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# Performance of 1mm<sup>2</sup> Silicon Photomultipliers

- Thursday, 24 April 2008

A silicon photomultiplier (SPM) is a new type of semiconductor detector that has the potential to replace the photo- multiplier tube (PMT) detector in many applications. In common with a PMT detector, the output of an SPM is an easily detectable current pulse for each detected photon and can be used in both photon counting mode and as an analogue (photocurrent) detector. However, the SPM also has a distinct advantage over PMT detectors. The photon-induced current pulse from a PMT varies greatly from photon to photon, due to the statistics of the PMT multiplication process (excess noise). In contrast, the current pulse from an SPM is identical from photon to photon. This gives the SPM a distinct advantage in photon counting applications as it allows the associated electronics to be greatly simplified. Identical pulses also mean that the SPM can resolve the number of photons in weak optical pulses, so-called photon number resolution. This is critical in a number of applications including linear-optics quantum computing.

A silicon photomultiplier is an array of photon counting microcells connected to a common output^{[1, 2, 3]}. Each photon counting microcell consists of a Geiger-mode photodiode connected in series with an integrated quenching element. A Geiger-mode photodiode is a photodiode engineered to operate above the breakdown voltage of the junction

^{4}. Under these conditions, the photodiode is sensitive to single photons and a photo- carrier generated in the depletion region can result in the entire junction breaking down — Geiger breakdown — by avalanche multiplication producing a large pulse of current. Once the photodiode has detected a photon, it must be reset such that it is ready to detect the next photon. Resetting the photodiode after Geiger breakdown is known as quenching and can be achieved by passive elements or active quench circuits. In a silicon photomultiplier, quenching is achieved by an integrated polysilicon series resistor.

Each Geiger-output pulse has a duration of typically 40 — 60ns and contains around a million charge carriers and is usually amplified to a useful level (10 — 100mV) by a simple, fast voltage amplifier. The SPM detector can be used in single photon mode, pulse detection mode, and analogue mode for slowly varying or continuous optical signal above the single photon level.

The main performance parameters of an SPM are its photon detection efficiency (PDE), dynamic range, noise rate, and pulse or gain uniformity.

### Photon Detection Efficiency

The PDE is determined by the detection efficiency of the individual photon counting microcells and the geometrical efficiency, or fill factor, and can be written as

*PDE(λ,V)=η(λ)⋅ε(V)⋅F*

where η(λ) is the quantum efficiency of silicon at a given wavelength, ε(V) is the carrier Geiger avalanched initiation probability and F is the SPM fill factor. The quantum efficiency of silicon is 80+% over much of the visible spectrum while the avalanche initiation probability of an electron can be as high as 70%. The quantum efficiency and avalanche initiation probability make up the detection efficiency of the individual photon counting microcells. The fill factor is the ratio of the total active area of all the microcells and the total area of the SPM. The SPM fill factor is determined by design constraints and the size of the microcells. In the SPM design there is a fundamental trade-off between the microcell size, the fill factor and the total number of microcells for a given area. The total number of microcells and the PDE determine the dynamic range of the SPM.

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