1 Introduction

Time division multiplexing (TDM) is a high readiness readout technology that has been broadly used in bolometer [1,2,3] and microcalorimeter [4] experiments and is being developed as the readout technology for the X-ray Integral Field Unit (X-IFU) of the ATHENA Satellite mission [5] and CMB-S4 [6]. Our latest generation multiplexer (mux21) is designed to be symmetric for compatibility with differential readout [7], utilizes two layers of switching to reduce the number of row address wires [8], and uses half of the power [9] and 60% of the area compared to the previous generation of TDM (mux15). Mux21 has been implemented in our 4-column × 34-row chips, which achieved (2.02 ± 0.03) eV resolution at 5.9 keV reading out NASA TES arrays [7], and in linear multiplexer chips for CMB-S4 (mux21_S4).

The packaging considerations for large focal plane arrays, especially in mass constrained space applications, favor reductions in multiplexer area. Close packing to minimize chip area has been achieved in mux15 chips, but at the cost of having physical nearest neighbor crosstalk at the level of 0.37% proportional crosstalk due inductive coupling between components in adjacent cells, a level of crosstalk that reduces event throughput in microcalorimeter applications. In this paper, we report techniques to reduce physical neighbor (PN) crosstalk in close-packed TDM cells. We present nearest PN crosstalk levels below 0.01% in our 2-dimensional (2D) multiplexers for X-IFU and below a background of 0.005% for our CMB-S4 demonstration chips.

2 Physical Neighbor Crosstalk in Time Division Multiplexing

Each TDM multiplexing unit reads out the currents of dc voltage biased TESs sequentially by measuring SQUIDs one at a time [10], accomplished in modern TDM architectures by opening a flux actuated switch (FAS) [11] to activate each TES’s corresponding first stage SQUID ammeter (SQ1) [12]. As shown in Fig. 1Left, our FAS-based TDM architectures use superconducting transformers to transfer flux from the TES circuit coil to the SQ1, with a dummy-SQ1 [10] without Josephson junctions used to cancel the parasitic coupling between the TES circuit and the SQ1 feedback coils (FB1). The superconducting washers of these transformers are coupled to TES bias circuit coils with many turns, making these features far larger than the SQUIDs.

Fig. 1
figure 1

Left, a circuit diagram showing the split transformer washer architecture used in mux15 and the monolithic washer architecture used in our most recent chips to couple SQ1 to the TES current coils. Right, an optical image of two cells of a linear multiplexer designed for bolometer readout (mux21_S4), which uses a monolithic washer. The eight large rectangles in the center of each cell are where coils carrying the TES current are coupled to the superconducting transformer washer, marked by a dashed box in the circuit diagram. The polarity of each lobe, labeled in the figure, is chosen, so the washer and TES circuit coils of adjacent cells have zero mutual inductance

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PN crosstalk proportional to a neighboring pixel’s TES current (ITES, adj) occurs when the neighboring bias circuit is inductively coupled to the affected pixel’s superconducting transformer washer or SQ1 SQUIDs. As shown in Fig. 1Right, the lobes of the transformer washers are orders of magnitude larger than those of the first order gradiometric SQUIDs, making the washer the primary consideration for proportional PN crosstalk.

Low passed derivative crosstalk arises from inductive coupling between neighboring bias circuits, particularly the Nyquist (LNyq) and TES current coils of the transformer. This parasitic coupling introduces a voltage proportional to dITES, adj/dt across the inductor, resulting in a shift in TES current proportional to dITES, adj/dt with an additional lowpass filter applied by the TES circuit. Since ITES is nearly constant in bolometric applications, derivative crosstalk is primarily a concern for microcalorimeter readout.

Recent reductions in PN crosstalk come from the use of lobe polarity encoding. The lobe polarity encoding scheme shown in Fig. 1Right uses eight lobe monolithic washers. The top four lobes of the even cell have polarity identical to those in odd cells but have the polarity of the bottom four lobes reversed. Due to symmetry, there will be near zero mutual inductance between odd and even washers.

3 Crosstalk in Linear Multiplexers

Linear multiplexers, which are widely used in ground-based experiments [3, 4], are motivated by the use of wire bonds to interface the multiplexer chips to the sensor array. The need for a perimeter bond pad pair for every TES read out prevents the use of a square 2D grid of readout cells, as the perimeter pad area available only scales with the perimeter of the chip, and instead favors chips consisting of a single line of readout cells.

We performed crosstalk measurements using a microcalorimeter variant of mux15 (mux18d) and the newer crosstalk protected monolithic design in an otherwise identical multiplexer (mux19a). X-rays fluoresced from a Mn target were measured by a NASA TES array with an event rate of greater than 15 counts per second per TES to promote near coincident events. Performing pulse processing using optimal filtering [13], we plot the shift in measured pulse energy versus time offset between events measured by two different pixels as shown in Fig. 2 for nearest PN crosstalk (PNN) in a microcalorimeter variant of mux15 (mux18d) and mux19a, with 0.37% and 0.02% shifts in energy during coincident events, respectively. A third plot is shown for second nearest PN crosstalk (2PNN), which is representative for both multiplexers. 2PNN crosstalk has a different energy profile due to it being mostly derivative rather than proportional, meaning it is likely on the TES bias circuit chip.

Fig. 2
figure 2

Crosstalk in a linear multiplexer reading out microcalorimeters. Top-Left, Top-Right, and Bottom-Left, Event histograms with bins defined by the impacted pixel’s energy (Evictim) and the separation between the arrival time of the impacted (victim) and the influencing (perpetrator) pixels for physical neighbor pairs. A 7.2 ms pulse analysis window is used, with pulse arrival occurring in the middle of the window. Mux19a’s encoding scheme greatly reduces nearest neighbor (PNN) coincident crosstalk to 0.02% from Mux18d’s 0.37%. Second nearest neighbor (2PNN) crosstalk is unchanged but has a profile consistent with inductive coupling on the TES bias circuit. Bottom-Right, A crosstalk map of a 28-pixel mux19a multiplexing unit showing percent shift in energy during coincident events, indexed by timing order. Time neighbors are chosen to mostly correspond to second nearest physical neighbors

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A crosstalk map for a mux19a multiplexing unit is shown in Fig. 2Bottom-Right. Time nearest neighbor (TNN) crosstalk, determined by the analog bandwidth of the TDM readout chain and row durations (trow) [9], dominates at a 2% level for X-IFU-like trow = 160 ns. TNN crosstalk levels in more recent systems are presented in Ref. [7] for a range of trow, measuring crosstalk of 0.79% with trow = 160 ns and 0.11% with trow = 336 ns. In microcalorimeter readout, large crosstalk pairings primarily impact event throughput, as affected events can be removed using cuts based on relative arrival time [14]. Mux18d requires cuts on four source pixels: same pixel, TNN, and two PNN. Mux19a requires only same pixel and TNN cuts.

Our most recent linear multiplexer is a CMB-S4 demonstration chip (mux21_S4), shown in Fig. 1Right, which uses a symmetrized two-layer switching TDM architecture [7]. Mux21_S4 has a TES current coil to SQUID inductance (Min) of 1260 pH, compared to Min = 690 pH of the mux15 bolometer chip (mux15b), with increases in Min motivated by scaling models predicting higher achievable multiplexing factors [7]. Adjacent pixel proportional crosstalk measured in mux21_S4 has been studied by applying a triangle wave signal with a 734 ms period on an input. Crosstalk was not significantly different from distant neighbors at 0.005%.

4 Crosstalk in 2D Multiplexers

2D multiplexers, consisting of readout cells arranged in a close-packed grid, become viable with the use of indium bump bonds [15] to interface the multiplexer chip to other components. Since bump bonds can be placed in the center of chip, TES current pads can be located within each multiplexer unit cell and the sensor to readout interface scales naturally with the grid. Kilopixel scale 2D TMD chips were bump bonded directly to sub-arrays for SCUBA2 [1] and HAWC +  [2], while much smaller chips will be bump bonded to interface chips for X-IFU [5].

The crosstalk reduction scheme in a 2D multiplexer is shown in Fig. 3left, which includes both multiplexer and bias circuit components. Reducing the number of SQUIDs in each SQ1 from four to two, means area is roughly split evenly between the multiplexer and bias circuit, providing flexibility in implementation. We use a polarity encoding scheme to place x-adjacent transformer lobes and Nyquist coils in a line. Less sensitive components like SQ1, dummy-SQ1, switches, and the bias resistor (Rbias) can be used as buffer regions separating the large inductive components of y-adjacent cells.

Fig. 3
figure 3

Left, our 2D crosstalk reduction scheme in a 2 × 2 grid, with the polarity of the Nyquist coils (blue rectangles) and transformer washer lobes (orange squares) shown. Polarity encoding is used for crosstalk reduction x-adjacent neighbors. The placement of less sensitive components provides separation between large y-adjacent inductors. Right, pulse records were triggered by the arrival of a pulse in the top left cell to measure the TES current response in the other three. Each plot is the average of 950 records

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We measured crosstalk in a close-packed grid of pre-rescope X-IFU pixels using the 2 × 3 pixel chips and the NASA GSFC array [16] used in Ref. [7]. To obtain a lower noise floor than the high rate crosstalk measurement in Sect. 3, we performed a TES pulse measurement using an X-ray event in a perpetrator pixel to trigger pulse records for the rest of the pixels in the multiplexing unit. 950 pulses were measured at an incident X-ray rate of 0.6 counts per second, which is low to avoid coincident events. We wired pixels so that multiplexer neighbors did not correspond to TES array neighbors and kept multiplexer physical neighbors separated in time. Figure 3Right shows crosstalk below 0.01% in both nearest pixels as well as in the closest diagonal, a level with no significant effect on energy resolution or throughput for X-IFU.

5 Conclusion

We have presented physical neighbor crosstalk reduction techniques used in recent TDM chips and tested their effectiveness in measurements. We have demonstrated physical nearest neighbor crosstalk levels limited by a 0.005% background in adjacent pixels of preliminary linear multiplexers for CMB-S4 and levels below 0.01% for a pre-rescope X-IFU-like 2D multiplexer.