Resistive Silicon Detectors Overview

• RSDs are silicon sensors with a continuous gain implant and resistive readout that enable 4D tracking with full sensor coverage.
• They employ charge-sharing techniques—analyzing amplitude, delay, and waveform features—to achieve micron-level spatial and sub-40 ps timing resolutions.
• Recent AC and DC-coupled developments demonstrate scalable, uniform performance and enhanced radiation tolerance for future collider experiments.

Resistive Silicon Detectors (RSDs), also referred to as Resistive AC-Coupled Silicon Detectors and AC-LGADs, are LGAD-based $n$-in-$p$ silicon sensors in which a continuous gain layer and a resistive read-out surface generate built-in charge sharing among several neighboring electrodes. In this architecture, the hit position is reconstructed from the analog pattern of amplitudes, delays, and waveform features rather than from isolated binary pixel hits, while internal avalanche multiplication preserves fast timing and high signal-to-noise ratio. The concept was developed for 4D tracking, namely simultaneous measurement of hit position in the sensor plane and time of arrival, and was later extended to DC-coupled variants intended to improve signal containment, waveform shape, and scalability (Tornago et al., 2020, Arcidiacono et al., 29 May 2025).

1. Historical development and conceptual emergence

The immediate antecedent of modern RSDs was a resistive charge-division microstrip concept in which metallic electrodes were replaced by resistive polycrystalline-silicon electrodes, so that the longitudinal coordinate could be reconstructed from the relative amplitudes at the two strip ends. In that proof-of-concept, the basic estimator was

$y = L \times \frac{A_2}{A_1 + A_2},$

and the average spatial resolution along the strip was reported as $1.1\%$ of strip length for $2.8\ \Omega/\mu$m and $1.2\%$ for $12.2\ \Omega/\mu$m, corresponding to roughly $225~\mu$m and $232~\mu$m for a $6$ MIP signal (Bassignana et al., 2011). That work did not yet constitute a modern RSD in the LGAD sense, but it established the soundness of resistive charge division in silicon and validated circuit-level modeling as a design tool.

The explicitly LGAD-based RSD program emerged later as an effort to combine the timing capability of thin gain sensors with analog position encoding and $p$0 fill factor. The first demonstration of fine-pitch Resistive AC-Coupled Silicon Detectors reported working $p$1 matrices at $p$2m, $p$3m, and $p$4m pitch with $p$5 fill factor, using a resistive $p$6-type implant together with a coupling dielectric layer (Mandurrino et al., 2019). A full characterization of the first production, RSD1, then showed that the architecture could reach micron-level spatial resolution together with picosecond timing; the best reported result was $p$7m and $p$8 ps for the $p$9 structure at gain $y = L \times \frac{A_2}{A_1 + A_2},$0 (Mandurrino et al., 2020).

The next stage was the consolidation of the operating principles and reconstruction formalism. A combined analysis of laser and beam data established that RSDs are $y = L \times \frac{A_2}{A_1 + A_2},$1-in-$y = L \times \frac{A_2}{A_1 + A_2},$2 silicon sensors with a resistive $y = L \times \frac{A_2}{A_1 + A_2},$3 implant and AC-coupled pads, and reported spatial resolutions ranging from about $y = L \times \frac{A_2}{A_1 + A_2},$4m for the $y = L \times \frac{A_2}{A_1 + A_2},$5–$y = L \times \frac{A_2}{A_1 + A_2},$6 pad-pitch geometry to about $y = L \times \frac{A_2}{A_1 + A_2},$7m for the $y = L \times \frac{A_2}{A_1 + A_2},$8–$y = L \times \frac{A_2}{A_1 + A_2},$9 matrices, with temporal resolution of $1.1\%$0 ps for $1.1\%$1m-pitch devices in beam conditions (Tornago et al., 2020). The second FBK production, RSD2, then shifted the emphasis from proof of principle to geometry optimization and response uniformity (Mandurrino et al., 2021).

2. Device architecture and signal-formation physics

In the AC-coupled implementation, RSDs are defined by three structural elements: a continuous gain implant, a resistive $1.1\%$2 cathode, and a dielectric coupling layer on top of the silicon. The continuous gain implant extends over the full active area, removing the gain interruptions associated with segmented LGADs; the resistive cathode spreads the multiplied charge laterally while providing a path to DC discharge through peripheral contacts; and the dielectric layer sets the AC coupling capacitance $1.1\%$3, thereby controlling signal formation and sharing among channels (Mandurrino et al., 2021). This architecture eliminates segmentation implants such as JTE and $1.1\%$4-stop from the multiplication structure and thereby approaches $1.1\%$5 fill factor (Mandurrino et al., 2019).

The signal-formation picture is that of a distributed current divider. In one formulation, the signal current seen by pad $1.1\%$6 is

$1.1\%$7

where $1.1\%$8 is the impedance from the hit point to pad $1.1\%$9 (Cartiglia et al., 2023). In the AC-RSD implementation, the prompt signal is induced on the resistive $2.8\ \Omega/\mu$0 layer by the drifting carriers, then propagates laterally toward the grounded pads, and finally discharges through the RC network, producing a slower opposite-polarity lobe. The sharing is described as isotropic and does not require floating electrodes or an external magnetic field (Tornago et al., 2020). A common misconception is therefore that RSDs behave like ordinary segmented pixels with improved interpolation; in fact, segmentation is moved to the read-out side, while the multiplication structure remains continuous.

The waveform polarity and the spatial response are both consequences of this RC architecture. AC-RSDs characteristically produce bipolar signals, and the balance between the first lobe and the undershoot depends on the effective $2.8\ \Omega/\mu$1 network (Mandurrino et al., 2019). Hits directly under metal pads can collapse the sharing pattern toward a single dominant channel, whereas controlled charge sharing in the inter-pad region is what carries most of the spatial information (Siviero et al., 2020).

The DC-coupled evolution, DC-RSD, removes the dielectric and places the read-out electrodes directly on the resistive $2.8\ \Omega/\mu$2 layer. It is described as a thin LGAD with a DC-coupled resistive read-out, producing $2.8\ \Omega/\mu$3–$2.8\ \Omega/\mu$4 ns long unipolar signals and enabling leakage-current removal at each electrode (Arcidiacono et al., 29 May 2025). In this architecture, isolating trenches are introduced to contain the signal within a predetermined number of electrodes, addressing several limitations identified in AC-RSDs, including bipolar signals, baseline fluctuations, and hit-position-dependent spread beyond the nearest pads (Menzio et al., 2022).

3. Reconstruction formalisms and algorithmic approaches

The reconstruction problem in RSDs is intrinsically multichannel. In the earliest strip-like implementation, longitudinal position was obtained from the two-end charge-division relation, while the transverse coordinate remained defined by strip segmentation (Bassignana et al., 2011). In two-dimensional pad arrays, the first analytical approaches modeled the fractions of total signal observed on neighboring pads as functions of distance and geometry, and position was reconstructed by minimizing

$2.8\ \Omega/\mu$5

over an $2.8\ \Omega/\mu$6-$2.8\ \Omega/\mu$7 grid (Tornago et al., 2020).

For four-pad pixels, two reconstruction schemes recur in the literature. The Signal-Weighted Position method uses the amplitude-weighted centroid,

$2.8\ \Omega/\mu$8

whereas the Discretized Position Circuit method uses left-right and top-bottom amplitude imbalances,

$2.8\ \Omega/\mu$9

$1.2\%$0

In RSD2 analyses, these measured coordinates are often corrected with a migration map built from training data (Arcidiacono et al., 2022). Template or look-up-table reconstruction is a related strategy: a table of signal-sharing fractions is built from calibration data, and each event is matched to the most probable position. That method is used both in AC-RSD beam studies and in the first DC-RSD beam analysis (Menzio et al., 2024, Arcidiacono et al., 29 May 2025).

Machine learning was introduced because analytical sharing laws become difficult to derive reliably once waveform propagation, geometry, and metal structures are all included. The first ML application used a Multi-Output Regressor with Gradient Boosting Regressor as estimator, taking as inputs the four pad amplitudes and their normalized values; it reported spatial resolution below $1.2\%$1m for a $1.2\%$2m-pixel sensor (Siviero et al., 2020). A later Random Forest approach for RSD2 used the measured amplitudes on all read-out channels as inputs, with $1.2\%$3 decision trees and an $1.2\%$4 train-test split in which all events from a given scan point were assigned entirely to either training or test. In one implementation the input vector was the $1.2\%$5-channel amplitude pattern $1.2\%$6, and two independent regressors were trained for $1.2\%$7 and $1.2\%$8 (Siviero et al., 2022).

Time reconstruction is likewise multichannel. In large-pixel RSD2 analyses, the individual pad times are corrected for position-dependent delay and setup offsets, then combined with an amplitude-squared weighting. In DC-RSD beam tests, each electrode time is measured with a constant fraction discriminator at $1.2\%$9, then corrected for signal-propagation delay and setup offset before forming the event time (Arcidiacono et al., 2022, Arcidiacono et al., 29 May 2025).

4. Reported performance and scaling with geometry

The defining empirical result of the RSD program is that the spatial resolution is routinely far better than the read-out pitch would imply for binary operation. In conventional digital read-out, the natural reference is $12.2\ \Omega/\mu$0; RSD papers repeatedly report performance about a factor of $12.2\ \Omega/\mu$1 better than that benchmark for matched geometries (Tornago et al., 2020).

Representative device	Pitch / geometry	Reported performance
Resistive microstrip proof-of-concept (Bassignana et al., 2011)	$12.2\ \Omega/\mu$2m pitch, $12.2\ \Omega/\mu$3 mm strip length	$12.2\ \Omega/\mu$4–$12.2\ \Omega/\mu$5 of strip length for $12.2\ \Omega/\mu$6 MIP
RSD1 best result (Mandurrino et al., 2020)	$12.2\ \Omega/\mu$7 structure	$12.2\ \Omega/\mu$8m, $12.2\ \Omega/\mu$9 ps at gain $225~\mu$0
Combined RSD laser/beam study (Tornago et al., 2020)	$225~\mu$1–$225~\mu$2 to $225~\mu$3–$225~\mu$4 geometries	$225~\mu$5–$225~\mu$6m spatial; $225~\mu$7 ps at $225~\mu$8m pitch
First 16-channel RSD2 pad-array result (Siviero et al., 2022)	$225~\mu$9 array, $232~\mu$0m pitch	$232~\mu$1m; $232~\mu$2 within $232~\mu$3m
Large-pixel RSD2 TCT study (Arcidiacono et al., 2022)	$232~\mu$4 and $232~\mu$5m$232~\mu$6	$232~\mu$7m and $232~\mu$8 ps; $232~\mu$9m and $6$0 ps at gain $6$1
DESY beam test with FAST2 (Menzio et al., 2024)	$6$2m pitch	$6$3m; $6$4 ps dominated by FAST2
First DC-RSD prototype result (Arcidiacono et al., 29 May 2025)	$6$5m square pixel	$6$6m, $6$7 ps at gain $6$8

Several systematic trends recur. Resolution improves with gain until a constant term dominates; for $6$9m-pitch RSD2 matrices characterized with Random Forest regression, the total spatial resolution was about $p$00m at gain $p$01, with the performance plateauing after $p$02 V (Tornago et al., 2022). In large-pixel RSD2 devices with cross-shaped electrodes, spatial resolution scales at roughly $p$03 of the pixel size while time jitter remains in the $p$04–$p$05 ps range at gain $p$06 (Arcidiacono et al., 2022). The first DC-RSD prototypes likewise achieved position resolution better than $p$07 of pitch for all tested devices (Arcidiacono et al., 29 May 2025).

The residual distributions are not always Gaussian. In the first $p$08, $p$09m-pitch RSD2 study, the worst-reconstructed regions clustered near the metal-pad arms, and $p$10m$p$11 maps of residual width showed that global non-Gaussianity was driven by local distortions close to those structures (Siviero et al., 2022). That observation established electrode geometry and metal coverage as first-order determinants not only of mean resolution but also of uniformity.

5. Geometry optimization, detector generations, and strip-like variants

RSD development has been strongly geometry-driven. RSD1 established the principle, but studies of that first production showed that the sharing pattern was not fully uniform: near the sensor edges the signal typically involved only one or two pads, whereas in the central region it mostly involved three or four (Mandurrino et al., 2021). RSD2 was therefore designed to produce the same number of pads sharing a signal across the whole detector. The layouts included staggered cross-pads with asymmetrical arms, staggered star-pads, and a regular square array with cross-pads; the arm thickness $p$12 was typically $p$13–$p$14m, and the interpad distance $p$15 covered roughly $p$16–$p$17 of the pad pitch (Mandurrino et al., 2021).

Within that program, cross-shaped electrodes became a central design element. For the $p$18m$p$19 and $p$20m$p$21 RSD2 pixels, the cross-shaped layout was reported to improve the response uniformity considerably by surrounding the pixel while minimizing metal coverage (Arcidiacono et al., 2022). A DESY beam test of a $p$22m-pitch RSD2 matrix with cross-shaped electrodes found $p$23m spatial resolution together with $p$24 fill factor and homogeneous resolutions over the whole matrix surface (Menzio et al., 2024). By contrast, a comparison among three $p$25m-pitch RSD2 layouts—“Swiss crosses”, “flakes”, and “boxes”—found compatible spatial resolutions within errors, so no geometry could be claimed superior on the basis of those measurements alone (Tornago et al., 2022).

A further design branch extends RSD principles toward strip-like operation. Novel H-shaped read-out pads with $p$26m pitch were introduced as a hybrid between strip-like and pixel-like readout, intended to limit charge spread to two neighboring electrodes (Grimm et al., 29 May 2026). In Top-TCT characterization with a $p$27 nm pulsed laser, a $p$28m scan step, and a simple linear-fit plus $p$29-minimization reconstruction, the one-dimensional spatial resolution reached a plateau of approximately $p$30m, about $p$31 of pitch; the best reconstruction occurred in the center region between the electrodes, while performance degraded near electrode edges (Grimm et al., 29 May 2026). This suggests that RSDs are not restricted to square-pixel tilings and can be adapted to channel-count-constrained tracker layers.

6. DC-coupled evolution, irradiation behavior, and research directions

The DC-RSD program was initiated to address several limitations attributed to AC-coupled RSDs: non-uniform resolution across the sensor area, bipolar signals with long discharge tails, baseline fluctuations, and the collection of full-sensor leakage current only at the periphery in large or irradiated devices (Arcidiacono et al., 29 May 2025). The DC-coupled concept keeps the thin LGAD gain structure and resistive charge sharing but implants the electrodes directly into the resistive $p$32 layer. In simulations and first prototypes, this has been associated with unipolar output, controlled signal containment, and scalability to large pixels and large-area systems (Menzio et al., 2022).

The design methodology has relied heavily on simulation. One route combined Weightfield2 for bulk LGAD signal formation with LTspice for lateral spreading on the resistive network; for a $p$33m-wide detector, a combined spatial-temporal compromise gave $p$34 and $p$35, and the broader study reported expected time resolution of $p$36–$p$37 ps and space resolution of $p$38–$p$39m even up to $p$40 (Menzio et al., 2022). A full 3D TCAD campaign with Synopsys Sentaurus was then used to optimize the first FBK DC-RSD production, exploring $p$41 sheet resistivity, contact resistance, pad geometry, pitch, and isolation schemes; in that study, $p$42–$p$43 emerged as a favorable range, and isolating trenches were found to collect the charge almost entirely within the four pads of the affected pixel (Moscatelli et al., 14 Aug 2025). The first DC-RSD1 production at FBK, within the 4DSHARE project, comprised $p$44 p-type $p$45-inch epitaxial wafers of active thickness $p$46m, with several options for $p$47 resistivity, gain implant dose, and Si-Al DC contact; $p$48 wafers were reported as fully functional (Arcidiacono et al., 29 May 2025).

Radiation tolerance has become a distinct research direction. An irradiation study of RSD2 devices exposed sensors to $p$49, $p$50, and $p$51 in $p$52 MeV neutron equivalent fluence with both protons and neutrons, then used $p$53-$p$54, $p$55-$p$56, Van der Pauw measurements, and TCT to examine gain-layer and resistive-layer evolution (Elicabuk et al., 17 Apr 2025). The extracted degradation coefficients from $p$57-$p$58 data were lower than typical standard-LGAD acceptor-removal coefficients, and the study argued that donor removal in the resistive $p$59 layer is a key contributor to this behavior. Preliminary TCT results for a W14 sensor showed normalized charge-sharing profiles and $p$60-drop points that were remarkably similar before and after irradiation, suggesting that the charge-sharing mechanism remained essentially unchanged in that sample (Elicabuk et al., 17 Apr 2025).

The principal application domain remains future 4D tracking. Across the literature, RSDs are discussed in the context of next-generation collider systems, including the EIC, FCC-ee, CEPC, and FCC-hh, because they combine large-pixel operation with high spatial precision, fast timing, low material budget, reduced channel count, and $p$61 fill factor (Grimm et al., 29 May 2026, Arcidiacono et al., 29 May 2025). A plausible implication is that further progress will depend less on demonstrating the basic effect of resistive sharing—which is already well established—and more on controlling its uniformity, containment, and post-irradiation stability through geometry, read-out architecture, and resistive-layer engineering.