Evolution of silicon trackers

small compared to the signal current. So, if the quiescent current has to be below 0.1 µA, the voltage applied must not exceed 30 µV. Not only that this voltage is difficult to keep stable but also the speed of the charge collection would be incredibly slow.

The solution is to increase the resistivity of the sensor. This is achieved by doping the silicon like a diode and operate the sensor in reverse bias. Thus, the silicon becomes an insulator, and the quiescent current is very low. The high resistivity allows applying high bias voltages—often in the range of sev- eral hundred volts—which lead to a fast collection of the charge carriers. The collection time in a fully depleted sensor is defined in [49] by

tc≈

d2

µcV (3.1)

where d is the thickness of the sensor, µcthe mobility of the charges and V the

applied voltage.

Figure 3.3 shows the cross section of a typical p-in-n silicon detector. An n-type substrate builds the base in which the strips are doped as p+-type regions. An insulation layer of silicon dioxide (SiO2) is placed above the strips, then alu-

minum electrodes are added on both sides. Due to the insulation layer, the electrodes are de-coupled from the bias voltage. The AC-coupled signal is then amplified and further processed by the detector electronics. Some silicon detec- tors have the amplifiers and some data processing, e.g. filtering, discretization, integrated with the pixels—these are called Monolithic Active Pixel Sensors (MAPS).

The outer tracker of the original CMS consists of p-in-n silicon detectors with thicknesses of 320 µm and 500 µm [7]. The bias voltage at the sensors is up to 500 V, and the sensor readout is DC-coupled. For the CMS outer tracker at the HL-LHC, n-in-p sensors are under development [5]. Both AC- and DC-coupled readout will be used: AC-coupled readout for the strip sensors and DC-coupled readout for pixel sensors.

3.2. Evolution of silicon trackers

First experiments with particle detectors based on semiconductors took place at the Bell Telephone Laboratories in Murray Hill, New Jersey in 1950 [50]. A pn-junction of a germanium detector in reverse bias was bombarded by alpha

particles, and the generated charge was collected and amplified—basically, the same principle as applied today. Around 1960, monocrystalline silicon became available, and the research continued mainly with silicon detectors [51]. In the early 1970s, the development of particle strip detectors started. Among others, the Kernforschungszentrum Karlsruhe was involved, and a striped silicon detector for digital position encoding was presented in [52]. However, these first sensors were not used in high-energy physics experiments but as spectrometers for energy measurement.

The first high-energy physics experiment that included a silicon strip detector as a tracker was the NA11 experiment at CERN in 1980 [53]. The goal of this experiment was to study the production and properties of charmed particles, i.e. composite particles that contain at least one charm quark. The short lifetime of these particles of the order of 10−13_{s requires a detector with high spatial}

resolution. To fulfill this and other requirements, a silicon strip detector with 1200 strips was developed of which every third was read out. NA11 was a fixed target experiment where a beam of protons hit a block of beryllium. Particles produced by collisions of the protons with beryllium atoms were detected by six strip detectors located upstream the beryllium target. In total, the tracker had 2400 readout channels.

In 1989, the “Detector with Lepton, Photon and Hadron Identification” (DEL- PHI) experiment at the LEP included the first silicon tracker similar to the one at CMS. Silicon strip detectors were arranged on a barrel-like structure around the electron-positron interaction point [54]. Three layers of in total 96 detector modules provided about 73 000 readout strips. Later in 1997, the detector was upgraded with better modules and, endcaps with pixels and mini strips were added [55].

Currently, the silicon trackers of the two large state-of-the-art experiments have millions of channels: CMS has more than 9.6 million strips and 66 million pixels, and ATLAS has 6.2 million strips and 140 million pixels. During the upcoming upgrades of CMS and ATLAS, the number of readout channels will be increased again. The CMS silicon outer tracker at the HL-LHC alone will provide data from more than 260 million readout channels to the track trigger. In addition, there are the pixel channels of the inner tracker.

The development of silicon detectors over the last 25 years shows that the experiments include larger and larger silicon trackers. Figure 3.4 shows the evolution of the silicon trackers from the NA11 experiment up to the recent plans for the Phase-II upgrades of CMS and ATLAS. The driving force behind the increasing channel number is, on the one, hand the desire for ever higher

3.2. Evolution of silicon trackers 1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 103 104 105 106 107 108 109 1010 ATLAS - Phase-II CMS - Phase-II ATLAS CMS GLAST AMS-02 DØ Zeus CDF-II BaBar DELPHI (97) CDF-I Mark II DELPHI (89) NA11/NA32

ATLAS - Phase-II CMS - Phase-II CMS - Phase-I ATLAS CMS DELPHI (97) Year Num ber of channels Strip detectors Pixel detectors

(a) Number of readout channels of silicon trackers.

1980 1985 1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 10−2 10−1 100 101 102 103 104 ATLAS - Phase-II CMS - Phase-II ATLAS CMS GLAST AMS-02 DØ CDF-II DELPHI (97) CDF-I Mark II DELPHI (89) NA11/NA32 ATLAS - Phase-II CMS - Phase-II CMS - Phase-I ATLAS CMS DELPHI (97) Year Area (m 2) Strip detectors Pixel detectors

(b) Active area of silicon trackers.

Figure 3.4.: Evolution of readout channels (a) and area (b) of silicon trackers in high- energy physics experiments. Sources: [5, 7, 24, 51, 53–68].

spatial resolution in the detection of the particle tracks and, on the other hand, the increasing particle density at high-energy, high-luminosity colliders. Under such conditions, a higher channel number facilitates to distinguish between the separate tracks.

However, an increased channel number causes also higher data rates.

ratedata∝ nchannel· fc (3.2)

The collision rate (fc) is chosen as high as possible to maximize the number of

recorded events. Moreover, the amount of data (ratedata) that can be processed

on-line with reasonable effort is limited by the current technology. Then the number of channels (nchannel) may not be freely chosen but depends on the

current data processing technology. Therefore, it is interesting to compare the increase of readout channel numbers of strip detectors with the increase of transistors on chip predicted by Moore’s law [69]. Figure 3.4 (a) shows the evolution of the number of tracker channels. The number of strip readout channels increases by a factor of 1.6 every two years, whereas the number of transistors on a chip increase by a factor of 2 every eighteen months. The readout channel number thus increases slightly slower than the transistor count on chips. All data can be found in Appendix D.