Tracking particles at fluences 5-10 · 10 16 n eq / cm 2

This paper presents the possibility of using very thin Low Gain Avalanche Diodes (LGAD) (25 − 50μm thick) as tracking detector at future hadron colliders, where particle fluence will be above 1 · 10 neq/cm. In the present design, silicon sensors at the High-Luminosity LHC will be 100200 μm thick, generating, before irradiation, signals of 1-2 fC. This contribution shows how very thin LGAD can provide signals of the same magnitude via the interplay of gain in the gain layer and gain in the bulk up to fluences above 1 · 10 neq/cm: up to fluences of 0.1-0.3·10 neq/cm, thin LGADs maintain a gain of ∼ 5-10 while at higher fluences the increased bias voltage will trigger the onset of multiplication in the bulk, providing the same gain as previously obtained in the gain layer. Key to this idea is the possibility of a reliable, high-density LGAD design able to hold large bias voltages (∼ 500V). 1. Properties of Silicon sensors exposed to fluences above 1 · 10 neq/cm In the past several years, a lot of effort has been devoted to the study of the properties of Silicon sensors irradiated with fluences up to 1 − 2 · 10 neq/cm. The extrapolation of these results to fluences above 1 ·10 neq/cm depicted a very difficult situation: very high leakage currents, strong decline of charge collection efficiency, and a steep increase of the bulk doping. However, during the extensive experimental campaigns aimed at the development of the Silicon trackers to be operated at HL-LHC, it was found that a simple linear extrapolation does not predict accurately the situation above 1 − 5 · 10 neq/cm : charge collection does not decrease due to trapping linearly with fluence and it remains still fairly high (above 50%), detectors can hold very high biases (almost 1000V) allowing for charge multiplication to compensate charge trapping, the bulk doping does not increase linearly with fluence, and the leakage current increase is reduced. Overall, several preliminary measurements are suggesting that damage in Silicon sensors does not increase linearly for fluences above ∼ 5 ·10 neq/cm, however, sensors that are thicker than 50-100 microns still suffer from high leakage current, distortion of the electric field, charge trapping, and the impossibility of reaching full depletion. A comprehensive review on the effect of radiation damage in Silicon can be found in [1]. ∗Corresponding author Email address: cartiglia@to.infn.it (N. Cartiglia) Preprint submitted to Elsevier September 2, 2019 ar X iv :1 90 8. 11 60 5v 1 [ ph ys ic s. in sde t] 3 0 A ug 2 01 9 From a phenomenological point of view, the non linearity of the damage with fluence is expected: at high enough fluences, impinging particles will start hitting areas of Silicon that have already been hit previously and the resulting damage will happen on already damaged Silicon. The geometrical distribution of the damage created by a particle in Silicon is fairly complex: Figure 1 [2, 3] shows two examples of the effects of a 1 MeV neutron. An interacting neutron creates several clusters of damaged Silicon, with interstitial (I) or vacancy states (V); each cluster extends several tens of Angstroms, much more than the Silicon lattice constant (5.4 Å). Figure 1: Spatial distribution of the damaged produced by a 1 MeV neutron in Silicon. The complete calculation of the probability of clusters overlap as a function of fluence is beyond the scope of this contribution, however, a simpler 2-dimensional approach can be used to gain insights into this problem. The probability for an impinging particle on one cm of Silicon to hit a location not already hit by any of the preceding particles can be calculated in the following manner, Figure 2 left side: • A particle hit on the Silicon surface is identified by a square , ao, of a given area, for example 1 Å. • For a particle, the probability of imping on a specific square is phit = 10 −16cm2 cm2 = 10−16. • Consequently, the probability of not-impinging on a specific square is pmiss = 1 − phit = (1.− 10−16) • The probability for a particle to hit a square ao missed by all n previous particles is pmiss = (pmiss) n = (1.− 10−16)n. The resulting trend is shown in Figure 2 right side: for ao = 1 Å , after a fluence of 1 · 10 neq/cm the probability of hitting an empty square is reduced to 30%, indicating that saturation effects are likely. As shown in the plot, the probability of hitting an empty square as a function of fluence follows an exponential trend with parameter ao since the events follow a Poisson distribution. 2 Figure 2: Probability as a function of particle fluence of hitting a square of 1 Å2 not previously hit by any other particle. As the probability decreases, saturation effects in Silicon damage are more likely. According to this simple model, the transition from linear to saturation happens in one decade of fluence. Measurements have shown that up to fluences ∼ 1−3·10 neq/cm the damage is linear therefore the exploration of the properties of irradiated Silicon in the decade 3 − 30 · 10 neq/cm is of major importance to shed light on this topic. 2. Thin Silicon sensors Even though saturation effects might lead to better than foreseen properties of Silicon sensors at fluences above 5 · 10 neq/cm, it is clear that the decrease of the carriers lifetime, the increase of leakage current and that of the bulk doping will severely impact operation. One way to minimize these negative effects is the use of thin p-bulk (25 50 μm) Silicon sensors: • High leakage current is responsible for noise increase and the distortion of the electric field due to the trapping of the charge carriers, forming the so-called ”double junction”. Thin sensors minimize this problem: as shown in [1], the first 50 μm of Silicon bulk near the n-p junction maintains a linear electric field up to 1 · 10 neq/cm, • The increase of bulk doping with fluence raises steeply the depletion voltage in 200300 μm thick Silicon sensors: after 1 · 10 neq/cm the depletion voltage in a 300 (200) μm thick Silicon sensor is V ∼ 1400V (620V). Conversely, thin sensors can be depleted even after very high fluences: Figure 3 shows the depletion voltage after a fluence of 1 · 10 neq/cm as a function of sensor thickness assuming a standard geff = 0.02 or a saturated geff = 0.01 value of the acceptor creation coefficient (for additional comments on the meaning of geff see eq.2 and the discussion in chapter 5 of [4]). It is very important for reliable operation that the voltage of full depletion can be reached since it assure always a constant active volume and a field high enough to provide good carriers velocity everywhere in the volume • In thin sensors, even if the carriers lifetimes becomes very short, charge collection efficiency remains fairly high: assuming an electron (hole) lifetime of 0.2 ns (0.15 ns) 3 Figure 3: Depletion voltage after a fluence of 1 ·1017 neq/cm as a function of sensor thickness assuming a standard g = 0.02 or a saturated g = 0.01 value of the acceptor creation coefficient. as predicted to be after a fluence of ∼ 1 · 10 neq/cm, charge collection efficiency in a 50 μm thick sensor is still almost 80%. Regardless of the advantages listed above, thin sensors (20 30 μm) are not suitable for operation since the signal is too small: the most probable value of charge released by a minimum ionizing particle is of the order of 0.3 fC while the newest ASICs developed by the RD53 collaboration, see for example [5], require at least 1 fC of charge to detect a hit. For this reason, thin sensors can only be employed if they have an internal mechanism of charge multiplication. As shown in Figure 4, 3D sensors manage to break the proportionality between drift path and signal amplitude by drifting the charge carriers perpendicularly to the direction of charge deposition: internal gain in thin sensors manages to achieve the same results by multiplying the charge carriers. Figure 4: Thin sensors with internal gain and 3D sensors manage to break the proportionality between drift path and signal amplitude. 1http://rd53.web.cern.ch/rd53/