[Paper Review] Study of the internal mechanisms of Pixelized Photon Detectors operated in Geiger-mode

H. Otono, H. Oide+5 more|ArXiv.org|Aug 19, 2008

Advanced Optical Sensing Technologies17 references3 citations

TL;DR

This paper proposes a new dynamic model for Pixelized Photon Detectors (PPDs) operating in Geiger-mode that explicitly incorporates the transient avalanche multiplication and quenching processes. By solving coupled circuit equations involving diode capacitance $C_d$, quenching resistor $R_q$, and parasitic capacitance $C_q$, the model successfully reproduces experimentally observed waveforms—particularly the sharp spike component at low temperatures—matching measured data at 77K, 200K, and 300K with calibrated parameters only from 77K data.

ABSTRACT

In the 1990s, a novel semiconductor photon-sensor operated in Geiger-mode was invented in Russia (Silicon PhotoMultiplier), which consists of many tiny pixels and has a single photon level sensitivity. Since then, various types of the sensor with this scheme, Pixelized Photon Detectors (PPD), have been developed in many places in the world. For instance, Hamamatsu Photonics K.K. in Japan produces the PPD as a Multi-Pixel Photon Counter. While the internal mechanisms of the PPD have been intensively studied in recent years, the existing models do not succeeded to fully reproduce the output characteristic, such as waveforms at low temperature. We have developed a new model with the transient multiplication and quenching of the realistic avalanche process and have succeeded in reproducing the output waveform of the PPD at various temperature. In this paper, we discuss our improved model.

Motivation & Objective

• To address the limitations of existing PPD models in explaining the sharp spike component observed in output waveforms at low temperatures.
• To develop a physically accurate model that captures the transient behavior of avalanche multiplication and quenching in Geiger-mode PPDs.
• To reproduce the experimentally observed output waveforms across multiple temperatures (77K, 200K, 300K) using a single set of calibrated parameters.
• To validate the model’s consistency with the linear $G$–$\Delta V$ relationship observed in real PPDs.

Proposed method

• Formulate a dynamic circuit model with three key components: diode capacitance $C_d$, quenching resistor $R_q$, and parasitic capacitance $C_q$ between the diode and $R_q$.
• Derive and solve two coupled differential equations: one for diode voltage $V_d(t)$ and one for charge $q(t)$ on $C_q$, based on Kirchhoff’s laws and the current through $R_q$.
• Use the amplifier’s gain $A$ and input impedance $Z_{\text{input}}$ to scale the output current into measurable voltage, accounting for system bandwidth effects.
• Calibrate $C_d$ and $C_q$ using the spike pulse height at 77K, where the effect of $C_q$ is most sensitive, and apply the same values to all temperatures.
• Account for signal distortion due to the measurement system’s bandwidth (1.4 GHz for the Suhner QLA connector), which shapes the rise and fall times of the spike.
• Validate the model by comparing simulated waveforms with measured data across 77K, 200K, and 300K, using measured $R_q$ values at each temperature.

Experimental results

Research questions

• RQ1 Why does the traditional PPD model fail to reproduce the sharp spike component observed in PPD waveforms at low temperatures?
• RQ2 How do the transient dynamics of avalanche multiplication and quenching contribute to the formation of the spike component in PPD output waveforms?
• RQ3 Can a physically consistent model incorporating $C_q$, $C_d$, and $R_q$ reproduce the measured waveforms across multiple temperatures with a single calibration?
• RQ4 Does the proposed model preserve the experimentally observed linear relationship between gain $G$ and overvoltage $\Delta V$?
• RQ5 What is the role of the system bandwidth in shaping the leading and trailing edges of the spike component?

Key findings

• The proposed model successfully reproduces the sharp spike component in PPD output waveforms at 77K, which the traditional model fails to explain.
• The spike component’s amplitude and timing are primarily determined by the parasitic capacitance $C_q$, calibrated to 2 fF from the 77K waveform.
• The diode capacitance $C_d$ is determined to be 20.2 fF from the recovery time constant $R_q C_d$ at 77K.
• The model reproduces waveforms at 200K and 300K using the same $C_d$ and $C_q$ values calibrated at 77K, with only $R_q$ adjusted to measured values.
• The model predicts a linear $G$–$\Delta V$ relationship consistent with experimental data, confirming its physical consistency.
• The bandwidth of the measurement system (1.4 GHz) is found to govern the rise and fall times of the spike component, matching observed distortion.