Analyzing the time distribution of external cross-talk for an SiPM-based TOF-PET detector

In the pursuit of developing the fastest time-of-flight positron emission tomography (ToF-PET) detectors, understanding and minimizing noise factors that significantly influence the timing performance of such detectors are vital. Currently, state-of-the-art ToF-PET detectors are silicon photomultiplier (SiPM)-based scintillation detectors, which introduce SiPM-specific noise sources, such as cross-talk. Cross-talk can occur in three scenarios, namely, direct, delayed, and external cross-talk. Although there have been technological developments to address direct and delayed cross-talk, external cross-talk remains challenging to study because it often gets combined with the signal and other noise sources. This work aims to deepen our understanding of external cross-talk by measuring its probability and time distribution across different detector configurations. For this purpose, we conduct dark count measurements with high-frequency electronics and an oscilloscope for readout. We investigate two Broadcom NUV-MT SiPMs, one with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mn>2</mml:mn><mml:mo>×</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> and one with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mn>3.8</mml:mn><mml:mo>×</mml:mo><mml:mn>3.8</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> active area, and couple each to three bismuth germanium oxide (BGO) crystals of different lengths ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m8"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m9"><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m10"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> ) wrapped in Teflon. Additionally, we test the SiPM without coupling, with direct Teflon™ wrapping and coupled with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m11"><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m12"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> crystal without wrapping. Our findings indicate that adding a reflector significantly increases the cross-talk in scintillation detectors. The cross-talk probability increases by a factor of 1.4 to 1.9, with the lower end of this range corresponding to the coupling with the longest crystal ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m13"><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m14"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> ). Our setup successfully resolved the shift in cross-talk arrival time for crystals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m15"><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m16"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> and longer. Additionally, we have found that the minimal delay time for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m17"><mml:mrow><mml:mn>15</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m18"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m19"><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m20"><mml:mrow><mml:mi mathvariant="normal">m</mml:mi><mml:mi mathvariant="normal">m</mml:mi></mml:mrow></mml:math> crystals corresponds to the time taken for passing through the crystal twice and that changes in signal slope only occur after this delay time. This behavior is observed for crystals of any size in a few-photon measurement.