SiPM Model

SiPM model

The model used is extracted from S. Seifert et al, "Simulation of Silicon Photomultiplier Signals", IEEE trans. on nucl. science, vol. 56, no. 6, dec. 2009, p3726-3733.

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The switch is closed by an incoming trigger and opened when the current flowing through it is bellow a given value Iq.

Model parameters

The parameters have been characterized at 20C before irradiation :
Parameter Value
Rq 140e+3
Cg 12.65e-12
Cd 0.131e-12
Cq 0.015e-12
The bias voltage Vbias is 72.9 with a breakdown voltage Vbr 1.2 to 1.3V bellow (71.6V). The gain in these condition is 9*10^5 e/PE (with e = 1.602*10^-19 C, the charge per fired cell is then Qc = 1.44*10^-13 C).

Verilog-a model


`include "constants.vams"
`include "disciplines.vams"

module sipmmodel(p,n,csw,ncsw);
  inout p, n, ncsw;
  inout [0:87] csw;
  electrical p,n, ncsw;
  electrical [0:87] csw;
  electrical [0:87] inode;
  electrical [0:87] inodebr;
  electrical [0:87] inodesw;

  parameter real Cg=12.65e-12 from [0:inf);
  parameter real Cq=15e-15 from [0:inf);
  parameter real Rq=140e3 from [0:inf);
  parameter real Cd=131e-15 from [0:inf);
  
  parameter real Rd=1e3 from [0:inf);
  parameter real Vbr=71.6 from [0:inf);
  parameter real Iq=7.5e-6 from [0:inf);

  parameter real Vthre = 0.5 from [0:inf);

  genvar i;

  analog begin
    // Capacite parasite
    I(p,n) <+ ddt(Cg*V(p,n));

    // Cellule SiPM
    for(i=0;i<88;i=i+1)
    begin
      I(p,inode[i]) <+ ddt(Cq*V(p,inode[i]));
      I(p,inode[i]) <+ V(p,inode[i])/Rq;

      I(inode[i],n) <+ ddt(Cd*V(inode[i],n));
      if (V(csw[i],ncsw) > Vthre)
        V(inode[i], inodesw[i]) <+ 0.0;
      else
        if (I(inode[i], inodesw[i]) > Iq)
          V(inode[i], inodesw[i]) <+ 0.0;
        else
          I(inode[i], inodesw[i]) <+ 0;
      V(inodesw[i],inodebr[i]) <+ Vbr;
      I(inodebr[i],n) <+ V(inodebr[i],n)/Rq;
    end
  end
endmodule
Note 1 : The value for Iq has to be refined

Note 2 : n has to be put at Vbias, ncsw at gnd

Note 3 : p is the SiPM output

Note 4 : csw allow to choose which cell is fired (active when V(csw) > 0.5V)

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