Resultado de las Encuestas a los Socios de la Asociación de Mujeres “Las

The crosstalk probability for the MPPC has been measured by A. Vacheret at Imperial College London by using a pulsed laser which can be focused onto a single MPPC pixel. Since only one pixel is illuminated by the laser, any peaks larger than a single avalanche can be attributed to crosstalk with neighbouring pixels. These events can be differentiated from afterpulses, where several peaks are visible rather than a single large peak.

The probabilities for an avalanche to induce 1, 2 and 3 crosstalks, as well as the inclusive CT probability, have been measured. This was done for a pixel in the centre of the device (“normal” pixel), one on the edge, and one in the

corner. Because the pixels have different numbers of neighbours, the data put fairly detailed constraints on any crosstalk model for the device.

Implementation of a crosstalk model in the simulation is a compromise between achieving good agreement with the data, consistency with the underlying physics believed to be taking place, and computational efficiency. In principle, crosstalk photons may be rescattered between pixels before causing an avalanche, and the probability of getting crosstalk will depend on the position of the initial avalanche within the primary pixel (this is supported by data taken at Imperial by scanning the laser across the pixel faces). Including a detailed microscopic model would be computationally prohibitive, however, and is not required to achieve good agreement with the data. We instead considered a model where the probability of generating a crosstalk photon from a primary avalanche is a quadratic function of the device overvoltage. The pixel fired by this photon is determined by assuming a finite range R for the crosstalk photon, and choosing the secondary pixel using a probability distribution e−r/R_{, where r is the distance from the centre of the} primary pixel to the centre of the candidate pixel. This model accounts for the lower crosstalk probability for pixels near the device edge, by allowing the photon to be lost by scattering into “pixels” off the edge of the device.

The quadratic parameters for the crosstalk probability in the model were derived by fitting the inclusive crosstalk probability for a normal pixel, giving

PCT(Vo) = 0.0356Vo+ 0.0598Vo2, (3.14)

forVo in volts. A toy MC was then used to calculate the CT probabilities for the

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Inclusive CT Probability 0 0.05 0.1 0.15 0.2 0.25 0.3 Data Model Normal pixel Normal pixel Edge pixel Edge pixel Corner pixel Corner pixel

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Single CT Probability 0 0.05 0.1 0.15 0.2 0.25 0.3 Data Model

Normal pixel Normal pixel

Edge pixel Edge pixel

Corner pixel Corner pixel

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Double CT Probability 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Data Model

Normal pixel Normal pixel

Edge pixel Edge pixel

Corner pixel Corner pixel

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Triple CT Probability 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Data Model

Normal pixel Normal pixel

Edge pixel Edge pixel

Corner pixel Corner pixel

Figure 3.6: Inclusive, single, double and triple crosstalk probabilities (differentiated on plot axes), as a function of voltage for normal, edge and corner pixels. Results are from the Imperial test stand. The simulation results are also shown.

of 0.4 times the pixel pitch was found to best match the data — this value was chosen by eye since no error information was available to allow fitting the data. The results for this range value are shown in Figure 3.6. There is a plateau in the crosstalk probabilities for the corner pixel which is not matched by the simulation — this is not completely understood, but for empirical purposes it is not very important, since these pixels form a very small subset of all pixels in the device.

Another model has also been considered, where the number of crosstalk photons produced is decided using a Poisson distribution, rather than generating only one photon with a given probability. When this model is tuned to the in-

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Inclusive CT Probability 0 0.05 0.1 0.15 0.2 0.25 0.3 Data Model Normal pixel Normal pixel Edge pixel Edge pixel Corner pixel Corner pixel

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Single CT Probability 0 0.05 0.1 0.15 0.2 0.25 0.3 Data Model Normal pixel Normal pixel Edge pixel Edge pixel Corner pixel Corner pixel

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Double CT Probability 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Data Model Normal pixel Normal pixel Edge pixel Edge pixel Corner pixel Corner pixel

Overvoltage / V 0.6 0.8 1 1.2 1.4 1.6 1.8 Triple CT Probability 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Data Model Normal pixel Normal pixel Edge pixel Edge pixel Corner pixel Corner pixel

Figure 3.7: Crosstalk probability plots as in Figure 3.6, with the preferred model replaced by a model with the crosstalk photons generated on a Poisson distribution. Agreement with data for higher crosstalk multiplicities is poor.

clusive probability as before, however, the probabilities for high CT multiplicities are greatly overestimated, as shown in Figure 3.7. This is true for all values of the range parameter. The disagreement of this model with the data may be due to not taking into account the position of the primary avalanche within its pixel — it is possible that crosstalk photons are much more likely to scatter into the neighbour closest to the avalanche, and so even if several photons are produced, the probability for them to scatter into different pixels is low.

The data presented here are from a preliminary version of the laser analysis, which is currently in its final stages. They give a rather larger value for crosstalk

in a “normal” pixel than is compatible with total correlated noise measurements from, e.g. the UK QA tests in Chapter 4, once afterpulsing is subtracted. This is thought to be because the incident light may be rescattered by the epoxy window on the MPPC and hit adjacent pixels, causing additional crosstalk. This is sup- ported by results for crosstalk from dark noise (also from Imperial), which give an inclusive crosstalk probability of0.09_±0.01at an overvoltage of 1.33 V. Because of the discrepancy between the light-induced and dark noise crosstalk measure- ments, and the large prediction of the former with respect to total correlated noise measurements, the crosstalk probability in the simulation is scaled so that it agrees with this dark noise measurement, but other parameters are as tuned on the laser data. This method is not quite correct as the probabilities for higher crosstalk multiplicities scale non-trivially with the inclusive probability, but this represents the current state-of-the-art for this measurement.