2.3.1.

Pixel design

The LMS TES pixel design is based around the same Mo/Au bilayer technology developed for Athena/X-IFU. However, to optimize for high resolution over a narrower energy range, we implemented several adjustments. First, the absorber composition is changed from the thick Bi $(5\mu \mathrm{m})/\mathrm{Au}(1\mu \mathrm{m})$ design that Athena/X-IFU uses, to $0.54\mu \mathrm{m}$ Au-only design. The Bi/Au composite design was needed to provide low heat-capacity ($C$) with high stopping power for x-rays at energies up to 12 keV. The reduced energy range of LEM means we can achieve unity stopping power at 1 keV with a significantly thinner Au absorber and without the need for an additional Bi layer. Simultaneously, the lower heat-capacity of this design enables improved spectral resolution over LEM’s narrower energy range ($\mathrm{\Delta }E\propto \surd C$). Using single layer, Au absorbers have some significant benefits; it makes the fabrication easier and eliminates any possible ageing effects associated with the oxidization of the Bi,¹⁵ which can adversely affect the energy resolution. Au has near unity reflectivity to long wavelength radiation (compared to 40% for Bi²⁵), which makes the absorbers less sensitive to stray power loading and shot noise.

Previously, we have developed a process to fabricate mechanically robust absorbers as thin as $\sim 0.2\mu \mathrm{m}$ thick on the same pixel pitch as LEM; thus the $0.54\mu \mathrm{m}$ baseline for LEM is comparatively straightforward. Figure 3 shows the total absorber quantum efficiency (QE = vertical stopping power × fill fraction) as a function of energy. Also shown is a scanning tunneling microscope (SEM) of a LEM absorber demonstrating a thickness of $0.54\mu \mathrm{m}$ Au with $1.5\mu \mathrm{m}$ gaps between pixels. This provides 99% fill-factor and 100% vertical stopping power at an energy of 1 keV which is needed to satisfy the LEM effective area requirements.

Fig. 3

(a) Total QE of the LMS pixels as a function of energy. This is defined as the vertical stopping power multiplied by the array filling fraction. (b) SEM image of a LEM absorber with the appropriate pitch ($290\mu \mathrm{m}$), thickness ($0.54\mu \mathrm{m}$), and gaps between pixels ($1.5\mu \mathrm{m}$) needed for LEM.

In addition, the transition temperature, $T_C$, of the devices is reduced from 90 to 55 mK (the LEM cryogenic chain supports 40 mK heat-sink temperature with high cooling capacity). Lower $T_C$ enables low total heat capacity and low thermal noise ($\mathrm{\Delta }E\propto T^{3/2}$) while ensuring the pixels are sufficiently slow to match the bandwidth and dynamic range of the TDM readout. The single pixels and hydras are implemented with the same TES geometry and absorber thickness. Because the hydras have 4 pixels for 1 TES, they have $\times 4$ the heat capacity of the single pixels and $\times 2$ worse energy resolution. The Athena/X-IFU TES consists of a Mo/Au proximity effect bilayer of size $50\mu \mathrm{m}\times 50\mu \mathrm{m}$ with Nb biasing leads and Au “banks” that run along the edges of the TES to ensure uniform edges.^26,27 For LEM, we have reduced the width of TES to $15\mu \mathrm{m}$ and adjusted the bilayer thickness, in combination this has enabled us to achieve the desired transition temperatures in the range 55 to 60 mK. Figure 4 shows a schematic diagram of a LEM hydra showing the anatomy of the TES pixel. The TES sits atop of a $0.5\mu \mathrm{m}$ thick SiN membrane that provides the weak thermal link to the heat-bath. The absorbers are supported above the TES and membrane using 6 Au pillars. The single pixel devices have a square $200\mu \mathrm{m}$ membrane, whereas the hydra has a single four-leaf clover shaped membrane of spatial extent of $450\mu \mathrm{m}$. In the hydra design, 1 absorber is directly coupled to the TES via 1 of its support columns, whereas the other 3 are decoupled using Au links (200 nm thick and $2\mu \mathrm{m}$ wide) of varied lengths, tuned to provide the desired hydra pulse shapes. We have successfully demonstrated hydras with up to 25 absorbers for mission concepts such as NASA’s Lynx.⁶ Because of the large number of absorbers, the Lynx hydra design necessitated a complex thermal network, where the pixels are arranged in hierarchical “tree” geometry. The 4-pixel design we are pursuing for LEM, however, is arranged in a “star” geometry where all pixels connect directly to the TES. This design is straightforward to implement, making the layout, modeling, and analysis, comparatively simple.

Fig. 4

(a) Schematic layout of a hydra showing the key components of the pixel design. The inset shows an optical micrograph of the TES before the membrane has been back etched and the absorbers deposited. (b) Measured resistance versus temperature curves for three TES pixels with widths of 50 (Athena/X-IFU design), 30, and $15\mu \mathrm{m}$. We have baselined the $50\mu \mathrm{m}\times 15\mu \mathrm{m}$ TES for both the LEM single pixels and hydras.

Figure 4 also shows the measured resistance versus temperature curves for three TESs of different widths (derived from current–voltage measurements), but all fabricated with the same Mo/Au bilayer deposition. The reduction in transition temperature with width is attributed to the lateral proximity effect from the metal banks along the edge of the TES. The normal conducting Au banks proximitize laterally into the superconducting Mo/Au TES, suppressing the effective transition temperature of the device.²⁸ As the Mo/Au width is decreased, the $T_C$ suppression from the banks increases. A consequence of the increased aspect ratio of the device is that its normal state resistance is also increased. The higher resistance of the baseline LEM TESs compared to the $50\times 50\mu \mathrm{m}$ devices baselined for Athena/X-IFU does not directly affect the performance of the pixels, but it does change the dimensioning of the readout and bias circuit parameters, such as the shunt resistor ($R_s$) used to voltage bias the TES, the bandwidth limiting Nyquist inductance ($L$) used to optimally match the bandwidth of the pixels to that of the readout, and the mutual inductance that couples the TES circuit to the SQUID readout ($M_{\text{in}}$). These will be discussed further in Sec. 2.4 and in Ref. 13.

The reduction of the TES width has added benefits to the LMS design related to the magnetic field sensitivity of the pixels. A TES is sensitive to the magnetic field perpendicular to the plane of the detector. Time varying magnetic fields, $\mathit{\delta }B$, inside the focal plane assembly can result in changes in the detector response from event-to-event,²¹ which ultimately manifests as a drift in the measured photon energy $\mathit{\delta }E$. This can degrade the spectral resolution of the detector and complicate the calibration of the energy scale. In general, a device with reduced perpendicular area should be less sensitive to external magnetic fields. However, the dependency of the energy gain sensitivity, $\mathit{\delta }E/\mathit{\delta }B$, on geometry is complicated by inhomogeneity of the current flow through the TES and the self-induced magnetic field generated from the current flowing in the TES and bias leads. For our TESs of lengths in the range 50 to $75\mu \mathrm{m}$, we have empirically found that $\mathit{\delta }E/\mathit{\delta }B$ scales non-linearly with the width of the device.²⁷ The gain sensitivity also scales approximately linearly with photon energy and is not strongly dependent on device parameters such as heat-capacity or transition shape. Thus, the lower energy range of the LEM pixels and the reduced pixel width are both beneficial in reducing the gain sensitivity. We have recently measured $\mathit{\delta }E/\mathit{\delta }B=7\mathrm{meV}/\mathrm{nT}$ at 1.5 keV on LMS pixels of width $15\mu \mathrm{m}$,²⁹ almost $\times 300$ lower than the $2.0\mathrm{eV}/\mathrm{nT}$ at 7 keV measured for Athena/X-IFU pixels of width $50\mu \mathrm{m}$.²¹ The low field sensitivity of the pixels is important to the LMS focal plane assembly design, enabling a reduction in the magnetic shielding requirements, and thus smaller, lower mass magnetic shields.

2.3.2.

Implementation in hybrid arrays

Hybrid arrays may include pixels of different pitch, absorber composition, and TES transition temperature (or shape) fabricated on a single substrate, and thus enable the flexibility to design different parts of the focal plane to achieve different performance requirements. The hybrid focal-plane array for LEM provides better spectral resolution and count-rate capability in the central portion of the array using single pixel TESs while the use of hydras in the outer portion of the array maximizes the FoV, without adding significant technical complexity to the focal plane array and assembly. Since the TES design, the absorber pitch and the absorber thickness are the same for both the single pixels and hydra portion of the array, the implementation of the LMS hybrid array is straightforward. The only differences are the need for different SiN membrane geometries for the hydras and single pixels, and the addition of a metal link layer to connect the hydra absorbers to the TES. The SiN is released from the substrate using a deep reactive ion etch (DRIE) from the backside of the Si wafer. We have successfully optimized our DRIE process to simultaneously back-etch the different sized membranes needed for single pixel and hydras in a large format (1k-pixel) hybrid array. Different back-etch geometries have been studied for the hydra, including a simple large square membrane and a four-leaf clover geometry. The clover leaf membrane was designed to match more closely the size of single pixel membrane and thus make it easier to fabricate, since the etch rate depends on the size of the opening. However, no difference was observed in the yield between the large square membrane and clover-leaf design, and in practice either geometry can be used. Figure 5 shows an optical photograph of a 1k LMS array that includes a central region of 256 pixels surrounded by 192 4-pixel hydras. Also shown is a zoom-in view of the backside of the chip showing both the pixel types. The features of the TES are visible through the membrane, showing the outline of the TES, hydra links, and the absorber support contacts. This image shows the clover-leaf membrane design for the hydra.

Fig. 5

Photograph of a 1k-pixel LMS hybrid array that includes both single pixel and hydra devices. Also shown is a zoom-in of the backside of the chip showing both pixel types. Visible is the Si frame, SiN membranes, and through the membranes the outline of the various TES features can be seen.

The measured energy histograms for representative pixels in a prototype LMS array of 1k pixels are shown in Fig. 6. We achieved a full-width-at-half-maximum spectral resolution of $\mathrm{\Delta }{E}_{\mathrm{FWHM}}=0.90\pm 0.02\mathrm{eV}$ in a single pixel and $1.92\pm 0.02\mathrm{eV}$ for a 4-pixel hydra (4 pixels summed) measured using $\mathrm{Al}\text{-}\mathrm{K}\alpha$ x-rays (1.5 keV). Furthermore, the position discrimination was successfully demonstrated in the hydras down to energies of $\sim 200\mathrm{eV}$. The detailed characterization of these first pixels (including noise properties, pulse shape, transition shape, etc.) are reported in Ref. 29. These results demonstrate that the LMS pixel designs can achieve the desired performance requirements in a large format hybrid array and were key to establishing TRL-5 for the LMS detector.

Fig. 6

Energy histograms for (a) a single pixel and (b) a four-pixel hydra (all 4 pixels summed) measured in a prototype LEM 1k pixel array. Data are measured using a fluorescent $\mathrm{Al}\text{-}\mathrm{K}\alpha$ x-ray source which emits photons of energy 1.5 keV. The dashed lines are the assumed natural line shapes for the $\mathrm{Al}\text{-}\mathrm{K}\alpha$ complex from literature^30–32 and the solid lines are the fits to the data points. To avoid potential bias in the fitted energy resolution from the $\mathrm{K}\alpha$ satellite lines whose positions are not well established, we fit to a limited energy range around the $\mathrm{K}{\alpha }_{\mathrm{1,2}}$ emission peaks only. The fitted energy resolutions are $\mathrm{\Delta }{E}_{\mathrm{FWHM}}=0.90\mathrm{eV}$ and $\mathrm{\Delta }{E}_{\mathrm{FWHM}}=1.92\mathrm{eV}$ for the single pixel and hydra respectively. Further details on the pixel performance can be found in Ref. 29.

2.4.1.

Detector and readout parameters

The baseline properties of the LMS pixels are listed in Table 2 and are derived from the characterization presented in Ref. 29. Since the TES design is the same for both pixel types, the TES transition shape (parameterized by the transition parameters $\alpha =T/R\partial \mathrm{R}/\partial \mathrm{T}$, $\beta =I/R\partial \mathrm{R}/\partial \mathrm{I}$) and noise properties are also very similar. The hydras naturally have $\times 4$ the total heat-capacity and have larger thermal conductance ($G_b$) to the heat-bath. For a TES on a thin SiN membrane, $G_b$ scales by the phonon emitting perimeter of the device. Thus, the absorber support pillars that contact the membrane, and the metallic thermal links both contribute to a factor of almost $\times 2$ higher $G_b$ in the hydra pixels. Typically, a large inductance ($L$) is used in series with the TES to slow the rise of the pulse and reduce the dynamic range requirement for the readout, enabling the lowest possible readout noise.⁴ The important dimensioning parameter is the “slew-rate” of the pixel, which is the maximum change in current in the TES circuit $\mathrm{dI}/\mathrm{dt}{|}_{\max }$, at the maximum energy range of interest (which is 2 keV for LEM). For the hydra, this is set by the pixel directly coupled to the TES with the fastest rise-time. Based on our characterization of the single pixels and the hydras, we find that the peak slew-rates are roughly the same for a given circuit inductance $L$ and x-ray energy. This is convenient because it means that the same TDM chips can be used to readout both pixel types. We budget $65\mathrm{mA}/\mathrm{s}$ at 2 keV for the LMS with a baseline shunt resistance value of $R_s=100\mu \mathrm{\Omega }$ and a circuit inductance of $L=1.51\mu \mathrm{H}$. To accommodate the peak slew-rate within the dynamic range requirements of the TDM readout (while multiplexing 60 rows in a TDM column), we choose a mutual input coupling of the TES to the first stage SQUID input of $M_{\text{in}}=820\mathrm{pH}$. These components are situated on the TDM readout chips and are easily accommodated in pre-existing Athena/X-IFU designs, requiring only minor adjustments. Details of the readout noise contribution to the total system performance will be discussed in Sec. 2.4.2. Further information of the TDM development for Athena/X-IFU and LEM can be found elsewhere.^4,13

Table 2

Pixel, bias-circuit, read-out parameters and performance metrics for the LMS pixels.

2.4.2.

Energy resolution budget

Table 3 shows the currently assumed ERB for the LMS detector. The detector performance requirements for the LMS are 1.3 and 2.5 eV FWHM at 1 keV for the single pixels and hydras, respectively. The energy resolution of the LMS is dominated by the intrinsic energy resolution of the pixels themselves; however, many system parameters contribute to the overall performance of the instrument. The ERB contains both in-band noise terms (such as noise from the detector and readout) as well as contributions due to drifts in the system gain that cannot be readily corrected, and thus contribute noise. The root-sum-squared (RSS) of all the uncorrelated contributions provides the current best estimate (CBE) of the total system performance. We hold margin for each subsystem contribution in as well as holding additional unallocated margin at the system level. This ensures that the overall performance requirements are met. The CBE is 1.2 eV for the single pixels and 2.27 eV for the hydras, leaving 0.5 and 1 eV of unspecified margin, respectively. The budget is based on direct measurement when possible, and modeling/analysis based on the baseline LEM architecture and experience from developing the Athena/X-IFU resolution budget. The budget and margins will continue to evolve as the actual performance of each subsystem is measured. The detailed apportionment in the noise budget between the LMS subsystems is complex, and here we briefly outline the key components.

Table 3

LMS ERB at 1 keV.

Readout noise

The second largest contributor ($0.46/0.68\mathrm{eV}$) is from the warm and cold readout electronics (including noise from the front-end TDM SQUIDs, second stage amplifier SQUIDs, digital to analog converters (DACs), analog to digital converters (ADCs), and the room temperature low noise amplifier). Due to the inherent mismatch between the large open loop bandwidth needed to rapidly switch between TDM rows and the individual pixel bandwidth, broadband noise sources will be aliased into the signal band. The total broadband white noise level scales with the square-root of the number of rows in a TDM column. This is typically the dominant source of noise from the readout chain. We have conservatively chosen a total non-multiplexed white noise level of $0.35\mu {\mathrm{\Phi }}_0\surd \mathrm{Hz}$, referred to flux in the first stage SQUID (this is slightly higher than the $0.32\mu {\mathrm{\Phi }}_0\surd \mathrm{Hz}$ used for Athena/X-IFU to accommodate additional margin). For LEM, we have 60 rows in a TDM column, which gives a multiplexed aliasing factor of $\sim 14$. With the preferred choice of $M_{\text{in}}=820\mathrm{pH}$, the budgeted TES referred white noise after multiplexing is then $12\mathrm{pA}/\surd \mathrm{Hz}$.^4,13 To accurately assess the contribution of the noise on the pixel energy resolution, we have added randomly generated white noise to measured datasets in the limit of low readout noise. Figure 7 shows the RSS resolution broadening as a function of the white noise level. At the budgeted noise allocation of $12\mathrm{pA}/\surd \mathrm{Hz}$, the RSS contributions to the total resolution are $\sim 0.40$ and $\sim 0.60\mathrm{eV}$ for the single pixel and hydra, respectively, which we adopt in our ERB. Other small contributing terms include $1/f$ noise, narrow band noise from the SQUID and TES biases (not subject to the aliasing factor), and conducted susceptibility from electromagnetic interference (EMI) that couples to the readout chain.

Fig. 7

RSS energy resolution degradation as a function of broad-band white readout noise for LMS single pixel and hydra detectors. The vertical line indicates the total budgeted white noise level of $12\mathrm{pA}/\surd \mathrm{Hz}$ referred to the TES input.

2.4.3.

Count-rate accommodation

Photon arrival times are Poisson distributed and the count-rate accommodation of the detectors can be determined from a statistical analysis. The total time interval in which a single event can be accepted is $\mathit{\delta }t=\mathit{\delta }{t}_p+\mathit{\delta }{t}_n$, where $\mathit{\delta }{t}_p$ is the time needed for the previous event to have decayed to a negligible level and, $\mathit{\delta }{t}_n$, the time required to process the event before the arrival of the next. The latter is defined as $\mathit{\delta }{t}_n=t_{\text{rec}}-t_{\mathrm{pre}\text{-}\mathrm{trig}}$, where $t_{\mathrm{rec}}$ is the record length used by the digital optimal filter to determine the pulse height and $t_{\mathrm{pre}\text{-}\mathrm{trig}}$ is the time before the trigger point (accounting for the fact that the trigger point is not at the very start of the record). The fraction of the events that can be accepted for a given rate, $r$, is then $f={\mathrm{e}}^{-r\mathit{\delta }t}$. Based on the pixel properties listed in Table 2, we choose $\mathit{\delta }{t}_p=55\mathrm{ms}$ for the hydras and $\mathit{\delta }{t}_p=35\mathrm{ms}$ for the single pixels (since they are faster pixels). However, we adopt identical record lengths of $t_{\mathrm{rec}}=79\mathrm{ms}$ (8192 samples) for both. These define the high-resolution event grades. In digital optimal filtering, the choice of record length affects the achievable energy resolution.³³ The shorter the record length, the more degraded the resolution. In the ERB, this is already included as a 1.5% and 2% degradation factor for the single pixels and hydras, respectively (affecting the pixel and readout related noise terms). To maximize the instrument throughput, we can define additional event grades that have shorter record lengths, and thus slightly degraded resolution. Following similar definitions that were used for the Astro-H/SXS event grading scheme,³⁴ we define mid-resolution events with a record length of ¼ the high-resolution. We also define a low-resolution event grade that finds the raw pulse peak and only requires a few samples to measure. The event grades are defined in Table 4. Note that these definitions are preliminary and will be further updated as the instrument and observational needs are refined (additional intermediate event grades may also be considered). Events that do not satisfy the three primary event grades are defined as high/mid/low resolution secondary events (pile-up events landing on the tail of the previous pulse) and are not easily used for spectroscopy. The measured energy of the secondary events depends on the energy of the previous pulse and the time separation between them. As part of our future studies, we will explore methods to correct such events in post-processing, which may enable their use for spectroscopy and increase throughput at higher rates. Figure 8 shows the event grading branching ratios as a function of count-rate. The inner array of single pixels offers around ×6 higher count-rate accommodation (per 15″ pixel) compared to the hydras. This is in-part because of the larger $\mathit{\delta }{t}_p$ exclusion window needed for the hydras (because the hydras pulse time constant is larger). However, the main reason is because the hydra has 4 pixels for a single TES. Consequently, they can accommodate ×4 fewer events per 15″ pixel compared to the single pixel TESs.

Table 4

Event grading scheme for the LMS microcalorimeter. δtp=55  ms for hydra pixels and 35 ms for single pixels.

Fig. 8

Event grade branching ratios as a function of count-rate per 15 arcsec pixel for (a) single pixels and (b) hydras. High- and mid-resolution events dominate at lower count-rates before secondary events quickly dominate as the rate increases. Here, we show the total of all high/mid/low resolution secondaries combined.