3D Diamond Pixel Sensors: Design & Performance

• 3D diamond pixel sensors are advanced detectors that embed electrodes inside diamond to shorten carrier drift distances and mitigate trapping.
• They employ two main architectures—laser-induced full-carbon columnar sensors and RIE-fabricated interdigitated detectors—to optimize timing and charge collection.
• High-performance simulations and beam-test validations confirm sub-100 ps timing and enhanced radiation hardness for applications in HL-LHC and nuclear medicine.

Searching arXiv for the specified papers and closely related work on 3D diamond pixel sensors. 3D diamond pixel sensors are diamond radiation detectors in which the charge-collecting electrodes are brought into the bulk, so that carrier drift is governed primarily by the inter-electrode geometry rather than by the full sensor thickness. In the literature summarized here, this class includes full-carbon columnar devices with electrodes engraved orthogonal to the crystal surface by femtosecond laser-induced graphitization, as well as diamond detectors with embedded 3D interdigitated electrodes produced by reactive ion etching and metallization. The central motivation is to combine diamond’s low leakage, radiation hardness, and fast carrier transport with a 3D field configuration that shortens drift paths, mitigates trapping, and, in recent devices, supports timing below 100 ps in harsh environments (Anderlini et al., 13 May 2026, Hoeferkamp et al., 2022).

1. Conceptual basis and device classes

The defining feature of a 3D diamond sensor is that the relevant collection distance is set by the electrode spacing inside the bulk, rather than by the substrate thickness. In the Snowmass review, 3D geometries are framed as a response to trap-limited operation at HL-LHC doses, where the average free-carrier drift distance falls below 50 μm. Under those conditions, a planar geometry forces charge transport over 250–500 μm, whereas a 3D geometry reduces the typical path to 25–100 μm, with proposed 25 μm × 25 μm cells engineered so that the longest drift path is 25 μm in the saddle-point region and 17.5 μm elsewhere (Hoeferkamp et al., 2022).

Two architectural lineages are prominent. One is the full-carbon columnar sensor, in which electrodes orthogonal to the surface are created directly inside the diamond by femtosecond laser-induced graphitization. The other is the 3D interdigitated detector, in which vertical grooves are etched into single-crystal CVD diamond and selectively metallized so that the groove sidewalls become embedded electrodes. Both geometries aim to reshape the electric and weighting fields to shorten carrier travel and broaden the effective active region, but they do so through different materials and process stacks (Anderlini et al., 13 May 2026, Forneris et al., 2016).

Within high-energy instrumentation, the technology is explicitly associated with HL-LHC and beyond, where the ambition is to preserve charge collection at fluences beyond those usually tolerated by planar devices. In parallel, the full-carbon columnar variant is also presented as relevant to Nuclear Medicine and dosimetry, where radiation hardness, low dielectric noise, and operation without cooling are material advantages already emphasized for diamond (Anderlini et al., 13 May 2026).

2. Geometry, materials, and fabrication routes

The full-carbon columnar approach forms electrodes by driving a local phase transition from diamond to a mixture of graphite and amorphous carbon using femtosecond laser-induced graphitization. In the Snowmass summary, RD42 reports 130 fs laser pulses at 800 nm with a 2 μm focus spot, and a Spatial Light Modulator is used to correct spherical aberrations. The reported outcome is a column diameter of 2.6 μm and a column formation yield of at least 99.8% across a device, with column resistivity in the range 0.1–1 Ω·cm (Hoeferkamp et al., 2022).

A representative fast-timing device used for validation in the GPU-accelerated simulation study was a prototype 6×6 3D pixel matrix with a pitch of 55×55 μm², approximately 12 μm electrode diameter, about 30 kΩ electrode resistance, equivalent resistivity 0.75 Ω·cm, and 500 μm bulk thickness. In that architecture, both readout columns and bias columns are laser-graphitized. The reported reduction in electrode resistance is central, because lower-resistance full-carbon electrodes reduce RC delays and accelerate signal propagation along the columns (Anderlini et al., 13 May 2026).

The RIE-based 3D interdigitated route uses a different process sequence. A single-crystal CVD diamond film is oxidized at 500 °C in air for 1 hour, covered with a 1 μm thick Ni hard mask, and etched in CF₄/O₂ plasma with 25% CF₄ in O₂, 20 sccm total flow, 20 mbar pressure, and 200 W RF power. The etch rate is reported as 3.8 μm/h, giving grooves of about 6 μm depth. After Ni removal, a 50 nm Cr layer is evaporated and selectively removed from the top surface so that the metal remains only in the grooves, forming two interdigitated combs of embedded Schottky electrodes. The demonstrated geometry uses 10 μm finger width, 10 μm gap, and a pitch of about 20 μm (Forneris et al., 2016).

Architecture	Reported fabrication or geometry	Reported outcome
Full-carbon columnar pixel sensor	fs-laser graphitization; 6×6 matrix; 55×55 μm² pitch; ~12 μm electrode diameter; 500 μm bulk	time resolutions better than 100 ps
RD42 laser-microstructured 3D diamond	130 fs, 800 nm, 2 μm focus; 50×50 μm² fabricated; 25×25 μm² under design	2.6 μm columns; ≥99.8% yield; 0.1–1 Ω·cm
3D interdigitated diamond detector	RIE grooves ~6 μm deep; 10 μm finger width; 10 μm gap; 50 nm Cr in grooves	higher CCE and wider active area than planar reference

These process routes define two distinct conceptions of “3D” in diamond. The columnar pixel family places resistive electrodes fully inside the bulk and directly motivates dynamic signal-propagation modeling. The interdigitated family uses embedded metal sidewalls to reshape the depletion region laterally. A plausible implication is that future 3D diamond pixel development may continue to draw from both traditions: laser-defined internal electrodes for pixelated timing layers and etched sidewall geometries for aggressive field engineering.

3. Electrostatics, carrier transport, and induced-signal formation

Several material properties of diamond explain why 3D geometries are attractive. The Snowmass review lists a bandgap of about 5.5 eV, electron–hole pair creation energy of about 13 eV, relative permittivity of about 5.5–5.7, room-temperature mobilities of about 1800 cm²/V·s for electrons and 1600 cm²/V·s for holes, saturation velocity of about $2 \times 10^7$ cm/s, thermal conductivity of about 2000 W/m·K, and radiation length of about 12.1 cm. The corresponding detector implications reported there are very low leakage at room temperature, low-noise operation, fast drift, and low multiple scattering for a given thickness (Hoeferkamp et al., 2022).

For charge yield, the same review gives the standard estimate

$Q \approx \frac{(dE/dx)\cdot t}{w},$

with $t$ the sensor thickness and $w \approx 13$ eV for diamond. Because $w$ is larger than in silicon, the raw signal is smaller for equal deposited energy, so 3D architectures are used to preserve effective charge collection efficiency under trapping by shortening the drift time. The trapping dependence is summarized there as

$\mathrm{CCE} \sim \exp(-t_{\mathrm{drift}}/\tau),$

which makes reduced drift distance directly beneficial in irradiated material (Hoeferkamp et al., 2022).

In the interdigitated geometry, the field is described as laterally “parallel-plate” across the 10 μm gaps between opposing groove sidewalls. For a 50 V bias over a 10 μm gap, the reported field scale is $E \approx 5 \times 10^6$ V/m, large enough that drift velocity can approach saturation, while the effective path to the nearest sidewall is only about 5–10 μm. This is the physical basis for the observed increase in charge collection efficiency and wider active area relative to planar surface electrodes (Forneris et al., 2016).

For induced current, the classical Ramo–Shockley form quoted in the Snowmass summary is

$i(t) = q \cdot v(t) \cdot E_w.$

That static weighting-field formulation is sufficient when electrode impedance and propagation effects can be neglected. In the recent full-carbon 3D pixel study, however, the dominant timing contribution is reported to arise from propagation and dispersion along the resistive readout columns rather than from the bias columns. This requires an extended formulation, written there as

$$i(t) = -\frac{q}{V_w}\int_0^t \vec{H}(\vec{x}(t'), t-t') \cdot \vec{v}(t') \, dt',$$

where $\vec{H}(\vec{x}, t)$ is a four-dimensional correlation function that acts as a time-dependent weighting field. In that treatment, dynamic weighting potentials are obtained from a differential equation derived as a quasi-static approximation of Maxwell’s laws, so impedance-induced delay and dispersion enter the induced current explicitly (Anderlini et al., 13 May 2026).

A recurrent misconception is that 3D timing is governed only by carrier transit in the bulk. The recent simulation and beam-test comparison indicate that, for these resistive-electrode diamond pixels, signal propagation along the readout column can be the dominant term in the timing budget. Static weighting potentials then miss the key effect rather than merely refining it (Anderlini et al., 13 May 2026).

4. Modeling, numerical methods, and high-performance computing

The recent simulation framework for columnar 3D diamond pixels is an end-to-end chain that starts from a text description of electrode geometries in OpenSCAD, converts them to STL, and voxelizes them onto regular 3D grids. The electrostatic field is computed with an iterative pseudo-spectral Laplace solve, alternating potential and charge-density updates through 3D FFTs and a custom CUDA kernel that multiplies or divides by $Q \approx \frac{(dE/dx)\cdot t}{w},$0 directly in spectral space to reduce GPU memory footprint. The resulting static fields are exported in CSV and imported into Garfield++, which uses HEED for stochastic energy deposition and integrates electron and hole trajectories in the electrostatic field (Anderlini et al., 13 May 2026).

The dynamic weighting-field computation is more specialized. The correlation function $Q \approx \frac{(dE/dx)\cdot t}{w},$1 is advanced with a forward-Euler time-marching scheme under the quasi-static Maxwell approximation. Boundary conditions are imposed using fundamental solutions: arrays containing Green’s function contributions from point charges are rescaled and translated to represent electrode boundary sources, and their superposition forms the external potential contribution $Q \approx \frac{(dE/dx)\cdot t}{w},$2. The bulk update again uses FFT-based pseudo-spectral steps, and the time-dependent $Q \approx \frac{(dE/dx)\cdot t}{w},$3 maps are stored in HDF5. For waveform synthesis, Garfield++ trajectories are combined with $Q \approx \frac{(dE/dx)\cdot t}{w},$4 through a per-carrier CUDA convolution kernel, with the weighting-field arrays stored in GPU texture memory to exploit hardware linear interpolation along each path (Anderlini et al., 13 May 2026).

The same study describes orchestration and distribution as part of the sensor-research infrastructure. Snakemake manages the workflow as a DAG of micro-steps; Arrow is used for trajectory compression with about 80% size reduction and lower deserialization overhead; Kubernetes with Kueue and InterLink-defined virtual nodes dispatch jobs to INFN-CNAF and the TeRABIT Padova HPC bubble; CVMFS, Apptainer, and CVMFS Unpacked provide software and containers; and a centralized S3-compatible storage based on Deuxfleurs Garage at Cloud@CNAF handles data exchange. The reported effect is a reduction in time-to-insight from about one week to a few hours for typical geometries, making concurrent geometry scans practical (Anderlini et al., 13 May 2026).

Earlier 3D diamond modeling used a different scale and objective. The interdigitated detector study employed COMSOL Multiphysics 4.3 in a 2D finite-element cross-section, solving Poisson and stationary drift–diffusion equations with Schottky boundary conditions, then synthesizing IBIC response by convolving simulated CCE$Q \approx \frac{(dE/dx)\cdot t}{w},$5 with a SRIM-2008 Bragg profile for 1 MeV protons and a Gaussian beam spot of 7 μm FWHM. That methodology was sufficient to reproduce measured CCE maps and bias dependence, but it did not address the impedance-limited propagation problem that becomes central in resistive columnar pixels (Forneris et al., 2016).

5. Experimental performance, validation, and radiation hardness

Radiation hardness is one of the primary motivations for 3D diamond. In the Snowmass review, after $Q \approx \frac{(dE/dx)\cdot t}{w},$6 n/cm² a 3D diamond device with 50 μm × 50 μm cells is reported to show “better than three times less charge loss” than a planar diamond detector when both are normalized to the same unirradiated relative charge, and the unirradiated 3D device shows twice the charge of the unirradiated planar device. The programmatic target stated there is to extend radiation tolerance to fluences above $Q \approx \frac{(dE/dx)\cdot t}{w},$7 hadrons/cm² by moving to 25 μm × 25 μm cells and minimizing the longest drift paths (Hoeferkamp et al., 2022).

The interdigitated 3D detector provides a complementary performance demonstration at shallow penetration depth. Under IBIC with a 1 MeV proton micro-beam, the 3D device shows maximum CCE increasing with bias and saturating at about 0.85 for $Q \approx \frac{(dE/dx)\cdot t}{w},$8 V, whereas the planar reference reaches about 0.55 at $Q \approx \frac{(dE/dx)\cdot t}{w},$9 V without clear saturation in the tested range. The study also reports a wider active area, detectable signal in the inter-finger gap at higher bias, and qualitatively improved energy resolution relative to the planar structure (Forneris et al., 2016).

For fast-timing columnar pixels, the most specific validation comes from the CERN SPS 2021 beam test of a 6×6 3D diamond pixel matrix with 55×55 μm² pitch, approximately 12 μm readout electrode diameter, approximately 30 kΩ electrode resistance, and 500 μm thickness. Under those conditions, the state-of-the-art time resolution is reported to be well below 100 ps. The simulation framework with time-dependent weighting fields reproduces the key timing behavior because it captures impedance-induced delays that static weighting potentials miss; the agreement with measurements is presented as evidence that the dynamic weighting-field approach is necessary for accurate timing predictions in this device class (Anderlini et al., 13 May 2026).

The same study also reports geometry scans that clarify which design parameters actually control timing. Varying the bias electrode diameter from 6 μm to 14 μm in 2 μm steps changes the nominal resistance according to

$t$0

yet the time resolution shows no significant dependence on $t$1. By contrast, reducing bulk thickness, and therefore shortening the readout electrode length, lowers the asymptotic time resolution at a given signal amplitude. The reported interpretation is that propagation along the resistive readout columns dominates the timing response, while the bias-column contribution is practically negligible in the studied geometry (Anderlini et al., 13 May 2026).

6. Design trade-offs, applications, and open problems

Several design rules now emerge directly from the reported results. First, shortening readout electrodes by reducing bulk thickness improves the asymptotic timing floor, provided sufficient signal amplitude is maintained for efficiency. Second, reducing bias electrode diameters to the fabrication limit does not significantly degrade timing in the studied full-carbon geometry. Taken together, these changes are expected to improve time resolution by approximately 10% with minimal fabrication impact (Anderlini et al., 13 May 2026).

These results also correct a common oversimplification in discussions of 3D sensors. It is not generally true that all geometric reductions are equally important. In the reported full-carbon pixel architecture, the dominant levers are readout electrode resistance and readout electrode length, whereas bias electrode diameter can be minimized chiefly to reduce crystal-damage risk without a substantial timing penalty. In the interdigitated architecture, by contrast, groove depth, gap, and field reach determine how much of the deposited charge is brought into the high-field region, so deeper etches are specifically identified as desirable for particles with longer stopping ranges (Forneris et al., 2016, Anderlini et al., 13 May 2026).

Application domains are explicitly broader than collider tracking. The full-carbon columnar study identifies High Energy Physics, Nuclear Medicine, and dosimetry as motivating areas. For fast timing layers and beam monitors in HEP, the attraction is robustness after irradiation together with sub-100 ps timing. In Nuclear Medicine, the cited advantages are radiation hardness, low noise, and operation without cooling. In dosimetry and beam monitoring, the full-carbon 3D architecture is presented as combining fast response with durability (Anderlini et al., 13 May 2026).

Important limitations remain. The quasi-static approximation used for time-dependent weighting fields neglects full-wave effects and radiation, which limits applicability at very high frequencies or in strongly dispersive structures. Numerical stability and conditioning depend on voxel resolution, time-step choice, and boundary assembly accuracy, while memory bandwidth dominates the cost of boundary construction. Garfield++ path integration currently dominates runtime, and centralized S3-compatible storage becomes the bottleneck under high concurrency. On the device side, the Snowmass review notes that comprehensive metrics for 3D diamond pixels remain incompletely reported: sensor thickness beyond the stated cell geometries, bias and depletion voltages, breakdown behavior, hit efficiency, timing resolution for the RD42 structures, position resolution, capacitance, leakage current, power, TID tolerance, and integration with modern pixel ASICs are identified as active R&D topics rather than closed issues (Anderlini et al., 13 May 2026, Hoeferkamp et al., 2022).

The present state of the field therefore combines clear physical validation with unfinished engineering. The established core proposition is that embedding electrodes inside diamond shortens drift paths and can substantially improve charge collection under trapping; the newer result is that, in resistive full-carbon pixel sensors, accurate timing prediction additionally requires a dynamic treatment of signal propagation along the readout electrodes. This suggests that the next phase of 3D diamond pixel development will depend not only on microfabrication advances such as smaller columns, thinner bulks, and deeper grooves, but also on geometry–electronics co-optimization supported by fast, physically consistent simulation.