Improved SPICE electrical model of silicon photomultipliers D. Marano a,n , G. Bonanno a , M. Belluso a , S. Billotta a , A. Grillo a , S. Garozzo a , G. Romeo a , O. Catalano b , G. La Rosa b , G. Sottile b , D. Impiombato b , S. Giarrusso b a INAF, Osservatorio Astrofisico di Catania, Via S. Sofia 78, I-95123 Catania, Italy b INAF, Istituto di Astrofisica Spaziale e Fisica Cosmica di Palermo, Via U. La Malfa 153, I-90146 Palermo, Italy article info Article history: Received 22 February 2013 Received in revised form 8 May 2013 Accepted 22 May 2013 Available online 29 May 2013 Keywords: Electrical models Equivalent circuits Output pulses Silicon photomultipliers Transient waveforms abstract The present work introduces an improved SPICE equivalent electrical model of silicon photomultiplier (SiPM) detectors, in order to simulate and predict their transient response to avalanche triggering events. In particular, the developed circuit model provides a careful investigation of the magnitude and timing of the read-out signals and can therefore be exploited to perform reliable circuit-level simulations. The adopted modeling approach is strictly related to the physics of each basic microcell constituting the SiPM device, and allows the avalanche timing as well as the photodiode current and voltage to be accurately simulated. Predictive capabilities of the proposed model are demonstrated by means of experimental measurements on a real SiPM detector. Simulated and measured pulses are found to be in good agreement with the expected results. & 2013 Elsevier B.V. All rights reserved. 1. Introduction Silicon photomultipliers (SiPMs), also referred to as multi-pixel photon counters (MPPCs), are a contemporary rapidly developing class of solid-state detectors which have been gaining great interest and extensive diffusion in the fields of high-energy physics, nuclear medicine, and astrophysics. SiPM photo-sensors consist of a parallel array of photodiodes (SPADs), connected in parallel and operating above their break- down voltage. When an optical photon strikes one of the basic microcells, the related photodiode undergoes a Geiger avalanche and the released charge is collected onto a common electrode. The series quenching resistance integrated in each pixel slows the avalanche current by reducing the voltage drop across the diode terminals. When the current is quenched, the cell begins to recharge, recovering its preceding quiescent bias conditions. The peak amplitude of the SiPM output generated signal is directly proportional to the total number of microcells which is struck by optical photons [1–6]. The availability of an accurate electrical model can enrich understanding of the design and behaviour of the SiPM detector as a signal source, allowing a reliable interpretation of its static and dynamic characteristics and its physical interactions with the coupled front-end electronics. This work develops a new truthful SPICE electrical model of the SiPM sensors based on the peculiar physical features of each SPAD microcell composing the detector structure. Compared to pre- viously reported models, the proposed circuit configuration pro- vides a more accurate representation of the trigger generation processes underlying the transient response of the optical device to an incoming avalanche event. In Section 2 the novel SiPM electrical model is addressed. Simulation results are discussed in Section 3. Experimental valida- tion of the proposed model is performed in Section 4. Finally, Section 5 summarizes the paper conclusions. 2. Proposed electrical model The circuit electrical model which is typically associated to the single elementary SPAD microcell is illustrated in Fig. 1 [1–4]. The avalanche photodiode is modeled as a parallel connection between the internal resistance of the diode space-charge region R d , and the junction capacitance of the inner depletion layer C d . The integrated quenching resistance R q is associated with its parallel stray capacitance C q , and an additional parasitic capaci- tance C m across the microcell terminals is also introduced to account for metal lines and bonding pads. The above electrical model is easily extendable to the case when more than one microcell is fired by an avalanche event by connecting in parallel multiple SPAD elements. Avalanche triggering is modeled by means of an ideal DC voltage supply V BD with a series voltage-controlled switch S 0 . Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods in Physics Research A 0168-9002/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nima.2013.05.127 n Corresponding author. Tel.: +39 0957332213. E-mail address: davide.marano@oact.inaf.it (D. Marano). Nuclear Instruments and Methods in Physics Research A 726 (2013) 1–7