Photon Detection Efficiency Calculator (SiPM)

PDE is the probability that an incident photon at a given wavelength and overvoltage is actually recorded as a count. PDE = QE times FF times Ptrig, where QE is quantum efficiency (photon-to-electron conversion probability), FF is the geometric fill factor (fraction of chip area that is active silicon), and Ptrig is the avalanche trigger probability at the operating overvoltage. Typical SiPMs achieve PDE of 15 to 55 percent depending on wavelength and bias.

A SiPM is a solid-state photodetector consisting of thousands of single-photon avalanche diode (SPAD) microcells connected in parallel on a silicon chip, all reverse-biased above breakdown. When a photon triggers an avalanche in one cell, that cell produces a fixed charge pulse (gain = 10 to the sixth). The SiPM output is the sum of all firing cells. SiPMs are used in PET scanners, time-of-flight LiDAR, gamma cameras, dark matter detectors, and quantum optics experiments.

Fill factor is the ratio of the active avalanche area (the depleted region that can trigger a count) to the total chip area including guard rings, interconnects, and quenching resistors. A fill factor of 50 percent means only half of incident photons even reach active silicon. Increasing microcell size improves fill factor but reduces time resolution and increases cell capacitance. Modern SiPMs achieve fill factors of 60 to 80 percent.

DCR is the average rate of avalanche events that occur without any incident photon, caused by thermal generation and band-to-band tunneling of electron-hole pairs in the depleted region. DCR is expressed in kilohertz or megahertz per square millimetre and increases with temperature (doubles roughly every 8 to 10 degrees Celsius) and with overvoltage. A typical 1 mm squared SiPM at 25 C and moderate overvoltage has DCR of 50 to 500 kHz.

For Poisson-distributed photon counts in an integration window t: signal counts = PDE times Phi times t, dark counts = DCR times t, and SNR = signal counts divided by square root of (signal counts plus dark counts). For PDE = 30 percent, incident rate 10 MHz, DCR = 100 kHz, window = 1 us: signal = 3 counts, dark = 0.1 counts, SNR = 3 / sqrt(3.1) = 1.70. Longer windows improve SNR but blur time resolution.

Overvoltage (Vov) is the bias voltage above the breakdown voltage Vbr: Vov = Vbias minus Vbr. Increasing Vov raises the electric field in the depletion region, increasing both the avalanche trigger probability (and thus PDE) and the gain (Q = C times Vov per discharge). However, higher Vov also increases DCR, optical cross-talk, and after-pulsing probability. The optimal operating point balances PDE improvement against noise increase, typically at Vov = 1 to 5 V above Vbr.

Both detect single photons, but a SiPM is a solid-state device (compact, rugged, insensitive to magnetic fields, low voltage at 25 to 70 V) while a PMT uses vacuum tube multiplication (fragile, affected by magnetic fields, requires kilovolt bias). SiPMs have PDE comparable to or better than PMTs at visible wavelengths and are now the preferred choice in most applications including PET scanners. PMTs still win on timing resolution and ultra-low DCR in large-area formats.

When a microcell avalanche fires, it emits a few secondary photons (Luminescence). If a neighbouring cell absorbs one of these photons, it too fires in the same clock cycle, creating a false coincident count. Cross-talk probability is typically 1 to 15 percent and increases with fill factor and overvoltage. Cross-talk produces an excess count multiplier, slightly overstating the detected photon number. Trenched-isolation SiPMs reduce cross-talk below 1 to 3 percent.

Breakdown voltage increases by about 20 to 50 mV per degree Celsius. A fixed bias therefore decreases effective overvoltage as temperature rises, reducing PDE and gain. DCR doubles roughly every 8 to 10 C. To maintain stable performance, either temperature-compensate the bias supply (track Vbr vs temperature) or actively temperature-stabilise the detector. Many PET and LIDAR systems include thermal compensation circuits.

Most silicon-based SiPMs peak at 400 to 500 nm (blue-green) where silicon absorption depth matches the depletion region depth. QE at 420 nm can reach 50 to 70 percent. At 800 nm (near-infrared) QE drops to 10 to 20 percent because photons penetrate deeper than the depletion region. Manufacturers optimise the depletion depth for specific applications: shallow junctions for blue-optimised PET detectors, deeper junctions for LIDAR at 905 nm.

After-pulsing occurs when carriers trapped in crystal defects during an avalanche are released after the cell has recharged, triggering a second avalanche. After-pulsing probability is typically 0.5 to 5 percent and increases with overvoltage. It creates correlated background counts that appear with a characteristic delay (10 to 100 ns) after a real event. In high-rate environments, after-pulsing inflates count rates and affects dead-time calculations.

Match the peak PDE wavelength to your scintillator or light source emission spectrum. Choose microcell density (cells per mm squared) to ensure less than 5 percent microcell saturation at your maximum expected photon burst size. Verify DCR is low enough to maintain the SNR required during your integration window. For timing applications, select SiPMs with single-photon time resolution (SPTR) below your required timing jitter, typically 100 to 300 ps FWHM for fast SiPMs.

Most commercial SiPMs achieve PDE of 15 to 55 percent at their peak wavelength (typically 400 to 500 nm) at recommended overvoltage. Examples: Hamamatsu S13360 series reaches 40 percent at 450 nm; SensL J-series reaches 41 percent at 420 nm; Broadcom AFBR-S4N44P044M reaches 50 percent at 500 nm. PDE drops to 10 to 30 percent at 650 nm and 5 to 15 percent at 800 nm. Always read the PDE versus wavelength curve at your specific operating overvoltage.