Avalanche Multiplication

The avalanche multiplication effect (or impact ionisation) is the most important mecha- nism in junction breakdown. This is because the avalanche breakdown voltage imposes an upper limit on the reverse voltage for most semiconductor devices (diodes). A thermally generated electron in the depletion region gains kinetic energy from the electric field. If the field is sufficiently high, the electron can gain enough kinetic energy that on collision with an atom, it can break the lattice bonds, creating an electron-hole pair. The newly created electron and hole both acquire kinetic energy from the field generating further electron-hole pairs.

Assuming all conditions for avalanche multiplication have been met (high electric field), the electron current In will increase with distance through the depletion region to

Mn≡

In(W)

Ino

. (5.16)

Similarly the hole current will increase fromx=W tox= 0.

Given that the avalanche breakdown voltage is defined as the voltage at whichMn

approaches infinity and knowing the field dependence of the ionisation rates, the critical field (maximum electric field at breakdown) can be calculated [133]. This combined with Poisson’s equation allows for the calculation of the breakdown voltage, VB for one-sided

abrupt junctions: VB = εcW 2 = sε2c 2q (NB) −1 (5.17)

This effect is of particular interest for detectors that have to be very radiation tolerant. Radiation tolerant devices are often designed to be operated at very high bias voltages to reach full or partial depletion. In fact, soft charge multiplication in electron collecting detectors has been seen after irradiation at very high bias voltages, increasing the signal and improving the performance of the devices. Significant work has been dedicated to explore the effects of charge multiplication and to enhance and control the process (Section 10.3 and Section 10.6).

p-n

Junction as a Particle Detector

High resolution silicon detectors are used in high energy physics to track particle tra- jectories. These detectors are all based on the p-n junction (see Section 5.4). The p-n

junction can function as a particle detector whilst operated in reverse bias mode, either fully or partially depleted. Particles which traverse and interact within the depleted region generate charge carriers. The potential difference across the device drifts these carriers to either side of the junction, electrons → n+ and holes→ p+ where n+ and p+ refer to very high concentrations of dopants in each type of silicon. The charge collected at either end of the junction can be read out (using amplifying electronics). The readout side of the junction can then be segmented to provide the required spatial hit resolution. A schematic diagram of a silicon particle detector is given in Figure 6.1.

Figure 6.1: Illustration of charge deposition from a particle within a double-sided silicon micro-strip detector.

Details on traditional types of segmentation for particle detectors are given in Sec- tion 6.1, followed by a description of charged and neutral particle energy loss (Section 6.2) and signal generation (Section 6.3) in silicon detectors.

6.1 Segmentation

In order to realise high resolution trajectory measurements, fine segmentation of the readout electrodes is needed. There are two main types of segmentation widely used is particle physics experiments, pixels and micro-strips.

Devices with a strip or micro-strip structure use long rectangular readout electrodes. To give an idea of its typical size, a typical micro-strip detector could feature electrodes 10µm wide with a pitch of around 100µm with lengths varying depending on the device longitudinal size. This segmentation doesn’t allow for two dimensional hits to be measured with a single device. Instead, multiple layers of devices are needed, with some of the devices rotated with respect to each other.

Pixelated devices use smaller electrode structures than strip or micro-strip detectors, but they can vary in size and shape depending on their use. Pixels are arranged in a regular two dimensional array, creating a grid like structure. This allows for the determination of two dimensional hit information from a single device. The readout electrode density is much higher compared to strip or micro-strip structures, which adds readout complications.

The major drawback from using pixel segmentation in devices is the added readout complication. Since strip and micro-strip electrodes are typically as long as the detector, the readout electronics can be positioned at one or either ends of the sensor. Pixelated detectors need a different arrangement for the readout electronics. The readout chip has the same or similar readout channel grid structure as the detectors electrode grid structure. This has a number of consequences:

• The readout chip needs to be directly attached to the sensor, as each detector electrode has to be connected to the relevant readout channel.

• The readout chip has to be more advanced due to the high channel density and the need for a larger readout bandwidth. This necessitates the use of smaller transistor technology which increases production costs

Nonetheless, particle physics central trackers require very high channel granularity to separate high multiplicity events very close to the interaction points. This is not possible using strip or micro-strip trackers. The ability of pixel detectors to measure two spatial coordinates of hits with a single device also reduces the number of detector layers needed, which is especially important close to the interaction point where space is limited and material has to be reduced to mitigate the effect of multiple coulomb scattering on the charged particles tracks.