Noise floor, dark count rate and temperature compensation in SiPM front ends

A silicon photomultiplier (SiPM) front end has its noise floor set by dark counts rising exponentially with temperature, correlated noise rising with overvoltage, and amplifier noise driven by large terminal capacitance. This note derives gain and pulse shape from the microcell model, quantifies dark counts versus threshold and temperature, derives gain drift and a compensation error budget, and covers front ends, laser-ranging thresholds in sunlight and characterisation.

Microcell model and overvoltage

Equivalent circuit and pulse shape

An analog SiPM is an array of single-photon avalanche diodes (SPADs), each biased through its own quench resistor R_q; densities run from about 100 to several thousand microcells per mm² [1]. In Klanner's model [2] a cell is a diode capacitance C_d, the quench resistor R_q and a parasitic C_q in parallel with it; when the cell fires, a switch discharges the diode down to the turn-off voltage V_off. The discharge takes well under 1 ns; the cell then recharges through R_q. The pulse has two time constants [2]:

(R_s: readout resistance, N: cell count.) If C_q ≪ C_d the fast component vanishes, as Klanner observes for 25 μm but not 50 μm cells [2]. For a front end with input resistance R_in, the fast part of the voltage is [3]:

Sharing charge with thousands of idle cells, the fast pulse loses amplitude with area but keeps its speed [3]. Including series resistance, the manufacturer note gives τ_R ≈ C_cell·(R_Q + N·R_S), with a 90 %→10 % time of ≈ 2.2·τ_R [4]. With 1070 pF on a 3 mm J-Series part (5676 cells) [5], a 50 Ω sense resistor adds ≈ 54 ns, comparable to the 45 ns cell constant; hence 10 Ω for 6 mm sensors [4] (10 Ω × 4140 pF ≈ 41 ns).

Gain and overvoltage dependences

Integrating the whole pulse gives the gain [2]:

Manufacturer notes write G = C·ΔV/q with the overvoltage ΔV = V_bias − V_BD [1]. Gain is set by V_off, while the I–V curve yields the breakdown voltage V_BD; the gap was ≈ 1 V for a 15 μm cell and shrinks with cell size [2]. Datasheet check:

• S13360-3050CS: 1.7 × 10⁶ at 3 V [6] gives C_cell ≈ 91 fF (Hamamatsu arrives at the same value [8]); 3600 × 91 fF ≈ 327 pF against 320 pF in the datasheet.
• S14160-3050HS: 2.5 × 10⁶ at 2.7 V, 3531 cells [7] gives 148 fF and ≈ 524 pF in total (datasheet: 500 pF).
• MicroFJ-30035: 2.9 × 10⁶ at 2.5 V and 6.3 × 10⁶ at 6 V [5]. The slope gives C ≈ 156 fF and the zero crossing sits ≈ 0.49 V below the datasheet V_BD, so the overvoltage that sets gain is ≈ 3 V. Indicative only (rounded typical values).

Overvoltage moves every noise parameter at once. For the J-Series, going from 2.5 V to 6 V takes photon detection efficiency (PDE) from 38 % to 50 %, dark counts from 50 to 150 kHz/mm², optical crosstalk from 8 % to 25 % and afterpulsing from 0.75 % to 5 % [5]. PDE saturates while noise keeps rising, so the operating point is an application-specific optimum [7]; larger cells trade capacitance, recovery time and dynamic range for fill factor, PDE and gain [1].

Dark count rate: sources, temperature and threshold

Generation mechanisms

Dark counts (dark count rate, DCR) are discharges triggered by thermally generated carriers reaching the high-field region, indistinguishable from photon-triggered ones [1]. Gundacker and Heering model primary dark counts as Shockley–Read–Hall (SRH) generation through band-gap states; near room temperature they change by roughly a factor of two per 10 °C, like silicon dark current [3]. At low temperature the reduction saturates because the high field makes trap-assisted tunnelling dominant, and that term depends strongly on the internal field [3]. A large share of counts comes from a few “screamer” cells that an analog SiPM cannot disable [3].

Temperature dependence

Over −40 to +40 °C at fixed relative overvoltage, Otte et al. measure doubling intervals of T₂ = 5.3 °C (Hamamatsu S13360-3050CS), 5.9 °C (SensL J-Series) and 7.0 °C (FBK NUV-HD) [9]; the manufacturer note, also at constant overvoltage, states 50 % less per 10 °C of cooling [1], which disagrees for the same family. A 20 °C rise means ×13.7 with T₂ = 5.3 °C but ×4 with 10 °C. References: S13360-3050CS at 25 °C, 3 V, 0.5 p.e., 500 kcps typical, 1500 kcps maximum [6]; J-Series at 21 °C, 50 kHz/mm² at 2.5 V [5], i.e. ≈ 0.47 MHz on 3.07 × 3.07 mm². Holding overvoltage constant does not hold DCR constant: compensation fixes gain, not dark counts [1].

The DCR–threshold staircase and correlated noise

Plotting the dark pulse rate against discriminator threshold gives a staircase whose plateaus are the 1, 2 and 3 p.e. rates [1]. The first plateau is the DCR; the ratio of the second to the first is the prompt crosstalk probability [8]. On Hamamatsu's typical curve, raising the threshold by 1 p.e. drops the DCR by about an order of magnitude [8]; onsemi shows dark triggers becoming negligible at ≈ 3 p.e. [1].

In a geometric chain model, where each discharge fires a neighbour with probability p, the number of discharges M per primary obeys P(M = n) = (1 − p)pⁿ⁻¹ and P(M ≥ n) = pⁿ⁻¹, so:

At 8 % crosstalk the 1.5 p.e. step is 12.5 times lower; at 3 %, 33 times. With high DCR and long tails, pile-up inflates the 1.5 p.e. count and overstates crosstalk [8].

The resolution penalty from correlated noise is captured by two quantities [2]: the excess charge factor ECF = ⟨Q⟩/⟨Q_P⟩ and the excess noise factor ENF = (σ_Q/⟨Q⟩)²/(σ_P/⟨Q_P⟩)², where P denotes an ideal Poisson detector. With Poisson primaries and independent multiplicities, the compound Poisson process gives ENF = E[M²]/E[M]². For the geometric model, E[M] = 1/(1 − p) and Var[M] = p/(1 − p)², hence:

Afterpulses and delayed crosstalk add contributions that depend on the integration window, so ECF and ENF depend on the readout and the analysis window [2]. A long recovery reduces visible afterpulsing, and trench-isolated sensors keep ENF near one up to 5 V overvoltage [3].

Breakdown-voltage temperature coefficient and bias compensation

Deriving gain drift

Breakdown voltage rises linearly with temperature: the carrier mean free path shortens and a higher field is needed to sustain the avalanche [3]. Let β = dV_BD/dT. Differentiating (3) at fixed V_bias, with capacitance taken as temperature-independent:

Coefficients: 54 mV/°C for the S13360 (given for the recommended operating voltage) [6], 34 mV/°C for the S14160 [7], 21.5 mV/°C for the J-Series [5]. Gundacker and Heering tie the spread to junction depth: ≈ 20 mV/°C for shallow junctions with ≈ 25 V depletion voltage, ≈ 60 mV/°C for wide ones at ≈ 75 V [3]. From (7): 1.8 %/°C (S13360-3050CS, 3 V), 1.26 %/°C (S14160, 2.7 V), 0.86 %/°C and 0.36 %/°C (J-Series, 2.5 and 6 V). In relative terms [9]: with V_BD shifting ≈ 0.1 %/°C, gain moves 1 %/°C at 10 % relative overvoltage and 0.5 %/°C at 20 %, PDE only 0.2–0.3 %/°C at 90 % breakdown probability. Over wide ranges V_BD(T) is not linear [10].

Open-loop compensation

The common approach is a temperature sensor, a microcontroller and a DAC or programmable high-voltage supply applying V_bias(T) = V_bias(T₀) + β(T − T₀) [4]. Eigen et al. derive the coefficient from the constant-gain condition

using 0.1 V scans in a climate chamber (0.2 °C stability) and a two-dimensional fit, since dividing separately fitted slopes ignores their covariance [11]. With a regulator built around a 2.5 ppm/°C tracking divider and a ≈ 2 ppm/°C reference, gain stayed within ±0.5 % over 20–30 °C for all Hamamatsu and CPTA sensors tested, whereas single-parameter compensation failed for KETEK sensors with long pulses and strong afterpulsing [11].

Closed-loop methods

Closed loop trims bias against a measured gain indicator rather than trusting β and the sensor-to-die offset: the spacing of adjacent peaks in the single-photon spectrum is q·G* [2], measurable with a low-level pulsed LED or with the dark counts themselves. If peaks are not resolved, the method of moments, G* = σ_Q²/(q⟨Q⟩·ECF·ENF), applies; Klanner finds it suited to in-situ calibration and monitoring of many SiPMs, given known ECF, ENF and linear response [2]. Statistics take seconds, so the loop is slow; the practical architecture is open-loop feedforward plus slow closed-loop trim.

Table 1. Gain stability error budget (derived). Sensitivity is 1/V_ov.

A low β does not shrink relative uncertainty: for the J-Series, the method-dependent 18.9–22.0 mV/°C spread [9] dominates. Bias-path series resistance adds a light-dependent error: Hamamatsu's example uses 1 kΩ and 0.1 μF [6], a 0.3 V drop at the ≈ 0.3 mA daylight current derived below. Bias-filter resistors should stay small [4].

Front-end topologies: bandwidth, noise and capacitance

50 Ω / voltage mode

Standard-output current is converted to voltage across R_S and amplified by a 50 Ω RF amplifier; onsemi recommends 50 Ω for 1, 3 and 4 mm parts, 10 Ω for 6 mm, followed by a ≈ 1 GHz, 20 dB low-noise amplifier [4]. Orders of magnitude (derived): at G = 2.9 × 10⁶, Q = 0.46 pC and the slow-component peak current is ≈ Q/τ ≈ 10 μA (τ = 45 ns), ≈ 0.5 mV across 50 Ω. In 100 MHz the 50 Ω thermal noise is ≈ 9 μV and a 1 nV/√Hz amplifier adds ≈ 10 μV, ≈ 0.03 p.e. rms in total. The fast component (2) shrinks with area, but 1 GHz bandwidth is easy [3]; timing jitter σ_t = σ_v/(dv/dt) depends on slope at threshold [3].

Transimpedance amplifier

A transimpedance amplifier (TIA) offers a virtual ground and DC information, but nanofarad source capacitance pushes it to its bandwidth and noise limits. For a Butterworth response (Q = 0.707) [12]:

and, for wideband pulse applications, the equivalent input current noise density is [12]:

The last term grows with capacitance and bandwidth. Example (derived): with C_S = 1 nF and GBP = 1.6 GHz, (9) gives ≈ 16 MHz at R_F = 1 kΩ and ≈ 50 MHz at 100 Ω. (10) assumes post-filtering below the TIA bandwidth [12], so take F = 50 MHz: with e_N = 1 nV/√Hz the last term is ≈ 0.18 nA/√Hz, ≈ 1.3 μA rms integrated, about 0.13 of a 10 μA single-p.e. peak and four times the 50 Ω chain. Gundacker and Heering give the same limit for current mode: a 1 nF sensor into 1 Ω is a first-order ≈ 159 MHz pole [3]. For single-p.e. resolution or fast timing on a large SiPM, a low-impedance current mode or RF voltage amplifier is preferred; an op-amp TIA suits moderate-bandwidth DC current measurement.

Capacitive fast output

onsemi sensors add a third terminal capacitively coupled to every cell, with no net charge or DC information [4]: 40 pF against 1070 pF on a 3 mm J-Series part, 1.5 ns FWHM [5]. Its amplitude scales with fired cells [1]; timing and energy can be read from both outputs simultaneously [4].

Noise floor and threshold in pulsed laser ranging

Solar background rate

For a Lambertian target the radiance is L = ρE_λΔλ/π; the collected power and primary background count rate are (derived):

The ASTM G173-03 AM1.5 global spectrum gives 0.817 W·m⁻²·nm⁻¹ at 905 nm [14]. Take the optics of onsemi's rangefinder model, 15 mm aperture, ±5 nm (10 nm full width) filter and 0.1° full cone angle of view (its demonstrator's 1 mm sensor and 40 mm lens give the stated 1.4°) [13], and assume ρ = 0.5, T_o = 0.8. With A = 1.77 × 10⁻⁴ m² and Ω = π(θ/2)² = 2.39 × 10⁻⁶ sr, P_b ≈ 0.44 nW ≈ 2.0 × 10⁹ photons/s. The example is mixed and indicative only: the ≈ 30 % PDE is the model's “next generation” sensor [13]; gain, cells, crosstalk and DCR are 3 mm J-Series values. Blue-sensitive parts are far weaker at 905 nm (1.8 % for the MicroFC-10020 in the same table) [13], and R_b, I_b scale with PDE. Here R_b ≈ 6 × 10⁸ s⁻¹, ≈ 1300 × the J-Series DCR, and I_b = qG·ECF·R_b ≈ 0.30 mA (p = 0.08). Occupancy R_bτ_r/N ≈ 0.5 % costs little PDE, but the bias drop (Table 1) and self-heating matter; onsemi treats a narrow filter and small field of view as essential [13].

Background fluctuation: a derivation in photoelectron units

Let h(t) be the single-photoelectron response normalised to 1 p.e. peak. With Poisson primaries at rate R_b and geometric multiplicities, Campbell's theorem gives for the baseline (derived):

The variance mirrors Klanner's dark charge-spectrum width [2]. For an exponential response ∫h² = τ_s/2. With the unshaped slow component (τ_s = 45 ns), σ_x ≈ 4.2 p.e.; DC-coupled single-pole 5 ns shaping (pole-zero cancellation) gives σ_x ≈ 1.4 p.e. and a mean offset of ≈ 3.3 p.e. Hamamatsu's 100 pF/51 Ω CR filter for DCR measurement [8] blocks DC, so the mean offset vanishes (AC coupling loses the average current [2]); on the 45 ns pulse it gives ∫h² ≈ 2.3 ns and σ_x ≈ 1.3 p.e. Shaping cuts the fluctuation as √τ_s while a laser pulse shorter than τ_s keeps its peak.

Threshold selection and false alarms

At night (R_b ≈ 0) the floor is set by DCR and crosstalk. At a 1.5 p.e. threshold the false-trigger rate is (derived):

Terms: crosstalk, and pile-up of two dark counts within an effective window τ_w. With DCR = 0.47 MHz, p = 0.08, τ_w = 5 ns: ≈ 38 + 1.1 kHz, ≈ 5 % false alarms per shot in a 200 m gate (1.33 μs); at 2.5 p.e. crosstalk drops to ≈ 3 kHz. In daylight the baseline fluctuates ≈ 1.3–1.4 p.e. rms; with the Poisson tail the threshold must sit several σ above the mean, roughly 5–8 p.e. with AC coupling (plus the ≈ 3.3 p.e. offset if DC-coupled), multiplying the signal needed. An adaptive threshold beats a fixed one; onsemi's multi-shot histogramming targets the same problem [13].

Table 2. Single-shot noise budget in p.e. (3 mm J-Series, 2.5 V; τ_s = 5 ns; derived).

In the dark, DCR adds little variance, yet at 0.5 p.e. every dark count is a false alarm: the threshold comes from the staircase, not the rms noise.

Measurement and characterisation

Infrastructure

I–V and C–V measurements belong on a temperature-controlled chuck in a light-tight, shielded, humidity-controlled box [2]. For ≲ 10 mV precision, 100 mV steps around V_BD are recommended; a typical source meter's ±10 mV setting accuracy and saw-tooth deviation limit it [2]. Temperature scans run in a climate chamber whose stability (e.g. 0.2 °C) dominates the temperature uncertainty [11]. Light comes from a picosecond pulsed laser or pulsed LED; readout is a ≈ 1 GHz amplifier with a counter or digitiser [8]. Dew condensation must be controlled in cold measurements [6].

Breakdown voltage from the I–V curve

onsemi defines V_BD as the voltage intercept of a straight-line fit to √I versus V [5]. Hamamatsu's mass testing uses the log(I)–V inflection V_peak, whose offset from V_BR is type-specific and calibrated once against the gain–voltage line, under DC light to suppress surface leakage [8]. Klanner defines six methods, compares four, finds dark and illuminated results within ±20 mV, and recommends the inverse log-derivative minimum under DC light for 50 mV-level results [2]. Otte et al. show that even the temperature coefficient is method-dependent: 29.9 mV/°C from gain, 28.9 from the I–V derivative and 32.5 from the second derivative for the FBK sensor [9].

Gain from the single-photon spectrum

A charge spectrum is recorded with low-intensity pulsed light; the spacing of adjacent peaks is q·G*. If the integration window is shorter than the pulse, G* = G·f_Q with f_Q ≤ 1 [2], so gains measured with different windows are not comparable. Peak width grows as σ_N² = σ₀² + Nσ₁², with σ₁ driven mainly by cell-to-cell V_off variation [2]. The zero of the gain–voltage line is V_off, not V_BD [2].

DCR–threshold scan

A counter records each threshold (2 s each for the S13360-3050CS, longer for low DCR) [8]. Pile-up from long tails distorts the steps, hence a CR filter after the amplifier [8]. With a digitiser, the fraction f_0.5 of gates of length t_gate exceeding 0.5 p.e. gives:

It is exact only at 0.5 p.e.; the interval (Δt) distribution between consecutive pulses gives a more precise DCR plus afterpulse probability and time constant [2].

References

1. onsemi, “Introduction to the Silicon Photomultiplier (SiPM),” Application Note AND9770/D, Rev. 9, Aug. 2023. https://www.onsemi.com/pub/collateral/and9770-d.pdf
2. R. Klanner, “Characterisation of SiPMs,” Nuclear Instruments and Methods in Physics Research A, vol. 926, pp. 36–56, 2019, doi:10.1016/j.nima.2018.11.083. https://arxiv.org/abs/1809.04346
3. S. Gundacker, A. Heering, “The silicon photomultiplier: fundamentals and applications of a modern solid-state photon detector,” Physics in Medicine & Biology, vol. 65, no. 17, 17TR01, 2020. https://doi.org/10.1088/1361-6560/ab7b2d
4. onsemi, “Biasing and Readout of ON Semiconductor SiPM Sensors,” Application Note AND9782/D, Rev. 3, Apr. 2019. https://www.onsemi.com/pub/Collateral/AND9782-D.PDF
5. onsemi, “J-Series SiPM Sensors,” Data Sheet MICROJ-SERIES/D, Rev. 7, Aug. 2021. https://www.onsemi.com/pub/Collateral/MICROJ-SERIES-D.PDF
6. Hamamatsu Photonics, “MPPC S13360 series,” Datasheet, KAPD1052E07, Jul. 2025. https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/ssd/s13360_series_kapd1052e.pdf
7. Hamamatsu Photonics, “S14160/S14161 series,” Datasheet, KAPD1064E04, Nov. 2024. https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/ssd/s14160_s14161_series_kapd1064e.pdf
8. A. Ghassemi, K. Sato, K. Kobayashi, “Technical guide to silicon photomultipliers (MPPC),” Hamamatsu Photonics, Nov. 2022. https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/ssd/mppc_kapd9005e.pdf
9. A. N. Otte, D. Garcia, T. Nguyen, D. Purushotham, “Characterization of three high efficiency and blue sensitive silicon photomultipliers,” Nuclear Instruments and Methods in Physics Research A, vol. 846, pp. 106–125, 2017, doi:10.1016/j.nima.2016.09.053. https://arxiv.org/abs/1606.05186
10. S. Piatek, “How does temperature affect the performance of an SiPM?,” Hamamatsu Photonics technical note, Jan. 4, 2017. https://hub.hamamatsu.com/us/en/technical-notes/mppc-sipms/how-does-temperature-affect-the-performance-of-an-SiPM.html
11. G. Eigen, J. Cvach, J. Kvasnicka, I. Polak, A. Træet, J. Zalieckas, “Gain stabilization of SiPMs with an adaptive power supply,” Journal of Instrumentation, vol. 14, P05006, 2019, doi:10.1088/1748-0221/14/05/P05006. https://arxiv.org/abs/1902.06261
12. X. Ramus, “Transimpedance Considerations for High-Speed Amplifiers,” Texas Instruments Application Report SBOA122, Nov. 2009. https://www.ti.com/lit/pdf/sboa122
13. onsemi, “SiPMs in Direct ToF Ranging Applications,” White Paper TND6254/D, Rev. 5, Dec. 2024. https://www.onsemi.com/pub/collateral/tnd6254-d.pdf
14. National Laboratory of the Rockies (NLR), “Reference Air Mass 1.5 Spectra (ASTM G173-03).” https://www.nlr.gov/grid/solar-resource/spectra-am1.5