Empujes del terreno sobre el elemento de contención

Silicon photomultipliers (SiPM) are based on an array of Geiger mode Single Photon Avalanche Diodes (SPAD) elementary cells connected together to form an array of in- dependent identical microcells. A SPAD is a variation of a p-n junction as shown in Fig. 4.1. SPAD devices with planar structure are manufactured using a compatible CMOS

Figure 4.1: Cross section of the basic SPAD device structure [128]. The junction has dimensions of few micrometers and the active area dimensions range from 20µm to 200µm. p+ represents the device anode and n+ the cathode. The p+ layer (close to p) is an intrinsic thick lightly p-type doped layer. Another p+ implant is used to form the anode contacts at the edge of the structure. A ring heavily doped with phosphorus and deeply diffused surrounds the device providing electrical isolation.

(Complementary Metal-Oxide Semiconductor) technology with seven photolithographic steps. The starting silicon wafers used have double epitaxy: a lightly doped p-layer is grown over a heavily doped buried p+ layer. The p+ anode is realized by means of an ion implantation process and the implant dose is selected in order to obtain a break- down voltage in the range 20-40V. The n+ cathode overlaps the p region in order to form a virtual guard ring, preventing premature edge breakdown. Another p+ implant is used to form the anode contacts at the edge of the structure. A ring heavily doped with phosphorus and deeply diffused surrounds the device providing electrical isolation

(known as a polysilicon frame). The active area dimensions range from 10 µm to 100

µm. [128]

When a p-n junction photodiode is reversed biased, an electric field exists in the vicinity of the junction that keeps electrons confined to the n side and holes confined to the p side of the junction. When an incident photon of sufficient energy (>1.1 eV in the case of silicon) is absorbed in the region where the field exists, an electron-hole pair is generated. Under the influence of the field, the electron drifts to the n side and the hole drifts to the p side, resulting in the flow of photocurrent in the external circuit. When a photodiode is used to detect light, the number of electron-hole pairs generated

per incident photon, known as the quantum efficiency, is at best unity. Losses due to reflection or absorption in zero field regions usually lower the quantum efficiency. SPAD detects light by using the same principle. The difference between a SPAD and an ordinary p-n junction photodiode is that a SPAD is designed to support high electric fields. When an electron-hole pair is generated by photon absorption, the electron (or the hole) can accelerate and gain sufficient energy from the field to collide with the crystal lattice and generate another electron-hole pair, losing some of its kinetic

energy in the process. This process is known as impact ionization. The electron can

accelerate again, as can the secondary electron or hole, and create more electron-hole pairs, hence the term “avalanche”. After a few transit times (i.e. time of transit of the charged particles inside the depletion layer to the high-field regions before triggering an avalanche), a competition develops between the rate at which electron-hole pairs are being generated by impact ionization and the rate at which they exit the high- field region and are collected. If the magnitude of the reverse-bias voltage is below a value known as the breakdown voltage, electron-hole pairs are collected causing the

population of electrons and holes to decline. Because the average photocurrent is

strictly proportional to the incident optical flux this mode of operation is known as linear mode and it is the standard operational mode of Avalanche Photodiode (APD). When the p-n junction is reverse biased above the breakdown voltage (see Fig. 4.2, point A) (known asGeiger mode) the electrons and holes multiply by impact ionization faster, on average, than they can be extracted, leading to a gain much higher than the one in linear mode (106 instead of 102). The population of electrons and holes in the high-field region grows exponentially in time with a rise time of hundreds of picoseconds and producing an associated photocurrent of the order of milliamps. The SPAD will remain in a metastable state until a photon arrives and generates an avalanche (Point B in Fig. 4.2). This avalanche is quenched by suitable quenching circuit (Point C), which lowers the bias voltage below the breakdown voltage (labeledVBR in Fig. 4.2).

Afterwards the excess bias voltage can be restored. During this time, which is known as thedead time (or recovery time) of the diode, the device is insensitive to any other incoming photons.

The breakdown is not a destructive phenomenon such as the dielectric breakdown that occurs when the field is strong enough to dislocate atoms in the material. Simply connecting a SPAD to a low-impedance power supply, however, gives no way either to

Figure 4.2: Current voltage characteristics of an avalanche photodiode operated in Geiger mode. The devise is biased above the breakdown voltage (Point A). The diode will remain in a metastable state until a photon arrives and generates an avalanche (Point B). This avalanche is quenched by a quenching circuit (Point C), which lowers the bias voltage below the breakdown voltage (labeledVBR). Courtesy of Thorlabs.

detect the turn-on or to shut off the avalanche so that the SPAD is ready to detect another photon. Shutting off the avalanche current (i.e. lowering the voltage below the breakdown voltage), is called quenching, and is accomplished in one of two ways: passive quenching andactive quenching.