# Glossary of silicon photomultipliers (SiPM) terms

This glossary defines the key technical terms used in describing aspects of silicon photomultipliers (SiPM).

**Glossary of silicon photomultiplier (SiPM) terms**

**A silicon photomultiplier (SiPM) is a relatively new (developed in 1990) photonic device with unique features and characteristics. This page has an alphabetized glossary of the key technical terms used in describing all aspects of SiPMs**

By Slawomir Piatek, Hamamatsu Corporation & New Jersey Institute of Technology

*Note: Silicon photomultipliers (as they are commonly known) are manufactured by Hamamatsu under the brand name of Multi-Pixel Photon Counter.*

**Afterpulsing probability (P _{ap}):** A microcell recovering from Geiger discharge may retrigger before completing the recovery—this is afterpulsing. The most likely cause of afterpulsing is the release of trapped charge in the avalanche region of the recovering microcell. The probability of afterpulsing, P

_{ap}, also depends on overvoltage and temperature.

**Avalanche:** A process occurring in a high-field (electric) section of the depletion region by which energized electrons and holes can impact-ionize silicon atoms leading to multiplication of unbound charge.

**Avalanche photodiode:** This is a type of photodiode that operates near the breakdown voltage on the I-V characteristic. A single microcell of a SiPM consists of a series combination of an avalanche photodiode and quenching resistor.

**Bias voltage (V _{BIAS}):** The reverse voltage applied across the terminals of a SiPM. If this voltage is larger than the breakdown voltage, the SiPM operates in Geiger mode. The value of V

_{BIAS}determines the overvoltage.

**Breakdown voltage (V _{BD}):** A reverse voltage that divides the operation of an avalanche photodiode between the linear mode (the reverse bias voltage is less than the breakdown voltage) and Geiger mode (the reverse bias voltage is larger than the breakdown voltage). The operation of a SiPM requires Geiger mode, so the device is always biased above its breakdown voltage.

**Charge carrier:** Either electron or a hole. In a semiconductor device, a current can be due to motion of electrons, holes, or a combination of both.

**Crosstalk probability (P _{CT}):** A discharge in a microcell emits photons capable of triggering nearly simultaneous discharges in neighboring microcells; this is known as optical crosstalk. The probability of crosstalk P

_{CT}rapidly increases with overvoltage, which imposes a realistic limit on overvoltage and, consequently, on the gain.

**Dark rate (υ _{d}):** This is a rate of discharges triggered by thermally generated charge carriers in and outside of the avalanche region. The value of υ

_{d}depends on overvoltage and temperature.

**Depletion region:** Joining a p-type semiconductor and an n-type semiconductor results in the formation of a PN junction. The depletion region is the region straddling the physical boundary (known as the metallurgical boundary), which is characterized by negligible concentrations of charge carriers—electrons and holes. A built-in electric field exists in the depletion region, pointing from the n to the p side. The field is due to immobile space charge, positive on the n side and negative on the p side. The space charge is due to ionized dopant atoms.

**Dynamic range:** It expresses a relationship between the number of microcells experiencing Geiger discharge, N_{fired}, and the number of photons, N_{γ}, in an infinitesimally short pulse (δ-illumination) impinging on the device with N_{tot} microcells. This relationship is

where ξ is the photon detection efficiency. The equation shows that for ξ ⋅ N_{γ} ≪ N_{tot} the relationship is linear; otherwise, N_{fired} asymptotically approaches N_{tot} as ξ ⋅ N_{γ} → ∞. N_{tot} is therefore the key parameter that determines the dynamic range of a SiPM.

**Electron:** A fundamental particle, a constituent of matter, and carrier of a negative electric charge equal to -1.6 x 10^{-19} C. Unbound and mobile electrons give rise to electrical currents.

**Excess noise figure (F):** This quantity 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.

**Fill factor (f):** The ratio of the light-sensitive area of a microcell and the total area of a microcell is known as fill factor.

**Forward bias:** A SiPM is a two-pronged device with one terminal called "anode" and the other "cathode." If the electric potential on the cathode is lower than that on the anode, the SiPM is said to be forward biased.

**Gain (μ):** It is the number of electron-hole pairs produced in a discharge (avalanche) of a single microcell. The relationship μ = (ΔVC_{J})/e shows that μ depends linearly on overvoltage ΔV and junction capacitance C_{J}.

**Geiger mode:** When the bias voltage on an avalanche photodiode exceeds the breakdown voltage, the avalanche photodiode is said to operate in this mode. The avalanche is self-sustaining and the theoretical gain is infinity. The avalanche photodiodes in a SiPM operate in Geiger mode.

**Hole:** A pseudo-particle (the absence of a bound electron) that has a positive electrical charge of 1.6 x 10^{-19} C. Holes can be mobile and, thus, responsible for electrical currents. The concept of "hole" is especially useful in semiconductor devices.

**Jitter (σ _{t}):** This quantity is a measure of the spread in transit times. A histogram of, for example, 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.

**Junction capacitance (C _{J}):** This is the capacitance of the avalanche photodiode's depletion region. It depends on the cross-sectional area of a microcell and on the applied reverse voltage. For a fully depleted junction, C

_{J}is on the order of ~100 fF.

**Microcell:** The smallest light-sensitive unit of a SiPM. A microcell consists of an avalanche photodiode in series with a quenching resistor. All of the microcells in a SiPM are connected in parallel.

**One photoelectron waveform (1 p.e.):** An output current pulse in response to a discharge in a single microcell is known as 1 p.e. waveform. If two distinct microcells discharge at the same time, the resulting waveform would be 2 p.e., and so on for three, four, etc.

**Overvoltage (ΔV):** The difference between the bias voltage (V_{BIAS}) and the breakdown voltage (V_{BD}) is referred to as overvoltage. If ΔV > 0, the avalanche photodiodes in a SiPM are in Geiger mode. Overvoltage is the key adjustable parameter affecting the operation and performance of a SiPM.

**Photon detection efficiency (ξ):** It is the probability that a SiPM produces an output signal in response to incident photon. It is a product of quantum efficiency η(λ), Geiger discharge probability P_{G}, and geometrical fill factor ƒ; namely ξ = η(λ)P_{G}ƒ. Photon detection efficiency is a function of wavelength and overvoltage.

**Pixel:** The same as microcell. The term "microcell" is preferable because the term "pixel" may imply that a SiPM is an imaging device—but it is not.

**Pixel pitch:** Center-to-center distance between two adjacent microcells. If the microcells are square and there is no dead space between them, the pitch also gives the size of a microcell. Thus, a 25 μm pitch means that a microcell has an area of 25 μm x 25 μm.

**PN junction:** When a p-type semiconductor makes a physical contact with an n-type semiconductor, the resulting junction is called the PN junction. The actual physical boundary between the two semiconductors is called the metallurgical boundary. The PN junction is the key structure in the operation of many semiconductor devices, including SiPMs.

**Quenching resistance (R _{Q}):** Each microcell is a series combination of an avalanche photodiode (APD) and R

_{Q}. The role of the resistor is to restore the voltage on the APD back to V

_{BIAS}after the microcell experienced a discharge (avalanche). The value of R

_{Q}can be determined from the slope of the linear part of the forward-bias I-V characteristic obtained under dark conditions. It is typically on the order of 100-300 kΩ.

**Recovery time (τ _{r}):** A microcell that has experienced a Geiger discharge recovers back so that the bias voltage on the avalanche photodiode is again V

_{BIAS}. This recovery has a characteristic time τ

_{r}, which is approximately equal to R

_{Q}C

_{J}. For typical values of R

_{Q}(~150 kΩ) and C

_{J}(~100 fF), τ

_{r}is ~ 15 ns.

**Reverse voltage:** A SiPM is a two-pronged device with one terminal called "anode" and the other "cathode." If the electric potential on the cathode is higher than that on the anode, the SiPM is said to be reverse biased.

**Transit time (τ):** 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.