Internal Charge Amplification (ICA) Overview

• Internal Charge Amplification (ICA) is the field-driven avalanche multiplication of charge carriers inside detector media, enabling improved detection sensitivity.
• ICA techniques span cryogenic high-purity germanium, millikelvin impurity ionization, and CMOS pixel sensors, each exploiting unique carrier dynamics under high fields.
• By integrating gain directly within the sensor, ICA enhances low-energy event detection and timing resolution while mitigating reliance on external amplification.

Internal Charge Amplification (ICA) denotes the multiplication of charge carriers inside a detector medium, prior to external electronic amplification. Across the literature, the term covers a family of related but nonidentical phenomena: avalanche multiplication in cryogenic high-purity germanium (HPGe), impact ionization of impurity-related charged states in millikelvin germanium, and controlled avalanche gain in monolithic CMOS pixel sensors. The common element is field-driven generation of secondary carriers within the detector volume; the specific initiating states, carrier asymmetry, operating temperature, field geometry, and stability conditions differ substantially between implementations (Mei et al., 2017, Acharya et al., 2022, Mei et al., 2 Mar 2026, Pernegger et al., 19 Dec 2025).

1. Conceptual scope and defining criteria

In the most general sense, ICA is avalanche multiplication of charge carriers inside a semiconductor crystal. A carrier accelerated by an electric field acquires sufficient kinetic energy between inelastic collisions to impact-ionize, thereby creating secondary electron–hole pairs. In cryogenic HPGe, this is treated as a detector-internal gain process that lowers the effective threshold by boosting primary charge above front-end noise; in monolithic CMOS pixels, it is implemented as controlled multiplication under the collection electrode; in the millikelvin planar-Ge observation, the amplified channel is not conventional band-to-band avalanche but impact ionization of impurity-related charged states with meV-scale ionization potentials (Mei et al., 2 Mar 2026, Acharya et al., 2022).

Context	Medium/device	Amplifying process
(Mei et al., 2017)	Cryogenic Ge multistrip detector	Impurity ionization followed by avalanche multiplication in high-field regions
(Acharya et al., 2022)	Planar HPGe at $\sim 40$ mK	Hole impact ionization of impurity-related charged states
(Mei et al., 2 Mar 2026)	Cryogenic HPGe design framework	Avalanche-onset modeling via SFF and physics-informed ionization law
(Pernegger et al., 19 Dec 2025)	Monolithic CMOS MAPS in 180 nm process	Controlled avalanche multiplication under in-pixel gain layers

A standard onset condition for sustained ICA is the Townsend criterion

$\int_0^d \alpha(E,T)\,dx \approx 1,$

with $\alpha(E,T)$ the impact-ionization coefficient and $d$ the multiplication width. In electron- or hole-initiated APD-style treatments, the mean multiplication and excess noise depend on the ionization coefficients for the two carrier types; in favorable unipolar limits, the excess noise remains modest rather than diverging with gain (Mei et al., 2 Mar 2026).

The literature also distinguishes ICA from two adjacent concepts. First, it is distinct from external electronic gain, because the multiplication occurs in the detector material before readout. Second, it is not synonymous with a single microscopic channel. The 2022 millikelvin Ge work explicitly separates its observed effect from conventional avalanche multiplication across the $\sim 0.7$ eV Ge bandgap, emphasizing instead the role of acceptor-derived dipole and cluster dipole states with binding energies less than $\sim 10$ meV (Acharya et al., 2022). This suggests that “ICA” is best understood as a device-level category defined by internal carrier multiplication, not as a unique microscopic mechanism.

2. Cryogenic germanium ICA for MeV-scale dark-matter detection

A prominent ICA proposal uses germanium at helium temperature to detect MeV-scale dark matter by converting sub-eV depositions into amplified charge signals. In that design, dark-matter interactions first deposit sub-eV to $\sim 100$ eV through nuclear or electronic recoils; the deposited energy is predominantly dissipated into phonons, including LA phonons at $\sim 0.037$ eV and TA phonons at $\sim 0.026$ eV. These phonons can ionize shallow donor and acceptor impurities whose binding energies are approximately $0.01$ eV: boron $\int_0^d \alpha(E,T)\,dx \approx 1,$0 eV, aluminum $\int_0^d \alpha(E,T)\,dx \approx 1,$1 eV, gallium $\int_0^d \alpha(E,T)\,dx \approx 1,$2 eV, and phosphorus $\int_0^d \alpha(E,T)\,dx \approx 1,$3 eV. The resulting carriers are then accelerated in localized high-field regions near narrow anode strips until they exceed the Ge bandgap and initiate impact ionization, producing an avalanche (Mei et al., 2017).

The basic avalanche condition is expressed as

$\int_0^d \alpha(E,T)\,dx \approx 1,$4

where $\int_0^d \alpha(E,T)\,dx \approx 1,$5 is the local electric field, $\int_0^d \alpha(E,T)\,dx \approx 1,$6 is the mean free path for inelastic scattering, and $\int_0^d \alpha(E,T)\,dx \approx 1,$7 is the Ge bandgap. In the proposed planar multistrip detector, the localized field near the anodes exceeds a critical value $\int_0^d \alpha(E,T)\,dx \approx 1,$8 V/cm. With $\int_0^d \alpha(E,T)\,dx \approx 1,$9 at $\alpha(E,T)$0 K and an avalanche region of length $\alpha(E,T)$1, the heuristic gain model

$\alpha(E,T)$2

gives $\alpha(E,T)$3. The design therefore couples impurity-ionization charge creation to intrinsic avalanche gain, rather than relying on the $\alpha(E,T)$4 eV average energy per electron–hole pair required in pure Ge at 77 K (Mei et al., 2017).

The operating-temperature logic is central. After depletion at 77 K and cooling to $\alpha(E,T)$5–4 K, shallow impurities freeze into neutral states, and thermal generation becomes negligible because $\alpha(E,T)$6 eV at 4 K, far below the impurity binding energies. The phonon absorption probability is written as

$\alpha(E,T)$7

with measured impurity ionization/excitation cross section $\alpha(E,T)$8. Using these inputs, the analysis finds that at 1.5 K and $\alpha(E,T)$9, $d$0 eV of phonons can generate more than 12 carriers, while at 4 K and $d$1, at least one carrier is produced. ICA gain of $d$2 then converts single- or few-carrier events into detectable signals (Mei et al., 2017).

The detector concept is a multistrip planar Ge device of about 1 kg mass, with dimensions $d$3, fiducial volume $d$4, 15 anode strips of width $d$5 and length $d$6 cm, a common cathode of $d$7, and guard electrodes. Full depletion is achieved at $d$8 V at 77 K, and upon cooling to $d$9–4 K the local anode fields reach the required high-field regime. The amplified signal is read out using standard high-impedance JFET or HEMT charge amplifiers (Mei et al., 2017).

Projected performance is correspondingly aggressive. For a 1 kg-year exposure and an energy threshold of $\sim 0.7$0 eV, the projected sensitivity reaches a DM–nucleon cross section of $\sim 0.7$1 at a DM mass of $\sim 0.7$2 MeV/$\sim 0.7$3, and a DM–electron cross section of $\sim 0.7$4 at a DM mass of $\sim 0.7$5 MeV/$\sim 0.7$6. The projections assume light-mediator DM–electron scattering with the conversion $\sim 0.7$7, and incorporate a phonon detection efficiency normalized to 50%. Radiogenic and cosmogenic backgrounds are treated as negligible in the region of interest when counting single carriers; neutrino-induced nuclear recoils set a floor around $\sim 0.7$8 (Mei et al., 2017).

The same study identifies several practical constraints. Uniform impurity distribution, with Hall mobility $\sim 0.7$9 and net impurity $\sim 10$0, is required for predictable depletion and multiplication. Avalanche-generated phonons can produce delayed carriers and secondary avalanches, so the proposed mitigation is to reduce the electric field dynamically for $\sim 10$1 ms after the primary avalanche pulse. This is a distinctive feature of the 2017 concept: the gain mechanism is intrinsically useful for threshold reduction, but it must be actively managed to avoid runaway or breakdown (Mei et al., 2017).

3. Time-dependent impurity-state ICA in planar germanium at millikelvin temperature

A later experimental study reported the first observation of time-dependent ICA in a planar Ge detector at cryogenic temperature, specifically at mixing-chamber temperatures of $\sim 10$2–35 mK and $\sim 10$3–40 mK. Here the effect is not described as conventional band-to-band avalanche. Instead, it is attributed to impact ionization of shallow impurity-related charged states, specifically acceptor-derived dipole and cluster dipole states whose binding energies are less than $\sim 10$4 meV. Because these energies are orders of magnitude smaller than the Ge bandgap, modest bulk fields can give holes sufficient kinetic energy to ionize the charged states and create additional carriers (Acharya et al., 2022).

The detector was a planar HPGe crystal of 10 cm diameter, 3.3 cm thickness, and mass $\sim 10$5 kg, with four charge-readout electrodes on one face and a uniform Al electrode on the opposite face. A $\sim 10$6Am source provided the 59.54 keV $\sim 10$7-ray calibration line. “Charge energy” was defined as the measured energy assigned to that line, and the charge collection efficiency was written as

$\sim 10$8

with amplification inferred when $\sim 10$9 (Acharya et al., 2022).

The striking empirical feature was its polarity dependence. Amplification appeared only under positive bias, with holes drifting across the full detector thickness; no corresponding effect was observed under negative bias, where electrons drifted across the detector. The proposed microscopic cycle was

$\sim 100$0

followed by the amplifying process

$\sim 100$1

and then trapping or neutralization,

$\sim 100$2

The analysis emphasizes that electrons are trapped more severely than holes in this p-type Ge system, which explains why hole drift produces amplification while electron drift does not (Acharya et al., 2022).

The observed gain was transient. After a positive bias was applied, the charge response rose linearly for a few minutes and then decayed exponentially over tens of minutes; the abstract describes amplification in a time period of 30 and 45 minutes after bias application. The empirical fit used was

$\sim 100$3

In this parameterization, the exponential factor inside the brackets represents time-dependent multiplication driven by the evolving population of cluster dipole states, while the outer factor $\sim 100$4 represents damping from bulk-field degradation due to trapped charges (Acharya et al., 2022).

Quantitatively, ICA “kicks off” at +4.5 V in Run 67, corresponding to $\sim 100$5 V/cm across 3.3 cm, and at $\sim 100$6 V in Run 74, corresponding to $\sim 100$7 V/cm. The effect is stronger in Run 67 than Run 74 because the former used four $\sim 100$8Am sources and therefore had a higher event rate. Representative fit values illustrate the field dependence: in Run 67 at 4.5 V, $\sim 100$9, $\sim 0.037$0, $\sim 0.037$1, $\sim 0.037$2, and $\sim 0.037$3, giving $\sim 0.037$4 min; at 9.0 V, $\sim 0.037$5, $\sim 0.037$6, $\sim 0.037$7, $\sim 0.037$8, and $\sim 0.037$9, giving $\sim 0.026$0 min. Thus higher field increases the gain terms but shortens the decay time (Acharya et al., 2022).

The study also reports linear correlations of the fit parameters with electric field. For Run 67,

$\sim 0.026$1

$\sim 0.026$2

with $\sim 0.026$3 in V/cm. At fields $\sim 0.026$4 V/cm, the detector returns to time-independent behavior with $\sim 0.026$5, consistent with normal HPGe operation without visible ICA (Acharya et al., 2022).

The implications for threshold physics are important but explicitly conditional. The authors argue that if the amplification can be stabilized, an extremely low-energy detection threshold of $\sim 0.026$6 meV could be achieved for MeV-scale dark-matter searches. They further extrapolate, using Run 67 fits, that CCE could be increased by $\sim 0.026$7 at $\sim 0.026$8 V/cm, corresponding to bias $\sim 0.026$9 V across 3.3 cm and collection time $0.01$0s. The paper states that this extrapolation must be validated experimentally. The limiting issues are stability, space-charge dynamics, and the fact that avalanche breakdown in the reported setup occurred at $0.01$1 V in Run 67 and $0.01$2 V in Run 74 (Acharya et al., 2022).

4. Critical-field theory and predictive design at 77 K and 4 K

A 2026 treatment recasts ICA design in cryogenic HPGe around a single central quantity: the avalanche-onset critical electric field, $0.01$3. In that framework, reliable operation requires a predictive estimate of the field at which sustained internal amplification becomes both measurable and stable. For uniform-field test diodes, onset is defined by $0.01$4; in nonuniform fields it is governed by the path integral $0.01$5, typically dominated by hot spots (Mei et al., 2 Mar 2026).

The paper develops a unified framework that bridges a mobility-based single-free-flight (SFF) upper bound and a physics-informed (PI) impact-ionization model. In the SFF picture, a carrier accelerated for one momentum-relaxation time $0.01$6 gains

$0.01$7

and using $0.01$8 with the condition $0.01$9 yields

$\int_0^d \alpha(E,T)\,dx \approx 1,$00

The same design intuition can be written as

$\int_0^d \alpha(E,T)\,dx \approx 1,$01

Here $\int_0^d \alpha(E,T)\,dx \approx 1,$02 is an effective impact threshold, pragmatically taken between the Ge bandgap $\int_0^d \alpha(E,T)\,dx \approx 1,$03 eV and the mean pair-creation energy $\int_0^d \alpha(E,T)\,dx \approx 1,$04 eV in cryogenic Ge (Mei et al., 2 Mar 2026).

Using $\int_0^d \alpha(E,T)\,dx \approx 1,$05, electron $\int_0^d \alpha(E,T)\,dx \approx 1,$06, hole $\int_0^d \alpha(E,T)\,dx \approx 1,$07, and the quoted mobilities, the SFF upper-bound fields are estimated as follows: electrons, $\int_0^d \alpha(E,T)\,dx \approx 1,$08 V/cm and $\int_0^d \alpha(E,T)\,dx \approx 1,$09 V/cm; holes, $\int_0^d \alpha(E,T)\,dx \approx 1,$10 V/cm and $\int_0^d \alpha(E,T)\,dx \approx 1,$11 V/cm. The paper explicitly interprets SFF as an upper-bound reference rather than a complete transport model (Mei et al., 2 Mar 2026).

The PI model then incorporates nonparabolic Kane dispersion, energy-dependent inelastic scattering, intervalley transfer, and the high-energy lucky-drift tail. The impact-ionization coefficient is approximated by a Chynoweth/Okuto–Crowell form,

$\int_0^d \alpha(E,T)\,dx \approx 1,$12

with

$\int_0^d \alpha(E,T)\,dx \approx 1,$13

and the onset relation becomes

$\int_0^d \alpha(E,T)\,dx \approx 1,$14

Thickness leverage is therefore only logarithmic in $\int_0^d \alpha(E,T)\,dx \approx 1,$15, while onset in nonuniform devices is still governed by the highest local field (Mei et al., 2 Mar 2026).

A major contribution of this work is the calibration workflow. One route is transport-informed initialization: calibrate acoustic, optical, intervalley, and defect-assisted scattering so that measured low-field mobility $\int_0^d \alpha(E,T)\,dx \approx 1,$16 is reproduced, then compute $\int_0^d \alpha(E,T)\,dx \approx 1,$17 from the energy-relaxation integral. The second route is direct diode calibration via multiplication curves $\int_0^d \alpha(E,T)\,dx \approx 1,$18 in a slab of known $\int_0^d \alpha(E,T)\,dx \approx 1,$19, using

$\int_0^d \alpha(E,T)\,dx \approx 1,$20

A Chynoweth plot of $\int_0^d \alpha(E,T)\,dx \approx 1,$21 versus $\int_0^d \alpha(E,T)\,dx \approx 1,$22 then yields $\int_0^d \alpha(E,T)\,dx \approx 1,$23 and $\int_0^d \alpha(E,T)\,dx \approx 1,$24, after which TCAD field maps are used to de-rate bias targets for nonuniform fields and identify hot spots (Mei et al., 2 Mar 2026).

The model further emphasizes carrier asymmetry. In Ge, hole ionization coefficients can exceed electron coefficients in the high-field regime, so hole-initiated multiplication with small $\int_0^d \alpha(E,T)\,dx \approx 1,$25 reduces excess noise and favors stable operation. Example PI calibrations for holes give $\int_0^d \alpha(E,T)\,dx \approx 1,$26 and $\int_0^d \alpha(E,T)\,dx \approx 1,$27 V/cm, implying $\int_0^d \alpha(E,T)\,dx \approx 1,$28 V/cm; at 4 K, $\int_0^d \alpha(E,T)\,dx \approx 1,$29 and $\int_0^d \alpha(E,T)\,dx \approx 1,$30 V/cm give $\int_0^d \alpha(E,T)\,dx \approx 1,$31 V/cm. Comparable electron examples fall in the $\int_0^d \alpha(E,T)\,dx \approx 1,$32–$\int_0^d \alpha(E,T)\,dx \approx 1,$33 V/cm range at 77 K and $\int_0^d \alpha(E,T)\,dx \approx 1,$34–$\int_0^d \alpha(E,T)\,dx \approx 1,$35 V/cm at 4 K for $\int_0^d \alpha(E,T)\,dx \approx 1,$36–10 $\int_0^d \alpha(E,T)\,dx \approx 1,$37m (Mei et al., 2 Mar 2026).

The excess-noise relation used for hole-initiated multiplication is

$\int_0^d \alpha(E,T)\,dx \approx 1,$38

which approaches the minimum-noise limit $\int_0^d \alpha(E,T)\,dx \approx 1,$39 for $\int_0^d \alpha(E,T)\,dx \approx 1,$40. The design prescription is therefore not merely “reach high field,” but rather combine calibrated onset prediction, unipolar-favored multiplication, and field shaping that suppresses edge curvature, sidewall roughness, and other sources of microplasma breakdown (Mei et al., 2 Mar 2026).

5. Monolithic CMOS ICA in fine-pitch pixel sensors

ICA has also been realized in silicon monolithic active pixel sensors through the CASSIA project, which implements internal charge multiplication in a standard 180 nm TowerSemiconductor imaging CMOS process. In this context, ICA refers to controlled avalanche multiplication of the primary ionization charge inside the sensing diode, before any electronic amplification. The device is a true monolithic active pixel sensor (MAPS) in which the sensing diode, the avalanche gain region, and the readout circuitry are co-fabricated at fine pitch without process changes or added masks (Pernegger et al., 19 Dec 2025).

The baseline sensor uses a 30 $\int_0^d \alpha(E,T)\,dx \approx 1,$41m-thick depleted p-type epitaxial layer on a p$\int_0^d \alpha(E,T)\,dx \approx 1,$42 substrate, with a circular n$\int_0^d \alpha(E,T)\,dx \approx 1,$43 collection electrode of radius 20 $\int_0^d \alpha(E,T)\,dx \approx 1,$44m at the pixel center. A low-dose n-type implant shifts the p–n junction into the bulk and assists full depletion. ICA is introduced by placing p-type gain implants directly beneath the n$\int_0^d \alpha(E,T)\,dx \approx 1,$45 electrode using standard wells: a shallower deep p-well (DP) and a deeper extra deep p-well (XDP). The gain layer diameter is varied among 12, 20, and 28 $\int_0^d \alpha(E,T)\,dx \approx 1,$46m, and the electrode implant depth is adjusted as shallow, standard, or deep to shape the local high-field profile (Pernegger et al., 19 Dec 2025).

The biasing and operation are APD-like. The n$\int_0^d \alpha(E,T)\,dx \approx 1,$47 electrode is biased positive up to 160 V while the substrate and electronics p-well are grounded. Electrons drifting into the high-field region under the electrode undergo impact ionization. For $\int_0^d \alpha(E,T)\,dx \approx 1,$48, the multiplication is approximated as

$\int_0^d \alpha(E,T)\,dx \approx 1,$49

and the excess noise follows

$\int_0^d \alpha(E,T)\,dx \approx 1,$50

The project uses TCAD with Okuto–Crowell impact-ionization modeling rather than analytical fitting of $\int_0^d \alpha(E,T)\,dx \approx 1,$51 and $\int_0^d \alpha(E,T)\,dx \approx 1,$52 (Pernegger et al., 19 Dec 2025).

The measured behavior separates into proportional and Geiger regimes. Two voltages are defined from I–V curves: $\int_0^d \alpha(E,T)\,dx \approx 1,$53, the onset of proportional multiplication, and $\int_0^d \alpha(E,T)\,dx \approx 1,$54, the hard breakdown that marks Geiger/SPAD-like operation. The reported values depend strongly on implant geometry. For DP gain layers, M2 has $\int_0^d \alpha(E,T)\,dx \approx 1,$55 V and $\int_0^d \alpha(E,T)\,dx \approx 1,$56 V, S4 has $\int_0^d \alpha(E,T)\,dx \approx 1,$57 V and $\int_0^d \alpha(E,T)\,dx \approx 1,$58 V, and S5 has $\int_0^d \alpha(E,T)\,dx \approx 1,$59 V and $\int_0^d \alpha(E,T)\,dx \approx 1,$60 V. For XDP gain layers with standard n$\int_0^d \alpha(E,T)\,dx \approx 1,$61, M3 has $\int_0^d \alpha(E,T)\,dx \approx 1,$62 V and $\int_0^d \alpha(E,T)\,dx \approx 1,$63 V, whereas S6 has $\int_0^d \alpha(E,T)\,dx \approx 1,$64 V and $\int_0^d \alpha(E,T)\,dx \approx 1,$65 V. Deep-n$\int_0^d \alpha(E,T)\,dx \approx 1,$66 XDP variants S13 and S14 shift these values to $\int_0^d \alpha(E,T)\,dx \approx 1,$67 V and $\int_0^d \alpha(E,T)\,dx \approx 1,$68 V, respectively. The paper summarizes that LGAD-like operation starts at $\int_0^d \alpha(E,T)\,dx \approx 1,$69 between $\int_0^d \alpha(E,T)\,dx \approx 1,$70 and $\int_0^d \alpha(E,T)\,dx \approx 1,$71 V depending on implant geometry, and SPAD-like operation starts at $\int_0^d \alpha(E,T)\,dx \approx 1,$72 between $\int_0^d \alpha(E,T)\,dx \approx 1,$73 and $\int_0^d \alpha(E,T)\,dx \approx 1,$74 V (Pernegger et al., 19 Dec 2025).

The gain measurements are correspondingly large. In continuous-light measurements, M2 exhibits gain rising from 1 at $\int_0^d \alpha(E,T)\,dx \approx 1,$75 V to $\int_0^d \alpha(E,T)\,dx \approx 1,$76 at 62 V, while M3 begins amplification at $\int_0^d \alpha(E,T)\,dx \approx 1,$77 V, reaches photo-to-dark-current ratio $\int_0^d \alpha(E,T)\,dx \approx 1,$78 at $\int_0^d \alpha(E,T)\,dx \approx 1,$79 V, and exceeds 4000 gain at $\int_0^d \alpha(E,T)\,dx \approx 1,$80 V. Focused laser scans show uniform gain plateaus across the gain-layer footprint with gradual roll-off outside it, indicating that the effective gain-collection area can exceed the implant diameter at higher bias. For example, M2 reaches gains of 10, 100, and 1000 at 39.1, 41.1, and 44.8 V with 532 nm light, while M3 reaches the same nominal gains at 80.9, 84.5, and 89.2 V (Pernegger et al., 19 Dec 2025).

The readout implications are central to the sensor concept. For a minimum ionizing particle in the 30 $\int_0^d \alpha(E,T)\,dx \approx 1,$81m depleted silicon epitaxial layer, the estimated input charge is

$\int_0^d \alpha(E,T)\,dx \approx 1,$82

so the multiplied output charge spans roughly 3.8 fC at $\int_0^d \alpha(E,T)\,dx \approx 1,$83 to 38 fC at $\int_0^d \alpha(E,T)\,dx \approx 1,$84. In the prototype, off-chip readout used a CIVIDEC Cx-L amplifier with gain 6.68 mV/fC and ENC $\int_0^d \alpha(E,T)\,dx \approx 1,$85. The expected signal-to-noise scaling is approximately

$\int_0^d \alpha(E,T)\,dx \approx 1,$86

and timing jitter follows

$\int_0^d \alpha(E,T)\,dx \approx 1,$87

Because ICA increases both signal amplitude and the prompt current slew, it improves the intrinsic timing potential, although the reported laboratory timing spreads of 0.6–5 ns rms are dominated by the external amplifier rise time of 50–70 ns rather than the sensor itself (Pernegger et al., 19 Dec 2025).

The CASSIA work also reports room-temperature dark-count-rate behavior. DCR rises exponentially with temperature between $\int_0^d \alpha(E,T)\,dx \approx 1,$88 and $\int_0^d \alpha(E,T)\,dx \approx 1,$89C, consistent with thermally generated carriers. At room temperature, the normalized DCR is $\int_0^d \alpha(E,T)\,dx \approx 1,$90 Hz/$\int_0^d \alpha(E,T)\,dx \approx 1,$91 in LGAD and early SPAD regimes, increasing to $\int_0^d \alpha(E,T)\,dx \approx 1,$92 Hz/$\int_0^d \alpha(E,T)\,dx \approx 1,$93 at 120 V for M3. Shallow n$\int_0^d \alpha(E,T)\,dx \approx 1,$94 variants show substantially worse DCR, up to $\int_0^d \alpha(E,T)\,dx \approx 1,$95 Hz/$\int_0^d \alpha(E,T)\,dx \approx 1,$96. In the reported setup, a 300 k$\int_0^d \alpha(E,T)\,dx \approx 1,$97 bias resistor provided passive quenching in Geiger mode by limiting current to $\int_0^d \alpha(E,T)\,dx \approx 1,$98 nA; active quench and recharge circuits are reserved for later designs (Pernegger et al., 19 Dec 2025).

In detector-system terms, the significance of the result is that ICA was demonstrated in a fully monolithic 180 nm CMOS pixel using only standard wells in the process stack. The sensor can be operated in proportional LGAD-like mode for moderate gain and low DCR, or in SPAD-like mode for extremely high gain, and the multiplication region is localized under the electrode rather than at the periphery when the electrode-to-p-well spacing is properly engineered (Pernegger et al., 19 Dec 2025).

6. Cross-cutting constraints, misconceptions, and research directions

The literature shows that ICA is highly context dependent. Reported onset scales span very different regimes: $\int_0^d \alpha(E,T)\,dx \approx 1,$99–2 V/cm for impurity-state ICA in a 3.3 cm planar Ge detector at $\alpha(E,T)$00 mK, $\alpha(E,T)$01 V/cm in the localized avalanche regions of the 2017 multistrip Ge concept, and device-specific $\alpha(E,T)$02 and $\alpha(E,T)$03 values from $\alpha(E,T)$04 V to $\alpha(E,T)$05 V in 30 $\alpha(E,T)$06m monolithic CMOS pixels (Acharya et al., 2022, Mei et al., 2017, Pernegger et al., 19 Dec 2025). These are not contradictory numbers; they correspond to different multiplication widths, temperatures, carrier types, and microscopic ionization channels.

Several common distinctions emerge. First, ICA is not necessarily equivalent to near-breakdown Geiger operation. The CASSIA devices operate in both proportional LGAD-like mode and SPAD-like mode, with moderate multiplication in the former and regenerative multiplication in the latter (Pernegger et al., 19 Dec 2025). Second, ICA is not necessarily a steady-state avalanche phenomenon. The millikelvin Ge observation is explicitly transient, with gain set by time-dependent impurity-state populations and degraded by space-charge buildup (Acharya et al., 2022). Third, the carrier asymmetry matters. Hole-favored multiplication is desirable in the 2026 HPGe design framework because small $\alpha(E,T)$07 lowers excess noise, and the 2022 planar-Ge experiment observed amplification only for hole drift (Mei et al., 2 Mar 2026, Acharya et al., 2022).

Field shaping and material control are recurrent engineering constraints. In the 2017 Ge dark-matter concept, avalanche must be confined to narrow high-field regions near anode strips while maintaining bulk purity and impurity distributions suited for both depletion and phonon-induced impurity ionization (Mei et al., 2017). In the 2026 framework, the device bias must be de-rated with TCAD field maps to avoid hot spots and microplasma before the nominal mean field reaches the predicted onset (Mei et al., 2 Mar 2026). In CASSIA, too small an electrode-to-p-well spacing drives periphery breakdown rather than centered multiplication under the electrode (Pernegger et al., 19 Dec 2025).

Stability remains the principal open problem where the physics is most ambitious. The 2017 Ge detector proposes dynamic electric-field reduction for $\alpha(E,T)$08 ms after the primary avalanche pulse to suppress secondary avalanches generated by avalanche phonons (Mei et al., 2017). The 2022 planar-Ge work identifies stabilization of the cluster-dipole population and suppression of space-charge-induced field degradation as prerequisites for realizing the suggested $\alpha(E,T)$09 meV threshold regime (Acharya et al., 2022). The 2026 critical-field framework adds a more general prescription: calibrate $\alpha(E,T)$10 and $\alpha(E,T)$11 experimentally, favor unipolar multiplication, and operate only slightly above onset within a safe TCAD-validated bias window (Mei et al., 2 Mar 2026).

A plausible synthesis is that ICA is most mature as a design principle when it is formulated in terms of calibrated onset field, controlled multiplication geometry, and excess-noise management, and most exploratory when it relies on nonequilibrium impurity-state populations that are not yet stabilized. The published work therefore spans both detector engineering and unresolved condensed-matter transport physics. In germanium, the concept is closely tied to low-threshold rare-event searches; in CMOS, it is tied to timing-capable fine-pitch tracking. What links these domains is the same detector-level objective: to move gain into the sensor bulk so that smaller primary signals become measurable without relying solely on external front-end amplification (Mei et al., 2017, Mei et al., 2 Mar 2026, Pernegger et al., 19 Dec 2025).