Operating principles | **Main characteristics** | Modules & implementation | Tradeoffs & considerations | Product comparison

### Active Area

Active area is the light sensitive area of the device. For a single channel, it is the light sensitive area. You can tile and adjust your active area from 1mm to 25mm.

### PDE

Photon detection efficiency of the active area is a probability that a silicon photomultiplier (SiPM) produces an output signal in response to an incident photon. It is driven by the characteristics of the SiPM, namely, its geometrical fill factor, quantum efficiency, and probability of Geiger discharge. It is a function of overvoltage, ΔV, and wavelength, λ.

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*Figure 2: PDE comparison*

### Linearity and Microcell Sizes

Linearity is the relationship between the number of microcells experiencing Geiger discharge, Nfired, and the number of photons, Nphoton, in an infinitesimally short pulse (δ‐illumination) impinging on the device with Ntotal microcells. The equation shows that for PDE*Nphoton << Ntotal, the relationship is linear; otherwise, Nfired asymptomatically approaches Ntotal as PDE*Nphoton approaches infinity. Ntotal, or the total number of microcells available to fire, therefore directly relates to your linearity. Ntotal is a function of microcell pitch total channel active area. You can increase linearity by increasing active area size (while keeping microcell size the same) or reducing the microcell size (while keeping active area the same). Linearity is typically a tradeoff with PDE and other parameters.

*Equation 1: Linearity*

*Figure 3: Dynamic range corresponds with total number of microcells*

### Gain

It is the number of electron-hole pairs produced in a discharge (avalanche) of a single microcell and is designated as mu (μ). The relationship μ = (ΔVCJ)/e shows that μ depends linearly on overvoltage, ΔV, and junction capacitance, Cj. The variation in the gain mechanism is what contributes to the excess noise figure described below. Gain is a function of overvoltage, temperature, and microcell size.

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*Figure 4: Gain vs. overvoltage*

### Speed and Time Resolution

The pulse shape of the MPPC output is dependent on the design of the MPPC. The rise time will be driven by the series resistance, which is a function of active area size and package, and the junction capacitance, which is determined by the microcell size. The fall time is driven by the microcell recovery time. The microcell recovery time is a function of the quenching resistor, which is designed in the manufacturing process, and the junction capacitance, Cj.

Time resolution is often determined by jitter or time transit spread. Jitter is the measure of the spread in transit times. Transit time is the time elapsed between the instant a photon (or δ‐like illumination) strikes a SiPM and the instant that the output signal reaches a maximum value. Transit time depends on overvoltage and design architecture. A histogram of single-photon transit times has a Gaussian distribution. Jitter can be reported as the full-width at half maximum (FWHM) of the distribution or as the standard deviation of the distribution.

### Noise

There are four basic noise sources in MPPCs; thermally generated (dark), afterpulse, crosstalk and excess noise figure. The values are dependent on the design of the MPPC, active area, temperature, microcell size and overvoltage. **Thermally generated noise** is the rate of discharges triggered by thermally generated charge carriers in and outside of the avalanche region. The value of depends on overvoltage and temperature. **Afterpulse** is when a microcell recovering from Geiger discharge retriggers before completing the recovery. The most likely cause of afterpulsing is the release of trapped charge in the avalanche region of the recovering microcell and is therefore a result of the wafer material and process. The probability of afterpulsing also depends on overvoltage and temperature.**Crosstalk** is caused when an avalanche emits photons capable of triggering nearly simultaneous discharges in neighboring microcells. Crosstalk is a function of overvoltage and microcell size.**Excess noise figure** is the quantity which expresses the noise introduced by the multiplication process, or gain. There are several sources contributing to F in a SiPM: microcell-to-microcell gain variations, the stochastic nature of the gain, the occurrence of crosstalk, and of afterpulsing. F increases with overvoltage due to increasing probability of crosstalk and afterpulsing. In addition, F is likely to be a function of the incident light power because the occurrence of crosstalk and afterpulsing is correlated to the photon flux. The excess noise figure for SiPMs is around 1.1.

*Figure 5: Afterpulses*