Abstract:
A superconducting metallic glass transition-edge sensor (MGTES) and a method for fabricating the MGTES are provided. A single-layer superconducting amorphous metal alloy is deposited on a substrate. The single-layer superconducting amorphous metal alloy is an absorber for the MGTES and is electrically connected to a circuit configured for readout and biasing to sense electromagnetic radiation.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit under 35 U.S.C. Section 119(e) of the following co-pending and commonly-assigned U.S. provisional patent application(s), which is/are incorporated by reference herein: 
         [0002]    Provisional Application Ser. No. 61/381,895, filed on Sep. 10, 2010, by Charles C. Hays and Donald G. Naugle, entitled “Superconducting Metallic Glass Transition-Edge-Sensors,” attorneys&#39; docket number 176.67-US-P1/CIT-5448-P2. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
       [0003]    The invention described herein was made in the performance of work under NASA Contract Number NASI-1407 and is subject to the provisions of Public Law 96-517 (35 USC 202) in which the Contractor has elected to retain title. 
     
    
     BACKGROUND OF THE INVENTION 
       [0004]    1. Field of the Invention 
         [0005]    The present invention relates generally to imaging, and in particular, to a method, apparatus, and article of manufacture for fabricating and using a metallic glass transition-edge-sensor (MGTES) device. 
         [0006]    2. Description of the Related Art 
         [0007]    (Note: This application references a number of different publications as indicated throughout the specification by reference numbers enclosed in brackets, e.g., [x]. A list of these different publications ordered according to these reference numbers can be found below in the section entitled “References.” Each of these publications is incorporated by reference herein.) 
         [0008]    Actively cooled, direct radiation detectors, which exhibit improved image and energy resolution in the infra-red (IR) and x-ray wavelength regions, are a next-generation technology for advanced imaging, for both terrestrial and space applications. In this regard, NASA&#39;s Science Mission Directorate (SMD) is driven in part by the motivation for understanding the content and evolution of matter in the known universe. To support these goals, a broad spectrum of missions are planned to conduct measurements at submillimeter and far-infrared (FIR) wavelengths; e.g., the NASA proposed Background-Limited far-IR/Submillimeter Spectrograph (BLISS) and the SpicA FAR Infrared Instrument (SAFARI) instruments for Japan&#39;s Space Infrared Telescope for Cosmology and Astrophysics (SPICA) mission. SPICA requires actively cooled, direct radiation detectors, with very high sensitivity. Potential terrestrial applications for actively cooled, direct radiation detectors arrays are: 1) x-ray detectors for medical imaging; 2) chemical analysis for materials science (Scanning-electron-microscopy/Energy Dispersive Spectroscopy) at x-ray wavelengths; and 3) radiation detectors for nuclear forensics (e.g., Alpha-particle and gamma-ray detection). 
         [0009]    Membrane—isolated superconducting transition-edge sensor (TES) arrays are a leading sensor technology for such space applications (see [1]-[3]). To meet application requirements, the detectors must be formatted into large-scale high pixel density arrays, which will be read using superconducting quantum interference detector (SQUID) Multiplexer (MUX) technology. Detector arrays that use the current baseline transition edge sensor technology, i.e., state-of-the art (SOA) TES arrays, do not exhibit the performance requirements of the BLISS instrument. The BLISS instrument requires detectors with the following performance metrics: 1) fast response time τ (τ&lt;100 mS); 2) high pixel density arrays (at least 10 3  pixels); 3) TES films must exhibit stable T C &lt;100 mK; 4) must perform over a broad wavelength range 35 mm-433 mm; 5) low detector noise equivalent power (NEP) of the order NEP&lt;1×10 −19  W/√Hz; and 6) low 1/f noise level at low frequencies, f, below 10 Hz. 
         [0010]    TES-based microcalorimeter arrays are being developed for the mission listed above, as well as the NASA Beyond Einstein Program Constellation-X Observatory (Con-X, for measurements of x-ray spectra). SOA TES devices detect radiation by precisely measuring the temperature rise associated with the absorption of a photon, which raises the TES temperature. The temperature increase is detected by a superconducting thermistor, which is voltage-biased 10-20% into the superconducting transition curve at T=T C . The superconducting thermistors in SOA TES devices are typically based on: 1) elemental superconducting films; e.g., Titanium (Ti, T C =565 mK) or Iridium (Ir, T C =130 mK); and 2) proximity effect elemental metallic bilayer design; e.g., Mo/Au.  FIGS. 1A and 1B  illustrate an ordinary bilayer Mo/Au (Molybdenum/Gold) TES ( FIG. 1A ) and TES with stripes ( FIG. 1B ) (140 microns on a side, stripes spaced every 15 μm) of the prior art. In the single-layer elemental TES designs, the superconducting transition temperature T C  cannot be controlled, and is well above the desired operating temperature (˜50 mK) for space applications. The bilayer TES device functions as a single superconducting element via the proximity effect, and the superconducting transition temperature, T C , is controlled by the thickness of the superconductive film element. However, this TES device architecture has inherent problems, which are manifest in fabrication difficulties, control of the superconducting transition temperature, T C , and an excess noise equivalent power spectrum. 
         [0011]    In other words, while the techniques used to fabricate SOA TES single-layer elemental and TES bilayer designs are well developed, the TES device architecture exhibits a variety of problems: 1) device fabrication is difficult to control, resulting in variable superconducting transition temperature, T c , from element to element; 2) broadened transition widths, ΔT C ˜2-30 mK; and 3) SOA TES devices exhibit an excess noise equivalent power spectrum (NEP) (see [4]-[5]). 
         [0012]    SOA TES devices based on the bi-layer design are designed for operation at ˜50 mK, and the individual TES films must exhibit similar T c  values for good performance. In SOA TES devices, the T c  values are difficult to control because these devices are fabricated using thin-film synthesis techniques based on geometry. Achieving the control necessary to fabricate large arrays is technically challenging, as the T C  is a sensitive function of the properties of both layers, as well as the interface transparency. In Mo/Au proximity effect bilayer TES designs, the lack of control of the residual resistance ratio (RRR) for as-sputtered Au films impacts the T c  value, and post-annealing to improve the RRR contribute to un-controlled changes in T c . 
         [0013]    The e-beam deposition techniques used to fabricate bilayer TES devices are also manifest with challenges. Typically, Mo/Au films are e-beam deposited onto an LSN (low-stress silicon nitride) substrate maintained at 600° C.; the high substrate temperature is used to compensate for thermal expansion coefficient mismatch between the metal film and substrate. The remaining residual stress in these Mo-films is of the order 400 to 600 MPa (Megapascals). In these films, the residual stress shifted the superconducting transition temperature T c  by as much as 50 mK. 
         [0014]    SOA single-layer elemental design TES detectors; e.g., based on Ti or Ir, typically exhibit an excess noise-equivalent-power (NEP), which is 2× larger (or greater) than that predicted by theory. SOA bilayer design TES detectors typically exhibit an NEP which is 4-10× greater than that predicted by theory.  FIG. 2  illustrates excess noise in bilayer TES compared to the calculated Johnson noise of the TES and shunt resistor in the prior art. The source of this noise is unknown. Resolution of the excess noise is a global challenge for everyone in the field. 
         [0015]    In the SOA designs, there are factors intrinsic to their design, which may limit the reduction of the excess noise spectrum to acceptable levels. For example, in Mo/Au proximity effect bilayer TES designs, the residual stress state in the bilayers has ramifications on the excess noise exhibited by these films. Local fluctuations in the film stress state, on spatial length scales of the order of the superconducting coherence length ξ can increase quasiparticle carrier scattering in the metallic layer, which can introduce additional noise. Defects present in the elemental crystalline films (e.g., grain boundaries and dislocations) contribute to an increase in quasi-particle charge carrier scattering at low temperatures, thereby increasing the noise levels observed. Interlayer quasiparticle carrier scattering in metallic bilayers will also introduce additional noise. 
         [0016]    In addition to the technical challenges outlined above, another issue that limits the application of TES devices for terrestrial applications, is the low TES operating temperature, T op ˜100 mK. To actively cool TES arrays to this temperature range, complex and costly cryogenic cooling methods (e.g., dilution refrigerators) are required. A TES technology that would enable operation at 0.3 K or higher, would be very desirable, as this temperature can be achieved using closed-cycle refrigerator systems using  3 He or the newer adiabatic demagnetization refrigerator (ADR) system (e.g., a continuous adiabatic demagnetization refrigerator (ADR with 4-stages), a He 3 /He 4  dilution refrigerator, or a cryogenic cooling system that uses liquid  4 He). 
         [0017]    The performance limiting difficulties associated with the SOA TES devices are:
       T c  controlled only by superconducting proximity effect in metallic bilayer design and for these ultra-thin films the substrate surface roughness broadens the transition; therefore T c  value is difficult to control;   Energy resolution limited by low logarithmic sensitivity factor (α) values, manifest by large transition widths, ΔT c ;   Large excess noise values at high frequencies [1-20 kHz] (up to 20 times theoretical expectations), correspondingly reduces the high-frequency sensitivity;   Sources of large excess noise are unknown;   Fabrication techniques introduce wide variability in TES performance values;   SOA TES design itself introduces unavoidable extrinsic sources of excess noise; and   Expensive cryogenic technology required to achieve cooling to ˜100 mK.       
 
       SUMMARY OF THE INVENTION 
       [0025]    As described above, prior art TES detectors include many limitations including:
       T C  value difficult to manage;   Large excess high-frequency noise (often 2-10 times theoretical expectation) of unknown origin;   Complex fabrication process; difficult to reproduce for large arrays; and   Fabrication process introduces large residual stresses in bilayer films.       
 
         [0030]    Embodiments of the invention provide a new type of transition edge sensor that will meet the requirements for many terrestrial (e.g., spectroscopy) and space-based sensing applications in the IR and X-ray wavelength regions. The novel devices are based on single-layer thin-films of superconducting amorphous metal alloys—i.e., metallic glasses. Changes in chemical composition are used to control the T c  in amorphous metal alloys, in thin-film form. Superconducting metallic glass forming alloys with T c  values as high as 7.6 K have been reported (see [6]-[7]), and a number of systems exhibit T c &#39;s near 300 mK (e.g., Zr 40 Cu 60 ) (see [8]). In addition, superconducting metallic glasses typically exhibit very narrow transition widths ΔT c  ˜0.1-10 mK. For example, Johnson et at report that a splat-quenched Zr 75 Rh 25  metallic glass foil (45 μm thick) exhibits a superconducting transition at T c =4.562 K, and a transition width, ΔT c =7 mK, defined by the 10% and 90% points on the resistive transition curve (see [6]-[7]). 
         [0031]    Therefore MGTES devices in accordance with embodiments of the invention can be operated at higher temperatures than conventional TES devices. Temperatures in this range are achieved using closed-cycle cryogenic systems that use  3 He, resulting in an immediate decrease in overall operating cost for this type of cryogenically cooled detector array. In addition, the active element of MGTES device embodiments may be comprised of a single-layer alloy film, greatly simplifying the fabrication methodology used to fabricate a large array of MGTES devices. Further, intrinsic features associated with the disordered alloys used in MGTES device embodiments contribute to a significant reduction in the NEP values, and with an improved energy resolution. MGTES devices will be subject to lower 1/f noise values due to their narrow superconducting transition temperature widths, which will minimize the bias-induced noise. All of these benefits extend to terrestrial applications operating at higher temperatures (T&gt;100 mK). 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]    Referring now to the drawings in which like reference numbers represent corresponding parts throughout: 
           [0033]      FIGS. 1A and 1B  illustrate an ordinary Mo/Au (Molybdenum/Gold) TES ( FIG. 1A ), TES with stripes ( FIG. 1B ) (140 microns on a side, stripes spaced every 15 μm) and grating-style absorber for Far-Infrared Radiation Far-IR or Sub-mm Spectroscopy ( FIG. 1C ) of the prior art; 
           [0034]      FIG. 2  illustrates excess noise in bilayer TES compared to the calculated Johnson noise of the TES and shunt resistor in the prior art; 
           [0035]      FIG. 3  illustrates a schematic of a MGTES device architecture in accordance with one or more embodiments of the invention; 
           [0036]      FIG. 4  shows the superconducting transition observed in an amorphous Zr75Rh25 (At. %) splat-quenched foil in accordance with one or more embodiments of the invention; 
           [0037]      FIG. 5  illustrates the temperature dependence of resistivity curves for: A) crystalline metals, B) weakly-scattering metallic glasses, and C) strongly-scattering metallic glasses in accordance with one or more embodiments of the invention; 
           [0038]      FIG. 6  illustrates a mushroom-type absorber structure in accordance with one or more embodiments of the invention; 
           [0039]      FIG. 7  illustrates four TES sensors on a SiN thermally isolated island structure in accordance with one or more embodiments of the invention; and 
           [0040]      FIG. 8  illustrates distributed antenna-coupled small-volume arrays in accordance with one or more embodiments of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0041]    In the following description, reference is made to the accompanying drawings which form a part hereof, and which is shown, by way of illustration, several embodiments of the present invention. It is understood that other embodiments may be utilized and structural changes may be made without departing from the scope of the present invention. 
         [0042]    Superconducting metallic glasses exhibit a number of desirable properties for applications of embodiments of the invention, and will exceed the performance of the SOA for each TES figure of merit:
       Improved energy resolution;   Lower excess noise;   Amorphous alloy may be a self-absorber of radiation (with 4d and 5d transition metal additions to alloy(s));   Precisely controlled superconducting transition temperature, T c ;   Simplified detector architecture; and   Mechanically &amp; chemically robust design.       
 
         [0049]    Some of these advantages are detailed in Table 1: 
         [0000]    
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Comparison of performance of MGTES vs. State-of-the-Art. 
               
             
          
           
               
                 TES 
                 Current SOA 
                 MGTES (Super- 
                 Improvement 
               
               
                 Figure 
                 (bilayer 
                 conducting amorphous 
                 MGTES vs. 
               
               
                 of Merit 
                 geometry) 
                 metal thin film) 
                 SOA 
               
               
                   
               
               
                 Control of 
                 Difficult to 
                 Composition controls T C : 
                 Enabling 
               
               
                 T C   
                 control by 
                 Cu 35 Ti 65   
                 feature in 
               
               
                   
                 film thickness 
                 (At. %) − T C  = 58 mK 
                 amorphous 
               
               
                   
                   
                 Cu 60 Zr 40   
                 alloys 
               
               
                   
                   
                 (At. %) − T C  = 320 mK 
               
               
                 Intrinsic 
                 Quasiparticles 
                 Quasiparticles in 
                 Noise will be 
               
               
                 noise: 1/f, 
                 scattered by 
                 superconducting metallic 
                 near 
               
               
                 thermal 
                 grain boundaries, 
                 glass thin-films are 
                 fundamental 
               
               
                 fluctua- 
                 crystal defects 
                 not scattered from grain 
                 limit 
               
               
                 tions &amp; 
                   
                 boundaries or other 
               
               
                 Johnson 
                   
                 crystalline defects 
               
               
                   
                   
                 below T c . 
               
               
                 Excess 
                 Source unknown: 
                 In glassy metal films, 
                 Large 
               
               
                 NEP 
                 2X-10X larger 
                 noise levels are reduced 
                 reductions 
               
               
                   
                 than theoretical 
                 by homogeneity of single 
                 possible 
               
               
                   
                 expectation 
                 layer film 
               
               
                 Device 
                 metallic bilayer 
                 Single layer thin film 
                 Enabling 
               
               
                 Fabrica- 
                 design difficult 
                 thermistor easily 
                 features 
               
               
                 tion 
                 to synthesize for 
                 fabricated, lead 
               
               
                   
                 very thin films 
                 structures can be made 
               
               
                   
                   
                 from same alloy system; 
               
               
                   
                   
                 w/higher T C   
               
               
                   
               
             
          
         
       
     
       Basic MGTES Architecture 
       [0050]    To illustrate the design advantages of MGTES detectors in accordance with embodiments of the invention, the application of the MGTES detectors as x-ray radiation and infrared radiation (IR) detectors is described herein. For IR sensing, the device design would be very similar, except without the addition of an x-ray absorbing layer on the TES thermistor. In either case, each MGTES device may be run in the deep Electro-Thermal-Feedback (ETF) mode (see [1]). The MGTES detector arrays operate as micro-calorimeters, and are scalable to large arrays. The MGTES pixels are read out using superconducting quantum interference (SQUID) amplifiers. Based on MGTES design details, SQUID multiplexing techniques based on transformer ratio multiplexing can be explored (see [9]). As a starting point, for a discussion of MGTES alloys, the device architecture shown in  FIG. 3  is presented, which is similar to that employed in SOA TES arrays. Consequently,  FIG. 3  illustrates a schematic of a MGTES device architecture in accordance with one or more embodiments of the invention. 
         [0051]    An MGTES element  302  can be synthesized as a 140 μm×140 μm sized device, on a Low-Stress-Silicon-Nitride (LSN) substrate  304  of varying thickness (0.25 μm&lt;T LSN &lt;1 μm). To tune the thermal conductance G, membrane-isolated TES sensor designs are used, wherein the superconducting film  302  is deposited onto a thin Silicon-Nitride (Si—N) membrane  304 , which is thermally isolated by thin Si—N support beams  305  of low thermal conductance. The MGTES design has an advantage in that its superconducting leads  306  can be deposited using higher transition temperature compositions from the same alloy system as the TES element itself. 
         [0052]    Shown in  FIG. 3  is the SQUID  308  current readout, whose output is used in feedback to the bias voltage  310  to maintain the operating point (10%-20% bias point) on the MGTES transition curve. 
         [0053]    Superconducting metallic glass transition-edge sensors (MGTES)  302  can be fabricated using a single-layer glassy (amorphous) superconductive thin film as the active device element, which is overall a much simpler device architecture compared to the SOA multilayer TES designs. The simplified architecture greatly increases the ability to fabricate large arrays of MGTES detectors  302 , with minimal variation in T c , from one element to another. MGTES films may be deposited onto substrates held at or near room temperature, which greatly improves device yield compared to the SOA proximity effect TES devices, where the substrate temperatures are raised to 600-700° C. during the deposition process. MGTES films deposited onto substrates held between 77-300 K would exhibit very uniform amorphous structures for good glass forming alloys. 
       MGTES Alloys 
       [0054]    The superconducting metallic glass transition-edge sensors (MGTES) introduce the novel concept of using film chemistry modulations alone to control the transition temperature T c . This well-studied technique offers the possibility of smoothly tuning the superconducting transition temperature of the MGTES device, while also adjusting its composition for high physical and chemical stability. 
         [0055]    The energy resolution limit of the TES device (including Johnson noise in the film and the thermodynamic fluctuations between the detector and the heat bath) is given by reference [1]: 
         [0000]    
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       E 
                       FWHM 
                     
                   
                   = 
                   
                     
                       
                         k 
                         B 
                       
                        
                       
                         T 
                         2 
                       
                        
                       
                         C 
                          
                         
                           ( 
                           
                             1 
                             / 
                             α 
                           
                           ) 
                         
                       
                        
                       
                         
                           8 
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   
                     - 
                     1 
                   
                 
               
             
           
         
       
     
         [0000]    where C is the total heat capacity of the superconducting thin film and absorber. The factor n=d log P/d log T is the logarithmic derivative of the bias power with respect to temperature, typically, n=3-5. In Eqn.-1, α is the logarithmic sensitivity factor 
         [0000]    
       
         
           
             
               
                 
                   α 
                   = 
                   
                     
                       
                         
                            
                           log 
                         
                          
                         
                             
                         
                          
                         
                           R 
                            
                           
                             ( 
                             T 
                             ) 
                           
                         
                       
                       
                         
                            
                           log 
                         
                          
                         
                             
                         
                          
                         T 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           T 
                           R 
                         
                         ) 
                       
                        
                       
                         ⌊ 
                         
                           
                              
                             R 
                           
                           
                              
                             T 
                           
                         
                         ⌋ 
                       
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   
                     - 
                     2 
                   
                 
               
             
           
         
       
     
         [0056]    The α value in SOA TES devices based on polycrystalline films is typically 20&lt;α&lt;200. The α value is a measure of the sharpness of the superconducting transition, and it is strongly dependent on the properties and the state of the film. The α values in SOA TES devices are reduced, manifest by the complexity of the elemental metallic bilayer design, which results in a broadened transition widths of the order ΔT c ˜2-30 mK. 
         [0057]    The MGTES may exhibit a significantly improved energy resolution, because amorphous superconducting films can be fabricated with very narrow transition widths, as low as ΔT c ≈100 μK. Further, such transition widths may only be limited by intrinsic superconducting fluctuations. Due to the findings presented in numerous studies, it is accepted that for amorphous superconductors, the contribution to the transition width ΔT c  from superconducting fluctuations is well described using the Aslamazov-Larkin (AL) theory. As a means of estimating the performance of MGTES devices, the contribution to the transition width ΔT may be calculated using the Aslamazov-Larkin (AL) theory for superconducting fluctuations (see [10]). AL fluctuations contribute to broadening of the transition width, and are dominant near the lower end of the transition, i.e., near the zero in resistance. 
         [0000]        ΔT   c   /T   c =1.52×10 −5   ·R   □ (Ω)   Eqn.-3
 
         [0058]    The resistance per square R □ (Ω) was calculated from data presented in Ref. [11] by using its definition 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       R 
                       • 
                     
                      
                     
                       ( 
                       Ω 
                       ) 
                     
                   
                   = 
                   
                     ρ 
                     t 
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   
                     - 
                     4 
                   
                 
               
             
           
         
       
     
         [0000]    where ρ is the film resistivity in Ω-m, and t is the film thickness in meters. Narrow superconductive transition widths ΔT c  predicted by Eqn. 3 &amp; 4 above are somewhat universal to superconducting amorphous thin films.  FIG. 4  shows the superconducting transition observed in an amorphous Zr 75 Rh 25  (At. %) splat-quenched foil (e.g., of Ref. [7]) in accordance with one or more embodiments of the invention. The Zr—Rh and Zr—Cu alloys are model systems, and therefore are relevant for a discussion of the magnitude of superconductive fluctuations near T c . 
         [0059]    To estimate the performance of an MGTES device fabricated from amorphous Zr 75 Rh 25  and Zr 40 Cu 60  films, the AL theory is applied to calculate the superconductive transition width ΔT c . The results of these estimates are provided in Table 2. 
         [0000]    
       
         
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Alloy 
                 ρ 
                 t 
                 T c   
                 R □   
                 Calculated 
                 Calculated 
               
               
                 Composition 
                 (Ω-m) 
                 (Å) 
                 (K) 
                 (Ω) 
                 ΔT c (K) 
                 α 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Zr 75 Rh 25   
                 220e−8 
                 1000 
                 4.56 
                 22.0 
                 1.53e−3 
                 2980 
               
               
                 Zr 40 Cu 60   
                 163e−8 
                 1000 
                 0.3 
                 16.3 
                 0.24e−3 
                 1250 
               
               
                   
               
             
          
         
       
     
         [0060]    In Table 2, the Aslamazov-Larkin theory is applied to calculate the transition width ΔT c  and the calculated logarithmic sensitivity factor a in Zr 75 Rh 25  and Zr 40 Cu 60  films. 
         [0061]    As described above, narrow transition widths ΔT C  are somewhat universal to superconducting amorphous thin films. The electron transport and superconductive properties of amorphous metals are reported in reviews by Mizutani, Howson &amp; Gallagher, and Naugle (see [20]-[22]). Reports of superconductive behavior at low temperatures, T C &lt;1 K, in two alloy systems: Cu 35 Ti 65  (T C =58 mK) and Cu 60 Zr 40  (T C =320 mK) are useful. Based upon such alloys, a number of alloy compositions, with ternary additions, may exhibit T C &#39;s in the range T C ≈65-75 mK. 
         [0062]    The alloys in both of these systems are strongly scattering metallic glasses (i.e., amorphous metals), where the conduction is due to the d-band conduction. Such alloys exhibit a negative temperature coefficient of resistivity α r &lt;0, with resistivity values that are well above the Mooij correlation limit ρ≈150 μΩ-cm (see [12]). For alloys with resistivities above this limit, the temperature dependence, ρ(T), is small and can be tuned via composition. 
         [0063]    Using the calculated superconductive transition width, the logarithmic sensitivity factor a can also be estimated (and is included in Table 2 above): 
         [0000]    
       
         
           
             α 
             = 
             
               
                 
                   
                      
                     log 
                   
                    
                   
                       
                   
                    
                   
                     R 
                      
                     
                       ( 
                       T 
                       ) 
                     
                   
                 
                 
                   
                      
                     log 
                   
                    
                   
                       
                   
                    
                   T 
                 
               
               ≈ 
               
                 
                   ( 
                   
                     
                       T 
                       c 
                     
                     R 
                   
                   ) 
                 
                  
                 
                   ⌊ 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       R 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         T 
                         c 
                       
                     
                   
                   ⌋ 
                 
               
             
           
         
       
     
         [0064]    The predicted superconductive transition widths are ΔT c =1.53 mK and ΔT c =0.24 mK, for Zr 75 Rh 25  and Zr 40 Cu 60 , respectively. ΔT c &#39;s of this magnitude provide large logarithmic sensitivity factors, and the calculated results are promising. The estimated AL fluctuation spectrum contribution to ΔT c =1.53 mK for Zr 75 Rh 25 , is especially promising: 1) for the qualitative agreement with the experimentally determined ΔT c =7 mK value for a 45 μm thick foil; and 2) the large T c , which suggests the fabrication of MGTES arrays operating at higher temperatures. Temperatures in this range, ˜4 K, are commercially viable for medical imaging applications. 
         [0065]    The calculated logarithmic sensitivity factors are much greater than the known values for the SOA proximity effect bilayer TES devices. In calculating a for the amorphous superconductors, it may be assumed that ΔR/R≈1. This is reasonable for low bias points on the Zr 75 Rh 25  and Zr 40 Cu 60  transition curves. These alloys are strongly scattering metallic glass, where the conduction is due to the d-band conduction (see [11]). This alloy exhibits a negative temperature coefficient of resistivity α r &lt;0, with resistivity values well above the Mooij correlation limit ≈150 μΩ-cm (see [12]). For alloys with resistivities above this limit, the temperature dependence, ρ(T), is small and can be tuned via composition. 
         [0066]    The temperature dependence of resistivity curves for: A) crystalline metals, 
         [0067]    B) weakly-scattering metallic glasses, and C) strongly-scattering metallic glasses, are shown in  FIG. 5  in accordance with one or more embodiments of the invention. In other words,  FIG. 5  illustrates the schematic temperature dependence of the electrical resistivity, ρ e , for: A) crystalline metals, B) weakly-scattering metallic glasses, and C) strongly-scattering metallic glasses. In the strongly scattering alloys of the type C, at low temperatures quantum corrections to the temperature dependence of resistivity become important in the weak-localization regime (WLR). In the WLR, the electron propagation between scattering events is no longer classical as there is significant interference between scattered partial waves. There are two sources of correction; (a) the ‘localization’ effect, which considers the quantum interference effects and (b) the ‘interaction’ effect, which considers the modification of the e − -e −  interaction in the WLR. These ideas have been very successful in describing the behavior in various examples of disordered metals and they represent a fundamental difference between the transport properties of highly resistive metals and metals for which ρ&lt;100 μΩ-cm. In amorphous metals, the disordered structure is the primary electron scattering mechanism, so impurities and defects have little effect on the properties. Therefore, the Residual-Resistance-Ratio (RRR)=R(300 K)/R(4.2 K) for an MGTES device (in accordance with embodiments of the invention) may be of the order RRR≈1. Such an embodiment reduces the effects of film non-uniformities, providing narrow transitions. 
         [0068]    Amorphous superconductors have no long-range order, and so they show no anisotropy effects, Brillouin-zone effects or precipitation effects. Obviously, they also lack crystal interfaces (grain boundaries) and crystalline imperfections (dislocations, twins, stacking faults, and interstitial impurities). These properties have made superconducting metallic glasses popular for testing theories of transition widths, e.g., Naugle et al&#39;s results that agree well with the AL theory (see [13]-[14]) Thus, the use of the AL theory to predict ΔT c &#39;s is reasonable. Further, there is evidence of 2D effects in thin Cu—Ti films that may be examined. 
         [0069]    In high-quality MGTES thin films held under low-bias and low-T, smaller ΔT c  could be realized; with logarithmic sensitivity scaling as α≈[ΔT c ] −1  and values approaching α≈10000 possible. The impact of a larger logarithmic sensitivity α is immediate. The resolution of TES devices is given by Eqn. 1, shown again below (see ref. [3]). 
         [0000]    
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     
                       E 
                       FWHM 
                     
                   
                   = 
                   
                     
                       
                         k 
                         B 
                       
                        
                       
                         T 
                         2 
                       
                        
                       
                         C 
                          
                         
                           ( 
                           
                             1 
                             / 
                             α 
                           
                           ) 
                         
                       
                        
                       
                         
                           8 
                            
                           n 
                         
                       
                     
                   
                 
               
               
                 
                   Eqn 
                   . 
                   
                       
                   
                    
                   
                     - 
                     1 
                   
                 
               
             
           
         
       
     
         [0070]    Compared to the SOA TES with 50&lt;α&lt;200, the resolution of embodiments of the invention may be improved by factors proportional to 1/√{square root over (α′)} which could yield reductions of up to 250% in ΔE FWHM . 
         [0071]    Similarly, MGTES device embodiments may exhibit near-theoretical noise-equivalent-power (NEP) values. This performance improvement may arise from the intrinsic factors described above, and also extrinsic factors. For example, thin metallic glass films tend to grow with very little residual stress compared to polycrystalline metal films (where the stresses can be quite large) (see [15]). The work by R. R. Hake further summarizes the universal trend of narrow ΔT c &#39;s for metallic glasses, in almost bulk form, i.e., in melt-spun ribbon form (see [16] which reports work for binary transition-metal alloys based on zirconium (Zr)). Of particular note is a Zr 62 Co 38  (At. %) specimen with T c =2.10 K, and ΔT c =4 mK; which yields ΔT c /T c =1.91×10 −3 . 
         [0072]    In addition to the above, embodiments of the invention may utilize two early-transition-metal/late-transition-metal (ETM-LTM) alloy systems known to exhibit superconductive behavior below 1 K: 1) amorphous Cu 35 Ti 65  (At. %), which has T C ˜58 mK; and 2) amorphous Cu 60 Zr 40  may be used. Embodiments of the invention may use these alloy and near-neighbor compositions in the respective alloy systems (see refs. [18] and [19]). 
         [0073]    Performance metrics for the base amorphous metal systems that may also be examined, i.e., Cu 1-x Ti x  and Cu 1-x Zr x  (At. %), are shown in Table 3 (see refs. [18] and [19]): 
         [0000]    
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Summary of superconducting properties in the 
               
               
                 Zn 1-x Cu —Zr  and Cu—Ti alloy systems 
               
             
          
           
               
                   
                 Alloy 
                 T c  (K) 
                 ρ (Ω-cm) × 10 −6   
               
               
                   
                   
               
               
                   
                 Cu 35 Ti 65   
                 0.058 
                 — 
               
               
                   
                 Cu 50 Ti 50   
                 — 
                 230 
               
               
                   
                 Cu 60 Zr 40   
                 0.32  
                 183 
               
               
                   
                   
               
             
          
         
       
     
         [0074]    To estimate the performance of an MGTES device fabricated from an amorphous Cu 60 Zr 40  film, the AL theory can be applied to calculate the superconductive transition width ΔT c . This information is provided in Table 4: 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Transition width in Cu 60  Zr 40   
               
             
          
           
               
                 Cu-content 
                   
                   
                   
                   
                 Calculated 
               
               
                 (At. %) 
                 ρ (Ω-m) 
                 t (Å) 
                 T C  (K) 
                 R □  ( ) 
                 ΔT C (K) 
               
               
                   
               
               
                 60 
                 183e−8 
                 920 
                 0.3 
                 19.89 
                 90.7e−6 
               
               
                   
               
             
          
         
       
     
         [0075]    The predicted superconductive transition width is ΔT C =90.7 μK. In MGTES device embodiments, ΔT c &#39;s of this magnitude may provide large logarithmic sensitivity factors. This ΔT C  value yields the following conservative estimate for the logarithmic sensitivity factor α, 
         [0000]    
       
         
           
             α 
             = 
             
               
                 
                   
                      
                     log 
                   
                    
                   
                       
                   
                    
                   
                     R 
                      
                     
                       ( 
                       T 
                       ) 
                     
                   
                 
                 
                   
                      
                     log 
                   
                    
                   
                       
                   
                    
                   T 
                 
               
               ≈ 
               
                 
                   ( 
                   
                     
                       T 
                       c 
                     
                     R 
                   
                   ) 
                 
                  
                 
                   ⌊ 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       R 
                     
                     
                       Δ 
                        
                       
                           
                       
                        
                       
                         T 
                         c 
                       
                     
                   
                   ⌋ 
                 
               
               ≈ 
               3333 
             
           
         
       
     
         [0076]    This number is much greater than the value for the SOA proximity effect TES device. In calculating α, ΔR/R≈1 is assumed. It may be recognized that an a of this magnitude is not realized when biasing a TES device in the ETF mode but, one can expect that the large value intrinsic to superconducting amorphous films may enable lower biasing points or a reduced noise equivalent power value. 
         [0077]    Accordingly, embodiments of the invention may synthesize single-layer superconducting amorphous alloy films from the new class of multicomponent bulk metallic glass forming alloys, which exhibit a greater resistance to crystallization, and a higher glass-forming-ability (GFA). There are a number of reports of superconductive behavior for these alloys at temperatures below 1 K. Therefore, ternary, quaternary, and higher order alloying additions may be added to the binary alloys to tune the T C  value and examine the effect of alloying on the MGTES device performance. 
         [0078]    In view of the above, the single-layer superconducting amorphous metal alloy used in embodiments of the invention may consist of an early-transition-metal/late-transition-metal (ETM/LTM) alloy system that exhibits superconductive behavior. The early transition metal (ETM) elements may be drawn from elements in Groups IVB, VB, and VIIB of the periodic table, and the late-transition (LTM) metal elements may be drawn from elements in groups VIIIB, IB, and IIB of the periodic table. Such alloys may be deposited onto a substrate using sputtering, atomic-layer-deposition, electron-beam evaporation, or thermal evaporation. 
       MGTES Architecture for X-Ray and IR Radiation Detection 
       [0079]    As an efficient X-ray absorber, a modified laminated high fill-fraction array of Bi absorber structures may be employed, similar to that employed by Chervenak et al (e.g., the laminated Bi/Cu absorbers)(see ref [17]). This absorber consists of 8 total alternating individual Bi/Cu films, with layer thicknesses of 8.5 and 0.8 μm, respectively. This mushroom-type absorber structure is shown in  FIG. 6  in accordance with one or more embodiments of the invention. 
         [0080]    However, to improve the x-ray efficiency, a more efficient design may be adopted (e.g., a reduced Bi-thickness to increase intra-layer x-ray photon thermalization, coupled with an Au-interlayer instead of Cu). The electronic heat constant γ e  for Cu and Au are similar, 0.695 and 0.729 mJ/mol-K 2 , respectively. The higher Z of Au will improve the x-ray quantum efficiency. Measurements will be conducted to establish the heat capacity C. Depending on the superconducting metallic glass alloy used, MGTES device embodiments may utilize a self-absorbing MGTES superconducting thermistor element, using alloys selected from the Mo—Re, Mo—Ru, Zr—Rh, Cu—Sn, Pt—Zr, Pt—Ti, Hf—Ni, Hf—Cu, Hf—Pt, W—Cu, Ta—Cu, and similar superconducting alloys drawn from combination of 4d-3d transition metal alloys and 5d-3d transition metal alloys, and 5d-4d transition metal alloys, greatly simplifying the device design. Further, superconducting leads that connect the single-layer superconducting amorphous metal alloy to the circuit may be comprised of a different composition within the same alloy system as the superconducting amorphous metal alloys used as the thermistor element. For example, the superconducting leads may be made using Zr 76 Cu 24  (At. %) with T C =3.5 K; and the MGTES element (Thermistor) may be made using Zr 40 Cu 60  (At. %) with T C =0.32 K. 
       MGTES Device Exemplary Embodiments 
       [0081]    MGTES detectors may be designed for measurements conducted on a platform that operates at low temperatures (≈50 mK). Each MGTES device may be run in the deep Electro-thermal Feedback (ETF) mode, and the noise characteristics of our sensors may be tested as described by Irwin et al. [1]-[3]. Depending on the alloy system under investigation and characteristics of the amorphous alloys prepared, the noise performance on thermally isolated island structures or small volume isolation architectures may be investigated. Examples of both structure types are shown in  FIG. 7  and  FIG. 8 . In this regard,  FIG. 7  illustrates four TES sensors on a SiN thermally isolated island structure in accordance with one or more embodiments of the invention.  FIG. 8  illustrates distributed antenna-coupled small-volume e arrays in accordance with one or more embodiments of the invention. The left side of  FIG. 8  illustrates a meandering aluminum structure (G) that forms an array of slot antennas. The two sides can be connected periodically with an array of MGTES microbolometers (B), each with a normal state resistance of tens of ohms (see ref [10]). 
         [0082]    Conclusion 
         [0083]    This concludes the description of the preferred embodiment of the invention. The following describes some alternative embodiments for accomplishing the present invention. 
         [0084]    In view of the above, alloys used in MGTES device embodiments have significantly higher superconducting transition temperatures than the SOA TES devices based on thin films of Ti (T c ˜0.5 K), or multi-layer MoAu designs that exploit the superconducting proximity effect (T c ˜0.1 K). The complicated SOA TES device design requires a complex fabrication process; making it difficult to produce large arrays with uniform performance. The unexplained excess noise equivalent power (NEP) spectrum values observed in SOA TES systems (noise excess high-frequency noise, 4× over theoretical expectations) is introduced in part by the complicated multi-layer design and other factors intrinsic to the SOA TES design. SOA TES operating temperatures in the range T˜100 mK require complex cryogenic cooling systems; e.g., a continuous adiabatic demagnetization refrigerator (ADR with 4-stages) or a He 3 /He 4  dilution refrigerator. ADR systems for operation for T&lt;1 K are very expensive, and in the early stages of development. 
         [0085]    The superconducting transition temperature for some MGTES alloy films are T c &gt;4 K. Temperatures in this range, enable the use of cheaper, cryogen free cooling systems; e.g., pulse-tube-refrigerator (PTR) systems that are commercially available for the T&lt;70K and T˜4K temperature ranges. These systems do not vibrate like traditional Stirling or Gifford-McMahon cryocoolers. Another advantage of the MGTES concept is that the superconducting transition temperature is controlled by alloy composition alone, and not film thickness like in SOA TES systems. This affords a greater control over the T c  and a more robust, reliable detector. The width of the superconducting transition region in superconducting metallic glasses, ΔT c , is significantly less than in crystalline alloys. The unexplained excess noise equivalent power (NEP) spectrum values observed in SOA TES systems (noise excess ˜5-10% over theoretical expectations), will be reduced in MGTES systems due to: 1) the simpler device design (single thin film); 2) the intrinsically high electrical resistivity (yields RRR ˜1); and 3) the intrinsically narrow superconducting transition region in superconducting metallic glasses, ΔT c , which provides an increased energy resolution, provided by correspondingly larger logarithmic sensitivity factors α=d log R(T)/d log T≈[T c /ΔT c ]=3000 are possible. Compared to α≦100 in SOA TES designs. 
         [0086]    As described herein, embodiments of the invention provide the ability to use the MGTES detector in cryogenically cooled x-ray microcalorimeter detector arrays, for terrestrial applications. In this regard, a MGTES microcalorimeter array may establish a new paradigm as x-ray detectors for energy dispersive spectroscopy (EDS) systems in scanning electron microscopes. The MGTES device embodiments offer order of magnitude or better increase in energy resolution, i.e., decreased ΔE, compared to SOA TES or Si-drift detectors, ΔE˜10 eV vs. ΔE˜200 eV. Other applications include: 1) x-ray detectors for medical systems; and 2) MGTES microcalorimeters as radioactive α-particle or γ-ray detectors for Nuclear Forensics applications. 
         [0087]    In view of the above, the MGTES sensors of embodiments of the invention are a break-though superconducting transition-edge sensor with unprecedented performance. In particular, MGTES sensors may achieve the following improvements over that of the prior art:
       develop superconducting amorphous metal alloys, with tunable T C  for application to MGTES sensors;   MGTES sensors that take full advantage of the intrinsic fluctuation limits in amorphous superconductors; and   MGTES array resulting in enhanced energy resolution and reduced noise floor.       
 
         [0091]    The foregoing description of the preferred embodiment of the invention has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. It is intended that the scope of the invention be limited not by this detailed description, but rather by the claims appended hereto. 
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