Characteristics of thin p-MCz Si Microstrip Detector Irradiated upto a mixed fluence of 1017neq./cm2for the FCC

Silicon microstrip detectors can be used for the precise particle tracking in the inner tracking region of the detector used in the future high luminosity collider experiment. In the future experiments, hadron collider provides higher luminosities on the strip detector, and therefore, a detector requires very high radiation hardness. Within CERNRD50collaboration, MCz Si is identified as a prime radiation hard material for the fabrication of the p-Si microstrip detector. In this paper, we have used the experimentally verified four level deep-trap mixed irradiation model for p-MCz Si to investigate the effect of heavy irradiations up to a mixed fluence of 1017n eq./cm2 on the full depletion voltage, leakage current, and charge collection efficiency using SRH and CCE modelling. The changes in the characteristics were evaluated, and effect of the traps on the macroscopic performance of the detectors and possible improvement in the design and semiconductor technology of the p-Mcz silicon microstrip detector.


Introduction
The radiation hardness of silicon detectors has improved significantly in recent years.For the upgradation of Future Circular Collider (FCC) experiments high radiation tolerance of the detectors is required.Dedicated R&D programmes are needed to activatefor the reliable operation of the Si (striplets, macropixed) detectors in the high-fluence range.It is known that the radiation-induced defects/impurities changes the macroscopic properties of Si detector, usually raising the full depletion voltage of p-type silicon, increase of leakage current, and it is a result of the formation of trapping centres, which degrades the efficiency of charge collection [1][2][3][4][5][6][7].A conceptual design report for the FCC was submitted in January 2019 [9][10].This will investigate the new physics potential at very high energy at FCC. Targeted radiation testing campaigns and technological advancements are also undertaken to ensure proper operation of the detectors over many years in the challenging radiation environments of the experiments.
For a novel design of detector to be used in experiments to detect radiation, research is being donein a variety of fields, including characterization of microscopic defects in materials, and characterization of irradiated detectors, some of which include Deep-Level-Transient-Spectroscopy (DLTS), current/voltage (I/V), Thermally Stimulated Current (TSC) and capacitance/voltage (C/V) .The Magnetic Czochralski(p-MCz)Si detector has shown good performance on full-depletion voltage (Vfd), leakage current (IL), and Charge Collecting Efficiency (CCE).Thus, we need Radiation Damage Model to understand space charge behaviour, electron-hole trapping, ILand the performance of heavily mixed irradiated p-MCz silicon microstrip detector for FCC.This paper is outlined as follows: section 2 outlines the device model and the corresponding process parameters.Section 3outlines the mixed irradiation damage model for FCC.In section 4, we discuss SRH and CCE modelling for n+ p-MCz .In section 5, we present results, followed by discussion and finally conclusion in section 6.

Device Modelling
Cross-section area of the device is 0.0625 cm 2 x 150μm p-bulk (MCz Si) is utilized for the SRH and CCE modelling at very high mixed irradiation fluences, as shown in figure1.The detector's hardware specifications and investigational process parameters are shown in Table 1.The n + p-MCz device grounds the n+ strip while applying a negative voltage to the p+ side

Mixed irradiation Damage Model for FCC.
All the features and parameters are listed in Table 2.Acceptor E5 is situated in the upper-half of the band gap, whereas the acceptor H(152K) lies in the lower-half of the band gap.Similarly, the lower part of the band gap is where the CiOi donor is positioned, whereas the upper half of band gap donor E (30K) is situated.The capture cross-section of electrons (σn) and holes ( σp) along with introduction rate η are also displayed.
Using this model the SRH and CCE (theoretically) modelling has been done on the n+ p-silicon microstrip detector to extract the macroscopic performance of the detector at very high-extrapolated fluences.

SRH and CCE modelling
According to the Shockley-Read-Hall (SRH) recombination formulation, the effective doping concentration (Neff ), full depletion voltage (Vfd) and leakage current( IL )changes with the different doses of fluences.The theoretical calculation of Vfd by SRH for the p -bulk (MCz) Si detector is given by where,NA is the acceptor doping concentration, Here, nT (donor,acceptor) represents the defect levels steady state occupancy, NT is the defect concentration and ep,n, which is the emission rate for holes and electrons in the equation ( 2) and (3).
Here, q is elementary charge, detector/strip area is represented by A, thickness of the sensor is d intrinsic carrier concentration is ni and τg,eff is the effective generation lifetime.
The formulation of CCE is equal to the ratio of total collected charge Q and the induced charge Q0.
here, D is the thickness of detector and W is width of depletion region at a bias and (effective trapping time constant) is given by Here, Nt is density of deep levels [8], vtis thermal velocity and σe,h is trapping cross-section of electrons and holes.In eq. ( 7), drifting time tdr, depends upon τgen (generation lifetime),VB (bias voltage ),VD (depletion voltage ) and μi (mobility of electrons and holes).
In this paper, the following tdr is used for the assumption of the charge carrier generation by minimum ionizing (mips) particle in detector.= (8)

Results and Discussion
In this section, the experimentally verified mixed irradiated damage model is used in the SRH and CCE modelling to extract the macroscopic parameters (Vfd,IL,CCE) at extrapolated fluences for the FCC.

Full depletion voltage in mixed irradiated p-MCz
With the help of theoretical (SRH modeling) eq.1, eq.2 and eq.3 figure 2 shows the vfd variation as a function of equivalent fluences for the device depth of 150μm (thin detector).Table 3.Estimated mixed irradiation equivalent extrapolated fluences for FCC.
In table 3, ɸn is the fluence of neutron,ɸp is the fluence of proton and ɸeq (n+p) is the equivalent mixed (neutron +proton) fluence that we have estimated by eq.8The hardness factors for proton and neutron are Kp and Kn, respectively.ɸn ɸp ɸeq, (n+p) mixed 2×10 14 n/cm 2 1.29×10 15 p/cm 2 1×10 15 /cm 2 2×10 14 n/cm 2 1.58×10 16 p/cm 2 1×10 16 /cm 2 2×10 14 n/cm 2 1.60×10 17 p/cm 2 1×10 17 /cm 2 From figure 2 it can be observed that the Vfd increases enormously with an increasing mixed (neutron + proton) irradiation fluence.This is due tothe damage that is accumulated in mixed irradiated detector(neutron + proton), which means the damage introduced by E30 K (donor), is not compensated by H152K (acceptor) in detector.The Vfd is having an uncertainty of ±15% for the fluences up to 1×10 17 /cm 2 as expected.To operate the detector at FCC fluences, we need to compensate the defects effect on the Vfd for the proper detector biasing up to 1000V.In table 2, deep traps E5, H152K, CiOi, and E30K are the defects out of which the defect E30K lower the τ gen (effective generation life time), which increases the IL.For the FCC the IL at -50 0 C is not a serious issue at highly irradiated Si microstrip detectors.The experimental measurement has a ±25% error in the current.The rise in dark current is due to the deep acceptor E5 because it is near to the band gap.

Charge Collection EfficiencyCCE in mixed irradiated p-MCz
CCE modelling describes charge collecting behaviour in the severely irradiated detector.At very high fluence, the e and h-trapped in detector and degrades the ability to collect signals.
In figure 4(a), we can see the overall impact of CCE as function of fluence with an experimental uncertainty of ± 5%.It has been found that many deep traps for e.g.like CiOi, and E30K are not affecting too much CCE.Figure 5(b) shows that impact of E5 (acceptor) and H152K (donor) defects on the CCE, it is observed that E5 is given a very less CCE of the detector than H152K trap.This means that acceptor trap E5 mostly degrades the CCE of the p-MCz Si detector.

Conclusion
This paper reports the preliminary results on the extracted values of charge collection efficiency (CCE) , leakage current(IL),full depletion voltage (Vfd), to determine performance of the p-Si MCz microstrip detector at significantly high mixed irradiation fluence of 1×10 17 cm -2 for the upcoming phase of the FCC Experiment.
Using SRH and CCE modelling, it has been observed a very highVfd>>> 1000V, and a significant decrease in CCE of the detector is obtained.It has beennotedthat the E5 trap is highly dominating than other traps and it is giving a large degradation in the CCE of the detector.Finally, an ultra radiation hard Si microstrip detector (p-MCz)with the new doped-impurities is projected to mitigate the effect of high Vfd and high CCE for the FCC experiment.

Figure 3 depicts
Figure 3 depicts IL at high mixed irradiation fluences at 223 K.It has been confirmed that it increases as predicted, linearly.

Figure 3 .
Figure 3. Dependence of Leakage current on extrapolated mixed irradiation fluences.

Table 1 .
Physical parameters for the p-type MCz detector.