5. Upgrades of the Pixel Detector 37
6.2. Radiation Damage in Silicon
6.2.2. Impact on Sensor Performance
The microscopic defects accumulate over time and have an increasing impact on the sensor performance, which ultimately limits the lifetime of silicon sensors used in high energy exper-iments. The properties of the sensor are altered in three main ways that are important for detector operation:
• Recombination-generation centres increase the leakage current, which affects the signal to noise ratio, the power consumption and the cooling system of the pixel detector.
• Defects change the effective doping concentration of the sensor, which has an impact on the depletion voltage. Overall more p-type than n-type defects are created, which leads to type-inversion of the sensor.
• Trapping centres cause a decrease in the charge collection efficiency. A degrading hit efficiency is the result, which in the end has a negative impact on theb-tagging performance and track resolution of the detector.
The impact of radiation damage is not constant after irradiation has stopped, because the created defects can anneal. Silicon interstitial and vacancies can recombine as already mentioned, however, stable defects are also able to transform and become inactive, which is beneficial for the sensor performance. Inactive defects can also be reactivated and thus increase the impact of radiation damage again.
Leakage Current
An example of the increase in the leakage current per unit of volume ∆I/V in several types of silicon is shown in Figure 6.3. In these measurements the leakage current was measured before and after irradiation in order to estimate its increase. An important factor that needs to be taken into account for a precise measurement is the dependence of the leakage current on the temperature. In this case all current measurements were normalised to a reference temperature of 20◦ [62].
The increase in the measured leakage current is proportional to the particle fluence and it is clearly visible that it does not depend on the silicon type. The relationship between the leakage current and the collected fluence can thus be written as [62]:
∆I =αφeqV , (6.1)
whereV is the sensor volume andα is the current related damage rate.
Annealing effects are described by the current related damage rate, which is therefore a function of time,α(t). The value ofα was found to decrease over time [62]. From this it follows that annealing effects are exclusively beneficial for the leakage current. Several models exist to describe the impact of annealing, however, in general the long term behaviour ofα is described by a fit function [62]:
α(t) =αIexp
− t τI
+α0−β·ln t
t0
(6.2) whereαI,α0 and β are fit parameters and the time t0 is set to 1 minute.
6. Monitoring Radiation Damage in the Pixel Sensor
Figure 6.3.: The leakage current as a function of the neutron equivalent fluence shown for different types of silicon. The measurements were taken after heating the sensor to 60◦ degrees for 80 minutes in order to be comparable to other measurements [62].
The time constant τI is based on the Arrhenius equation, which describes reaction rates as a function of the temperature. It is expressed as:
1
τI =k0I·exp
− EI
kBTa
, (6.3)
with two fit parameters k0I and EI. Ta is the temperature at which the silicon sensors were stored during the annealing period. Ta is in general different to the temperature at which the leakage current is measured.
According to [62] the parameters of the fit have been determined to be:
αI = (1.23±0.06)·10−17 A/cm, k0I = 1.2+5.3−1.0·1013 s−1,
EI = (1.11±0.05) eV,
β = (3.07±0.18)·10−18 A/cm,
α0 = −(8.9±1.3)·10−17 A/cm + (4.6±0.4)·10−14 AK/cm· 1 Ta .
A growing leakage current increases the noise in the sensor as well as the power consumption.
Due to the fact that the leakage current can reach the magnitude of mA in highly irradiated sensors, it can cause thermal runaway. The heat dissipation caused by a current of this magnitude is large enough to increase the leakage current, leading to an even higher heat dissipation. This self amplifying loop can finally destroy the sensor. Thus, it is crucial to ensure proper cooling of silicon detectors during operation.
48
Effective Doping Concentration and Depletion Voltage
Acceptor-like defects and donor removal lead to a change in the effective doping concentration in the silicon bulk. Donor removal can occur if foreign donor atoms such as phosphorus are combined with a vacancy and thus create a new defect which has different electrical properties.
An example measurement for an initially n-type doped sensor is shown in Figure 6.4. The effective doping concentration as well as the depletion voltage decrease at the beginning up to the point of type-inversion. Afterwards the silicon is effectively p-doped and the doping concentration as well as the depletion voltage increases continuously with the particle fluence.
Figure 6.4.: Change in effective doping concentration / depletion voltage as a function of the neutron equivalent fluence. The measurements were taken directly after irradia-tion [56].
According to [62], the change in the doping concentration can be quantified with the following formulas (Equations 6.4 - 6.10). Several parameters of these equations are again estimated via fits. The reader is also referred to [62] for the estimation of the fit parameters that are mentioned in this paragraph. Furthermore, an additional short summary of the model and its parameters can also be found in [22]. The effective doping concentrationNeff(φeq, t(Ta)) is described as:
Neff(φeq, t(Ta)) =Neff,0−∆Neff(φeq, t(Ta)) , (6.4) where Neff,0 is the initial doping concentration and ∆Neff(φeq, t(Ta)) the change in the con-centration induced by irradiation. The effective doping concon-centration depends on the time and the fluence, where the time dependence is a function of the temperatureTa. The induced change
∆Neff(φeq, t(Ta)) can be written as:
∆Neff(φeq, t(Ta)) =NC(φeq) +NA(φeq, t(Ta)) +NY(φeq, t(Ta)) . (6.5) NC represents the stable defects and thus only depends on the fluence,NA is the part charac-terising the short term annealing, and NY is the reverse annealing component of the formula.
6. Monitoring Radiation Damage in the Pixel Sensor
The function for the stable damage consists of two parts. An exponential function leads to a decrease in the effective doping concentration until the minimumNC0 is reached. The decrease can be interpreted as donor removal, while the second term is linear and describes the creation of acceptor-like states in the silicon sensor:
NC =NC0(1−exp(−cφeq)) +gcφeq . (6.6) The values of the parametersNC0 and cdepend on the type of silicon that is used. Some values are listed in [62]. The factorgcis only slightly dependent on the silicon material and the average isgc= (1.49±0.04)·10−2 cm−1.
The short term annealing component is described as:
NA=φeq
Annealing times that are very short are often not important for the operation of silicon detectors.
Additional information on short annealing times is for example presented in [56]. Therefore all time constants except the longest decay time are generally neglected. This reduces Equation 6.7 to a single exponential function. The parameter of the amplitude is estimated as ga= (1.49± 0.04)·10−2 cm−1, while the time constant has a dependence of:
1 the change in the doping concentration in contrast to the annealing of the leakage current. The third term in Equation 6.5 describes this behaviour:
NY =NY,∞ 1− 1 is illustrated in Figure 6.5 and the impact of beneficial and reverse annealing is clearly visible.
The evolution of radiation damage in silicon can be slowed down by inducing oxygen into the silicon sensor [63], this is the case for the sensors in the ATLAS pixel detector [33]. However, after years of operation the maximum voltage of the power supplies is nevertheless reached and the sensor cannot be operated fully depleted any longer. Due to the n-in-n sensor design that is used in the ATLAS pixel detector it is possible to operate the detector partially depleted after type-inversion. Before type-inversion, the depleted region grows from the backside of the sensor as is shown in Figure 6.6(a). Thus, it is only possible to receive a signal if the sensor is fully depleted. After type-inversion the p-n junction is located at the pixel side and therefore the depleted region grows from the readout side as shown in Figure 6.6(b). This offers the opportunity to operate the detector after the maximum voltage has been reached, even though the sensor efficiency will of course decrease, since the collected charge depends on the size of the active region.
50
Figure 6.5.: Change in the effective doping concentration ∆Neff caused by annealing effects as a function of time. The temperature was set to 60◦ and the sample was irradiated with a fluence of 1.4·1013 cm−2 [62].
(a) (b)
Figure 6.6.: Schematic view of a silicon sensor before (a) and after type-inversion. The de-pleted region grows from the backside of the sensor before and from the readout side after type-inversion. Thus, it is possible to operate the sensor partially de-pleted after type-inversion.
6. Monitoring Radiation Damage in the Pixel Sensor
Charge Trapping
A fraction of the free charge carriers drifting towards the electrodes in the silicon sensor are trapped for a limited time by defects. If the trapping time is longer than the time available for readout, then the charge carriers do not contribute to the signal and its amplitude will decrease.
The trapping time depends highly on the type of trap, only traps with energy levels very close to the valence/conduction band might release the holes/electrons fast enough so that the charge collection is not affected [15].
Traps, and thus the charge carrier loss in the silicon sensor, are characterised by the trapping time constantτ+(φ), which describes the average time that a charge carrier stays trapped. It is inversely proportional to the fluence [56]:
1
τ+(φ) = 1
τ0+ +γφ . (6.11)
Both parameters have been measured and the values were found to beτ0+ = 0.51·106s−1±12%
andγ = 0.24 cm2s−1. The quoted values are valid for electrons and holes, however, they cannot be used above a fluence of φ= 8.8·1012 cm−2 [56].
Measurements that assess the radiation damage in the ATLAS pixel detector have been taken regularly until the LHC was shutdown in order to install several upgrades at the beginning of 2013. Results of the monitoring program are discussed in the following.