoms DC Magnetron Sputtering Sputtering System Sputtering of Au:Er Films SQUID Magnetometer Principles of a DC SQUID The SQUID Chip and Circuitry Magnetic Property Measurement System (MPMS) Refrigerator vi

8 4.3.1 Dilution Refrigerator ADR (Adiabatic Demagnetization Refrigerator) Setup for Low Temperature Experiment Magnetization Measurement at Low Temperatures Heat Capacity Measurement Fe Source Characterization of Au:Er Films Introduction DC Magnetization of Natural Au:Er Films Magnetization at High Temperatures and High Magnetic Field Magnetization at Low Temperatures Heat Capacity of Au:Er Film DC Magnetization of Enriched Er-doped Au Films Discussion Possible Cause for Low Temperature Anomaly in Magnetization Energy Resolution Using the Au:Er Films Prototype MMC Detector Array Introduction Meander Geometry Experimental Setup Detector Design and Fabrication Characterization of Sputtered Au:Er Films Film Sputtered at GSFC Au:Er Film Sputtered at SAO vii

9 6.5 Pulse Analysis Rise Time Decay Time Conclusions Summary and Outlook 113 Bibliography 118 viii

10 List of Tables 2.1 Comparison of energies to excite an energy carrier for x-ray spectrometers Sputter conditions for Au:Er films. A 1400 ppm natural Er-doped Au target was used for the depositions of film1 film3. A 800 ppm isotopically enriched with 166 Er-doped Au target was used for the depositions of film4 film7. The Ar gas of % purity was used for film1 film6, while the Ar gas of % purity was used for film Summary of the sputter conditions for Au:Er films at GSFC and SAO. For both cases, Ar gas was used for a sputter gas, and the deposition was done at room temperature Calculated values of Kapitza conductance by the acoustic mismatch model between Au and sapphire Electron-phonon coupling constant in different experiments and theories.107 ix

11 List of Figures 2.1 A thermal model of a calorimeter. The absorber and the temperature sensor are thermally connected with the thermal conductance G as. The absorption of an energetic particle cause the temperature rise of the absorber and the temperature sensor. The energy is then released to the thermal bath through the thermal link with the conductance of G Bath. Typically G as G Bath, namely, the thermalization time within the absorber and the thermometer is much shorter than the relaxation time to return to the thermal bath temperature The energy resolutions of different x-ray spectrometers. XRS is the microcalorimeter of Suzaku. XIS is a CCD detector of Chandra. LEG, MEG, and HEG are the grating spectrometers of Chandra. RGS is a grating spectrometer of XMM-Newton [10] XRS instrument on Suzaku [6]. (a) One pixel of ion-implanted Si thermistor. The absorber is not attached yet. (b) Full view of 6 6 array. HgTe absorbers were manually attached with epoxy The Constellation-X Observatory [13] x

12 3.1 Schematic diagram of metallic magnetic calorimeters (MMCs). The magnetization change of the magnetic sensor is read out as the flux change in the pick-up coil using a SQUID The magnetization vs. inverse temperature of Au:Er (left), and the specific heat vs. temperature (right). The Au:Er sample with 300 ppm enriched with 166 Er was used for both measurements. The solid lines are the theoretical calculated values with α = 5 [22] The ground state energy levels of 167 Er in Au as a function of magnetic field The specific heat capacity of Au:Er with 480 ppm Er of natural isotope abundance. The lines represent the calculated values with considering the contribution of the conduction electrons, RKKY interaction, and the hyperfine interaction [26] (a) Thermal model of a magnetic calorimeter consisting of the spin (with heat capacity C z ) and the electron (C e ) subsystems. (b) Spectral density of the energy fluctuations for C z = C e = 1 pj/k, τ 0 = 1 µs and τ 1 = 1 ms in the model described in (a) The sputter yield for Au as a function of Ar ion energy. The data points are from the works of Laegreid [33], Robinson [34], Andersen [35], and Brauer [36] xi

13 4.2 The energy distribution of thermally evaporated Au atoms at 1500 K and sputtered Au atoms with Ar + ions at 500 ev. For the energy distribution of thermally evaporated atoms, Maxwell speed distribution for Au gas atoms was used for the calculation. For the energy distribution of sputtered atoms, SRIM program was used, The program was run for 10 4 Ar + ions bombarded onto Au target at normal incidence. The probability of atomic collisions and removing Au atoms from the target surface with certain energies was simulated by a Monte Carlo randomization procedure. The numbers for the temperature and the Ar + ion energy is the typical values for thermal evaporation and sputtering, respectively. The average energy for the sputtered Au atoms is 100 times larger than that for the evaporated Au atoms Typical setup of the DC magnetron sputter system. The dotted line stands for the sputter chamber. Inside the chamber is pumped down to 10 7 Torr before the deposition. The target, which is made of the material to be sputtered, is electrically connected to the cathode. The cathode shield, which is electrically grounded, is necessary to prevent unnecessary sputtering from the target surface that doesn t face to the anode. The distance between the cathode ground shield and the target must be short (typically a few mm) not to have a glow discharge The magnetic field on DC magnetron sputter cathode The sputter deposition system used for this work. The chamber is equipped with two DC magnetron sputter cathodes, a translation stage, and a residual gas analyzer (RGA). The pressure gauge and the current controllers for the sputter guns can be seen in top-right in the picture. 46 xii

14 4.6 The process of etching Au:Er films to produce φ=50 µm disks. (a)cut and glue film (b)spin photoresist and bake (c)expose (d)develop (e)etch (f)liftoff (a)the schematic diagram of a DC SQUID. (b)i-v characteristics. (c)v Φ characteristics for a constant bias current I B. From [39] The circuit diagram to measure the change of the flux in the SQUID loop. The left side of the thick vertical line lies on the sample holder attached to the mixing chamber of the dilution refrigerator. The preamplifier and the SQUID controller are at the room temperature. The right side of the broken vertical line is in the SQUID controller QD550. In the flux-locked loop mode, the output voltage is proportional to the feed back current I f that cancels the flux change in the SQUID loop Schematic of the MPMS magnetometer. The magnetic field up to ±5 T can be applied to the sample. The sample mounted in the plastic straw is moved between the bottom of the coil and the top of the coil to induce supercurrent. The induced current is detected by a SQUID that is inductively coupled to the detection coil xiii

15 4.10 Experimental setup for the magnetization measurement. A Au:Er disk was wedge bonded onto a Au pad that was evaporated on the quartz wafer. The Au pad has windows where there is no Au so that one can see through the quartz to position the Au:Er over the SQUID pick-up loop. The quartz was tied to the brass bridge. Thin cigarette paper was inserted between the quartz and the brass bridge to adjust the distance between the Au:Er sensor and the SQUID chip. The distance between the Au:Er sensor and the pick-up loop on the SQUID chip was approximately 30 µm. Au wires were wedge bonded on the second Au pad on the quartz wafer and the brass bridge for good thermal link. A bundle of annealed Cu wires were bolted down between the brass bridge and the Cu sample holder for good thermal link The experimental setup for the heat capacity measurement. A 50 µm Au:Er disk is positioned inside the pick-up loop of the SQUID. A magnetic field can be applied by the superconducting magnet. The brass collimator holds an 55 Fe x-ray source. The distance between the x-ray source and the Au:Er is approximately 2 mm The x-ray energy spectrum of the 55 Fe source. The measurement was made in a field of 1.8 mt and the sample temperature of 61 mk The K α and K β peaks are identified. The red line is a Gaussian curve fit. The energy resolution for 5.9 kev x-rays at the full width at half maximum (FWHM) is 27 ev Magnetization vs inverse temperature of the target material in a field of 5 T. The Er concentration of the target is 1390 ppm determined from the measurement xiv

16 5.2 Magnetization vs measurement of film1, film2, film3, and the target material in a field of 5 T Magnetization vs inverse temperature of the target material and film2 in a field of 10 mt and 50 mt. The diamonds represent the target material, and the circles represents the film 2. The magnetization of the sputtered film follows that of the sputter target material Magnetization of the sputtered Au:Er films, using natural Er-doped Au target, in a field of 3.6 mt. The magnetization of the target material follows the calculated value for 1400 ppm Er doped in Au The heat capacity of film2 in the form of 50 µm diameter, 4.5 µm thick disk, in a field of 3.6 mt. The broken line is the calculated values for 1400 ppm natural Er-doped Au Magnetization vs inverse temperature of the sputter target, which is isotopically enriched with 166 Er doped in Au. The measurement was made in a field of 5 T. The line is the least square fit to the data. The Er concentration of the target from the fit is 800 ppm Magnetization vs inverse temperature of the target material and film4,5,6, and 7 in a field of 5 T Magnetization of four sputtered films deposited using enriched in 166 Erdoped Au target in a field of 2.3 mt Magnetization of the film sputtered with a small air leak ( 10 6 Torr) into the chamber. The measurement was made in a field of 5 T. The 1400 ppm natural Er-doped Au target was used for the deposition. The concentration of Er in the film was reduced to 560 ppm xv

17 6.1 The cross sectional view of the meander coil and the magnetic sensor. The width of the Nb meander stripes is w, and the pitch of the stripes is p as indicated in the figure. The current through the stripes flows perpendicular to the page and generates a non-uniform field in the magnetic sensor Distribution of the magnetic field in Au:Er sensor of 500 nm thick on the insulation layer of 740 nm thick. The current I b = 25 ma was applied through the meander coil. The average field is 3.0 mt [46] The transformer chip and sputtered Au:Er arrays. The size of both a meander coil and an Au:Er sensor is 250µm 250 µm. The Au:Er sensors at four corners of the 6 6 array can be read out with a SQUID. The meander coils of the corresponding sites are connected in series (also see Fig. 6.4). The edge of three Au:Er pixels out of four, that can be read out, are overlapped with Au thermal pad (referred as nonisolated pixel). One pixel does not overlap with the Au pad (referred as isolated pixel) The circuit diagram of the Au:Er array. The meander shaped pick-up coils are inductively coupled to the SQUID input coils on a separate chip. The SQUID chip consists of three independent 16-SQUID arrays Picture of the sample holder for MMC array. Two sets of MMC arrays can be mounted on the sample holder. Au:Er sensors sputtered at GSFC is on one transformer. Au:Er sensors sputtered at SAO is on the other one xvi

18 6.6 The magnetization vs. temperature of the sputtered Au:Er film at GSFC in a field of 5 T. The solid line is the fit to the data with the two parameters; Er concentration and temperature independent susceptibility. The dotted line is the fit to the data with Er concentration as a fitting parameters, while the temperature independent susceptibility is set to that of Au χ = The magnetization vs. temperature of the sputtered Au:Er film at GSFC. The measurement was done from 30 K down to 1.85 K in a field of 50 mt The magnetization of the Au:Er film. A current of 25 ma was charged in the meander coils. The dotted line is the calculated values for 600 ppm natural Er in Au with a current of I b = 25 ma The heat capacity of the sputtered Au:Er film. I b = 25 ma was applied through the meander coils. The dotted line is the calculated values for 600 ppm natural Er in Au of volume V = µm 3 with the current I b = 25 ma The magnetization of the 300 nm Au:Er film sputtered at SAO from room temperature down to 5 K, in a field of 5 T The magnetization of the 300 nm Au:Er film. A current of 25 ma was applied in a meander coil. The magnetization of the thicker films (film2: 4.5 µm and film3: 5.5 µm) presented in Fig was plotted for comparison The measured and calculated magnetization for 300 nm Au:Er film sputtered at SAO. A current of 25 ma was applied to produce a field. 95 xvii

19 6.13 The rise time on absorption of a 5.9 kev photon as a function of temperature. The inset is the signal rise with respect to time measured at 50 mk. The signal rise was measured with open loop mode (without the feed back current) of the SQUID (a) The simulated temperature distribution on 250 µm 250 µm Au:Er sensor at t =10 nsec, 0.1 µsec, 1 µsec, 3 µsec after a 5.9 kev photon is absorbed at the center of the Au:Er sensor. (b) The cross sectional view of Fig (a) in the x-z plane that passes the center of the Au:Er sensor. The temperature distributions at 10 nsec, 0.1 µsec, 1 µsec and 3 µsec are plotted as indicated in the figure The rise time and the fit calculated from the magnetization change of the sensor using the temperature distribution with respect to time. The inset is the magnification of the initial signal rise Pulses of an isolated and a non-isolated pixels. The pulse height is normalized relative to the peak of each pulse. Both pulses were measured at 45 mk Thermal conductance between the Au:Er film and the substrate. The circles are the measured values in this experiment. The broken line is the Kapitza conductance calculated by Swartz and CRESST [49] [52]. The dashed-dot line is the electron-phonon conductance with Σ = W/m 3 K 5 calculated for Au by Allen [56]. The line is the combined thermal conductance given by Eqn xviii

20 6.18 (left):the top view of the non-isolated pixel. The µm 3 Au:Er sensor (shown as red) is connected to the large Au pad (shown as yellow) of 0.3 µm thick. The sensor and the pad is divided into segments of volume of µm 2 base area, and the time evolution of the temperature of each segment was calculated. The magnetization change of the sensor with respect to time was calculated. (right): The simulated pulse decay. The solid lines are the simulation result at 52 mk (bottom) and 59 mk (top). The dashed lines are the measured pulses. The simulated and the measured pulse at 59 mk are given an artificial offset. The pulses were measured a field of 25 ma applied through the coil xix

21 Chapter 1 Introduction The field of x-ray astronomy has been rapidly developing with the advancement of technology. With the development of low temperature detectors, high energy resolution spectroscopy in the soft x-ray band is starting in the field. The x-ray spectra from astronomical bodies will provide us the temperature, density, and matter composition of plasmas. The spectroscopic investigation of space x-rays is expected to reveal high energy phenomena and the origin of the universe. In 1984 Moseley et al. showed the possibility of achieving a high energy resolution with calorimetric x-ray detection at low temperature [5]. The advantage of low temperature calorimetric detection is the signal enhancement due to the reduction of the heat capacity and the thermodynamic fluctuation noise at low temperature. A metallic magnetic calorimeter (MMC) is a type of calorimeter that uses the magnetization of a paramagnetic material as a temperature sensor. Upon an absorption of a particle, the temperature change leads to the magnetization change of the sensor material. The magnetization change is read out using a dc SQUID. In its present state of development, a dilute alloy of Er in Au (Au:Er) as a temperature sensor has shown a good energy resolution [14]. However, it is a single pixel detector, 1

22 2 where the magnetic sensor was processed to the size of 50 µm from bulk material and manually positioned in a SQUID pick-up coil. For the astronomical applications, the development of a technology that fabricates a large number of Au:Er sensors, such as by vapor deposition, is necessary. In this work, fabrication processes and properties of vapor deposited Au:Er thin films for MMCs were studied. The Au:Er films were also deposited directly on microfabricated chips of a four pixel MMC array detector. The performance of the prototype MMC detector array was analyzed. Chapter 2, following this chapter, describes the value to x-ray astronomy of high energy resolution x-ray spectrometers. This field is where microcalorimeters are most needed. Conventional spectrometers are introduced. The principles and different types of microcalorimeters that has been developing are presented. Lastly, two future missions in x-ray astronomy, planned to launch with a microcalorimeter, Constellation-X and XEUS are described. In Chapter 3, MMCs are discussed in detail. As a magnetic sensor, a dilute concentration of Er in Au (Au:Er) was used for this work. Physical properties of Au:Er such as magnetization and heat capacity are discussed. The influence in light of designing high resolution MMC detectors of the presence of the nonzero nuclear spin isotope 167 Er in natural Er is discussed. Lastly, this section contains a general discussion of possible sources of noise. The fundamental limit of energy resolution and possible achievable energy resolution are discussed. Chapter 4 outlines the experimental methods and apparatus used for this work. The principles of sputtering and the dc magnetron sputtering system at SAO for thin Au:Er film depositions are introduced. The fabrication process of Au:Er films sputtered under different conditions is presented. DC SQUIDs are used as a magnetic flux

23 3 to voltage transducer for measuring the magnetic moment in Au:Er films and for the signal read out in the mk temperature range. The principles of dc SQUID magnetometers and different types of magnetometers used in this work are presented. The operating temperature of MMCs are typically below 100 mk. Dilution refrigerators and ADRs are popularly used to cool down to low temperatures. The refrigerators and the low temperature experimental setup are also described. Chapter 5 discusses the experimental results of the properties of the sputtered Au:Er films described in the previous chapter. The magnetization of the films was measured with two different SQUID magnetometers for different temperature ranges. The measured values are compared with the theoretical calculations. The possible origins of the deviations in magnetization at low temperatures are discussed. The heat capacity of an Au:Er film is presented. A MMC detector array aiming for future x-ray astronomy spectroscopic missions has been developed at NASA, GSFC. The detector is fabricated using conventional photolithography technologies in semiconductor industry. In Chapter 6, the design and the results of the first test of a prototype MMC detector array developed at NASA, GSFC are presented. The detector design with meander-shaped pick-up coil is described. The experimental setup for low temperature measurement cooled down with an ADR is presented. The performances and the feasibilities of the detector array in x-ray astronomy missions are discussed. This thesis ends with the summary of the results and the perspectives towards a real instrument in Chapter 7.

24 Chapter 2 X-ray Spectroscopy in Astronomy 2.1 Introduction An x-ray is a high energy electromagnetic wave of wavelength Å, in the energy range of kev. Since the Earth atmosphere is opaque to x-rays, x-rays do not reach the Earth s surface but are absorbed in the atmosphere. The exploration of the universe in the x-ray band had to wait for the development of the detectors and the capability to launch them above the earth atmosphere. The first cosmic x-ray was discovered in 1962 by Giacconi, using a Geiger counter flown on a sounding rocket [1]. The first orbiting satellite Uhuru was launched in 1970, which cataloged 339 x-ray sources mainly from supernova remnants, Seyfert galaxies, and clusters of galaxies, using two scanning proportional counters. Einstein Observatory launched in 1978 had the first x-ray imaging capability with a Wolter-I design telescope and a microchannel plate detector. The typical x-ray detectors at the early stage were the Geiger counter, proportional counter, and gas scintillation proportional counter. The energy resolution was poor (E/ E = 5 10), and those detectors did not have enough resolving power for x-ray spectroscopy. ASCA (Advanced Satellite for 4

25 5 Cosmology and Astrophysics) satellite launched in 1993 was the first mission to use a CCD as a focal plane detector for imaging and spectroscopy in the energy range of kev. The energy resolution of the detector was E/ E = 50 at 6 kev. Fe K α peak was distinguished from K β line, which is about 10% higher in energy than K α. Some of the remarkable scientific objectives achieved were the study of broad Fe lines from active galactic nuclei (AGNs), the determination of heavy element abundances in clusters of galaxies, and spectroscopic analysis of interacting binaries. In the last decade, Chandra Observatory and X-ray Multi-Mirror mission (XMM-Newton) were launched in 1999 and 2000, respectively. Chandra has achieved the very high angular resolution 0.5, while XMM-Newton has a large effective area with three coaligned Wolter-I telescopes, each of which is made up of 53 nested Ni shells. Both satellites have sets of gratings for high resolution spectroscopy in the soft x-ray band (0.1 < E < 10 kev). The energy resolution of the gratings is E/ E = Future x-ray satellite missions are planning to use detectors with even higher resolution for simultaneous imaging and spectroscopy. The structure of plasmas will be revealed with the detectors. The X-ray spectroscopic observations are of increasing importance to understand high energy phenomena in the universe. The following sections introduces x-ray spectroscopy in astronomy. Sec. 2.2 outlines the primary x-ray generating mechanisms in the universe and what can be searched with high energy resolution detectors. The principles and some examples of x-ray detectors are also presented. Sec. 2.3 outlines microcalorimeters, which have been intensely developed for next generation of x-ray astronomy missions. Semiconductor thermistors, TESs (transition edge sensors), and MMCs (metallic magnetic calorimeters) are outlined in this section. Sec. 2.4 introduces Constellation-X and XEUS missions, future missions in x-ray astronomy, where microcalorimeters will be

26 6 on board for high energy spectroscopy. 2.2 X-ray Spectroscopy X-ray Processes in Astrophysics There are two types of x-ray spectra; a continuous spectrum and a non-continuous spectrum such as a line or an absorption spectra. A number of objects that emit x-rays have been found in the universe. The primary mechanism of generating x-ray spectra are the followings. Bremsstrahlung When a charged particle is accelerated by an electromagnetic field, it emits electromagnetic waves. This is called bremsstrahlung. It has a continuous spectrum. X-rays can be emitted by bremsstrahlung from hot plasmas (T> 10 6 K), at which temperatures the hydrogen and helium atoms are fully ionized. Blackbody Radiation Black body radiation is the thermal radiation given by Planck s law. It shows a continuous spectrum. When the temperature of the matter is K, it emits x-rays. Emission from optically thick plasma becomes the blackbody radiation. Inside a star or an accretion disk, the radiation and the surrounding matter are in thermal equilibrium. The x-ray spectra from those objects can be approximated by the blackbody radiation.

27 7 Synchrotron Radiation When a charged particle is moving in a magnetic field, the trajectory becomes a helix along the field with the cyclotron frequency ω = qb mc for non-relativistic (v c) particle. The charged particle also emits electromagnetic waves. For a relativistic particle, the emission is called synchrotron radiation. The spectrum is continuous. In supernova remnants, electrons are accelerated by the shock-wave of the explosion. The electrons can be accelerated to sufficiently high energy to emit x-rays. Inverse Compton Scattering When a relativistic electron elastically scatters a low energy photon, the energy of the electron may be transferred to the photon. The energy of the photon can be as high as in the x-ray band by repeating the scatter process. This is called inverse Compton scattering. The spectrum is continuous. In addition to the continuous spectra, the emission peaks and the absorption edges may be observed in the x-ray spectra. In a hot gas, an inner shell electron may be ejected by colliding with high energy electrons, photons, or nuclei. Then a characteristic x-ray is emitted when there is a transition of electron from outer shell to inner shell. The energy of the emitted x-ray photon is equal to the difference of the two electron energy levels. Since the energy of characteristic x-rays is intrinsic to a given element, the presence of the characteristic lines provides the information of the existence of certain elements. On the other hand, when a radiation passes through matter, absorption lines may be observed in the spectrum. The K shell emission and absorption lines of the abundant materials in the universe such as C, Ni, O, Ne, Mg, Si, S, Ar, Ca, and Fe lie in the kev x-ray band. The x-ray spectroscopy of the soft x-ray band gives the information on the abundances and the physical conditions

28 8 of hot plasma of these elements X-ray Astronomy with High Resolution Spectrometers Observation of x-ray spectra with high energy resolution will pioneer new fields in x-ray astronomy. High resolution detectors can not only identify the peaks in the spectrum from each element but also can show the fine structure of the spectrum, which gives the information of the density of plasmas, ionization processes and chemical abundances in the universe. Also the plasma may have, depending the condition of the plasma motion, a few ev energy (red or blue) shift. In the following we will review a few examples of what kind of physics can be studied with a high energy resolution spectrometer [3]. Thermal Doppler Broadening Ion temperature in a plasma can be determined by measuring the thermal Doppler width of emission lines. The radial velocity distribution in a thermal plasma is Gaussian with the variance σ 2 = kt ion /m ion, where T ion and m ion are the temperature and the mass of the ion, respectively. The resolving power to observe the broadening is E/ E = λ/ λ = c/σ = (m ion c 2 /kt ion ) 1/2 = 1000A 1/2 (T ion /10 7 ) 1/2, where A is the atomic weight of the ions. This indicates that a high spectral resolving power is required for high A. Determination of Radial Velocity Radial velocity spectroscopy can be performed in x-ray astronomy, as in the other electromagnetic wave bands, by measuring the frequency shift. To detect the velocity v of a few hundred km/sec, the energy resolution E/ E > 1000 would be required.

29 9 The velocity corresponds the orbital velocity of accompany stars of black holes and other binary systems. The mass of high density stars such as black holes, neutron stars, and white dwarfs can be determined from the orbital velocity of the accompany stars. Also the distance to the objects can be determined as accurate as 1 Mpc or better from the Hubble s law X-ray Spectrometers Spectrometers can be classified to two types; wavelength dispersive spectrometers (WDSs) and energy dispersive spectrometers (EDSs). WDSs such as transmission gratings, reflection gratings, and Bragg crystals, disperse photons at different angles depending on the energy of photons. The energy of the incident photons can be determined by measuring the angles of dispersed photons with a non-wavelength dispersive detector (typically a CCD). The gratings have a high resolving power but do not have imaging capability. Also the gratings typically have very low quantum efficiency ( 20%) since the photons that go to the zeroth order dispersion angle do not contribute in determining the energy of photons. In EDSs, the energy of a photon is used to produce signal carriers, which may be electrons and ions, electron-hole pairs, or quasiparticles. If an average energy to produce an electron is w, then the number of energy carriers N and its variance σ produced on absorption of an x-ray of energy E is, assuming that they follow Poisson statistics, N = E w (2.1) and σ = N = E w. (2.2)

30 However, the variance does not follow Poisson statistics since the production of each 10 energy carrier is not independent. Therefore, the Fano factor F (0 < F < 1)is introduced to correct the departure from Poisson statistics. The energy resolution is given by E = E σ N = wf E. (2.3) This expression suggests that the energy resolution becomes better for lower energy x-rays. Also detectors with small w produce a large number of the signal carriers, and high energy resolution can be achieved. The values of w for different x-ray spectrometers are listed in Tab In the following, three types of EDS are presented. Gas Proportional Counters In a proportional counter, an incident x-ray ionizes an gas atom (typically Ar or Xe) and emit a primary electron. The electron is accelerated by an electric field, ionizes more gas atoms and generating the secondary electrons. The gas proportional counter is operated in the voltage region such that the number of the secondary electrons, which is read out as a current, is proportional to the number of the primary electrons that is proportional to the energy of the incident photon. The energy resolution is 1 kev for 6 kev x-rays. In a gas-scintillation proportional counter, an x-ray is absorbed in a gas (typically Xe) and generate a photoelectron. The number of the primary electron is proportional to the energy of the incident x-ray photon. The primary electron is accelerated by an electric field and excite the gas atoms. The UV scintillation light due to the deexcitation is measured by photomultiplier tubes. The energy resolution is improved, compared to the gas proportional counter, by a factor of 2 3.

31 11 Detector Energy Carrier w [ev] Proportional Counter Electron 30 Semiconductor Detector Electron-hole pair 3 Superconducting Tunnel Junction quasiparticle Table 2.1: Comparison of energies to excite an energy carrier for x-ray spectrometers Semiconductor Detector Semiconductor detectors have a p-i-n junction. The x-ray should be absorbed in the intrinsic layer. On x-ray absorption, electron-hole pairs are generated, which are separated by an electric field and read out as a current. The average energy of producing an electron-hole pair is smaller than the ionization energy for proportional counters (e.g ev for Si). Therefore, higher energy resolution can be achieved due to smaller statistical fluctuations of the number of the electron-hole pairs. The charge coupled devices (CCDs) is an array of semiconductor detectors. CCDs can be used as an imaging sensor and the energy resolution is 130 ev at 6 kev. Superconducting Tunnel Junction (STJ) A STJ consists of two superconducting films separated by a thin insulator and, therefore, should be operated at low temperatures (typically T<4 K). Absorption of an x-ray breaks up in the superconductor Cooper pairs and generates quasiparticles. On the application of a voltage across the junction, the quasiparticle tunnel through the insulator and can be detected as a current. The energy gap of a superconductor is thousands times smaller than the ionization energy of a proportional counter. Therefore, a large number of energy carriers can be excited, and high energy resolution can be achieved. The energy resolution 2.4 ev at 0.5 kev has been obtained [2]. Since the energy resolution gets better for low energy photons, STJs can have comparable

32 12 energy resolution to the gratings but have imaging capability as well. 2.3 Microcalorimeters Principles of Microcalorimeters When energy is absorbed in matter, it eventually is converted into heat. An X-ray microcalorimeter is a detector that can measure an energy of a single x-ray photon as a temperature rise upon absorption. The microcalorimeter consists of two essential components; an absorber and a temperature sensor, which are connected to a thermal reservoir as shown in Fig The absorber and the temperature sensor are strongly thermally coupled so that the absorption of the incident particle thermalizes within the two components quickly. The temperature rise due to the absorption of a particle can be expressed in terms of the energy of incident photon E and the heat capacity of the detector C, T = E C. (2.4) The detector is weakly coupled to the thermal bath and the temperature of the thermometer and the absorber return to the temperature of the thermal bath after the absorption of an x-ray. The temperature change with respect time can be expressed as C d T dt = G Bath T (2.5) where G Bath is the thermal conductance between the detector and the thermal bath. Therefore, the temperature rise of the detector exponentially decays to the temperature of the thermal bath with the time constant τ = C G Bath. (2.6)

33 13 Absorber G as Heat Link Temperature Sensor G Bath Thermal Bath Figure 2.1: A thermal model of a calorimeter. The absorber and the temperature sensor are thermally connected with the thermal conductance G as. The absorption of an energetic particle cause the temperature rise of the absorber and the temperature sensor. The energy is then released to the thermal bath through the thermal link with the conductance of G Bath. Typically G as G Bath, namely, the thermalization time within the absorber and the thermometer is much shorter than the relaxation time to return to the thermal bath temperature. To obtain a large temperature change, the heat capacity of the detector should be small. Microcalorimeters operate at low temperature (typically below 100 mk), where the heat capacity of the detector and the noise associated with thermal fluctuations are small in order to achieve large signal response and high energy resolution. Different types of technologies for the temperature sensors have been developed to measure T. The absorber stops the incident particles. The absorbed particles interact with the absorber material and transfer the energy. The choice of a material for an absorber depends upon the application. The primary interaction mechanism of energy transfer for the photon of E < 100 kev is the photoelectric absorption. In the photoelectric absorption process, the cross section σ for absorbing a photon depends upon the

34 energy of the photon E and the atomic number of the absorber material Z, and is approximated by the expressed [4] 14 σ Z4 E 3. (2.7) Because of the strong dependence on Z, an absorber of a high Z material can be made to be thin to achieve good quantum efficiency. The material for an absorber should have high quantum efficiency and a low heat capacity. Also the thermal conductivity of the material may be important in choosing the material. For an x- ray microcalorimeter, metal absorbers such as Au [7] [14] and semi-metal absorbers such as Bi [7] have been used. The semi-metal absorber in Ref. [7] has a thin Au layer underneath the Bi absorber for a better thermal conductance. Semiconductor thermistors with HgTe absorbers were tested and demonstrated to have a good energy resolution [8]. In Ref. [9], superconducting absorbers, Sn and Ta were demonstrated for high energy resolution γ-ray TES detectors. A very long thermal relaxation time was observed using the superconducting absorbers, which limits the count rate. Beside the read-out noise, an intrinsic source of noise to microcalorimeters is the statistical fluctuations in the energy content of the detector coupled to the thermal reservoir. This is given by [5] E 2 = k B T 2 C (2.8) where k B is Boltzmann s constant and C is the heat capacity of the detector. Compared to Eqn. 2.3 for the expression of the energy resolution limited by the fluctuation of the number of energy carriers for conventional detectors, the energy resolution limited by the thermodynamic energy fluctuations for microcalorimeters does not depend upon the energy of the incident particles. Fig. 2.2 shows the FWHM (Full Width at Half Maximum) energy resolution in unit of ev for different x-ray spectrometers. The

35 15 energy resolutions of the Suzaku XRS microcalorimeter (see Sec ), the gratings on Chandra and XMM-Newton, and the CCD on Chandra are presented. As for the energy resolution around 6 kev, which is close to the characteristic x-ray of the Fe K lines, the XRS microcalorimeter has the best energy resolution. For the detection of low energy x-rays, the grating spectrometers are better in energy resolution than microcalorimeters. The following section describes the three types of microcalorimeters; semiconductor thermistors, transition edge sensors, and metallic magnetic calorimeters. The metallic magnetic calorimeters, which is the focus of this thesis, is presented in more detail in Chap. 3. Figure 2.2: The energy resolutions of different x-ray spectrometers. XRS is the microcalorimeter of Suzaku. XIS is a CCD detector of Chandra. LEG, MEG, and HEG are the grating spectrometers of Chandra. RGS is a grating spectrometer of XMM-Newton [10].

36 Semiconductor Thermistors Semiconductor thermistors utilize the temperature dependence of the resistance of highly doped semiconductor near the metal-insulator transition for a temperature sensor. At low temperatures, the conduction is due to variable range hopping, and the resistance increases with decreasing temperature. Neutron transmutation doped (NTD) Ge and ion-implanted Si have been developed for the thermometers. The resistance of the thermistors is very large (> 1 MΩ) at low temperatures, therefore, the change of the resistance of the thermistors can be read out using low noise field effect transistors. The best energy resolution achieved using the semiconductor thermistor is E FWHM = 3.2 ± 0.1 ev at 5.9 ev with a HgTe absorber [6]. A microcalorimeter array was launched on Suzaku x-ray observatory in Fig. 2.3 shows a photograph of detector array that was located at the focal planes of the focusing mirrors of the X-Ray Spectrometer (XRS) on Suzaku. XRS is 6 6 ionimplanted Si detector array with HgTe absorbers. The µm absorbers were attached by hand with epoxy. XRS covers field of view. XRS was unable to operate 19 days after the launch due to the loss of liquid helium for cooling down the adiabatic demagnetization refrigerator (ADR). The ADR on board, however, successfully reached 60 mk in space, and XRS achieved 6-7 ev energy resolution using a calibration source, as expected from the ground tests. Due to the poor thermal coupling between the conduction electron and the lattice of the thermistor at low temperatures, the count rate for a semiconductor thermistor is relatively slow (internal time constant 3 msec for Suzaku XRS). Therefore, a filter is needed when observing bright astronomical objects. For future missions, a calorimeter that can stand higher count rates will be necessary.

37 17 Figure 2.3: XRS instrument on Suzaku [6]. (a) One pixel of ion-implanted Si thermistor. The absorber is not attached yet. (b) Full view of 6 6 array. HgTe absorbers were manually attached with epoxy Transition Edge Sensors Transition edge sensors (TESs) are an alternative technology for the thermometer of a microcalorimeter, and are being actively investigated. TESs utilize the sharp change of the resistance of a metal at the transition from the superconducting to the normal state. The combination of superconducting and normal conducting thin bilayer metal films are used to obtain the desired transition temperature. The superconducting transition temperature is less for the bilayer films than that of the superconducting element alone due to the proximity effect. The transition temperature depends upon the thickness of the each layer and can be tuned to obtain the preferred transition temperature by choosing the appropriate thicknesses of the layers. Different combination of bilayer films such as Ti/Au, Ir/Au, Mo/Cu, and Mo/Au have been fabricated and tested. The energy resolution E FWHM = 2.1 ± 0.1 ev at

38 kev has been obtained, using Mo/Au TES with BiAu absorbers [7]. TESs must be operated in the very narrow transition region ( T of a few mk or less). For a steady operation, a constant voltage bias is applied to provide a negative electro-thermal feedback [11]. When a TES of resistance R is operated at a constant bias V b, the Joule heating of the device is V 2 b /R. On absorbing a particle, the resistance of the sensor increases as an consequence. The Joule heating decreases so that the TES returns to the original operating point. The electrical current through TES also decreases as the resistance of TES increases. The change of the current can be read out using a SQUID inductively coupled to the TES circuit. The time constant to recover the working temperature is given by τ eff = τ 1 + α/n (2.9) where τ is the thermal relaxation time without the electro-thermal feedback, n is 4 6 depending on the thermal impedance between the TES and the thermal reservoir, and α is the sensitivity defined as α = dlogr/dlogt. The value of α is typically Therefore, the thermal relaxation time can be one or two orders of magnitude shorter with the electro-thermal feedback than without the feedback. An advantage of TESs is that the sensor and absorber can be fabricated by the vapor-deposition processes. Therefore, it is suitable for fabricating detector arrays by developing multiplexing read out technology. However, for applications that requires large heat capacity absorbers, TESs may not be suitable. The heat capacity of TESs are small, and energy resolution will be significantly affected by attaching a large absorber.

39 Metallic Magnetic Calorimeters Metallic magnetic calorimeters (MMCs) use a paramagnetic material as a thermometer and is the central subject of this thesis. The detailed description on MMC is presented in Chap 3. A single pixel MMC, using Au:Er for a thermometer and an Au foil for an absorber, has achieved 2.7 ev energy resolution at 5.9 kev x-rays [14]. 2.4 Next Generation of Missions in X-ray Astronomy Constellation-X Constellation-X is the next generation NASA X-ray observatory designed as a followup to Chandra Observatory. Constellation-X is an x-ray spectroscopy mission. While Chandra s gratings have made a remarkable technological breakthrough in energy resolution, detectors with even higher energy resolution are required for identifying finer features of the spectra and line intensities to determine the elemental abundances in the universe. The baseline mission requirement for energy resolution is E/ E = 300 for 1 < E < 10 kev and E/ E = 3000 at 6 kev for detailed analysis of Fe line. One scientific goal for Constellation-X is the study of extremely strong gravitational effect of black holes. ASCA observed the broadened Fe emission line from an active galactic nuclei (AGN) [12]. The center of the AGN is considered to have a massive black hole, and gas near the black hole emits x-rays. The observation near the event horizon of the black hole will determine if the broadening is caused by the relativistic spacetime curvature due to the strong gravity near the black hole. This is also a test of general relativity in extremely strong gravity.

40 20 The soft x-ray spectroscopy of Constellation-X is complemented by Hard X-ray Telescopes (HXT) for observing the x-ray band (10 < E < 40 kev). The HXT uses the multilayer, for an x-ray reflector, which consists of alternating layers of high density materials (such as W and Pt) and low density materials (such as Si and C). By setting the thickness of the layers thinner in the depth direction, the multilayer mirror can provide the reasonably high reflectivity over wide energy bandpass. Figure 2.4: The Constellation-X Observatory [13] XEUS The main scientific instrument of the XEUS project (X-ray Evolving Universe Spectroscopy) by ESA (European Space Agency) and Japan is an x-ray telescope with an effective area of 6 m 2 at 1 kev, which is 100 times higher sensitivity than XMM- Newton, and having the energy resolution 1500 around 8 kev. The scientific goals

41 21 include the study of early black holes, the evolution of early galactic clusters. Also the structure of intergalactic medium will be studied by spectroscopic methods. The design is based on a large (10 m 2 ) single x-ray telescope, which would be assembled at the space station. Since the angle of total reflection becomes smaller as the photon energy increases, the focal length for the large diameter telescope is very long. Current design requires 50 m focal length with two separate spacecrafts; one for the mirror and the other for the detector. The two spacecrafts are required to maintain their relative positions with a 1 mm precision.

42 Chapter 3 Metallic Magnetic Calorimeters 3.1 Introduction Metallic magnetic calorimeters (MMCs) have been developed for high resolution x-ray spectroscopy. MMCs are based on the temperature dependence of the magnetization and using the very sensitive technology of SQUIDs to measure the magnetization change. MMCs are different from other microcalorimeters in several aspects. MMCs are not based on the transport property but are based on the thermodynamic equilibrium property, the magnetization. Heat is not dissipated in measuring the magnetization change using a SQUID. This property can be beneficial when designing detector arrays for x-ray astronomy. MMCs are suitable for certain applications that require large absorbers. The heat capacity of the magnetic sensor is rather large (compared to TES for example), therefore, large absorbers can be attached without degrading the energy resolution. This chapter outlines the properties of MMCs. Sec. 3.2 discusses the detection principles of MMCs, followed by, in Sec. 3.3, the physical properties of dilute alloy of Er in Au, which is the material most often used for the MMCs. In Sec. 3.4, noise sources and the fundamental limitation in the energy resolution for 22

43 23 MMC are described. 3.2 Detection Principles Metallic magnetic calorimeters employ a paramagnetic material diluted in a metal host as a temperature sensor. A detector consists of an absorber, a paramagnetic sensor that is strongly thermally connected to the absorber. These are weakly coupled to a thermal reservoir (see Fig. 3.1). The MMC is operated in a weak magnetic field. When a particle of energy δe is stopped in the absorber the temperature of the absorber and the sensor rises by δt = δe C total (3.1) where C total is the heat capacity of the magnetic sensor and the absorber combined. Then the magnetization of the magnetic sensor changes due to the temperature rise. The change of the magnetization is given by δm = M M δe δt =. (3.2) T T C total The magnetization change is read out by a SQUID as a change of the flux in a pick-up coil. For a cylindrical sensor of volume V positioned inside a circular pick-up coil of radius r, the relationship between the magnetization change δm and the flux change in the pick-up coil can be written as δφ = µ 0 GV r M T δe C total (3.3) where the geometrical constant G is the coupling between the two and depends upon the configuration of the detector. From Eqn. 3.2, the magnetic sensor should have a strong temperature dependence, M/ T, in magnetization and a small heat capacity

44 24 Particle Absorber B Magnetic sensor df Pick-up coil SQUID Thermal link Thermal reservoir Figure 3.1: Schematic diagram of metallic magnetic calorimeters (MMCs). The magnetization change of the magnetic sensor is read out as the flux change in the pick-up coil using a SQUID. to obtain a large response. The interactions among spins should be small to avoid a smaller temperature dependence in magnetization and the additional heat capacity associated with the interactions. Therefore, the magnetic moment is embedded in a metal host to reduce interactions among the spins. Having a metal rather than a dielectric material for a host material is advantageous for a fast thermalization time since the coupling of spins to the phonons is very weak below 1 K. The thermalization time is shorter than 1 µs below 100 mk because of the strong coupling between the spins and the electrons. The drawback for having a metallic host is an additional heat capacity of the conduction electrons and the indirect exchange interaction among the localized spins mediated by the conduction electrons. Most of the results to date have been worked out with Er for a magnetic ions and Au for a host material. The best energy resolution to date E FWHM =2.7 ev at 5.9 kev has been achieved [14] for a

45 single pixel Au:Er sensor with an Au absorber, which are manually assembled on a SQUID chip Physical Properties of Er in Au Free Er Ion Er has an incomplete 4f shell. When Er is diluted in a solid hosts, it becomes trivalent ions losing two 6s and one 5d electron. The electron configuration of an Er 3+ ion is [Kr]4d 10 4f 11 5s 2 5p 6. An Er 3+ ion substitutes for an Au atom of the Au fcc lattice site. The 4f electrons are shielded by the outer shells (5s 2, 5p 6 ) of larger radius and is well localized. The ground state of free Er 3+ has L = 6, S = 3/2, and J = L + S = 15/2 determined by Hund s rules. The higher energy state with J = 13/2 is approximately 9400 K above the ground state, and the admixture of the higher state can be neglected for the discussion of the properties of Au:Er at room temperature or below. The magnetic moment µ is proportional to the total magnetic moment J and can be written as µ = g J µ B J (3.4) where µ B is the Bohr magnetron, and g J is the Landé g-factor g J = 1 + J(J + 1) + S(S + 1) L(L + 1). (3.5) 2J(J + 1) For Er 3+, g J = 6/5. The magnetization M of an isolated ion under a magnetic field B is given by the Curie law 2 J(J + 1)B M = (g J µ B ) 3k B T (3.6)

46 where k B is Boltzmann s constant. The Curie law is a good approximation in describing the magnetization of Au:Er at high temperatures (T >100 K) Crystal Field Effect The energy levels of the J = 15/2 state of the Er 3 + ion in a cubic crystal field splits into three Γ 8 quartets, one Γ 6 doublet, and one Γ 7 doublet. The lowest energy of the multiplets is the Γ 7 Kramers doublet. The magnetization deviates from Curie law below 100 K because of the depopulation of the higher energy multiplets. Lea, Leask and Wolf [17] calculated the energy eigenvalues of J = 15/2 within a multiplicative factor. Ebina [18] included Zeeman and crystal field interaction together, and computed eigenvalues for two different orientations for external field with respect to the crystallographic axes. From the magnetization measurement [15] and ESR measurement [16], the ground state doublet has determined to have g = 6.8 and the first excited Γ g state is 16±6 K higher than the ground state. At sufficiently low temperatures, where only the ground state doublet is occupied, the properties of Er in Au can be approximated with the Curie law with the effective spin S = 1/2 and g factor g = 6.8. The heat capacity of the non-interacting two-level spin system with N spins of the energy splitting E = gµ B B is given by the Schottky expression ( ) E 2 e E/k BT C s = Nk B k B T (e E/k BT + 1). (3.7) 2 The heat capacity has a peak at about T 0.4E/k B, has the temperature dependence of T 2 at higher temperatures, and falls off exponentially ( T 2 exp( E/k B T)) at lower temperatures.

47 Exchange Interactions The picture of non-interacting spins for Au:Er is not adequate for quantitative analysis. Interactions among spins need be taken into account. Two types of interactions are relevant to discuss for Er in Au in the context of MMC. One type is the dipoledipole interaction. The other type of interaction is an indirect exchange interaction among localized spins mediated via conduction electrons of the host material, which is called the RKKY interaction. Dipole-Dipole Interaction The spin of a magnetic moment can be treated as a classical dipole moment. The interaction between two spins located at r i and r j can be expressed as where H dipole ij = Γ dipole 1 (2k F r ij ) 3 [ S i S j 3( S i ˆr ij )( S j ˆr ij ) ], (3.8) Γ dipole = µ 0 4π ( gµ B) 2 (2k F ) 3. (3.9) k F is the fermi wave number of conduction electrons of Au, r ij = r i r j is the distance between the two spins, and ˆr ij is the unit vector in the direction of r i r j. The factor with the fermi wave number has been introduced here in order to compare the magnitude of strength with RKKY interaction. The strength of the interaction is anisotropic since it depends upon the orientation of the two spins. RKKY Interaction The exchange interaction between the conduction electron of spin s and the localized 4f electrons of spin S can be written as H sf = J sf s S. (3.10)

48 This interaction produces polarization of the conduction electrons in the vicinity of an Er spins. This polarization falls at a neighbouring Er spins. The 1/r 3 ij falloff is sufficiently long enough range to cover a number of nearest-neighbour sites. As a result, two localized spins can interact via conduction electrons. It is called Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction [19][20][21]. The RKKY interaction between the two localized spins of S i and S j separated by r ij is [ Hij RKKY 1 = Γ RKKY cos(2k (2k F r ij ) 3 F r ij ) 1 ] sin(2k F r ij ) ( S i S j ) (3.11) 2k F r ij 28 and Γ RKKY = Jsf 2 4V0 2 m ekf 4 g 2 (g J 1) 2 h 2 (2π) 3 gj 2 (3.12) where V 0 is the volume per lattice point and m e is the effective mass of the conduction electrons. The RKKY interaction is oscillatory with respect to the separation distance between the two spins. The magnitude of the RKKY interaction is described using a dimensionless parameter α, which is defined as the ratio of the coefficient of the RKKY interaction to the dipole-dipole interaction α = Γ RKKY Γ dipole. (3.13) In order to determine the magnetization and the heat capacity of Er randomly distributed in Au, the probability of field distribution of the exchange interaction was calculated. Walker and Walstedt [23] [24] showed that the probability distribution could be approximated by the Lorentzian form for randomly distributed spins in a continuous medium. Enss [22] has derived the analytical expression for M/ T and the heat capacity C, using the expression for the probability distribution of the exchange field by Walker and Walstedt in a frame work of the mean field approximation, where the exchange interaction was in the Ising form H ex S 1z S 2z.

49 29 Fig. 3.2 shows the magnetization and the specific heat of Au:Er with 300 ppm enriched 166 Er as a function of temperature and inverse temperature, respectively [22]. The deviation in the magnetization plot from the Curie law is due to the interactions among the magnetic moments. The data fits well with the mean field calculation with α = 5. The specific heat shows the Schottky anomaly. However, the width of the peak is twice as wide as it is for the system with non-interacting spins. The theoretical calculation fits satisfactory to the measurement with α = 5. Figure 3.2: The magnetization vs. inverse temperature of Au:Er (left), and the specific heat vs. temperature (right). The Au:Er sample with 300 ppm enriched with 166 Er was used for both measurements. The solid lines are the theoretical calculated values with α = 5 [22] Effect of 167 Er isotope The isotope 167 Er is 23% abundant in natural Er and has the nuclear spin I = 7/2. The nuclear spin influences the magnetization and the heat capacity because of the hyperfine interaction with the 4f electrons. The isotope 167 Er doped in Au was studied in ESR experiment [25]. The spin Hamiltonian for the ground state of 167 Er is written

50 30 Energy [K] Magnetic Field [mt] F m F Figure 3.3: The ground state energy levels of 167 Er in Au as a function of magnetic field. as H = gµ B B S + AI S g N µ N B I (3.14) where the first and the third terms represent the electronic and nuclear Zeeman energies, respectively. The second term represents the hyperfine interaction energy. The hyperfine constant and the nuclear g factor were measured to be A/k B = K and g N = 29, respectively. The zero field energy splitting associated with F = 4 and F = 3 (F = I ± S) multiplets is 140 mk. The energy levels of the lowest energy state Γ 7 doublet can be calculated using those results. Fig. 3.3 shows the energy level scheme as a function of the applied magnetic field. The magnetization and the heat capacity of 167 Er is significantly different from those of Er isotope with zero nuclear spin in the temperatures and magnetic fields

51 31 where MMC is typically being operated. The contribution due to the hyperfine interaction is significant. The heat capacity of 480 ppm natural Er-doped Au was measured in a field from 1.9 mt up to 10.6 mt [26]. The measured heat capacity is shown in Fig. 3.4 along with the calculated values. Two maxima can be seen for the low field measurement. The one at lower temperature is due to the transition within F = 4 multiplet and to the contribution of the isotopes with zero nuclear spin. The one at higher temperature, which is smeared out at high field measurement, is due to the redistribution of the spins between F = 4 and F = 3 multiplets. The contribution of the isotope 167 Er to the heat capacity is about 50% of the total heat capacity at 50 mk. In designing a high sensitivity detector, the isotope 167 Er should be removed and Er needs to be enriched with the isotopes with zero nuclear spin. Figure 3.4: The specific heat capacity of Au:Er with 480 ppm Er of natural isotope abundance. The lines represent the calculated values with considering the contribution of the conduction electrons, RKKY interaction, and the hyperfine interaction [26].

52 Noise and Resolution Limit Noise limits the resolution of a detector. There are three intrinsic noise sources of a MMC; the SQUID noise, the magnetic Johnson noise of the conduction electrons of the sensor and the absorber material, and thermodynamic energy fluctuations between the spin system and the electron system of the detector and between the calorimeter and the thermal reservoir. Other factors that degrade the energy resolution are the fluctuation of the external magnetic field, the fluctuation of the calorimeter temperature, 1/f noise, and the background radiation. This section outlines the intrinsic noises and the limit of energy resolution SQUID Noise The SQUID has an intrinsic flux noise originating from the shunt resistances. The spectral power density of flux noise S Φs can be characterized in terms of the energy sensitivity ɛ. The relationship is [39] ɛ s = S Φ s 2L (3.15) and ɛ s = 16kB T L s C. (3.16) From those equations, one can obtain S Φs L s 3/4. However, in the low-temperature limit, the energy resolution of a SQUID should approach ɛ s > h, which leads to S Φs L s. Currently SQUIDs with flux noise of a few µφ 0 / Hz do not have to involve this complexity of the quantum limit. In the case that the energy resolution of an MMC is limited by SQUID noise, it can in the future be greatly improved by using SQUIDs with lower flux noise.

53 Magnetic Johnson Noise Since there is no power dissipation for MMCs in measuring the flux change of the sensor, there is no intrinsic Johnson noise in a sense of measuring a resistance. However, the magnetic Johnson noise, fluctuating thermal currents of the conduction electrons in a conductor in the vicinity of the pick-up coil and the SQUID, can induce a flux noise. The magnetic Johnson noise can be produced by the host material, the absorber, and by metallic construction materials in the vicinity of the pick-up coil. Varpula [27] and Gillespie [28] have calculated the fluctuation of a magnetic field caused by random motions of charged particles in a conductor. When a conducting sheet of conductivity σ and thickness t is located parallel to the plane of a circular pick-up loop of radius a, separated by the distance z, the spectral flux density is given by This expression is valid when the skin depth δ = of the conducting material. S φ = µ 0 πa 2 σkb T t 8πz(z + t). (3.17) 2/µ 0 σω is larger than the dimension The geometry in which a disk of radius r and the thickness t is sitting inside a loop of radius a is also of interest in the] context of magnetic calorimeter. In this case, the spectral flux noise in the loop is [22] S φ = µ 0 πr 2 CσkB T t 8πa 2 (3.18) where T is the temperature of the conductor and C is a numerical coefficient. C = 1 for small r/a and increases as the ratio r/a increases, reaching C = 1.5 at r/a = 0.8 and C = 2.2 at r/a = 0.95 [22]. We can now estimate the magnetic Johnson noise level using the expressions above. Consider, as an example, the 800 ppm Er-doped Au cylindrical sensor of radius 24 µm

54 34 and 5 µm thick positioned in the circular loop of radius 25.3 µm operated at 50 mk. The conductivity of Au 1 x :Er x can be estimated from Ref. [29]. The residual resistivity of Au:Er linearly depends upon the Er concentration, which can be expressed as ρ = x Ωm. Then from the Eqn. 3.18, the magnetic Johnson noise level is S φ Φ 0 / Hz. The contribution to the magnetic Johnson noise from the absorber also can be estimated. Suppose an Au absorber is attached on top of an Au:Er sensor, 5 µm above the pick-up loop of radius 25.3 µm. Assuming the thickness of the absorber is 5 µm and taking the value of conductivity to be that of Au, σ = Ω 1 m 1, the magnitude of the magnetic Johnson noise is S φ Φ 0 / Hz Thermodynamnic Energy Fluctuation The magnetic Johnson noise, although it can contribute to a degradation of the energy resolution, can be reduced significantly with a proper detector design. The fundamental limitation of the resolution is set by the thermodynamic fluctuation of the energy. The thermodynamic fluctuations of the energy for MMCs were calculated using the model shown in Fig. 3.5 (a). It consists of the spin system with the heat capacity C z and the conduction electron system of the absorber and the sensor with the heat capacity C e. The heat capacity C z is considered to be that of the Zeeman system. The contributions from the interactions among the spins are not taken into account for simplicity. The electron system of the absorber and the sensor can be combined together since the principal impedance of the heat flow is electron-spin coupling. The spin system is connected to the electron system with the thermal conductance G ze, and the electron system is also coupled to the thermal bath with the conductance G eb. We assume that thermalization time within each system is infinitely

55 35 fast. The energy fluctuation arise from the energy exchange between the spins and the electrons and the electrons and the thermal reservoir. The time constant associated with the energy exchange between the spins and the electrons is τ 0 = C eff /G ze, where the effective heat capacity is 1/C eff = 1/C z + 1/C e. The time constant τ 1 is the relaxation time between the calorimeter and the thermal bath and given by τ 1 = C tot /G eb, where the total heat capacity C tot = C z + C e. Usually τ 1 τ 0 since G ze G eb. (a) (b) 10 1 G ze Ce G eb Cz Noise S ez [ev/ Hz] Thermal Bath Frequency [Hz] Figure 3.5: (a) Thermal model of a magnetic calorimeter consisting of the spin (with heat capacity C z ) and the electron (C e ) subsystems. (b) Spectral density of the energy fluctuations for C z = C e = 1 pj/k, τ 0 = 1 µs and τ 1 = 1 ms in the model described in (a). The spectral noise density of the energy fluctuations of the spin system S Ez, using the model, was calculated for C z = C e = 1 pj/k, τ 0 = 1 µs, and τ 1 = 1 ms [30]. The result is shown in Fig. 3.5 (b). The origin of the plateau at lower frequencies is associated with the energy fluctuation between the electron system and the thermal bath with the roll off frequency 1/2πτ 1. The plateau at higher frequencies with the roll off frequency 1/2πτ 0 is due to the energy fluctuation between the spin and the electron systems. The expression for the energy resolution due to the thermodynamic

56 fluctuations was written in terms of the time constants τ 0 and τ 1 [30] and given by where ( 1 E rms = 4K B C e T 2 β(1 β) β = τ 0 τ 1 36 ) 1/4 (3.19) C z C z + C e. (3.20) The energy resolution E rms can be minimized when C z = C e. The energy resolution for the optimized calorimeter is then given by [30] E FWHM = k B C e T 2 2 ( τ0 τ 1 ) 1/4. (3.21) Using the values for the heat capacity and relaxation times for C z = C e = 1 pj/k, τ 0 = 1 µs and τ 1 = 1 ms, the energy resolution is estimated to be E FWHM = 1.4eV. The finite energy resolution comes from the energy fluctuation between the spin and electron system. The corresponding noise level that rolls off at high frequency in Fig. 3.5 (b) is S Ez = 1.65meV/ Hz. The flux noise in the pick-up coil due to the fluctuations of the energy is given by S Φ = β 1 S Ez δφ/δe, where δφ/δe is the sensitivity defined as the flux change per unit energy input. In Ref. [22], the sensitivity was calculated, for the optimized calorimeter that was designed to give the maximum sensitivity, to be δφ/δe = Φ 0 /ev. Therefore, for β = 1/2 the energy fluctuation of the high frequency plateau corresponds to the flux noise of SΦ = 0.33 µφ 0 / Hz.

57 Chapter 4 Deposition of Au:Er Films and Experimental Apparatus This chapter describes the deposition of Au:Er films and experimental apparatus used in this work. Au:Er films were sputtered using a dc magnetron sputtering system at SAO. Sec. 4.1 describes the principles of sputtering deposition. Then the deposition of Au:Er films is discussed. The SQUID plays an important role in characterizing the Au:Er films. Sec. 4.2 introduces the concept of the SQUID magnetometer and the circuitry. The latter part of the chapter discusses the apparatus and experimental setup for the low temperature measurements. For the characterization of the Au:Er films below 1 K, a dilution refrigerator and an adiabatic demagnetization refrigerator (ADR) were used. The principles of the refrigerators are introduced in Sec and Sec The experimental setup for the magnetization and the heat capacity measurement are discussed in Sec

58 Sputtering Deposition Introduction When an energetic particle is bombarded onto the surface of a target material, one or more atoms are ejected if the energy transfered to surface atoms is large enough to break the atomic bonds. This phenomenon is called sputtering. Thin films can be fabricated by accumulating the sputtered atoms on a substrate. Sputter deposition is now widely used technique for depositing thin films, cleaning surfaces, micromachining, depth profiling, and so on, which require microscopic erosion of a surface Sputter Yield An important parameter used to describe sputtering phenomena is the sputter yield. The sputter yield is defined as the number of emitted atoms from the target per incident ion. The sputter yield is influenced most by the acceleration voltage of the incident ions. There is a threshold energy for ions to sputter target atoms. At very low ion energies (E<30-50 ev), there is very little sputtering. Above the threshold energy, the incident ions have enough energy to knock the target atoms off the target. The incident ion impacts a target atom, and then generates a cascade of collisions until the energies of the ion and all the recoil atoms have less than the displacement energy of the target atoms. The energy range of about 50<1000 ev is used for most sputtering applications. The sputter yield is roughly proportional to the incident ion energy in this energy range. A number of researchers [33][34][35][36] have measured the sputter yields for vast range of energies of incident ions. The relationship between the sputter yield and the incident Ar ion energy for Au target is plotted in Fig Also the

59 39 number of sputtered atoms is proportional to the flux of the incident ions (namely, ion current). These facts suggest that the sputtering rate is proportional to the cathode power. At very high energies (E>10 kev), an incident ion is implanted into deep inside the target, and the energy of the ion diffuses away from the surface. Therefore, the sputter yield at this energy regime becomes smaller as the energy of incident ion increases. Ar, Kr, and Xe are commonly used for the sputter process gas because they are chemically inert and have high sputter yield Sputter yield [atoms/ion] Laegreid Robinson Brauer Andersen Ar ion energy [ev] Figure 4.1: The sputter yield for Au as a function of Ar ion energy. The data points are from the works of Laegreid [33], Robinson [34], Andersen [35], and Brauer [36].

60 Energy Distribution of Sputtered Atoms The average kinetic energy of the atoms thermally evaporated from the source of temperature T is of the order of kt. If T is an evaporation temperature for a metal (T 1500 K), then kt is about 0.1 ev. On the other hand, sputtered atoms come off the target by exchanging momentum with ions that have an energy of kev. Therefore, the energy of the sputtered atoms is a lot higher than that of thermally evaporated atoms. Fig. 4.2 shows the calculated kinetic energy distribution of Au atoms evaporated at 1500 K and simulated energy distribution of sputtered Au atoms with Ar + at 500 ev at normal incidence. The energy distribution of the Au atoms was calculated from a Maxwell distribution, while the energy distribution for the sputtered atoms was calculated using the SRIM (previously known as TRIM [37]) simulation program. The range of kinetic energy distributions is significantly different, and the average kinetic energy for the thermally evaporated Au atoms is 0.16 ev, while 18.4 ev for the sputtered Au atoms. The sputtered atoms are more energetic and have more mobility as adatoms on the substrate DC Magnetron Sputtering A DC sputtering system consists of two electrodes in a vacuum chamber. The electrodes are typically separated by a few to 10 cm. The cathode is set to be a material that is sputtered and is called a target. The chamber is filled with a sputter process gas. A gas atom can be ionized by a high energy cosmic ray or other ways, emitting a primary electron. If high voltage is applied between the electrodes, then the positive ion is accelerated toward the cathode. The primary electron or the secondary electrons, which are emitted from the cathode, create a cascade of ionization of the gas. As a result, a stable glow discharge is formed between the electrodes which enable a

61 41 1 Probability [a.u.] Kinetic Energy [ev] Figure 4.2: The energy distribution of thermally evaporated Au atoms at 1500 K and sputtered Au atoms with Ar + ions at 500 ev. For the energy distribution of thermally evaporated atoms, Maxwell speed distribution for Au gas atoms was used for the calculation. For the energy distribution of sputtered atoms, SRIM program was used, The program was run for 10 4 Ar + ions bombarded onto Au target at normal incidence. The probability of atomic collisions and removing Au atoms from the target surface with certain energies was simulated by a Monte Carlo randomization procedure. The numbers for the temperature and the Ar + ion energy is the typical values for thermal evaporation and sputtering, respectively. The average energy for the sputtered Au atoms is 100 times larger than that for the evaporated Au atoms.

62 42 constant sputtering process. The sputtering technique described above is limited in practice for the following reasons. The efficiency of generating the ions is low, hence, the deposition rate is slow. The secondary electrons can hit the substrate and raise the substrate temperature. The process gas pressure may be high so some portion of the sputtered atoms are scattered by the process gas without reaching the substrate. The DC magnetron sputter system, which was used in this work, overcomes these points by placing permanent magnets on the back side of the target. The diagram of the DC magnetron sputtering setup is shown in Fig The magnets generate the magnetic field parallel to the surface of the target (see Fig. 4.4). The magnetic field confines the secondary electrons, which are produced when ions hit the target surface, to the target region. The force exerting on a charged particle (electron or ion) is the Lorentz force F = e(e + v B) (4.1) where e and v are the charge and velocity of the electrons and E and B are the electric and magnetic fields, respectively. This is known as E B drift (see Fig. 4.4). The plasma density is highest in the region where the magnetic field is parallel to the target surface, and the target erosion is the highest. The motion of the electrons is confined in a region near the target in the presence of the magnetic field, which improves the probability of ionizing the process gas. The DC magnetron sputter system is operated at a pressure in the range of 0.1 to a few mtorr, which is about two orders of magnitude lower than the system without

63 43 Cathode ground shield Sputter chamber - V Permanent magnet Stainless cathode Target Polar piece assembly (copper) Ar plasma Substrate Platen Figure 4.3: Typical setup of the DC magnetron sputter system. The dotted line stands for the sputter chamber. Inside the chamber is pumped down to 10 7 Torr before the deposition. The target, which is made of the material to be sputtered, is electrically connected to the cathode. The cathode shield, which is electrically grounded, is necessary to prevent unnecessary sputtering from the target surface that doesn t face to the anode. The distance between the cathode ground shield and the target must be short (typically a few mm) not to have a glow discharge.

64 44 the magnets. The number of defects on the deposited film due to the presence of high density of the process gas can be reduced. Also the number of secondary electrons that hit the substrate is reduced so that the substrate temperature does not become high. The cathode, where many high energy ions hit, is usually water-cooled to prevent the target material from melting, and to prevent the temperature of the magnet from reaching the Curie temperature and quenching. Top view ExB drift path Side view Sputter target Magnetic field lines S N S Magnet N S N Figure 4.4: The magnetic field on DC magnetron sputter cathode.

65 Sputtering System To develop a focal detector array for x-ray astronomy, one must fabricate the detector photolithographically, including the Au:Er alloy sensors. There are many possible techniques to deposit Au:Er films. However, for MMC, the thickness of Au:Er sensors may be as thick as several µm, therefore, a fast deposition rate is required. Furthermore, the sensors may need to be deposited directly onto a SQUID or a transformer chip. Therefore, the temperature during the deposition must be kept low (T<100 C). Considering these facts, a DC magnetron sputter system is employed for this work to deposit Au:Er films. A DC magnetron sputter system for studying the properties of Au:Er film was developed at the Multilayer Facility at Smithsonian Astrophysical Observatory (SAO). The chamber has a cylindrical shape with 15 inches in diameter, 9.5 inches tall, and is made of stainless steel 304. Two cathodes were installed to the chamber; a 1 inch (AJA ST-10) and a 2 inch (AJA A320) dc magnetron cathode. The platen is attached onto a linear translation stage so that a substrate can travel under the two cathodes. The chamber is shown in Fig Sputtering of Au:Er Films Two cylindrical sputter targets were used in the present work. An Au target of one inch in diameter and inch tall was doped with natural Er, whose concentration was measured to be 1400 ppm. The other target of the same dimension was doped with isotopically enriched 166 Er, which has zero nuclear spin. Both targets were prepared at Ames Laboratory [38]. A photoresist-coated 3 inch Si wafer was used as a substrate. The photoresist layer was for liftoff of the Au:Er film after deposition. The photoresist (Shipley 1075) was

66 46 Ion gauge 2 cathode 1 cathode Translation stage Chamber RGA Figure 4.5: The sputter deposition system used for this work. The chamber is equipped with two DC magnetron sputter cathodes, a translation stage, and a residual gas analyzer (RGA). The pressure gauge and the current controllers for the sputter guns can be seen in top-right in the picture. spun on a Si wafer. The spin speed was 5000 rpm to form 10 µm thick layer over the wafer. Then the wafer was baked on a hot plate at 100 C for 3 minutes. The substrate was glued on a platen in the chamber using a thermo paste for a good thermal contact. The chamber was pumped down from atmospheric pressure by a rotary vane mechanical pump and a turbo pump. The base pressure before deposition was usually Torr. An ultra high pure Ar gas ( % and % purity) were used for a sputter process gas. The Ar gas flow was controlled by a mass flow controller (MFC) to keep a constant pressure during deposition. The pressure during

67 the deposition was mtorr and was measured with a capacitance manometer. The target was pre-sputtered for 10 minutes after ramping up the cathode current to remove impurities on the target surface and to get a stable condition for sputtering. The platen and the cathodes were cooled during the deposition by running water through them so that the deposition was done at room temperature. Au:Er films were deposited under different conditions. The sputter conditions are summarized in Table 4.1 Film Target Cathode Deposition Thickness Ar Target-Sub. Power Rate Pressure Distance [W] [Å/sec] [µm] [mtorr] [inch] film1 natural film2 natural film3 natural l.30 film4 enriched film5 enriched film6 enriched film7 enriched Table 4.1: Sputter conditions for Au:Er films. A 1400 ppm natural Er-doped Au target was used for the depositions of film1 film3. A 800 ppm isotopically enriched with 166 Er-doped Au target was used for the depositions of film4 film7. The Ar gas of % purity was used for film1 film6, while the Ar gas of % purity was used for film7. 47 After the deposition, the Au:Er film was lifted off in acetone. The film was used for the magnetization measurement with two different magnetometers. For the high temperature magnetization measurement, a part of the film was cut into square shape of the size of about 1 1 cm and was mounted into a plastic straw (see Sec ). For the low temperature measurement (see Sec. 4.4), where 50 µm pick up loop of a SQUID magnetometer was used, a part of the film was photolithographically etched to produce 50 µm disks. The process of etching is described in the following. Fig. 4.6 illustrates the etching process. (a)au:er foil was cut to cm

68 and was glued with GE varnish onto a cover glass slide. (b)the positive photoresist 48 (Shipley 1075) was spun on top of it at 5000 rpm for 30 seconds. Then it was baked on a hot plate at 100 C for 3 minutes. (c)the sample was mounted on a photolithography mask aligner. The sample was exposed under the ultraviolet light. The sample was covered with a mask, which had a pattern of arrays of circles to block the light. (d)the sample was developed in a developer (Microchem 452 developer) for 9 minutes. (e)an Au etchant (Transene GE-8148) was used to etch the Au:Er layer. (f)the photoresist layer was washed off in acetone. The 50 µm Au:Er disk was ready to use. 4.2 SQUID Magnetometer The SQUID (Superconducting QUantum Interference Device) is an extremely sensitive device for detecting magnetic flux. This section outlines the working principles of the SQUID and the SQUID magnetometers used in this work. A complete picture of the SQUID principles, design and fabrication is described in Ref. [39] Principles of a DC SQUID A DC SQUID has a superconducting loop interrupted by two Josephson junctions as shown in Fig. 4.7 (a). The junctions are shunted by the resistances R to suppress hysteric characteristics on the current-voltage (I-V ) relations. When the bias current I is applied below the superconducting transition temperatures, the supercurrent can flow through the loop and the junctions without raising the voltage V across it as long as the current is smaller than the critical current. The I-V characteristics of the SQUID loop depends upon the magnetic flux Φ externally applied through the

69 49 (a) GE 7031 Au:Er film (d) Glass slide (b) Photoresist (e) (c) Ultraviolet light (f) Photomask Figure 4.6: The process of etching Au:Er films to produce φ=50 µm disks. (a)cut and glue film (b)spin photoresist and bake (c)expose (d)develop (e)etch (f)liftoff

70 50 loop as is shown in Fig. 4.7 (b). The I-V characteristics changes periodically for the external magnetic flux between Φ = nφ 0 and Φ = (n + 1)Φ 2 0 (n is an integer) with the period of Φ 0 = Tm 2. It suggests that the SQUID can measure the very small changes of the magnetic flux. The SQUID can be operated by applying the constant bias current I B. In the Fig. 4.7 (c) the voltage across the SQUID loop is shown as a function of the external flux for a constant bias current. The period is Φ 0. The SQUID is operated at the steepest point on V -Φ curve, where the transfer function V Φ = V/ Φ with respect to the external flux is a maximum. Figure 4.7: (a)the schematic diagram of a DC SQUID. (b)i-v characteristics. (c)v Φ characteristics for a constant bias current I B. From [39] The SQUID Chip and Circuitry An IBM SQUID KSUP was used for the low temperature magnetization and the heat capacity measurements. The size of the silicon chip, where the SQUID is fabricated along with four other SQUIDs, is mm, and 625 µm thick. The Nb-AlO x -Nb trilayer junctions are shunted with 10 Ω PtRh resistors, which do not become superconducting at mk temperatures. The bias current at operation is less than 10 µa. The SQUID has two pick-up loops in series in a gradiometer configuration, such that a uniform field through the two loops produces no output. The diameter

71 51 of the pick-up loop is 50 µm. An etched 50 µm Au:Er film was positioned over one of the pick-up loop for the magnetization measurement, and was glued on a pick-up loop for the heat capacity measurement. The SQUID was operated in the flux-locked loop mode for both the magnetization and the heat capacity measurements. In the flux-locked loop mode, the feed back coil compensates the flux change in the SQUID loop to maintain a fixed working point of the SQUID. Fig. 4.8 shows a simplified diagram of the SQUID circuitry used for this work. The right side of the broken line is the SQUID controller QD550 by Quantum Design. The details of the circuit components that are not shown in the diagram are described in Ref. [40]. The SQUID and the step-up transformer are located on the sample holder, which is attached to the mixing chamber of the dilution refrigerator. The SQUID loop and the feed back coil are on the same chip. The modulation and the feed back share the same coil, which is a typical setup to simplify the circuit. The room temperature preamplifier is QD-Micro-Preamp, which is modified to optimize the impedance coupling between the modulation and the SQUID loop. The modulated signal and the voltage across the SQUID are coupled to to the room temperature preamplifier through the step-up transformer. The output signal from the preamplifier is sent to the mixer, where the DC component of the signal is extracted by the lock-in technique. The DC signal is amplified and feed back to compensate the flux change in the SQUID loop. The SQUID noise read out using QD550 controller is S Φ = 3.5µΦ 0 / Hz at 4.2 K Magnetic Property Measurement System (MPMS) A Magnetic Property Measurement System (MPMS) SQUID magnetometer by Quantum Design was used for part of the magnetization measurement in this work. The

72 52 SQUID controller I Bias B Step-up Transformer Mixer Pre-amp DC amp SQUID 500 khz Oscillator R fb V out Feedback/ modulation coil I f Low Temperature Room Temperature Figure 4.8: The circuit diagram to measure the change of the flux in the SQUID loop. The left side of the thick vertical line lies on the sample holder attached to the mixing chamber of the dilution refrigerator. The preamplifier and the SQUID controller are at the room temperature. The right side of the broken vertical line is in the SQUID controller QD550. In the flux-locked loop mode, the output voltage is proportional to the feed back current I f that cancels the flux change in the SQUID loop.

73 53 MPMS can apply a magnetic field up to ±5 T with superconducting magnet, and can vary sample temperatures from 1.8 to 400 K. The magnetization was measured at the Center for Material Sciences and Engineering (CMSE) at Massachusetts Institute of Technology. The DC magnetization technique was used to measure the magnetic moment of a sample. The sputtered film was cut to the size of approximately 1 1 cm and was folded a few times to mount on a clear plastic straw. The sample mass was mg. The straw was then attached to an end of the sample rod. The sample was moved through a superconducting second-order gradiometer in a discrete 32 steps over 4 cm. The measurement scheme for the MPMS is shown in Fig The induced current through the detection coil was measured with a SQUID, which was inductively coupled to the detection coil, to compute the magnetic moment of the sample. Measurements were performed between 1.85 and 300 K in a field up to 5 T. Plastic straw Detection coil Au:Er film 3 cm To SQUID pick-up coil Figure 4.9: Schematic of the MPMS magnetometer. The magnetic field up to ±5 T can be applied to the sample. The sample mounted in the plastic straw is moved between the bottom of the coil and the top of the coil to induce supercurrent. The induced current is detected by a SQUID that is inductively coupled to the detection coil.

74 Refrigerator An MMC typically operates at 50 mk or below. To cool down the MMC to low temperatures, a dilution refrigerator was used at Brown University, and an adiabatic demagnetization refrigerator (ADR) was used at NASA, Goddard Space Flight Center (GSFC). This section summarizes the two types of refrigerators Dilution Refrigerator Dilution refrigerator, utilizing the difference in physical properties of 3 He and 4 He, is a highly developed technique for achieving low temperatures below 1 K. The idea was first proposed by H.London [41][42]. The dilution refrigerator is widely used now for low temperature experiments because of the insensitivity to magnetic fields and capability of continuous operation at low temperatures. The 3 He- 4 He mixture undergoes a phase separation below 0.87 K, and form a 3 Herich phase and a 4 He-rich phase. At lower temperatures, the 3 He-rich phase becomes pure liquid 3 He while the 4 He-rich phase doesn t become pure liquid 4 He even at the absolute zero temperature but has finite (6.4 %) 3 He solubility in 4 He. The 3 He-rich phase floats on top of the 4 He-rich phase due to the difference in densities. The molar entropy of 3 He-rich phase is smaller than that of the 4 He-rich phase. If some 3 He is removed from the 4 He-rich phase, then cooling occurs when 3 He in the 3 Hephase is diluted into the 4 He-rich phase. The process described above accrues in the mixing chamber. In a real system, 3 He is pumped and selectively evaporated in a still that operates around 0.7 K. A dilution refrigerator can be operated continuously by circulating 3 He. The general principles and operation of dilution refrigerators in detail are presented in Ref. [31] and Ref. [32].

75 55 In this work, a dilution refrigerator manufactured by Oxford Instruments was used. A metal mixing chamber Kelvinox 25 was installed to make mechanical and thermal contact to the sample holder. The dilution refrigerator was attached to a top-loading cryostat, which has a separate vacuum can. The cryostat was inserted in a vapor cooled liquid helium storage dewar. The liquid nitrogen free dewar had a liquid helium boil-off of 7 to 8 liters in 24 hours. The 3 He recirculation rate was 14 µmole/sec, and the cooling power of the refrigerator at 100 mk was 12 µw. The base temperature of the refrigerator was mk with the sample holder attached to the mixing chamber ADR (Adiabatic Demagnetization Refrigerator) An ADR achieves low temperatures by controlling the entropy of a magnetic material. The spins of a magnetic material is random at high temperatures and the entropy is large. The maximum entropy of the system of spin I is given as S max = Rln(2I + 1) (4.2) where R is the gas constant. When an external magnetic field is applied to the system with contacting the system through a closed heat switch to the thermal reservoir, the material is magnetized and the entropy becomes smaller. The heat of magnetization T S can be dumped to the thermal reservoir. Then after opening the heat switch, the magnetic field is decreased adiabatically. This process is carried out at constant entropy and the temperature becomes lower as the magnetic field decreases. The ADR at GSFC for this experiment is a single stage ADR with a liquid nitrogen and a liquid helium tank. An FAA (Ferric Ammonium Alum) salt was installed. The base temperature below 30 mk can be achieved. The refrigerator can maintain the

76 56 temperatures below 50 mk for about > 10 hours. 4.4 Setup for Low Temperature Experiment A sample holder, which was attached to the mixing chamber of the dilution refrigerator, was prepared for the measurement of the magnetization and the heat capacity of Au:Er films in the mk temperature range. A one inch OFHC (Oxygen Free High Conductivity) Cu rod was machined to make a sample holder, where a SQUID chip, circuit board, magnet coil and samples were mounted. The 250 g Cu rod was annealed, after being machined, in vacuum at 950 C for 48 hours to increase the thermal conductivity and remove hydrogen impurities which may give significant heat loads to the system due to ortho-para conversion. A small magnetic field was applied using a superconducting coil. A Nb:Ti superconducting wire of 4.2 mil in diameter (including Cu clad and insulator) was wound along a plastic spool, which was mounted on the Cu holder. The tips of the wire were spot-welded after removing its copper clad to make superconducting loop. The critical current through the coil is 80 ma, which is probably limited by the quality of the welded junction. The magnetic field coil can produce a field of 0.05 mt on the central axis at the surface of the coil by running 1 ma through the coil. A SQUID chip and circuit board with printed gold-plated copper wires and a stepup transformer were mounted on the sample holder. An aluminum cover was used as a superconducting shield for the sample holder to achieve low noise environment for operating the SQUID.

77 Magnetization Measurement at Low Temperatures The magnetization of sputtered Au:Er films were measured under the condition such that heat dissipated by the SQUID did not influence the temperature of the Au:Er. The experimental setup for the magnetization measurement is illustrated in Fig A mm square Au pad was e-beam evaporated to 2000 Å thick on a z-cut quartz crystal of cm. An etched 50 µm Au:Er disk was manually placed on the Au pad and pressed with a wedge bonder tip for strong mechanical and thermal contact. The quartz wafer was tied to a brass bridge. Ten 25 µm Au wires were bonded onto the second Au pad on the quartz and the brass bridge for a strong thermal contact. A bundle of annealed OFHC copper wires were bolted down on the brass and the sample holder. The quartz was tied under the brass bridge with a few turns of manganin wire. Thin cigarette paper was placed between the brass and the quartz for the adjustment of the sample-squid chip distance. The Au:Er sample attached to the brass bridge was positioned under microscope so that the sample was located above the 50 µm SQUID pick-up coil without making contact to it. The Au:Er sample was positioned approximately 30 µm above the SQUID pick-up coil. There was not heat dissipation to the Au:Er sensor during the measurement using a SQUID. The SQUID was operated in the flux-locked loop mode during the measurement. The change of the magnetization of Au:Er sample due to temperature change gave a flux change in the SQUID pick-up loop, which was cancelled by a feed back current in a coil that was inductively coupled to the SQUID pick-up loop. The amount of the feedback current was proportional to the change in the magnetization. The magnetization was measured between the lowest accessible temperature of the dilution refrigerator and 0.7 K. The temperature was changed by either slowly heating up or

78 58 Brass bridge Cigarette paper Manganin wire Quartz Au:Er Au lms Pick-up coil Au wire Cu wire SQUID Copper sample holder Figure 4.10: Experimental setup for the magnetization measurement. A Au:Er disk was wedge bonded onto a Au pad that was evaporated on the quartz wafer. The Au pad has windows where there is no Au so that one can see through the quartz to position the Au:Er over the SQUID pick-up loop. The quartz was tied to the brass bridge. Thin cigarette paper was inserted between the quartz and the brass bridge to adjust the distance between the Au:Er sensor and the SQUID chip. The distance between the Au:Er sensor and the pick-up loop on the SQUID chip was approximately 30 µm. Au wires were wedge bonded on the second Au pad on the quartz wafer and the brass bridge for good thermal link. A bundle of annealed Cu wires were bolted down between the brass bridge and the Cu sample holder for good thermal link.

79 cooling down the mixing chamber to ensure the thermal equilibrium between the mixing chamber and the Au:Er sample. A RuO 2 thermometer was attached to the 59 sample holder, whose resistance was read out by AVS 47 resistance bridge. The SQUID output and the resistance of the thermometer were simultaneously recorded with digital voltmeters. The quantity that the SQUID measures is not an absolute value of the magnetization but is a change in flux. The relation between the two can be written as δφ = µ 0 GV r δm (4.3) where δφ is the change of flux in pick-up loop, µ 0 is the magnetic permeability of vacuum, G is a dimensionless factor that depends on the geometrical configuration of the Au:Er sensor and the pick-up loop, V is the volume of the sample, r is the radius of the pick-up loop, and the δm is the magnetization change of the sample. The coupling constant G is different in each measurement for the different Au:Er films since the the sample-squid distance and the alignment of the sample to the pick-up loop are different. The coupling constant is calculated in Ref. [44] for a cylindrical sensor aligned in a pick-up loop without a gap. According to the calculation, for cylindrical sensor of the radius 25 µm and the thickness 5 µm, the coupling constant is 0.8. The coupling constant G measured in this work is Heat Capacity Measurement The heat capacity of a sputtered Au:Er film was also measured. The setup of the measurement is drawn in Fig A 50 µm Au:Er disk was positioned directly on the SQUID pick-up coil and was glued with GE varnish. A magnetic field was applied by the superconducting magnet. A 55 Fe radioactive source was mounted on

80 brass collimator. If one can know the temperature rise of Au:Er due to the absorption of an x-ray photon, the heat capacity of the Au:Er disk is given by 60 C = δe δt (4.4) where δe is an energy input by an x-ray photon and δt is the temperature rise of Au:Er. When the temperature of the Au:Er changes by δt, its magnetization changes by δm, which is read out as the flux change in the SQUID pick-up loop δφ. Therefore, by using the magnetization vs. temperature relationship, which is measured in a separate experiment, δφ can be associated with δt. For acquisition of the pulse events, the output of the SQUID controller was passed to a Gage card, where the signal was converted from analog to digital. The Gage card was also used for triggering the signals. The triggered signals were stored in a hard drive of a computer. The temperature was stabilized within 0.2 mk by controlling the current on the heater attached to the mixing chamber. To determine the temperature rise, the pulse events due to an x-ray absorption was recorded and averaged for the pulses that has similar pulse height and pulse shape by offline analysis. This experiment could not distinguish the K α1 and K α2 peaks of the 55 Fe radioactive source, but it could distinguish K α and K β peaks. The energy spectrum was measured in a field of 1.8 mt, and the sample temperature was 61 mk. The spectrum is shown in Fig Fe Source An 55 Fe was used to characterize the heat capacity of the films. The source has a half life of 2.73 years. The K α transition line is the transition from the principal quantum number n=2 to n=1. The transition from 2 P 3 2 state is the K α1 line and the transition

81 61 x-ray source collimator magnetic field coil Au:Er sensor Cu holder Figure 4.11: The experimental setup for the heat capacity measurement. A 50 µm Au:Er disk is positioned inside the pick-up loop of the SQUID. A magnetic field can be applied by the superconducting magnet. The brass collimator holds an 55 Fe x-ray source. The distance between the x-ray source and the Au:Er is approximately 2 mm DE FWHM = 27 ev Count/2eV Energy [ev] Figure 4.12: The x-ray energy spectrum of the 55 Fe source. The measurement was made in a field of 1.8 mt and the sample temperature of 61 mk The K α and K β peaks are identified. The red line is a Gaussian curve fit. The energy resolution for 5.9 kev x-rays at the full width at half maximum (FWHM) is 27 ev.

82 from 2 P 1 2 is the K α2 line. The emission of energies from the source is M n -K α kev, M n -K α kev and M n -K β kev. The ratio of emission frequency is Mn-K α1 : Mn-K α2 : Mn-K β is 20:10:3. The x-ray source was mounted on the brass collimator of φ = 0.15 mm. Distance between the source and Au:Er sample is 2 mm. The count rate on the 50 µm Au:Er sample is 0.1 count/sec. 62

83 Chapter 5 Characterization of Au:Er Films 5.1 Introduction The physical properties of the sputtered Au:Er films described in Chapter 4 were studied. In light of building a sensitive x-ray detector, it is important to know the temperature dependence of the magnetization and the heat capacities of the Au:Er films. In this chapter, the measured magnetic properties from room temperature down to 40 mk and heat capacity of the films at low temperatures are presented. The heat capacity of film2 is presented. An anomaly in the magnetization observed at low temperatures is discussed in the latter part of the chapter. 5.2 DC Magnetization of Natural Au:Er Films Film1, film2, and film3 in Tab. 4.1 were sputtered using the natural Er-doped Au target. DC magnetization of the sputtered Au:Er films were measured and compared with that of the target material. The magnetization measurements were carried out at three different temperature ranges and magnetic fields; from room temperature 63

84 down to 5 K at very high fields, from 30 K to 1.8 K at intermediate fields, and below 0.8 K down to 40 mk at low fields Magnetization at High Temperatures and High Magnetic Field The magnetization of sputtered Au:Er films was measured first at high magnetic fields and at higher temperatures, using a Magnetic Property Measurement System (MPMS) by Quantum Design. The magnetization of the target material with natural Er in Au is shown in Fig The measurement was performed in a field of 5 T and the temperature range between room temperature down to 5 K. The solid line is the least-square fit to the measurement calculated with the crystal field parameters from Ref [43]. Two free parameters, Er concentration and temperature independent diamagnetism, were adjusted to fit the data. From the fit, the Er concentration of the target and the temperature independent magnetic susceptibility were determined to be 1390 ppm and , respectively. The value of the diamagnetic susceptibility can be compared to the susceptibility of Au χ Au = The difference can be due to the contribution from the sample mounting straw and other impurities in the vicinity of the straw and the sample. The magnetization of film1 film3 sputtered from the 1400 ppm Er-doped Au target in a field of 5 T is shown in Fig The magnetization of the films show an agreement with that of the target material within 10%, and is well characterized using the crystal field parameters as was done with the bulk Au:Er. The magnetization measurement of the target material and film2 in the temperature range between 1.85 and 30 K in a field of 10 mt and 50 mt is shown in Fig. 5.3.

85 65 Magnetization [A/m] Target 0 Fit Inverse Temperature [K 1 ] Figure 5.1: Magnetization vs inverse temperature of the target material in a field of 5 T. The Er concentration of the target is 1390 ppm determined from the measurement At these temperatures and fields, most of the Er 3+ ion occupies the ground state doublet and first excited quartet. The magnetization of the ground state doublet follows Curie s law with effective g factor g = 6.8 and spin S = 1/2. The magnetization of the target material and the sputtered film have a good agreement down to 1.85 K Magnetization at Low Temperatures The magnetization measurement at lower than 0.8 K was made with the SQUID setup in Fig and cooled down with a dilution refrigerator. The result of film1, 2 and 3 is shown in Fig. 5.4 plotted together with the target material and the mean

86 Magnetization [A/m] Target Film 1 Film 2 Film Inverse Temperature [K 1 ] Figure 5.2: Magnetization vs measurement of film1, film2, film3, and the target material in a field of 5 T.

87 film target Magnetization [A/m] mt 10 mt Inverse Temperature [K 1 ] Figure 5.3: Magnetization vs inverse temperature of the target material and film2 in a field of 10 mt and 50 mt. The diamonds represent the target material, and the circles represents the film 2. The magnetization of the sputtered film follows that of the sputter target material. field calculation. field calculation. The magnetization of the target material agreed with the mean Since the coupling between the Au:Er samples and the SQUID pick-up coil was different in each set of measurement, the different sets of data were normalized so that the magnetization curves at T >300 mk match each other. The magnetization of the films below 200 mk was less than that of the target material, which was well described with the mean field calculation. It is indicating that there may be a larger exchange interaction than expected from the mean field calculation among randomly distributed Er 3+ ions in the sputtered films The possible origin of

88 Magnetization [a.u.] Target and Calculated Film 1 Film 2 Film Inverse Temperature [K 1 ] Figure 5.4: Magnetization of the sputtered Au:Er films, using natural Er-doped Au target, in a field of 3.6 mt. The magnetization of the target material follows the calculated value for 1400 ppm Er doped in Au.

89 69 the enhanced interaction is discussed in the later part of this chapter Heat Capacity of Au:Er Film The result of the heat capacity measurement of film2 in a field of 3.6 mt is shown in Fig The heat capacity calculated with the mean field theory is plotted along with the measured values for comparison. The calculation includes Zeeman effect, exchange interactions, hyperfine interaction of nonzero nuclear isotope 167 Er, and conduction electrons of Au. The heat capacity of 23% abundant 167 Er isotope has a nuclear spin I = 7/2 and the hyperfine interaction with 4f electrons of Er 3+ contributes about 50% of the total heat capacity at the temperature range where the measurement was made. The measurement and the calculated values agree within 10% DC Magnetization of Enriched Er-doped Au Films We also used a Au:Er sputter target, in which the Er is isotopically enriched with zero nuclear spin 166 Er. From the high temperature and high magnetic field measurement using the MPMS magnetometer, the Er concentration of the target was determined to be 800 ppm (see Fig. 5.6). The temperature independent diamagnetic susceptibility of the target from the fit is χ = , which is close to the value of the susceptibility of Au. The magnetization of the four films (film4, 5, 6 and 7) sputtered under different conditions were measured, and plotted in Fig. 5.7 together with the target material. The measurement was carried out in a field of 5 T at temperature range of 300 K down to 5 K. The magnetization of all films show a good agreement with that of the target material at this field and the temperature range. Fig. 5.8 shows the magnetization of the four films below 0.8 K in a field of 2.3 mt. The different measurements were adjusted so that the slopes of the curves at high

90 70 x Heat Capacity [J/K] Sample Temperature [K] Figure 5.5: The heat capacity of film2 in the form of 50 µm diameter, 4.5 µm thick disk, in a field of 3.6 mt. The broken line is the calculated values for 1400 ppm natural Er-doped Au.

91 71 temperatures (T > 300 mk) match as was done for the measurement of the natural Au:Er films. All films have similar behavior in the magnetization. The magnetization is less than expected from the bulk Au:Er and the mean field calculation below 0.2 K Magnetization [A/m] Inverse Temperature [K 1 ] Target Fit Figure 5.6: Magnetization vs inverse temperature of the sputter target, which is isotopically enriched with 166 Er doped in Au. The measurement was made in a field of 5 T. The line is the least square fit to the data. The Er concentration of the target from the fit is 800 ppm. 5.3 Discussion The sputtered Au:Er films, using both natural Er-doped and isotopically enriched Erdoped Au target, showed the same magnetic properties as the target materials from

92 Magnetization [A/m] film4 500 film5 film6 film7 target Inverse Temperature [K 1 ] Figure 5.7: Magnetization vs inverse temperature of the target material and film4,5,6, and 7 in a field of 5 T. room temperature down to 1.85 K despite the variety of the sputtered conditions. Among the films sputtered using the natural Er-doped Au target, film1, which was sputtered at the slowest rate and lowest cathode power, showed more deviation from the target material behavior in the low temperature magnetization measurement. However, film3, which was sputtered at faster rate than film2 with the same cathode power but different target-substrate distance, showed the same magnetization as film2 below 0.8 K. Among the films sputtered using the enriched Er-doped Au target, film5 was sputtered at the highest cathode power. The magnetization of film5 was similar to

93 Magnetization [a.u.] Film 4 Film Film 6 Film 7 Target and Calculation Inverse Temperature [K 1 ] Figure 5.8: Magnetization of four sputtered films deposited using enriched in 166 Erdoped Au target in a field of 2.3 mt.

94 74 those sputtered at lower cathode powers. The film6 was sputtered at lower sputter gas (Ar) pressure compared to the sputter condition for film4. The magnetization of both films was very similar. The similar magnetization between film6 and film7 suggests that the switching the purity of the sputter Ar gas from % to % did not improve the quality of the films. Film2 and film4 were sputtered under similar conditions using the different Er concentration of the targets. For film2, which was sputtered with the natural Erdoped Au target, the slope of the magnetization curves of the films dm/d(1/t ) at 50 mk is 65% of the expected slope from the calculation. For film4, which was sputtered using the enriched Er-doped target, is 57% of the expected slope at 50 mk. The fact that the magnetization of the films in the higher temperatures (T < 30) K match the magnetization of the target materials means that the Er ions in the sputtered films experience a crystal field that is similar to Er ions in the target material. However, the magnetization of the films became significantly less below 200 mk than that of the bulk Au:Er Possible Cause for Low Temperature Anomaly in Magnetization Er Oxide Er is a very strong oxygen getter, and oxidation of Er during the deposition can affect magnetic properties of the film. A film was unintentionally deposited with what later was discovered the small air leak ( Torr) from room into the sputter chamber. The film showed a significantly smaller magnetization than the target material even near room temperature. The magnetization of the degraded film

95 75 deposited using the 1400 ppm natural Er-doped Au target is shown in Fig From the least-square fit, the apparent Er concentration of the film was reduced from 1400 to 560 ppm. A portion of sputtered Er may be oxidized during the deposition to form Er 2 O 3 or other forms of Er oxide. The magnetization of an Er oxide in Au crystal could be different from that of Er in Au. No literature was found on the measurement of magnetic properties of Er oxide diluted in Au. The partial pressure of O 2 in the sputter chamber without air leak before the deposition was measured with a residual gas analyzer and was Torr. The partial pressure of the oxygen impurity from the sputter gas during the deposition ( 3 mtorr) was, from the certificate of the manufacture of the gas, < Torr for % pure Ar gas and < Torr for % pure Ar gas. Since the magnetization of the films sputtered using either types of Ar gas showed the same property, the O 2 impurity in the Ar gas is not the cause of the anomaly. The sputtered film, film1 film7, did not show the degradation in magnetization down to 0.2 K, suggesting that there is very little effect of Er oxidation for these films at the temperature range. Segregation of Er in the films The deviation in magnetization of the films from the magnetization of bulk Au:Er at low temperatures indicate that the exchange interaction between the magnetic ions is somewhat enhanced. Although the results of high temperature magnetization measurements imply that the crystal field that Er ions feel is the same as that of the bulk Au:Er, the exchange interaction between Er ions can significantly influence on the magnetization at low temperatures. It is also possible that the Er ions in the sputtered films are not randomly distributed in Au, but are sitting closer to other Er

96 76 Magnetization [A/m] Target Film Fit 560 ppm, χ dia = 1.59x Inverse Temperature [K 1 ] Figure 5.9: Magnetization of the film sputtered with a small air leak ( 10 6 Torr) into the chamber. The measurement was made in a field of 5 T. The 1400 ppm natural Er-doped Au target was used for the deposition. The concentration of Er in the film was reduced to 560 ppm.

97 77 ions. If it is the case then the RKKY interaction is stronger, and a smaller change in magnetization is the result. As Eqn. 3.8 and Eqn. 3.9 suggest, the strength of RKKY interaction between two spins falls off, oscillating from positive to negative depending on the distance between the spins. The measured magnetization curve starts to deviate from the calculated values around 200 mk. The thermal energy at this temperature corresponds to the exchange energy of spins separated by about 10 Å. This distance includes a number of neighbouring sites in Au crystals. If the Er ions tend to clump and alter the distribution of the exchange energy from what is assumed in the mean field distribution, the magnetization will be strongly affected. Ning [45] studied gold alloys modified by rare earth (RE) additions. The author observed that in a cast Au-0.2Ce alloy, the concentration of Ce was low in the dendrite crystals and high between the dendrites. However, in annealed Au:Ce alloys, the dendritic segregation disappeared and the segregation of Ce along grain boundaries occurred. Also in Au-9Ni-Gd alloy, Gd is distributed at grain boundaries [45]. According to the author, the reason of the segregation is that the majority of Gd forms complex compounds, Au(Ni) x Gd. These Gd-containing compounds form a eutectic with the alloy matrix. The eutectic mixture has a low melting point and is distributed at grain boundaries. In sputtering, the sputtered atoms from the sputter target on bombardment of Ar ions of the energy 500 ev have an average kinetic energy of ev. The sputtered atoms from the target collide onto the substrate. Some atoms bounce off the substrate surface, but most of the atoms diffuse around on the surface and give the energy to the substrate until they lose the energy. While diffusing, some atoms can pair up with other atoms and diffuse on the surface as a cluster of atoms. Sputtered Er atoms may be settled at the grain boundaries after diffusion on

98 78 the surface, and therefore, the distances among Er tend to be closer to each other compared to those randomly distributed in the Au matrix as assumed in the mean field calculation. If this is the reason of the enhanced interaction, to avoid the segregation, it is necessary for sputtered Er atoms to lose their kinetic energy immediately after they reach the substrate surface. It would be helpful to sputter while keeping the substrate at low temperature Energy Resolution Using the Au:Er Films Although the response per unit energy input, dφ/de, for the sputtered films is 40% less than that of the bulk material, these films can still be used for real x-ray detectors. The performance will be degraded by an amount that is determined by the principal source of noise limiting the energy resolution. If the detection electronics is the cause of the noise, the resolution is worsened in proportion to the loss of signal response. On the other hand, if the noise is determined by intrinsic thermodynamic energy fluctuations between the various components of the detector, then the parameters of the detector can be adjusted somewhat to mitigate the loss of resolution. The optimization process discussed in Sec is recomputed to account for the diminished response of 40%. The loss in resolution for the detector discussed in that earlier section is reduced to 27%.

99 Chapter 6 Prototype MMC Detector Array 6.1 Introduction As we have seen in the previous sections, a detector for soft x-ray spectroscopy for future x-ray satellite missions requires not only high energy resolution but also imaging capability with more than a thousand pixels. To achieve this goal, the total detector needs to be fabricated using a thin film technology. A transformer chip for an MMC array has been developed at NASA Goddard Space Flight Center (GSFC). In this chapter, the design and the performances of the MMC detector array is presented. First, in Sec. 6.2 outlines the basis of a novel design for MMCs using a meander shaped pick-up loop, which fits in with the thin film technology. Then Sec. 6.3 outlines the low temperature experiment setup for the detector performed at GSFC. Au:Er films were deposited on the transformer chips. The depositions were done at GSFC and SAO on separate chips. The magnetic properties of those Au:Er films are discussed in Sec Sec. 6.5 discusses the rise and decay time of pulse signals obtained with an 55 Fe x-ray source. 79

100 Meander Geometry Most of the MMC results to date has been performed with a cylindrical Au:Er sensor and a circular pick-up coil for read out the flux change. However, an alternate geometry that potentially can achieve higher energy resolution has been developed. A meander-shaped pick-up coil and a thin film magnetic sensor on top of it can potentially have a better sensitivity since the spins of the magnetic sensor are on average closer to the pick-up coil and, therefore, have a better flux coupling to the pick-up coil. The meander geometry is feasible to large area detectors The magnetic field is provided to the sensor by applying a DC current through the same meander coil. When the temperature of the magnetic sensor rises on the absorption of a particle, the magnetization and consequently the permeability of the sensor changes. Then the self inductance of the meander pick-up coil changes, which leads to a change of the current through the SQUID that is inductively coupled to the pick-up circuit. The magnetic field generated by the meander coil is spatially non-uniform in the magnetic sensor that is located on top of the coil. The field is parallel to the meander above the meander strip but is perpendicular to the plane between the stripes as illustrated in Fig By reciprocity, the field distribution in the sensor produced by a current in the meander coil is that which maximizes the current generated in the meander when its magnetization of the sensor changes. The distribution of the magnetic fields over the film was calculated by a finite element method [44]. The magnetic field at position r and the current I 0 in the meander can be expressed as B(r) = µ 0 G(r/p) I 0 p. (6.1)

101 81 Nb Magnetic sensor B p Substrate w Insulation layer Figure 6.1: The cross sectional view of the meander coil and the magnetic sensor. The width of the Nb meander stripes is w, and the pitch of the stripes is p as indicated in the figure. The current through the stripes flows perpendicular to the page and generates a non-uniform field in the magnetic sensor. Here G(r/p) is a local coupling factor that depends upon the position and the geometry of a sensor and a pick-up coil. The relationship between the flux change d(δφ) in the meander pick-up coil due to the change of the magnetization δm(r) of the volume δv at position r in the sensor is G(r/p) d(δφ) = µ 0 δm(r)dv. (6.2) p Fig. 6.2 illustrates the calculated field distribution, using the finite element method, for µm 2 meander coil of the pitch p = 5 µm, the width w = 2.125, and 500 nm thick Au:Er film deposited on the 740 nm thick insulator [46]. The average field is 3.0 mt for a current of 25 ma through the meander. These are the same dimensions for the experiment carried out at GSFC, which will be described in the following sections. Compared to the cylindrical setup with hand-placed sensor described in Sec , the geometrical constant G for the flux coupling of the microfabricated meander geometry can be calculated with more confidence. Therefore, the absolute value of the flux change seen on the SQUID can be calculated, while in the cylindrical geometry there was an adjustable constant in the relationship between the magnetization change and the flux change in the SQUID loop.

102 P(B)/0.002 [1/T] B [T] x 10 3 Figure 6.2: Distribution of the magnetic field in Au:Er sensor of 500 nm thick on the insulation layer of 740 nm thick. The current I b = 25 ma was applied through the meander coil. The average field is 3.0 mt [46] 6.3 Experimental Setup Detector Design and Fabrication The detector consists of a flux transformer chip and a SQUID chip. On the transformer chip, an Au:Er sensor array was deposited and the meander shaped pick-up coils were employed. The pick-up coils were bonded with Al wires to the SQUID input coils to read out the signals. For a detector array of > 1000 pixels, heat sinking may be a big problem if magnetic sensors are on the same chip that dissipates heat. This design of using the transformer chip is advantageous for a detector array since there is no heat dissipation on the transformer chip and the transformer chip

103 83 is thermally isolated from the SQUID chip. The transformer chip for an MMC array has been designed and fabricated at NASA Goddard Space Flight Center (GSFC). The chip was fabricated using four inch and 500 µm thick Si wafers. An Al 2 O 3 layer was deposited onto the Si wafer for an etch stop. Then a Nb layer was sputtered and patterned by reactive ion etch (RIE) to meander shape. Each meander coil covers the area of 250 µm 250 µm and has an inductance L m = 3.9 nh, which was confirmed by measuring the L/R roll-off at liquid helium temperature, using the known inductance of a SQUID input coil and R being the resistances of Al bonding wires in a closed loop. The meander coils have pitch p = 5 µm with the line width w = µm. This provides the optimal condition (w/p) opt = to maximize the ratio of the flux response to the flux noise as shown in Ref. [44]. On top of the meander coils, an Al 2 O 3 layer of 740 nm thick was e-beam deposited for electrical insulation. Another Nb layer for the transformer coil and an Au layer for the heat sink pads were deposited and patterned on top of the insulation layer. Finally, a layer of Au:Er was sputtered on top of the Al 2 O 3 layer. A Cr layer was deposited before the deposition of Au:Er to provide adhesion to the Al 2 O 3. The sputter conditions and characterization of the Au:Er film will be discussed in Sec The picture of the transformer chip is shown in Fig The size of the transformer chip is 1.0 cm 1.2 cm. At the center of the chip, there are a 6 6 array of Au:Er deposited sensors. The size of an Au:Er pixel is 250 µm 250 µm. Two types of thermal connections between the Au:Er sensor and the thermal reservoir were made. One type has an Au layer, which serves as a heat sink and overlaps with the Au:Er film. This is referred as a non-isolated sensor. The other type also has an Au heat sink layer but it does not overlap the Au:Er sensor. This type is referred as an isolated sensor. The meander pick-up coils of the four Au:Er pixels at the corners of the 6 6

104 84 Heat sink pad Heat sink pad Isolated pixel Au:Er sensors 1.0 cm Non-isolated pixel 1.2 cm Figure 6.3: The transformer chip and sputtered Au:Er arrays. The size of both a meander coil and an Au:Er sensor is 250µm 250 µm. The Au:Er sensors at four corners of the 6 6 array can be read out with a SQUID. The meander coils of the corresponding sites are connected in series (also see Fig. 6.4). The edge of three Au:Er pixels out of four, that can be read out, are overlapped with Au thermal pad (referred as non-isolated pixel). One pixel does not overlap with the Au pad (referred as isolated pixel).

105 85 sensor array are connected in series and can be connected to SQUID input coils for reading out the signals. A simplified diagram of the circuit of the arrays is shown in Fig A DC bias current I b can be commonly applied through all the meander pick-up coils in series. The current provides the magnetic field applied to the Er spins. The two current leads could be shorted with Al wires to form a superconducting loop below the superconducting transition temperature of the Al wires around 1.2 K. The current was applied through the meander coil, while the SQUID chip and the Al wires were heated above 1.2 K with on-chip heater to make the electrical impedance much larger on the SQUID input coil side in order to prevent the current flowing through the SQUID input coil. Then the current was reduced after the system cooled down below the superconducting transition temperature of Al wires. Very little flux change was observed with the SQUID during the ramp down of the current. The current was maintained in persistent mode without the need to keep a current source attached, which would produce noise in the field. The inductances in the bias line are to suppress cross talk among the pixels. The meander coils are bonded to the input coils of the SQUIDs. A series of SQUID array (C3X16A) developed at PTB (Physikalisch-Technische Bundesanstalt) Berlin was used. The SQUID chip contains three independent 16 SQUID arrays so that three Au:Er pixels can be read out. The transformer and the SQUID chips were glued onto a gold-plated OFHC Cu sample holder. The Au heat sink pads on the chip were bonded with Au wires to the sample holder for a strong thermal connection. The picture of the sample holder is shown in Fig The temperature of the sample holder was measured with the Ge resistance thermometer. The sample holder was inserted to the Nb shielding box attached to the cold stage of the adiabatic demagnetization refrigerator (ADR).

106 86 Au:Er sensor Al wire Nb wire +I b -I b Transformer chip SQUID chip 16 SQUID arrays To SQUID preamp Figure 6.4: The circuit diagram of the Au:Er array. The meander shaped pick-up coils are inductively coupled to the SQUID input coils on a separate chip. The SQUID chip consists of three independent 16-SQUID arrays. There are two Be windows on the dewar. The x-ray source can be attached outside the refrigerator for pulse measurements. 6.4 Characterization of Sputtered Au:Er Films Au:Er films were deposited on two separate transformer chips at two different facilities. On one transformer chip, an Au:Er film was deposited using a DC magnetron sputter system at GSFC. On the other chip, a DC magnetron sputter system at SAO was used for the deposition. The films were deposited at room temperature, and Ar gas was used for a sputter gas at both facilities. At GSFC, a 500 nm thick Au:Er layer was deposited on the transformer chip,

107 87 Ge thermometer SQUID chip Transformer chip Figure 6.5: Picture of the sample holder for MMC array. Two sets of MMC arrays can be mounted on the sample holder. Au:Er sensors sputtered at GSFC is on one transformer. Au:Er sensors sputtered at SAO is on the other one. using a 1.5 inch sputter target of 1050 ppm natural Er-doped Au. The deposition rate was 4.5Å/sec with the cathode power 50 W. The Ar pressure during deposition was 5 mtorr. The quantum efficiency for x-ray absorption of the 500 nm thick Au:Er film is 35% for 5.9 kev x-rays. At SAO, a 300 nm thick Au:Er layer was deposited using the facility described in Sec The 1 inch 1400 ppm natural Er-doped Au sputter target was used. The quantum efficiency for 5.9 kev x-rays is 22%. The sputter conditions were the same as that of film7 in Tab. 4.1 except the film thickness was 300 nm and natural Er-doped Au target was used instead of enriched in 166 Er-doped target this time. The sputter conditions of the Au:Er films from the two facilities are summarized in Tab Er Concentration Power Rate Ar Pressure Thickness [ppm] [W] [Å/sec] [mtorr] [nm] GSFC SAO Table 6.1: Summary of the sputter conditions for Au:Er films at GSFC and SAO. For both cases, Ar gas was used for a sputter gas, and the deposition was done at room temperature.