Pith. sign in

REVIEW 2 major objections 5 minor 7 references

Signal Development for Saturated Ultrafast Sensors with Impact Ionization Gain

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Impact ionization keeps an idealized gain-30 LGAD's X-ray signals above electronic noise at frame rates up to 10 GHz.

desk verdict A clean idealized model of LGAD signal onset that supports a conditional 10 GHz advantage, with the main caveat being an unquantified small-space-charge limit. read the letter →

arxiv 1908.04953 v2 pith:UGZYLVUB submitted 2019-08-14 physics.ins-det

Bruce A. Schumm This is my paper · ORCID
classification physics.ins-det PACS 29.40.Wk
keywords LGADsensorsimpactionizationgainultrafastX-raydetectionseriesnoisesignaldevelopmentsaturateddriftvelocityhighframeratesilicondiode
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper develops a closed-form approximation for the first instants of signal formation in a silicon diode after an instantaneous, longitudinally uniform X-ray deposition. In a PIN diode the collected charge grows only linearly with the electronic shaping time, while in an LGAD the impact-ionization gain adds a term quadratic in that time. Because series readout noise grows as the inverse square root of the shaping time, the quadratic term is what lets an idealized gain-30 LGAD hold a signal-to-noise advantage over a PIN diode at frame rates up to 10 GHz. A simple Monte Carlo simulation of a 50 $\mu$m sensor with a 2 $\mu$m gain layer places the boundary at an effective collection time near 0.1 ns. The 10 GHz claim applies to high-flux saturated depositions; for single X-ray quanta the depth-dependent onset of gain limits the frame rate to below 2 GHz.

What carries the argument

The load-bearing identity is Eq. (11), built from the parallel-plate induced-charge picture under the assumption of constant saturated drift speeds. Its new content is the quadratic-in-$\tau$ term $\frac{1}{2}K A_e v_e^s \tau$ multiplying the linear collection term: carrier multiplication makes the carrier density grow during collection, so the induced charge accumulates faster than linearly immediately after deposition. The paper pairs the analytic expression with an elemental simulation of a 50 $\mu$m sensor containing a 2 $\mu$m gain layer tuned to an overall gain of 30, confirming a gain-onset time scale near 0.1 ns. The argument also uses the standard series-noise scaling, in which the minimal detectable charge worsens at least as fast as the $3/2$ power of the frame rate when the collected charge falls linearly with shaping time; the quadratic term is exactly what counteracts that degradation.

What would settle it

Pulse a gain-30 LGAD with a sub-nanosecond X-ray pulse and record signal amplitude versus shaping time down to ~0.1 ns. Eq. (11) predicts the gain contribution grows as $\tau^2$, so the LGAD-minus-PIN charge should increase by a factor of four when the shaping time doubles; if the advantage instead saturates or vanishes at high instantaneous flux, the saturated-velocity assumption or the quadratic gain term is wrong.

Watch

Extended reading notes

Core claim

The paper's central object is an equation for the short-time collected charge, Eq. (11). After a shaping time $\tau$, the collected charge for a PIN diode is proportional to $\tau$, while for an LGAD it carries an extra factor $1 + \frac{1}{2}K A_e v_e^s \tau$, so the gain contribution grows as $\tau^2$. Here $A_e$ is the thickness-averaged electron impact-ionization coefficient and $v_e^s$ is the saturated electron drift velocity, so the quadratic term defines the time scale on which gain develops. The paper claims that for an idealized LGAD with overall gain 30, this quadratic term keeps the collected charge above the series-noise floor for effective collection times down to about 0.1 ns, corresponding to frame rates near 10 GHz, where a same-thickness PIN diode would fall below threshold. It also states that this advantage does not hold in the granular single-quantum limit, where the spread in arrival times of carriers at the gain layer limits the frame rate to below 2 GHz.

Load-bearing premise

The formulas and the 10 GHz boundary assume that the space-charge field from the deposited electron-hole plasma stays small relative to the bias field, so electrons and holes keep constant saturated drift speeds throughout collection; if high-flux deposits screen the field and slow the carriers, the gain-onset time scale and the frame-rate boundary shift.

Editorial extensions

If this is right

  • If Eq. (11) is correct, LGAD sensors remain useful for high-flux X-ray imaging at frame rates near 10 GHz, while PIN diodes lose signal to readout noise at sub-nanosecond shaping times.
  • Because the gain term is quadratic in $\tau$, its relative contribution grows as the shaping time shrinks, so gain becomes more valuable as the frame rate rises.
  • The closed-form expression gives sensor designers a direct estimate of the gain-onset time scale $\frac{1}{2}K A_e v_e^s$ without running full simulations.
  • In the granular single-quantum regime, the same picture predicts a lower frame-rate ceiling below 2 GHz, set by the spread of electron arrival times at the gain layer.
  • The treatment extends to white-beam or particle-stream depositions, since its main geometric requirement is a longitudinally uniform initial pair distribution.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct experimental extension would measure LGAD pulse height versus shaping time on a pulsed X-ray source: Eq. (11) predicts the gain contribution doubles when $\tau$ doubles, so observing saturation of that growth would pinpoint where the approximation breaks.
  • The same quadratic-gain argument should transfer to other saturated-drift multiplication sensors, such as thin avalanche photodiodes, with the frame-rate boundary set by their own impact-ionization coefficients and drift speeds.
  • The paper does not quantify when space-charge screening slows carriers; the first testable signature of that breakdown would be a flattening of the gain-onset time scale at high deposited flux density.
  • The stated granular-limit delay of 0.5 ps is inconsistent with the stated 2 GHz bound unless the delay is read as the ~0.5 ns electron transit time across a 50 $\mu$m bulk; the 2 GHz figure is consistent with the longer value.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This manuscript develops a closed-form approximate expression for the short-time signal development of silicon diode sensors (PIN and LGAD) following instantaneous, longitudinally-uniform ionization. The derivation uses the Shockley-Ramo induced-charge framework with saturated drift velocities and a leading-order treatment of impact ionization, yielding a collected-charge expression, Eq. (11), with a term quadratic in the shaping time that encodes the gain contribution. An elemental Monte Carlo simulation, using all-orders gain-layer multiplication and literature values for drift velocities, compares relative collected charge for PIN and LGAD sensors of 50 μm thickness, with the LGAD gain-layer parameters tuned to give an overall gain of 30. The paper claims that, for such an idealized gain-30 LGAD, the impact-ionization gain provides an advantage over PIN diodes at frame rates up to about 10 GHz.

Significance. If the claims hold, the paper provides a simple analytic tool for estimating ultrafast signal development in silicon diodes and identifies a regime in which internal gain materially extends the achievable frame rate. The strengths include a derivation that follows transparently from the Shockley-Ramo theorem with clearly stated assumptions, a simulation that uses an all-orders treatment of gain-layer multiplication rather than the linearized analytic approximation, and explicit discussion of the granular limit. The specific prediction that a gain-30 LGAD retains an advantage at ~10 GHz is falsifiable and testable against device-level simulations or prototype measurements. The main limitations are the unspecified shaping constant K and the unquantified space-charge assumption, both of which affect the quantitative 10 GHz claim.

major comments (2)
  1. [Section 2, Eq. (11)] The constant K is introduced as a "dimensionless constant of order 1 that relates the shaping time to the effective charge collection time," but it is never defined, given a value, or related to a specific shaper response. The central claim that a gain-30 LGAD is advantageous at frame rates up to 10 GHz depends on the conversion between the simulation's "effective collection time" and the shaping time τ, and hence on K. Without a specification of K (for example, its value for a CR-RC or other shaper), the mapping between the 0.1 ns collection time shown in Figure 1 and the 10 GHz frame-rate statement is not reproducible. Please define K, give its value for the assumed shaping, or express the simulation results directly in shaping time.
  2. [Introduction, first paragraph] The assumption that the space-charge field "remains small relative to the field created by the reverse bias" is load-bearing for the constant-saturated-velocity forms of Eqs. (3), (6), (10), and for the simulation's fixed drift speeds. No quantitative criterion is given for when this assumption holds. In the high-flux regime the paper targets, this is not automatic: for example, a 10 keV X-ray pulse of about 5×10^3 photons per (100 μm)^2 pixel in a 50 μm detector produces a pair density ρ0 ~ 3×10^13 cm^-3, and at τ ~ 0.1 ns the space-charge field is of order e ρ0 (v_e - v_h) τ / ε_Si ~ 2×10^3 V/cm, already ~10% of the assumed 2×10^4 V/cm bulk field. Since the gain term in Eq. (11) scales with the saturated electron velocity, any field-induced reduction of v_e or α_e would shrink the quadratic term and shift the 10 GHz boundary. Please provide an explicit validity estimate in terms of incident flux and pair density, and qualify the central claim accordingly.
minor comments (5)
  1. [Section 3, granular limit paragraph] The text states that the arrival time of a single X-ray deposition would be spread over "between 0 and 0.5 psec," but for a 50 μm sensor with v_e = 100 μm/ns the transit time is 0.5 ns; this appears to be a typo and should read "0.5 nsec."
  2. [Figure 1] The x-axis is labeled "Effective Collection Time" without units; the text indicates nanoseconds, but the units should be shown on the axis.
  3. [Section 2, Eq. (1)] The denominator "3.62 λ" could be misread as 3.62 times the wavelength; explicitly write the units (3.62 eV) and note that λ is the attenuation length, with the expression giving the pair density in cm^-3.
  4. [References] Reference [2] is a colloquium slide deck; consider citing a peer-reviewed description of the Dynamic Mesoscale Materials Science Capability or a similar source if one is available.
  5. [Section 3, simulation description] The phrase "anode (holes) or cathode (electronics)" is confusing; the parenthetical likely should refer to the electrode that collects electrons, so a wording such as "cathode (electron-collecting electrode)" would clarify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation is self-contained and the 10 GHz claim is an output of assumed parameters, not a fitted target.

full rationale

The paper derives a closed-form signal expression from the Shockley-Ramo induced-charge theorem (Eq. 2) and literature values for saturated drift velocities and impact-ionization coefficients. The quadratic gain term in Eq. (11) follows by ordinary integration of Eq. (8), which itself comes from substituting the linearized gain expression Eq. (6) into the Ramo current integral. The simulation tunes the electron impact-ionization coefficient to produce an overall gain of 30, but that gain is a specified design input, not a parameter fitted to the frame-rate conclusion. The 10 GHz statement is a consequence of the chosen 50 um sensor, 0.1 ns collection time, and gain-30 configuration; it is not obtained by defining the gain from the frame-rate claim. The dimensionless constant K is an order-unity shaping parameter and is not fitted to the 10 GHz result. All citations are to standard external references (Canali, Cavalleri, Jacoboni, Robbins, Spieler); there are no self-citations and no author-invoked uniqueness theorem. The small-space-charge assumption is a stated physical idealization. Whether it holds at the high fluxes of interest is a legitimate physics concern, but it is not circular because the derivation does not assume the conclusion that LGAD outperforms PIN at 10 GHz. The paper therefore contains no load-bearing circular step.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The analysis is an idealized model with two explicit tuning knobs: the shaping constant K (left unspecified) and the gain-layer alpha_e (tuned to gain 30). The main physical premise, small space-charge field at high flux, is asserted without quantitative support. No new entities are introduced.

free parameters (3)
  • K (shaping-to-collection time constant) = unspecified, 'of order 1'
    Introduced in Eq (11) to relate shaping time to effective charge collection time. The 10 GHz claim depends on the product (1/2) K A_e v_e^s tau, so leaving K unspecified leaves the quantitative boundary unconstrained.
  • electron impact ionization coefficient alpha_e in gain layer = mean free path = 0.61 micrometers (gain 30)
    Chosen in Section 3 so that the idealized LGAD has an overall gain of 30. This input determines the temporal onset scale of gain and therefore the frame-rate advantage claim.
  • gain layer thickness = 2 micrometers
    Design parameter of the simulated LGAD, placed just below the cathode; sets the spatial extent over which impact ionization multiplies carriers and contributes to the gain-onset time.
assumptions (5)
  • domain assumption Space-charge field from the deposited plasma remains small relative to the reverse-bias field, so drift velocities stay saturated
    Stated in the Introduction and used in deriving Eq (3); if violated, the linear time development and the gain-onset time scale change.
  • domain assumption X-ray absorption creates an instantaneous, longitudinally-uniform distribution of electron-hole pairs (saturated limit)
    Definition of the saturated regime in the Introduction; real absorption profiles are exponential, so the result applies only to the idealized limit.
  • domain assumption Hole impact ionization is negligible (alpha_h = 0)
    Used in Eq (8) and in the simulation; standard for LGADs below breakdown but still a simplification.
  • domain assumption Leading-order linearization of multiplication in Eq (6), valid for t such that carrier transport is small relative to alpha(z) variation
    The analytic expression truncates gain growth to first order; the simulation uses all-orders exponential growth, so the closed form is approximate.
  • standard math Parallel-plate Shockley-Ramo induced-charge framework for collection current
    Eq (2) rests on the induced-charge theorem of Cavalleri et al. [4]; standard detector physics.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Signal Development for Saturated Ultrafast Sensors with Impact Ionization Gain." pith.science (2026). https://pith.science/paper/UGZYLVUB

@misc{pith2026190804953,
  author       = {Pith},
  title        = {Pith review of: Signal Development for Saturated Ultrafast Sensors with Impact Ionization Gain},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UGZYLVUB}},
  note         = {Machine review of arXiv:1908.04953}
}
read the original abstract

A closed-form approximate expression is presented for the short time-frame development of silicon diode sensor signals in the context of high frame-rate detection of incident X-ray fluxes, in the limit that the X-ray absorption profile generates a longitudinally-uniform distribution of electron-hole pairs in the detector bulk. The expression represents the immediate time development of signals from diode sensors both with (LGAD) and without (PIN) gain, and presents a temporal scale associated with the onset of gain. Principles limiting the detection frame rate in the presence of electronic readout noise are discussed. Making use of an elemental simulation, the relative advantage of LGAD vs. PIN diode sensors is explored as a function of the effective electronic collection time. It is found that for an idealized LGAD sensor with a gain of 30, the gain provided by impact ionization yields an advantage relative to PIN diode sensors for frame rates as high as 10 GHz.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

  1. [1]

    Wang, On the single-photon-counting (SPC) modes of imaging using an XFEL source, JINST 10, C12013 (2015)

    Z. Wang, On the single-photon-counting (SPC) modes of imaging using an XFEL source, JINST 10, C12013 (2015)

    work page 2015

  2. [2]

    C. W. Barnes, The Dynamic Mesoscale Materials Science Capability, Colloquium, Los Alamos National Laboratory, February 14 2019, https://204.121.60.11/science-innovation/science- facilities/dmmsc/_assets/docs/PTColloq%2020190214_public.pdf

    work page 2019

  3. [3]

    Canali, M

    C. Canali, M. Martini, G. Ottaviani and A. A. Quaranta, Measurement of the average energy per electron -hole pair generation in silicon between 5-320oK, IEEE Trans. Nucl. Sci. 19, 9-19 (1972). 7

    work page 1972

  4. [4]

    Cavalleri, G

    G. Cavalleri, G. Fabri, E. Gatti and V. Svelto, On the induced charge in semiconductor detectors, Nucl. Instr. & Meth. 21, 177-8 (1963); https://doi.org/10.1016/0029-554X(63)90106-X

    work page doi:10.1016/0029-554x(63)90106-x 1963

  5. [5]

    Spieler, Semiconductor Detector Systems, Oxford University Press, Oxford, U.K., (2005)

    H. Spieler, Semiconductor Detector Systems, Oxford University Press, Oxford, U.K., (2005)

    work page 2005

  6. [6]

    Jacoboni, C

    C. Jacoboni, C. Canali, G. Ottaviani, and A. A. Quaranta, A review of some charge transport properties of silicon, Solid State Electronics 20, 77-89 (1977)

    work page 1977

  7. [7]

    Robbins et al., Electron and hole impact ionization coefficients in (100) and in (111) Si, Journal of Applied Physics 58, 4614 (1985); https://doi.org/10.1063/1.336229

    V.M. Robbins et al., Electron and hole impact ionization coefficients in (100) and in (111) Si, Journal of Applied Physics 58, 4614 (1985); https://doi.org/10.1063/1.336229

    work page doi:10.1063/1.336229 1985

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.