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In this paper, we present an improved circuit model for single-photon avalanche diodes without any convergence problems. The device simulation is based on Orcad PSpice and all the employed components are available in the standard library of the software. In particular, an intuitionistic and simple voltage-controlled current source is adopted to characterize the static behavior, which can better represent the voltage-current relationship than traditional model and reduce computational complexity of simulation. The derived can implement the self-sustaining, self-quenching and the recovery processes of the SPAD. And the simulation shows a reasonable result that the model can well emulate the avalanche process of SPAD.

Weak signal detection has been well developed over the past several decades [

A traditional way to build model is using simple circuit to express SPAD behaviors. A basic SPAD model is proposed in [

In this paper, an enhanced SPAD model is proposed with Orcad PSpice. A voltage controlled current source (VCCS) is used to replace the piecewise linear voltage generator in [

In this paper, we present an improved SPAD model based on the traditional models implemented in [_{SPAD}, replaced the piecewise linear voltage generator in [_{AC}, two stray capacitances C_{CS} and C_{AS}, two voltage-controlled switches S_{1} and S_{TRIG}, a current-controlled switch S_{SELF}, two resistances R_{1} and R_{2}, three external interfaces “Cathode”, “Anode” and “Photon”, and one internal port “Sub”. All these component are from the standard library of Orcad PSpice and can be easily used by designers. The core parts of the SPAD model are I_{SPAD} and capacitances, the former mimics the static behavior while the latter emulates the dynamic behavior. Among them, junction capacitance controls the quenching and recovery time, while stray capacitances affect the signal extraction. Moreover, the switch S_{1}guarantees that the avalanche process can only be triggered in Geiger model, avoiding incident photon. With the S_{TRIG} and S_{SELF}, the model can implement avalanche processes.

As shown in _{B} is about 21.54 V [

the static I - V behavior, however, since the curve is not continuously differentiable function, the convergence problems will cause terrible consequences. There- fore, this paper presents a new means to rebuild the character, through making polynomial fitting of the measurement points and encoding the parameters into a VCCS to characterize the static I - V relationship. It has the following advantages: 1) The fitting curve is a continuous differentiable function that will avoid the convergence problems in simulation. 2) VCCS is an intuitionistic representation of I-V relationship than voltage generator. 3) The codes input to I_{SPAD} are very simple which have no complicated judgment statement as show in Equation (1)

Among them, “b_{n}” is nth order of the voltage I_{SPAD} (n = 1, 2, 3…); “a_{0}” is the constant term, and “a_{n}” are the coefficients of corresponding terms (n = 1, 2, 3…). The coefficients are calculated in MATLAB, from which also reducing the computational complexity. The PSpice properties of I_{SPAD} is shown in

The model is operated with PQC, which supply voltage V_{A} is beyond SPAD breakdown voltage V_{B}. Initially, the SPAD is reverse biased at V_{A}, the voltage-controlled switch S_{TRIG} and the current-controlled switch S_{SELF} is open, and

Property | Value |
---|---|

PSpice Template | G^@REFDES % + % − VALUE = {@Func} |

Func | @a_{0} + @a_{1} * @b_{1} + @a_{2} * @b_{2} |

b_{1} | V(%+, %−) |

b_{2} | @b_{1} * V(%+, %−) |

a_{0} − a_{n} | Input by the designer |

there is no current flow through the diode model. A short pulse source simulates single photon to trigger the “Photon” input port. Once triggered, the switch S_{TRIG} gets close due to the voltage division of R_{1} and R_{2}. Then, the current sharply rises to macroscopic level, which beyond the threshold level of S_{SELF} and makes it closed. With the suppression of QPC, the current will drop slowly but not be cut off unless it is lower than threshold, even S_{TRIG} is opened. When the current is lower than the threshold, the S_{SELF} opens. With the charging of capacitances the model returns back to the initial state, waiting for the next photon trigger.

In the simulation, this paper uses the I - V characteristics of a Si SPAD reported in [_{L} in PQC is 100 kΩ and the signal extracting resistance R_{S} is 50 Ω.

_{S} as a function of the time when excess voltage V_{ex}(V_{ex}=V_{A} − V_{B}) increases from 3 V to 5 V. As shown in figure, the avalanche voltage increases as the Vex increases. The phenomenon of avalanche signal is as we expected, a burst rise is generated in the first place, then it drops gradually until the current is lower than threshold. It significantly simulates the self-sustaining and self-quenching process.

We proposed a SPAD model based on Orcad PSpice and all the components are available in the standard PSpice library. A voltage-controlled current source is adopted, which can overcome the convergence problems, intuitionistic represent the I-V relationship, and decrease the amount of code to reduce the computational complexity. Cooperated with the PQC, the model can certainly simulate

static and dynamic behaviors, including self-sustaining, self-quenching and recovery process.

Tian, Y.C., Tu, J.J. and Zhao, Y.L. (2017) A PSpice Circuit Model for Single-Photon Avalanche Diodes. Optics and Photonics Journal, 7, 1-6. https://doi.org/10.4236/opj.2017.78B001