Orthogonal-Strip Planar HPGe Detectors

• Orthogonal-strip planar HPGe detectors are semiconductor devices featuring dual-sided orthogonal segmentation that enable sub-mm resolution through virtual pixel formation and charge sharing.
• They integrate advanced signal modeling and timing analysis to reconstruct two-dimensional and three-dimensional event topologies, crucial for gamma-ray imaging and 0νββ background discrimination.
• Design trade-offs involve optimizing strip pitch, crystal thickness, and channel count to balance spatial resolution, topology preservation, and practical readout complexity.

Orthogonal-strip planar high-purity germanium (HPGe) detectors are position-sensitive semiconductor detectors in which a planar HPGe crystal is contacted on its two opposite faces with orthogonal strip electrodes. Strips on the top face run along $y$ and measure $x$; strips on the bottom face run along $x$ and measure $y$. The intersection of an $x$-strip and a $y$-strip defines a virtual pixel, enabling two-dimensional imaging without a true pixel array. Because electrons drift to one face and holes to the opposite face, each face records a one-dimensional projection of the event along the coordinate transverse to the strip orientation, and the two projections can be combined to recover two-dimensional topology; timing and pulse-shape analysis extend the method to three-dimensional localization. The architecture has been developed for gamma-ray imaging, Compton reconstruction, medical imaging, and gamma-ray astronomy, and has more recently been studied as a topology-sensitive platform for distinguishing neutrinoless double beta decay ($0\nu\beta\beta$) events from single-electron backgrounds in $^{76}$Ge (Zhang et al., 2 Mar 2026, Zhang et al., 24 Jul 2025, Rogers et al., 2 Feb 2026).

1. Geometry, segmentation, and readout principle

The defining feature of the orthogonal-strip planar HPGe detector is double-sided strip segmentation. In the configuration studied for $0\nu\beta\beta$ discrimination, a planar crystal is instrumented on both faces with orthogonal strip sets; combining the energy collected on a top strip with that on a bottom strip provides a two-coordinate association, while charge sharing can support sub-strip centroiding when the cloud size is comparable to the pitch. With strip pitch $p$, the naive sampling-limited position resolution is $x$0 and similarly for $x$1, absent centroiding from charge sharing. Charge sharing improves centroid resolution but can also blur topological features if the diffusion width becomes large compared with $x$2, so pitch and thickness are coupled design parameters rather than independent conveniences (Zhang et al., 2 Mar 2026).

Several representative geometries appear in the recent literature. A simulation study of $x$3 event discrimination used a cylindrical baseline crystal of diameter $x$4 mm and thickness $x$5 mm, and examined strip pitches of $x$6 mm, $x$7 mm, and $x$8 mm while varying thickness from $x$9 to $x$0 mm in steps of $x$1 mm. A three-dimensional pulse-shape reconstruction study used a cylindrical active volume of $x$2 mm diameter and $x$3 mm thickness with eight strips per face, $x$4 mm pitch, $x$5 mm inter-strip gaps, and a $x$6 mm guard ring on each plane. The COSI double-sided strip detector uses a planar crystal of thickness $x$7 mm and lateral instrumented width $x$8 mm, segmented into $x$9 strips per face at $y$0 mm pitch, with strip width $y$1 mm and interstrip gap $y$2 mm; the orthogonal strip sets define $y$3 analysis pixels of $y$4 mm$y$5 (Zhang et al., 24 Jul 2025, Rogers et al., 2 Feb 2026).

Readout is inherently asymmetric in charge type but symmetric in information content. In one formulation, a triggered pair of strips collects charge while neighboring strips record induced image signals; the collection signals encode the directly collected electrons and holes, and the image signals encode position through weighting-potential asymmetry and polarity evolution. In another formulation, used for topology classification, the detector is reduced to two strip-energy vectors, one per face, so that the classifier operates on complementary one-dimensional projections rather than on a full pixelized image (Zhang et al., 24 Jul 2025, Zhang et al., 2 Mar 2026).

2. Contact technology, fabrication, and detector integration

Fine orthogonal segmentation in large-area HPGe is closely tied to contact technology. A fabrication route developed at Lawrence Berkeley National Laboratory coats all HPGe surfaces with a high-resistivity thin film of amorphous Ge (a-Ge) or amorphous Si (a-Si) by RF diode sputtering in Ar/H$y$6. The amorphous layer provides electron/hole injection blocking at the contact and also serves as full-surface passivation; metallic Al electrodes patterned on top define the segment geometry. Because segmentation is defined in the metal while the underlying amorphous coating uniformly passivates the surface, very fine strip pitches and narrow gaps are achievable on both faces without introducing lateral leakage or surface channels. The guard ring is part of the metal pattern and is critical for yield and stability (Amman, 2020).

The fabrication flow begins with crystal preparation by cutting, lapping, and chemical polish etching. The paper reports coarse lapping with $y$7 grit SiC ($y$8m) and fine lapping with $y$9 grit Al$x$0O$x$1 ($x$2m), followed by a chemical polish etch in $x$3 vol HNO$x$4:HF for approximately $x$5 min and a surface preparation etch in the same mixture for approximately $x$6 s immediately prior to sputtering. Amorphous semiconductor deposition is performed in two steps and two vacuum cycles: a “top and sides” deposition on a rotating off-axis fixture, and a “bottom” deposition on a centered water-cooled stage. Al metallization can then be patterned either by shadow masks or by photolithography; the latter is reported for fine-pitch patterns with blanket Al of approximately $x$7–$x$8 nm per face, S1818 photoresist spun at $x$9 rpm for $y$0 s, baked at $y$1C for $y$2 min, exposed for $y$3 s at $y$4 mW/cm$y$5 or $y$6 s at $y$7 mW/cm$y$8, developed for about $y$9 s, and wet-etched in $0\nu\beta\beta$0 HF diluted $0\nu\beta\beta$1 with DI H$0\nu\beta\beta$2O for about $0\nu\beta\beta$3–$0\nu\beta\beta$4 min (Amman, 2020).

Large-area orthogonal-strip implementations demonstrate the practicality of this process. The COSI detectors use $0\nu\beta\beta$5 strips per face at $0\nu\beta\beta$6 mm pitch and approximately $0\nu\beta\beta$7 mm thickness, with high voltage up to $0\nu\beta\beta$8 kV. The GRIPS detectors use $0\nu\beta\beta$9 strips per face at $^{76}$0 mm pitch, $^{76}$1 mm interstrip gaps, and approximately $^{76}$2 mm thickness, also with high voltage up to $^{76}$3 kV. In routine operation, the high-voltage side strips are biased through $^{76}$4 G$^{76}$5 resistors and AC-coupled through high-voltage-rated C0G/NP0 capacitors, while the low-voltage side strips are near ground and can be directly DC-coupled to preamplifiers. The depletion relation used for planar devices is

$^{76}$6

with $^{76}$7; a $^{76}$8 mm detector is reported to reach full depletion around $^{76}$9 V for $0\nu\beta\beta$0 (Amman, 2020).

The practical integration literature also identifies characteristic failure modes. Incomplete side amorphous coverage or undercoating correlates with excessive guard-ring leakage and detector failure; leaving a high-voltage-side output floating can raise the node to near high voltage through capacitive division and trigger destructive interstrip breakdown cascades; microphonics are reduced by placing high-voltage bias and coupling components on the detector board near the detector; and interstrip shorts in fine-pitch devices can arise from photoresist defects or trapped bubbles during Al etching (Amman, 2020).

3. Charge transport, signal formation, and modeling frameworks

Signal modeling in orthogonal-strip planar HPGe detectors is based on drift, diffusion, space-charge effects, weighting potentials, and front-end shaping. A simulation framework developed for $0\nu\beta\beta$1 discrimination combines Geant4 version 4.11.2, using the physics list G4EmStandardPhysics_option4 and a production range cut of $0\nu\beta\beta$2m, with a hybrid numerical–analytical transport model. Geant4 generates discrete interaction points $0\nu\beta\beta$3 per event, with $0\nu\beta\beta$4 tens to $0\nu\beta\beta$5, and each interaction point is treated as a macro-particle consisting of an electron and hole cloud pair. SolidStateDetectors.jl is then used to compute drift trajectories and inter-cloud Coulomb repulsion under the imposed electric field, while each macro-particle’s internal spreading is modeled analytically as a Gaussian of width

$0\nu\beta\beta$6

The carrier-density evolution is described by the drift–diffusion equation

$0\nu\beta\beta$7

with the Einstein relation $0\nu\beta\beta$8 (Zhang et al., 2 Mar 2026).

For strip-energy classification, the induced current is not computed event-by-event. Instead, the total projected energy density on a readout axis $0\nu\beta\beta$9 is written as

$p$0

and the energy collected by strip $p$1 is obtained by integration over the strip interval. Internal self-repulsion within each macro-particle is neglected; the study states that dominant broadening from thermal diffusion and inter-cluster repulsion is captured. The transport model reproduces full SolidStateDetectors.jl simulations with residuals within approximately $p$2 keV and relative standard deviation of charge collection for MeV-scale events within approximately $p$3, while reducing computational cost from hours per event to seconds per event (Zhang et al., 2 Mar 2026).

Waveform-based position reconstruction studies use a more explicit field-and-electronics stack. In the three-dimensional maximum-likelihood work, SolidStateDetectors.jl computes electric fields and weighting potentials from the full three-dimensional geometry, with impurity concentration set to $p$4 cm$p$5 at the detector bottom and a linear gradient of $p$6 along $p$7. Charge induction follows Shockley–Ramo,

$p$8

and the induced charge is evaluated as

$p$9

Carrier diffusion and self-repulsion are modeled, simulated pulses are convolved with an RC preamplifier response with $x$00s, and Gaussian electronic noise is added (Zhang et al., 24 Jul 2025).

The COSI depth-calibration study extends the same physical structure to ASIC timing emulation. It solves the full three-dimensional device with as-built geometry, p-type doping, and $x$01 V bias; simulates charge-cloud drift and induction with $x$02 ns sampling, including diffusion and self-repulsion; and processes the resulting waveforms through a SPICE model of the COSI ASIC. The ASIC chain consists of a preamplifier, a second-order Butterworth low-pass at $x$03 MHz, a slow shaper with $x$04s peaking used for energy, and a fast shaper with $x$05 ns peaking used for timing pickoff (Rogers et al., 2 Feb 2026).

4. Event topology and background discrimination in $x$06Ge $x$07 searches

The central motivation for using orthogonal-strip planar HPGe in $x$08Ge $x$09 searches is that the signal and a problematic class of backgrounds differ topologically even when both are single-site-like in conventional pulse-shape analysis. In the Geant4-based discrimination study, signal events are $x$10 decays of $x$11Ge generated with BxDecay0; the two emitted electrons share the $x$12 keV $x$13-value, individual electron energies peak near half of $x$14 keV, and the opening-angle distribution peaks at $x$15, favoring back-to-back emission. Background events are single electrons with initial kinetic energy of $x$16 keV. The physical distinction is that $x$17 tracks typically exhibit two Bragg peaks, giving a two-blob topology in projected profiles on both faces, whereas a single-electron background yields one Bragg peak and one-blob projected profiles. Point-contact and BEGe detectors rely on pulse-shape analysis such as $x$18 to distinguish multi-site from single-site events; because both $x$19 and single-electron events are SSEs, they are difficult to separate in that framework (Zhang et al., 2 Mar 2026).

The machine-learning implementation uses a balanced dataset of $x$20 signal and $x$21 background events with an $x$22 training/testing split. Events are selected by requiring the total reconstructed energy on both planes to lie within the $x$23 keV region of interest, with a $x$24 keV per-strip threshold. Each detector face contributes a centered, zero-padded $x$25-element strip-energy vector. The classifier is a dual-branch convolutional neural network in TensorFlow/Keras: each branch contains three one-dimensional convolutional layers with $x$26, $x$27, and $x$28 filters; kernel sizes $x$29, $x$30, and $x$31; ReLU activations; and batch normalization after each convolution, followed by global average pooling. The two branches are concatenated, passed through a fully connected layer with dropout, and terminated by a sigmoid output. Training uses Adam with initial learning rate $x$32, binary cross-entropy loss, and early stopping with patience $x$33 epochs; evaluation uses ROC curves, AUC, and a Kolmogorov–Smirnov test on response distributions (Zhang et al., 2 Mar 2026).

For the baseline detector of $x$34 mm thickness and $x$35 mm pitch, the reported performance is AUC $x$36, background rejection $x$37 at fixed signal efficiency $x$38, and K–S $x$39 between training and test response distributions. Pitch is a dominant topology-control parameter: at fixed thickness $x$40 mm, the AUC degrades from $x$41 at $x$42 mm to $x$43 at $x$44 mm, and at $x$45 the background rejection decreases from $x$46 to $x$47. Thickness produces a different trade-off: thicker crystals improve full-energy peak efficiency $x$48 by increasing containment, but increase drift time and therefore diffusion width, smearing the topology. Using the sensitivity-inspired figure of merit

$x$49

the optimal thickness at $x$50 mm is reported as $x$51 mm (Zhang et al., 2 Mar 2026).

A related strip multi-electrode HPGe study shows a complementary discrimination paradigm based on waveform morphology rather than projected strip-energy vectors. In a planar $x$52 mm diameter, $x$53 mm thick device with seven strips on one face, the pulse-shape discrimination proceeds in two tiers: rejection of multi-electrode collection events, followed by an $x$54 cut on the remaining single-electrode collection events, with $x$55 and threshold $x$56. In simulation with $x$57Th, the double-escape peak at $x$58 keV has acceptance $x$59 after all cuts, while the single-escape peak at $x$60 keV has acceptance $x$61, corresponding to a suppression factor of approximately $x$62. For simulated $x$63 events in the $x$64–$x$65 keV window, the survival rate is $x$66, while suppression factors are approximately $x$67 for $x$68Ge, $x$69 for $x$70Co, $x$71 for $x$72Th, and $x$73 for $x$74U. This indicates that topology-sensitive strip detectors can also be used as a complement to conventional pulse-shape discrimination for backgrounds that remain problematic after standard SSE/MSE separation (Jingzhe et al., 2023).

5. Three-dimensional localization: pulse-shape inference and timing-depth calibration

Orthogonal-strip planar HPGe detectors support three-dimensional reconstruction because the strip intersection provides two lateral coordinates while waveform features provide depth sensitivity. In the maximum-likelihood reconstruction study, the depth-sensitive parameters are the signed net-area sums

$x$75

and

$x$76

computed over a fixed $x$77 ns window from $x$78 ns to $x$79 ns that covers the rise edge. With fixed lateral position, increasing $x$80 changes the collection-signal shape from concave to convex and flips neighboring image-signal polarity from positive through bipolar to negative. Lateral position is reconstructed through integral-based asymmetries,

$x$81

with $x$82 computed from cathode-plane image signals and $x$83 from anode-plane image signals. The joint parameter vector is $x$84, and the position estimate is obtained by maximizing a multivariate normal likelihood with mean $x$85 and covariance $x$86 evaluated on a $x$87 mm grid within a representative central pixel (Zhang et al., 24 Jul 2025).

Under $x$88 keV events with $x$89 keV RMS electronic noise, the MLE framework reduces the maximum $x$90 reconstruction bias from $x$91 mm to $x$92 mm in the central region and from approximately $x$93 mm to approximately $x$94 mm near the electrodes. The maximum reconstruction bias in $x$95 is reduced from $x$96 mm to $x$97 mm. The achieved resolution ranges from approximately $x$98 mm to approximately $x$99 mm in $x$00 and from approximately $x$01 mm to approximately $x$02 mm in $x$03, with the lateral degradation localized to a $x$04–$x$05 mm band below the cathode where the weighting-potential gradient is small. The study also reports that integral-based parameters mitigate noise sensitivity: as noise RMS increases from $x$06 to $x$07 keV, average $x$08 resolution degrades linearly from $x$09 mm to $x$10 mm with $x$11, whereas amplitude-based CTD degrades exponentially from $x$12 mm to $x$13 mm (Zhang et al., 24 Jul 2025).

A separate depth-calibration program has been carried out for the COSI satellite detector geometry. There, depth is inferred from the collection-time difference between the two faces,

$x$14

with timing derived from the peak of the $x$15 ns fast shaper. Because of the small-pixel effect and the contribution of the opposite carrier near the faces, $x$16 is approximately linear over the central approximately $x$17 of the thickness and steepens within $x$18–$x$19 mm of each face. Simulated mapping is generated by injecting charge at depth increments of $x$20 mm across the $x$21 mm thickness and processing the waveforms through a SPICE model of the COSI ASIC. To align simulation with data, an affine correction is introduced,

$x$22

and depth is reconstructed through inversion of the simulated mapping (Rogers et al., 2 Feb 2026).

Using flood irradiation with $x$23 keV and $x$24 keV gamma rays, per-pixel fits recover a mean stretch of approximately $x$25 at $x$26 keV and $x$27 at $x$28 keV, with pixel-to-pixel standard deviation approximately $x$29, and an offset distribution centered near $x$30 ns with standard deviation approximately $x$31 ns. The mean depth resolution at the detector center is approximately $x$32 mm FWHM at $x$33 keV and approximately $x$34 mm FWHM at $x$35 keV, and more than $x$36 of pixels achieve $x$37 mm at $x$38 keV and $x$39 mm at $x$40 keV. These numbers quantify the depth performance obtainable when orthogonal-strip geometry is combined with detailed field simulation, ASIC-aware waveform modeling, and per-pixel calibration (Rogers et al., 2 Feb 2026).

6. Design trade-offs, comparisons, and limitations

The most explicit detector-design trade-off reported for orthogonal-strip planar HPGe in $x$41Ge $x$42 searches is the balance among strip pitch, crystal thickness, spatial resolution, topology preservation, and channel count. For an $x$43 mm diameter face, $x$44 mm implies approximately $x$45 strips per face and approximately $x$46 channels total; $x$47 mm implies approximately $x$48 strips per face and approximately $x$49 channels total; and $x$50 mm implies approximately $x$51 strips per face and approximately $x$52 channels total. The steep scaling of channels favors $x$53 mm as a practical high-resolution compromise, while the topology study recommends thickness $x$54 mm at that pitch as the optimum of the adopted sensitivity-inspired figure of merit. In the absence of charge sharing, the pitch-limited sampling resolutions are approximately $x$55 mm for $x$56 mm, $x$57 mm for $x$58 mm, and $x$59 mm for $x$60 mm; in practice, longer drift in thicker crystals increases diffusion width according to $x$61 and can blur blob multiplicity (Zhang et al., 2 Mar 2026).

Comparison with other Ge detector technologies is central to the interpretation of orthogonal-strip performance. Point-contact and BEGe detectors distinguish multi-site from single-site events through pulse-shape analysis such as $x$62, but both $x$63 and single-electron backgrounds are SSEs and therefore hard to separate. Segmented coaxial Ge improves localization but typically at coarser segmentation than microstrips and does not natively provide sub-mm two-dimensional topology across the bulk volume. Orthogonal-strip planar HPGe uniquely provides sub-mm two-dimensional imaging of charge deposition patterns such as two-blob versus one-blob topologies, at the cost of increased channel count and planar form factor. The strip multi-electrode study further suggests that orthogonal-strip topology-based rejection can be complemented by conventional pulse-shape analysis to catch multi-site gamma backgrounds, while the strip topology addresses the remaining SSE-like single-electron backgrounds that PSA struggles to suppress (Zhang et al., 2 Mar 2026, Jingzhe et al., 2023).

The present literature also defines the current limitations with unusual clarity. The $x$64 topology study assumes a uniform average electric field of approximately $x$65 V/cm, does not model nonuniformities or fringe fields, neglects guard rings and dead layers, applies only a $x$66 keV strip threshold without explicit shaping-time or electronic-noise modeling, and uses projected strip energies rather than full Shockley–Ramo current signals. It also neglects trapping, recombination, impurity gradients, and intra-cluster Coulomb self-repulsion, and leaves temperature implicit. The three-dimensional MLE study is restricted to a representative central pixel, with edge pixels and near-contact regions identified as more difficult because of non-monotonic parameter–position relations and weighting-potential structure. The COSI depth-calibration study excludes one anomalous low-voltage strip, notes larger stretch at very edge pixels, and restricts the analysis to single-pixel events; extension to shared-charge clusters requires modeling of transient induced signals and capacitive cross-coupling among neighboring strips. Across these studies, future work is directed toward realistic three-dimensional field and weighting-potential calculations for detailed electrode geometries, explicit pulse-shape simulation, timing-enhanced reconstruction, and advanced machine-learning models such as Siamese networks, transformers, or graph neural networks (Zhang et al., 2 Mar 2026, Zhang et al., 24 Jul 2025, Rogers et al., 2 Feb 2026).

A recurring misconception is that orthogonal-strip detectors are simply strip versions of ordinary spectroscopy-grade planar HPGe. The recent literature does not support that simplification. Their defining value is not merely segmentation, but the joint use of orthogonal projections, charge sharing, weighting-potential asymmetries, and timing or waveform observables to reconstruct interaction topology and depth. A plausible implication is that orthogonal-strip planar HPGe occupies a distinct regime within Ge detector design: it is neither a true pixel array nor a conventional low-channel-count spectrometer, but a virtual-pixel architecture whose scientific utility depends on whether the experiment benefits more from sub-mm topological information than from the reduced complexity of simpler contact schemes.