2.1.

LXM Subarray Types

The “main array” will provide an energy resolution of better than 3 eV over the energy range of 0.2 to 7 keV, with pixel sizes that vary in scale from 0.5 arc sec in the innermost 1 arc min “enhanced array” to pixels that are 1.0 arc sec extending out to a 5 arc min field-of-view. A different subarray called the “ultra-high-resolution (UHR) array” will provide an energy resolution of 0.3 eV up to 0.75 keV in a 1 arc min region off to the side with 1 arc sec pixels.

The x-ray absorber pitches corresponding to 0.5 or 1.0 arc sec are 25 and $50\mu \mathrm{m}$, respectively. The use of hydra designs with $5\times 5$ absorbers per sensor is assumed for the main and enhanced arrays, and the UHR array has 1 absorber per sensor. The extent of the main and UHR arrays cover $60\times 60$ sensors, whereas the enhanced array covers $24\times 24$ sensors.

2.2.

High Inductance MMC Sensors

With practical fabrication constraints on microstrip wiring linewidth, spacing, and insulation thickness, we estimated that the stray wiring inductance expected for a full-scale LXM main array would be $\sim 2.5\mathrm{nH}$ for wiring within the array, plus 3.5 nH for fan-out to microwave SQUID multiplexer resonator arrays, or 6 nH totally. As described in Ref. 4, the expected stray inductance level motivated us to design and fabricate higher inductance MMC sensors, achieved by reducing the linewidth and pitch of the niobium sensor coils to 400 nm lines on an 800-nm pitch, for which the sensor inductance is 8 to 13 nH, depending on Nb thickness (200 to 500 nm). Our prototype variations include sensor designs with a range of meander pitches from 0.8 to $5\mu \mathrm{m}$.

2.3.

Waffle Sensor Geometry for MMC Hydras

A simple but fundamental rule for optimization of MMC sensitivity² is that the volume of the Au:Er sensor should be increased (for greater signal) until the (mostly magnetic) heat capacity of the sensor equals the heat capacity of the x-ray absorber (set by the operating temperature, absorber material, pixel area, and absorber thickness required to stop the maximum x-ray energy with high efficiency). To maintain good magnetic coupling with the reduced pitch in the high inductance sensor coils, the thickness of the Au:Er layer needs to be scaled proportionately to about 130 nm for 800-nm pitch. Given volume and thickness of the Au:Er, the requisite area of the sensor is determined and is found to cover most of the area of the main and enhanced hydra unit cells and a smaller fraction of the available area in the UHR sensors. Therefore, the heat capacity of the Au:Er layer need not be reduced below the optimal value when making the Au:Er thinner for good magnetic coupling to sensor meander coils with pitch as fine as 800 nm.

Consequently, we chose a waffle-shaped geometry for our MMC hydras in which a square hole in the Au:Er is introduced around the location of the support stem for each absorber, with sufficient size for the hole to contain a metallic (Au) thermal link between the absorber stem and the Au:Er temperature sensor, with a unique thermal conductance for the each link in the hydra so that differences in pulse shape allow one to determine the x-ray photon hit location. Figure 1 shows the Au:Er waffle shapes for the main and enhanced arrays. The UHR sensor has a simple annular shape with one hole in the Au:Er as shown.

Fig. 1

Layout of (a) main, (b) enhanced, and (c) UHR MMC sensors. The Au:Er sensor (green shaded), Au thermal links (red shaded) between sensor and x-ray absorber support stems, and Au x-ray absorbers (green open) are shown. Absorber size is 50, 25, and $50\mu \mathrm{m}$, respectively, for main, enhanced, and UHR sensors, whereas the overall hydra unit cells shown have sizes 250, 125, and $50\mu \mathrm{m}$.

The Au:Er material has a relatively low residual resistance ratio because it intentionally contains impurities (the erbium ions). As a result, the expected thermal diffusion time for a bare Au:Er waffle is not fast enough compared to the pulse rise times calculated for an initial hydra design. Figure 2 shows the improvement in thermal diffusion time when a pure Au layer is added on top of the Au:Er waffle to aid rapid thermalization. We included a 600-nm Au capping layer to speed up the time constant sufficiently for the hydra design without increasing the overall heat capacity significantly. In this calculation, we used the measured residual resistivity and specific heat of our sputtered Au:Er films, and the measured residual resistivity versus thickness for our electron-beam evaporated Au films, to compute the thermal diffusivity of the composite structure. Figure 2 shows the expected thermal diffusion time across a main array Au:Er waffle, estimated as distance across the waffle squared divided by diffusivity. A finite-element calculation of the 2-D thermal diffusion gave a similar conclusion that a 600-nm capping layer is suitable.

Fig. 2

Calculated thermal diffusion time across the Au:Er main array waffle sensor as a function of the thickness of a pure Au capping layer added to speed thermalization. The thermal diffusion time (curve) is compared with the fastest expected hydra pulse rise time (lower horizontal line) and the overall hydra decay time constant (upper horizontal line).

4.1.

MIT Lincoln Lab Eight-Layer Multilayer Process

A promising multilayer Nb process has been demonstrated by MIT/Lincoln Lab (LL). MIT/LL has developed a process that supports eight superconducting Nb metal layers for superconducting electronics.¹⁵ Each Nb metal layer is defined by deep ultraviolet (DUV) lithography to achieve submicron line/space resolution. The submicron DUV photolithography requires high planarity of circuit layers because of the small depth-of-focus in modern photolithography. Therefore, the MLT/LL fabrication process utilizes chemical mechanical polishing to ensure all metal layers are deposited on a surface with topography height of less than 40 nm. The planarization also simplifies the addition of multiple metal layers by making the process modular—the process for the eighth metal layer can be the same as the process for the second metal layer. Through the use of this process, MIT/LL has integrated over 800,000 Josephson junctions in a single chip.¹⁶ This high level of integration has been achieved for the first time in this technology and demonstrates the high-yield of high-density superconducting wiring at MIT/LL.

Multilayer buried wiring can also be utilized to lower the crosstalk without increasing the line-spacing of the wires. For high-density wiring with small linewidths, crosstalk can be an issue. By surrounding the signal lines with grounded shielding layer, crosstalk can be reduced by a large factor. The mutual inductance crosstalk between two superconducting Nb striplines, which are $1\mu \mathrm{m}$ apart and $0.25\mu \mathrm{m}$ wide, has been reduced to $-41\mathrm{dB}$ using upper and lower ground planes, with data being in agreement with simulations.¹⁷

A third benefit of the multilayer buried wiring approach is that there is a planarized surface on top of the wiring on which to fabricate the main microcalorimeter pixels, with generally more space for the pixel designs and heat-sinking. This makes the subsequent fabrication process dramatically easier and even opens up pixel geometries. For example, MMC flux transformers and electrical crosstalk barriers could be introduced, which could not be realized on planar wiring.

4.2.

Automated (Algorithmic) Wiring and Sensor Layout

In a first trial integrating buried wiring fabricated at MIT/LL with MMCs fabricated at Goddard Space Flight Center (GSFC), we took an existing mask layout, which we had developed for fabrication of small arrays ($5\times 5$) of high-inductance, nonhydra MMCs, and had the Nb microstrip and ground plane fabricated at MIT/LL using two Nb metal layers. In our second generation buried wiring prototype, connections to every sensor in the three LXM subarrays are implemented using four buried superconducting Nb layers. This provides high wiring density, low inductance, high yield, reduced cross-talk (shielding ground planes), and ability to fan out wires from enhanced and UHR arrays underneath main array pixels. However, to take advantage of the array scale enabled by the wiring process, we needed to approach the mask layout task differently.

Our LXM prototype has 55,800 x-ray pixels, thermally linked to 5688 sensors, with wires from each sensor brought outside the array perimeter. Since the complexity of the design exceeds the capability for manual mask layout, we automated the mask layout process with custom algorithmic techniques developed by one of us for a variety of detector fabrication projects at the Detector Systems Branch at Goddard.

The first step in the algorithmic approach was topological layout of wiring paths in muntins between pixels. The basic wiring scheme we employed has long been used in hand layout of small TES microcalorimeter arrays.¹⁸ So that the required wiring pitch is relaxed, one can route the wires to attempt to equalize the number of wire-pairs in each muntin, with ideally at most $N/4$ wire-pairs in any muntin in an $N\times N$ sensor array. In determining wiring paths for one octant of a square array, starting from the muntin nearest the center line of the array, if routing wires from sensors near top of a muntin will exceed the $N/4$ goal, then one moves the path for those wires over to the next muntin to the right, and repeats this process for each muntin working from left (center line) to right (outer corner) in the octant. Success of the algorithm was shown for specific examples (e.g., for $N=16$) worked out by hand but with no proof that the $N/4$ goal could always be achieved. For our LXM arrays with $N=60$ or 24, this process is too tedious to complete manually but is rapidly solved with a computer algorithm. For even numbers $N$, we found that the $N/4$ goal is achieved only for $N\le 18$. With the division we chose for upper and lower octants, we found that for $N=20$ up to 38, one additional wire-pair per muntin is required to avoid wire paths being shifted outside the octant under consideration. For $N=40$ up to 74, two additional pairs are required, whereas for $N=76$ up to at least 200, three additional pairs suffice. Figure 4 shows the topological designs for $N=60$ and 24. A data structure describing the topology can be saved and reused, e.g., for the main and UHR designs that both have $N=60$.

Fig. 4

Topological wiring schemes for one quadrant of an $N\times N$ sensor array for (a) $N=60$ or (b) 24.

Details of actual wire paths and sensor features were then also created algorithmically. In our main array design (Fig. 5), the Au:Er film is patterned in the “waffle” geometry described above, which leaves holes for a support stem to each absorber, and a customized Au thermal link between absorber and Au:Er. The high feature density of the LL process allows not only fabrication of sensor meander coils, with pitch as narrow as $0.8\mu \mathrm{m}$, but also the packing of twin-microstrip wiring for the $60\times 60$ sensor array into a single layer (over a ground plane) between hydras using $0.7\mu \mathrm{m}$ lines and $0.7\mu \mathrm{m}$ spaces (shown as $1.0\mu \mathrm{m}$ lines and $0.4\mu \mathrm{m}$ spaces in Fig. 5 but later modified).

Fig. 5

(a) LXM main array sensor design with successive close-ups of one Au:Er waffle sensor, the Nb sensor coil that meanders to fill the area under the Au:Er waffle, and the interconnection to a twin-microstrip wire pair over a Nb groundplane in an adjacent muntin. (b) Details of the Nb wiring in the muntin, which is partially covered by a Au heat sinking grid.

The multilayer wiring provides even more benefits in our enhanced array design (Fig. 6). While the sensor meanders for this $24\times 24$ array are on the same layer as for the main array, in order to have close proximity and therefore good magnetic coupling to the Au:Er, the wiring for the enhanced array uses two additional layers through near the center of an enhanced array hydra connect the meander to a deeper wiring layer hidden by an additional intervening ground plane. The advantages are: (1) fan-out of this array’s wiring is beneath and hidden from the main array and (2) the intra-array wiring is also hidden from the sensor meander, allowing room for the desired sensor meander area, and for greater spacing between twin-microstrip pairs, thereby reducing crosstalk.

Fig. 6

(a) LXM enhanced array sensor design with successive close-ups of one Au:Er waffle sensor, the top level Nb sensor coil that meanders to fill the area under the Au:Er waffle, and the interconnection to lower wiring layers, through near the center of the waffle, to a twin-microstrip wire pair and ground plane. (b) Details of the Nb wiring in lower level muntins, which are shielded from the main array wiring and sensors by the intervening ground planes.

Our UHR design (Fig. 7) assumes the use of the same additional ground plane and wiring layers as the enhanced array. However, this $60\times 60$ sensor array has sensor cell size 1/5 that of the main array, leading to an aggressive packing of the intra-array wiring, which could be relaxed if six Nb layers were used instead of four. For this first LXM prototype fabrication run, we chose to cover as much of the sensor cell area as possible with the Au:Er and meander coil so as to keep the sensor inductance $>1\mathrm{nH}$, even though this gives a sensor heat capacity higher than optimal. Even for the nonhydra UHR sensors, we included a thermal link, between the absorber and the Au:Er sensor, to enable us to control the size of the x-ray pulse slew rate, without introducing too much internal thermal noise [Fig. 1(c)].

Fig. 7

(a) LXM UHR array sensor design with successive close-ups of one Au:Er annular sensor plus the top level Nb sensor coil that meanders to fill the area under the Au:Er annulus, and the interconnection to lower wiring layers, through vias near the center of the sensor, to a twin-microstrip wire pair and ground plane. (b) Details of the Nb wiring in lower level muntins, which are shielded from the main array wiring and sensors by the intervening ground planes.

The superconducting wiring from every sensor in the large arrays is brought out to the perimeter of the main array as it would be in LXM. Past that point, only selected sensors have their connections brought out to bond pads for SQUID readout to test this generation of devices. The fanout of the wiring is to two rows of 28 bond pad pairs along each long edge of the chip for a total number of 112 testable sensors. The spacing of the pads and the selection of testable pixels is arranged so that currently available NIST μMUX chips can connected with wire bonds to readout 20 sensors per cool-down, or alternatively PTB/Magnicon dc SQUID chips can be connected to readout eight sensors per cool-down, with a mixture of the three array types sampled in each case.

6.1.

Performance Characteristics of Initial Small Arrays with 2 Wiring Layers

We have measured the performance of devices from our first buried wiring run, with high inductance sensors and two Nb layers. The prototype MMCs were fabricated with various geometries of 0.8-, 1.2-, 1.6-, and $5.0\text{-}\mu \mathrm{m}$ pitch (line width is one half of the pitch). Each main array hydra has one $136\times 136{\mu \mathrm{m}}^2$ Au:Er sensor and twenty-five $50\times 50\times 2.8\mu {\mathrm{m}}^3$ gold absorber. As explained above, we separated the Nb coil and Au:Er sensor with a conservative 200 nm thickness of insulator. To expedite measurements, we also compromised by using the available PTB dc SQUIDs despite the inductance mismatch between their input inductance of 1.8 nH and our high-inductance meander coils. We measured this early version of buried wiring MMCs in a nonoptimal set-up currently purely for studying the different pitches and to verify the buried wiring process, and were pleased to see that the devices worked, and had a high critical current of 40 mA through the multilayer, fine-pitch wiring. We (i) measured Au:Er magnetization signal (change in SQUID flux from high temperature to the operating temperature) for various bias currents and sensor meander pitch, (ii) computed the total heat capacity $C_{\text{tot}}$ and thermal conductance $G_{\mathrm{b}}$ of the MMC sensor to the heat bath from x-ray pulse heights and decay times, and (iii) measured energy x-ray resolution in a spectrum of $\mathrm{MnK}\alpha$ x-rays. The measured magnetization and heat capacity were in agreement with estimated values based on a numerical simulation of the Au:Er sensor at various temperatures. The measured thermal conductance of the pixels to the solid substrate, which consists of multiple layers of ${\mathrm{SiO}}_2$ and Nb, was 50% of the value predicted from a simple acoustic mismatch model without accounting for the multilayer structure. Further details of the measurements and results are given in Ref. 9.

6.2.

MMC Hydra Optimization and Projected Performance for LXM

The first two wafers we have completed from the second generation, four-layer buried wire fabrication run used wafers with a 50 nm top insulation layer thickness, and are expected to give better energy resolution due to the improved magnetic coupling, and use of readout SQUIDs with appropriately matched input inductance. In addition, half the sensors in our large-scale arrays include Au thermal links to an intra-array heatsink to control the thermal conductance between sensor and heat bath and reduce thermal crosstalk. We have completed simulations of the expected response and energy resolution for the hydra sensors in the second-generation design, including the effects of position errors in the hydras. Figure 10 is an example of a magnetic field calculation from which the detector responsivity can be predicted.

Fig. 10

Magnetic field lines in a cross-section through an MMC, calculated using a finite-element method approximating the Nb as perfect conductors, for 1 mA of current. Shown is the region around two Nb traces with counterflowing current in the middle of the coil. Nb traces are 400-nm wide and 200-nm thick. Coil pitch is 800 nm. Also shown is the region filled by a 130-nm thick Au:Er sensor 50 nm above the Nb, but the influence of the Au:Er on the magnetic field distribution is not included in the calculation.

Results of our hydra simulations show that the main and enhanced array sensor designs can achieve the Lynx 3-eV resolution goal, with good position resolution down to about 200 eV x-ray energies. Figures 11 and 12 show the results of simulations for the energy resolution and the accuracy of determining the x-ray absorption location in a $5\times 5$ MMC main array for LXM, assuming a SQUID coupled energy sensitivity $100\hslash$ with input inductance matched to $0.8\text{-}\mu \mathrm{m}$ pitch sensor with 50-nm insulation thickness, operating at 40 mK. The sensor meander coil inductance is 7.7 nH, whereas the stray inductance in the large array and fanout to the microwave SQUIDs is 5.9 nH. The SQUID input coil is assumed to have been designed to have self-inductance 13.6 nH for optimal matching to the sensor plus stray inductance. The erbium concentration is 900 ppm, and the meander current is 14.8 mA. The 25 conductance values of the thermal links in the hydra have been designed to minimize the worst-case probability of an error in determining the position of the pixel hit by a 200 eV x-ray while not overly degrading the worst-case energy resolution among the 25 pixels. Here, the position error for a given pixel means the probability that a photon absorption event is incorrectly assigned a different pixel due to noise changing the best match to an optimal filter template.

Fig. 11

Simulation predicting the FWHM energy resolution of the $5\times 5$ hydra sensor with 800-nm pitch meander coils in the MMC main array in LXM. The energy resolution without errors in position correlation is dE, whereas dEx includes the effect of uncertainty in determining the x-ray absorption location in the $5\times 5$ hydra for an x-ray energy of 200 eV. For x-ray energies much larger than 200 eV, the energy resolution approaches dE.

Fig. 12

Probability of an error in determining the position of the x-ray absorption in MMC hydra for the LXM main array, for 200 eV x-ray energy, as a function of the normalized link conductance. Also plotted is the worst energy resolution among the hydra pixels for high and low x-ray energies. The worst-case position error is minimized (29%) with an optimized value for the overall normalized conductance value 0.5 (and with an optimized distribution of the relative conductances for each of the 25 individual links). The energy resolution shown in Fig. 11 is for a normalized conductance value 1.0, for which the worst-case position error is 40%.

To estimate the energy resolution and position error, we have used the correlated energy-position optimal filter algorithm.¹⁹ From this algorithm, the theoretical energy resolution $\mathrm{\Delta }E$ and the 1-sigma position resolution $\mathrm{\Delta }i$ are given as follows:

We calculated the position error and energy resolution for each pixel for hydra designs with various sets of thermal link conductances. Based on fabrication constraints, we bounded the ratio between highest and lowest link conductances, and then considered varying the overall conductance scale of a design characterized by the “normalized thermal conductance” parameter used in Fig. 12. (One can think of varying the normalized thermal conductance by changing the gold thickness used for the thermal links.) We iteratively distributed the relative conductances within the permitted range of ratios and varied the normalized thermal conductance so as to try to minimize the worst-case position error. As shown in Fig. 12, the position errors of all pixel are below 29% at a normalized conductance of 0.5. However, for that hydra design, the estimated energy resolution varies from 3.25 to 4.48 eV FWHM as the x-ray energy ranges down to 200 eV. As a practical trade-off between position error and energy resolution requirements, we chose the design for a normalized thermal conductance value 1.0, for which the energy resolution range is 2.85 to 3.37 eV FWHM and the maximum position error is 40% at 200 eV.