Comparing radiation tolerant materials and devices for ultra rad-hard tracking detectors

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1 Nuclear Instruments and Methods in Physics Research A 579 (27) Comparing radiation tolerant materials and devices for ultra rad-hard tracking detectors Mara Bruzzi a,, Hartmut F.-W. Sadrozinski b, Abraham Seiden b a INFN Florence Dipartimento di Energetica S. Stecco, Via. S. Marta 3, Firenze, Italy b SCIPP, University of California Santa Cruz, Santa Cruz, CA 9564, USA Available online 11 June 27 Abstract The need for ultra-radiation hard semiconductor detectors for the inner tracker regions in high energy physics experiments of the future generation can be satisfied either with materials which are inherently more radiation hard than float zone silicon or with special detector structures with improved radiation resistance. This report compares directly the data on the performance of rad-hard materials and devices proposed for the superlhc. r 27 Published by Elsevier B.V. PACS: 29.4.Wk; Fk; 29.4.Gx Keywords: Radiation damage; Semiconductor tracking detectors; Silicon strip detectors; SuperLHC 1. Introduction The possible increase of the luminosity of the Large Hadron Collider to 1 35 cm 2 /s (superlhc) [1] will result in an increase in the fluence position sensitive detectors have to withstand. For example, in the innermost tracker layers, tracking detectors would be exposed to hadron fluences of up to cm 2 during a 5- to 1-year operation. An intense research programme is under way to increase the radiation hardness of semiconductor detectors, so that they can survive such extreme levels of irradiation. In recent years, the research has been pursued along different paths, concentrating either on the development of silicon materials and high bandgap semiconductors (SiC, diamond) with increased radiation hardness or on the development of new, device-engineered, ultra-rad hard detectors such as 3D structures [2,3]. In this paper we will discuss and compare recent results on the performance of ultra-radiation-hard detectors. The main radiation damage phenomena in semiconductor detectors are: the increase of the leakage current with Corresponding author. Tel.: ; fax: address: bruzzi@fi.infn.it (M. Bruzzi). the irradiation fluence due to the creation of generationrecombination centres, the change in the effective doping concentration at large fluences (leading to an increased depletion voltage and possibly the inversion of the space charge sign), and finally a shortening of the carrier lifetimes due to increased trapping at radiation-induced defects (with corresponding loss of charge). We will analyse these important parameters of the detectors after irradiation with high fluence of fast hadrons ( cm 2 ). 2. Expected radiation levels Expected radiation levels for superlhc have been widely discussed in the high-energy physics scientific community. Possible parameterisation with the radius for 25 fb 1 integrated luminosity are given in Fig. 1 [4,5]. As usual, the radiation effects due to different particle species are taken into account by weighting the individual fluence with a relative damage factor and then quoting the fluence in terms of 1 MeV neutrons equivalents. A tentative division in three main tracker geometries (pixels, strips and long strips) is indicated, following suggestions given in Ref. [6]. For ATLAS, neutrons are the dominant particles in the outer tracker layers, and pions are most abundant in /$ - see front matter r 27 Published by Elsevier B.V. doi:1.116/j.nima

2 M. Bruzzi et al. / Nuclear Instruments and Methods in Physics Research A 579 (27) fast hadron fluence [cm -2 ] the pixel layers, while in the short strip layers both are important. 3. Leakage current pixels short strips long strips Data after Giannotti et al. [1] Data after ATLAS RTF [4] f = 1 14 x 115 R CMS [5] Best fit of RTF Data R [cm] 12 Fig. 1. Fast hadron fluence (in 1 MeV neutron equivalents) expected for an integrated luminosity of 25 fb 1 (5-years operation) and tentative division in optimised geometries for tracking detectors [6]. The leakage current I in semiconductor detectors is mainly caused by the presence of generation recombination deep levels which introduce a strong dependence on the absolute temperature T: IðTÞ /T 2 exp E (1) KT with E a typical activation energy characterising the main electrical conductivity process in the semiconductor bulk. In silicon the characteristic activation energy is close to half the semiconductor bandgap, which proves that the most active generation centres are those at midgap. In SiC and CVD diamond films, characterised by a lower crystalline purity than Si, the transport processes are generally dominated by native deep traps whose activation energies are lower than half the gap. Evaluating leakage currents at room temperature for diamond and SiC detectors we find that they should be lower by approximately a factor 1 13 and 1 5, respectively, than that of a Si detector with the same active volume. The experimental current actually measured can be nonetheless much higher than that expected from this calculation due to a nonoptimised manufacturing process or to the occurrence of larger microscopic defects in the material. Typical examples in SiC are dislocations and micropipes, while in diamond the most relevant contribution to the current is due to the passivation of dominant native defects, responsible for setting up persistent currents during and after irradiation. Since the irradiation causes the creation of deep levels within the energy gap of semiconductors, the increase of these defects can lead to a compensation of the original dopants and of the native dominant defects in the semiconductor bulk, increasing the importance of the midgap states for the evaluation of the leakage current. In diamond and SiC, where the activation energy before irradiation is mainly related to the presence of native defects, the effect of compensation by radiation-induced deep levels will bring the activation energy to move closer to midgap. As a consequence, the leakage current in such materials can be observed to decrease with increasing fluence of irradiation. As an example, in Ref. [7] the authors report how the room temperature current density of epitaxial SiC pn junctions made on 55 mm thick epitaxial layer decreased from 6 to 2 na/cm 2 after an irradiation of 1 16 n/cm 2. In silicon, the activation energy does not change significantly with irradiation, so the current is expected to increase proportionally with the increasing concentration of radiation-induced defects at midgap. This effect is well parameterised in terms of the leakage current density J as a function of the fluence F: JðFÞ ¼aFd (2) with a the damage constant (usually referred to 1 MeV neutron irradiation), and d the depleted thickness. As the leakage current after irradiation depends on the annealing history of the detector, the damage constant is evaluated after a prescribed anneal history and we have: að6 C; 8 minþ ¼ð3:99 :3Þ1 17 A=cm at the reference temperature of 2 1C after a thermal treatment of 8 min at 6 1C [8]. Thus, the effect of the high-fluence irradiation is to increase the volumetric current up to values far beyond the operational limits of the detector. The exponential dependence of the current with temperature given by Eq. (1) is used to lower the leakage current of silicon detectors after irradiation by keeping the detector cold (typically they are kept at in the range of 1 to 3 1C). As a comparison between different detector materials, Fig. 2 shows typical leakage current densities for Si, SiC and diamond as a function of the fluence (1 MeVn equivalent). The SiC device has a thickness of 55 mm, data are redrawn from Ref. [7]. The current density of the Si device (3 mm thick) has been calculated using Eqs. (1) and (2) at 3 1C, a maximum applied voltage of 6 V and an effective doping generation rate b ¼.5 cm 1 [9] (see below). The knee observed around a fluence of cm 2 occurs when the detector ceases to be fully depleted. The data for diamond are from Ref. [9] and are for a 3 mm thick polycrystalline CVD diamond detector produced by Element Six measured after pumping the device with a 6 Co source at 3 K at.2 V/mm. We note that the leakage current of a detector made with a highbandgap material being very low at room temperature and essentially constant or even decreasing with the fluence is one of the most advantageous features of these materials when compared to silicon.

3 756 ARTICLE IN PRESS M. Bruzzi et al. / Nuclear Instruments and Methods in Physics Research A 579 (27) Leakage Current Density [A/cm 2 ] 1x1-3 1x1-5 1x1-7 1x Operational voltage Si 3µm; V fd = 6V -3 C SiC 55μm +2 C pcvd diam 3μm +2 C Fluence [1MeV n/cm 2 ] Fig. 2. Typical leakage current density for Si, SiC and diamond as a function of the fluence (1 MeV n equivalent). The SiC device has a thickness of 55 mm, data are redrawn from Ref. [7]. The current density of the Si device (3 mm thick) has been calculated using Eqs. (1) and (2) at 3 1C and considering a maximum applied voltage of 6 V. The knee observed around a fluence of cm 2 occurs when the detector ceases to be fully depleted. Data for polycrystalline CVD diamond (3 mm thick) are taken after pumping the device with a 6 Co source at 3 K [8]. SiC detectors are used in the form of Schottky or pn junctions. Due to intrinsic limitations in the production of the epilayer, N eff is about 1 14 cm 3 or higher. Notwithstanding the low resistivity of this material before irradiation, data reported on a 55 mm thick layer show that it becomes almost intrinsic already after a 1 MeV neutron irradiation up to cm 3 [7], and remains almost intrinsic for any further increase of the fluence. This suggests a generation rate of radiation-induced defects far higher than in silicon. Diamond detectors are produced by evaporating metals on opposite surfaces of the sample. Due to the exceptionally high resistivity (up to 1 16 O cm) of the material the electrical conductivity of the device shows an ohmic behaviour. The operational voltage used for diamond detectors is that corresponding to an average electric field of 1 V/mm and is independent of irradiation levels. The operational voltage of a silicon detector coincides at low fluence with the full depletion voltage V fd determined by capacitance voltage measurements. After irradiation, the formation of radiation-induced defects changes the effective doping concentration N eff, defined by N eff ¼ 2ðV fd þ V bi Þ qw 2 (3) with e being the (static) permittivity of silicon, q the elementary charge, V bi the built-in potential, W the detector thickness. In p-on-n silicon detectors, an exponential decrease of N eff and consequently V fd with the fluence F is observed in the low fluence range while for higher fluences an increase of V fd with F is observed. This increase has been measured to be linear with a slope b (see below). In the very high fluence range (F41 15 cm 2 ) V dep reaches values as high as V for 3 mm thick detectors, so that it becomes practically impossible to fully deplete the irradiated detector. This phenomenon has been ascribed in n-type Si to the radiation-induced generation of deep acceptor-like states, which, contributing with a negative term to N eff, leads for sufficiently high fluences to the inversion of the sign of the space charge [8]. The fluence at which a minimum in N eff and V fd occurs is called inversion fluence. In this simple picture, the change in sign of N eff is attributed to the shift of the junction from the front side of the detector, near the p contact, to the back side, close to the n contact. However, it was shown that, for fluence higher than the inversion one, irradiated Si detectors appear to be sensitive on both sides. To explain this experimental fact the irradiated detector is assumed to contain a double junction: one is still located at the p contact, with N eff 4, and a second at the n contact, characterised by N eff o. In these conditions it becomes important where the region of maximum electric field is located. If the high electric field region has shifted to the back electrode, the sample will be definitely typeinverted, and the voltage required to maximise the collected charge will be much higher than the full depletion voltage to overcome the low field region during the drift. Thus, at high fluences, p-on-n detectors need to be fully depleted or over-depleted to maximise the collected charge. Detectors with double junctions are characterised by a lower constant field region in the centre of the detector. The extent and strength of this field will determine how much of the charges drifting from the back plane will be trapped (see below). The rate of increase of the full depletion voltage with the fluence in n-type silicon can be decreased by reducing the formation rate of the radiation-induced acceptor-like defects. This approach has been investigated within the RD48 [1] and RD5 [2] CERN collaborations by using n-type diffusion oxygenated float zone silicon (DOFZ). The standard FZ Si material is characterised by the presence of a concentration of interstitial oxygen content, of the order of 1 16 cm 3, while DOFZ can be oxygenenriched up to approximately cm 3 [8]. During the irradiation, oxygen acts as a sink of vacancies, thus diminishing the rate of formation of the defects related to di-vacancy, usually characterised by deep acceptor-like energy levels. Results have been encouraging especially in case of gamma- and 24 GeV proton-irradiation, where the lattice damage is mainly caused by point-defects, while with neutrons we see essentially no beneficial effect of the oxygen content, since in that case clusters, large aggregates of defects with energy levels close to midgap, are the dominant products of the irradiation. An alternative method to reduce the rate of increase of the full depletion voltage with the fluence and possibly to eliminate type inversion in n-type silicon is to increase the

4 M. Bruzzi et al. / Nuclear Instruments and Methods in Physics Research A 579 (27) rate of formation of radiation-induced donor defects. This research line has been investigated within RD5 by using n-type high resistivity Czochralski (Cz) and magnetic Czochralski (MCz) silicon. These materials are characterised by the presence of a high concentration of interstitial oxygen, typically up to cm 3.It has been suggested that the enhanced radiation-induced donor generation in these materials is related to the presence of interstial oxygen dimers O 2i, not present in DOFZ, which act as precursors for the formation of shallow donors [11]. In Fig. 3(a) we show the dependence of the full depletion voltage on the fluence after irradiation with 24 GeV protons (CERN, Geneva) [12] and reactor neutrons in Ljubljana, Slovenia [13]. Both curves show a pronounced minimum in the full depletion voltage curve at the inversion fluence. To determine the actual electric field distribution after the inversion fluence, where the detector should be considered as type-inverted, a transient current technique (TCT) experiment [14] has been performed with twin p-on-n single pad detectors made with n-type 1 ko cm Magnetic Czochralski silicon after irradiation with 24 GeV protons up to cm 2 and 1 MeV neutrons up to cm 2. Reconstruction of the electric field profile shows that there are three regions to consider in the n-type heavily irradiated detector (see Fig. 3(b)). Considering the partially depleted detector, (the proton irradiated data refer to V rev ¼ 28 V with V fd 5 V, and the neutron irradiated data to V rev ¼ 2 V with V fd 4 V), we observe two space charge regions, one at each contact, separated by a region with fairly low constant electric field produced by the reverse current flowing in the high resistivity neutral detector bulk, behaving like a resistor (TCT measurements are taken at T ¼ 295 K). For the proton irradiated detector, at the p + contact there is an extended space charge region with a positive charge while the negatively charged region at the n + contact is rather narrow. In the neutron-irradiated detector, the main high electric field region is placed at the back electrode. Thus the simple double junction picture of the irradiated detectors is confirmed, and the notion of type-inversion is traced back to the relative importance of the high field regions on the p + and n + contacts. As defects induced by radiation in Si are dominantly deep acceptor-like traps, type inversion is not expected in n-on-p Si detectors. Thus, p-type detectors have the critical advantage over customary p-on-n devices that the high electric field region is always at the readout electrode: the detector can be operated under-depleted, i.e. the bias voltage does not have to exceed the depletion voltage for efficient charge collection. On the other hand, the depletion voltage is expected to be higher since the radiationgenerated acceptors add to the initial doping density, while in n-type they compensate it. Under this assumption a number of n-on-p detectors have been up to now produced on p-type FZ, diffusion oxygenated FZ and MCz Si [15 17]. First productions of strip detectors with polysilicon biasing on p-type Magnetic Czochralski Si have V fd [V] Electric Field [V/cm] p + 4x1 4 n + 3x1 4 2x1 4 1x shown a non-uniformity of the full depletion voltage along the wafer. This effect is probably related to the thermally activated formation of oxygen aggregates (thermal donors) [17,18]. Studies to optimise the manufacturing process of p-type MCz Si detectors are still under way (Fig. 3). 5. Collected charge. 5.x x x1 15 Fluence 1 MeV n eq [cm -2 ] 24 GeV protons 2.1x1 15 cm -2 Reactor neutrons 5x1 14 cm -2 x [μm] 24 GeV/c protons Reactor neutrons Fig. 3. (a) Full depletion voltage of n-type MCZ Si as a function of the fluence after irradiation with a 24 GeV protons [12] and reactor neutrons [13]. (b) Electric field profile as determined by TCT in n-type MCz silicon after irradiation with 24 GeV protons up to cm 2 and with cm 2 1 MeV neutrons. TCT Measurements carried out at Ioffe Inst. S. Petersburg on two single pad detectors produced at ITC-IRST Trento by the SMART-INFN Collaboration. All the MCz Si wafers are from Okmetic, Finland. Fig. 4 shows the charge collected by single pad and microstrip detectors made with different rad-hard materials, after irradiation with fast hadrons up to the fluence of 1 16 cm 2 (normalised to 1 MeV neutron equivalent values) [3,7,15,18 2]. Detector thickness, operational temperature and shaping times of the electronic read-out system are listed in the legend. All data refer to a measurement performed with minimum ionising (mip) particles (mostly

5 758 ARTICLE IN PRESS M. Bruzzi et al. / Nuclear Instruments and Methods in Physics Research A 579 (27) # electrons p MCz Si 3μm; 1ns; -3 C; 8V p FZ Si 28μm; 25ns; -3 C; 8V n EPI 75μm; 25ns; -3 C; 3V 3D Si; 235μm; laser;-1 C;16V scvd Diam 77μm; 25ns; 2 C; 1V/μm pcvd Diam ; 25ns; 2 C; 1V/µm n EPI SiC 55μm;2μs; 2 C; 8V MeV n fluence [cm -2 ] Fig. 4. Collected charge with different materials after irradiation with fast hadrons up to the fluence of 1 16 cm 2 redrawn from Refs. [3,15,18 2]. The two curves are simulations employing different trapping constants: cm 2 /ns (broken line) and cm 2 /ns (solid line), respectively. electrons from a 9 Sr source) except for 3D devices that are measured with a laser source. Before irradiation the most probable value of the collected charge for Si, SiC and diamond are, respectively, 73, 55 and 36 e/mm. Data for p-type FZ Si from Ref. [15] have been normalised to 3 mm thickness. Both data for p-type Fz and MCz Si are taken before to annealing. For silicon, we considered only those data with an applied voltage sufficiently high (typically up to 8 9 V) to ensure full charge collection either by depleting the detector completely or to the thickness beyond which the charges are lost due to trapping. We normalised the data of radiation damage for polycrystalline CVD diamond (pcvd) and single crystal CVD diamond (scvd) to a most probable charge collection at zero fluence of respectively 8 e (pcvd) and 24 5 e (scvd, 77 mm-thick) [3]. We note that SiC is definitely less radiation hard than both diamond and silicon, at any fluence range. In terms of collected charge, diamond does not seem to be more radiation hard than silicon, and single crystal diamond seems to degrade more than polycrystalline CVD diamond films [3]. From the plot shown in Fig. 4, it is evident that for fluences below cm 2, thick, planar, p-type MCz and FZ detectors exhibit superior performance in terms of radiation hardness. Beyond this fluence threshold, the highest charge collection values are measured for 3D devices [21], characterised by columnar pn junctions inside the silicon bulk [22]. Up to now only 3D detectors on standard n-type FZ Si with a thickness of 235 mm have been tested with high radiation (although only with a laser source, which introduces a uncertainty about the absolute normalisation) [2]. These devices show, at cm 2, a signal of 713 e, which is much larger than that of a 75 mm thick epitaxial silicon (32 e) [18] and of a polycrystalline diamond (28 e measured at cm 2 ) [3]. The similarity of charge collection loss with fluence between the different materials is striking, and thus suggests to ascribe it to a charge trapping mechanism common to the different materials. In a simplistic model, useful to describe the behaviour qualitatively, only a part N(F) of the deposited charge N is collected. The reduction is both due to the inability to fully deplete the detector, so that depleted thickness d is less than the total detectors thickness, W, and due to trapping: d NðFÞ ¼N W expð cft sþ (4) where the trapping is described as an exponential decay with a factor depending on the ratio between the trapping time t t, and the transit time t s of the incident mip particle. At fluences below 1 15 neq/cm 2, the trapping time is measured to be inversely proportional to the fluence: 1=t t ¼ cf. (5) A much more thorough treatment of trapping in both pad and strip detectors, for electrons and holes including annealing can be found in Ref. [23]. Since in n-on-p type detectors the signal is mostly due to electron transport, we concentrate here on electron trapping only, and simulate the collected signal simply with a step-wise transport of electrons in a field of a p-type microstrip detector. Early estimations of the trapping parameter c, the constant for neutron damaged n-type pad detectors, in Eq. (5) gave c 1 ¼ cm 2 /ns, using the transient current technique (TCT) [23]. The dotted line in Fig. 4 has been calculated using this value, giving a bad description of the data. If we evaluate the fluence dependence of the collected charge in proton damaged p-type microstrip detectors [15] in terms of trapping, we find a trapping collected charge (#e) Fluence [1MeV n/cm 2 ] 4V 6V 8V Fig. 5. Predicted collected charge for 3 mm-p-type Si detectors as a function of the fluence for three different operational voltages. The curve is calculated employing c 2 ¼ cm 2 /ns as the trapping constant c.

6 M. Bruzzi et al. / Nuclear Instruments and Methods in Physics Research A 579 (27) constant of c 2 E cm 2 /ns. The solid line in Fig. 5 has been calculated using c 2 ¼ cm 2 /ns giving a good description of the data. Among possible explanations for the discrepancy between directly measured and extracted trapping parameters c we mention the saturation of the fluence dependence Eq. (4), and the existence of complicated field configurations inside the heavily irradiated detector, as described in the previous section. 6. Detector performance Most detector performance parameters depend on the signal-to-noise ratio S/N. While the signal S depends only weakly on the detector geometry for a given thickness (changing mainly due to charge sharing between neighbouring detector elements), the noise is dependent on the geometry of the detector element being read out, since both the capacitance and the leakage current scale with the length. To determine the detector performance as a function of the fluence we make the distinction between two main detector regions, depending on the radial distance from the collision point, as indicated in Fig. 1. Detectors in the inner region, where pixel layers are foreseen, should withstand fast hadron fluences in the range cm 2, while detectors in the outer region, where short/long strips will operate, must work after fluence lower than about cm Outer region As we already discussed, thick, planar detectors made on p-type MCz and/or FZ silicon are most promising in this fluence range. Using an approximate linear fluence dependence for the depletion voltage of 3 mm thick silicon strip detectors (SSD): V dep ¼ V þ bf (6) with V the pre-rad depletion voltage determined by the resistivity of the wafer. Its present value of the order 15 2 V should be reduced in the future. There is uncertainty about the slope b in Eq. (6). We estimate from Ref. [24] b ¼ V/cm 2 for MCz, b ¼ V/cm 2 for FZ. The depleted detector thickness d is given by the physical thickness W when the bias voltage V bias is larger than the depletion voltage V fd and scales like the square root of the ratio V bias /V fd when it is smaller. d ¼ W; V bias XV fd rffiffiffiffiffiffiffiffiffiffi V bias d ¼ W; V bias ov fd. ð7þ V fd Fig. 5 shows the charge collection simulated for three different depletion voltages as a function of the fluence (with V ¼ 161 V and 3 mm-thick detector), taking into account Eqs. (6) and (7). The line added to the plot is the best fit found for the collected charge in Fig. 4. We observe in Fig. 5 that the operational voltage is only slightly affecting the collected charge as a function of the fluence. This is due to the fact that the signal is affected both by the inability to deplete the detector and by trapping, as expressed in Eq. (4). Beyond a fluence of about 1 15 neq/cm 2, trapping which is almost bias independent becomes more important than the ability to deplete the detector. Still, a bias of 6 V is preferred over 4 V because of better charge collection, while 6 V is preferred over 8 V because of reduced heat generation, at about the same charge collection efficiency. In case the slope b in the fluence dependence of the depletion voltage Eq. (6) is increased by a factor 2, the points in Fig. 5 for bias voltage in Fig. 5 needs to be raised from 4 to 6 V and from 6 to 8 V to yield the same charge. S/N S/N um, -2deg, 4V 3um, -2deg, 6V 3um, -2deg, 8V 1.E+12 1.E+13 1.E+14 1.E+15 1.E+16 Fluence [neq/cm 2 ] um, -2deg, 4V 2um, -2deg, 6V 2um, -2deg, 8V 1.E+12 1.E+13 1.E+14 1.E+15 1.E+16 Fluence [neq/cm 2 ] Fig. 6. Signal-to-noise ratio S/N for p-type MCz Si short strip SSD as a function of fluence for two detector thicknesses: (a) 3 mm, (b) 2 mm. The operating voltage is varied from 4 to 6 to 8 V. The leakage current constant is set to a p ¼ A/cm. The operating temperature is set at 2 1C. The strips are 3 cm long with a pitch of 8 mm.

7 76 ARTICLE IN PRESS M. Bruzzi et al. / Nuclear Instruments and Methods in Physics Research A 579 (27) The RMS noise value s Noise of the detector can be parameterised in the form: s 2 Noise ¼ðA þ BCÞ2 þð2it s Þ=q (8) where C is the total capacitance, and the second term is due to the leakage current I (with t s the shaping time and q the electron charge). For A and B we will adopt numbers characteristic of the ATLAS silicon tracker (SCT), A ¼ 5 e, and B ¼ 6 e /pf, which are also typical for a recent CMOS design in Deep submicron CMOS [25]. An ATLAS SCT shaping time of t s ¼ 2 ns is assumed. The largest contributor to the capacitance, the interstrip capacitance, depends on the geometry of the implants, the starting material (n-type vs. p-type) and on the way the surface is processed, for example p-stop implants vs. p- spray and the p-spray dose. A recent study on the effects of radiation on the surface properties of p-type SSD, e.g. the interstrip capacitance and isolation and the breakdown voltage indicate that ionising radiation of a few 1 krad improves the surface parameters so that they become comparable to n-type detectors [26]. The dependence of the total capacitance on the bias, i.e. on the depletion depth of the detector is deemed to be small for fluences up to neq/cm 2, where the depleted thickness is 2 mm or more. A minor point of interest is the question if the relatively small back plane capacitance becomes independent of bias as the neutral bulk of the silicon detector is almost intrinsic and the space charge is due to very deep levels, which do not react to high frequency signals. The temperature dependence of the noise in Eq. (8) is due to the temperature dependence of the leakage current Eq. (1). Fig. 6 shows the signal-to-noise ratio S/N as a function of fluence neq for short strips (6 pf) for two detector thicknesses (3 and 2 mm), and three maximum bias voltages (4, 6, 8 V), for an operating temperature of 2 1C. As mentioned above, the detectors need to be biased at their depletion voltage or at the maximum voltages, whichever is smaller. The choice of the maximum bias voltage plays a role only in the fluence range of neq/cm 2 : much below that fluence, the depletion voltage of 3 mm detectors is below 4 V, and much above that fluence, the trapping effects limit the depth of the effective active region. There seems to be no advantage to using thinner detectors Innermost region One of the main limitations in the performance of heavily irradiated Si pixel detectors is the high leakage current reached at these fluence levels. We already observed that this can be partially mitigated by decreasing the temperature. Fig. 7 shows the typical leakage as a function of the temperature of a Si pixel with area 5 3 mm 2 operated at 6 V: at R ¼ 5 cm and 5 fb 1 ( cm 2 ) and R ¼ 7 cm, 25 fb 1 ( cm 2 ). The inset shows the dependence of the leakage current on the radius at T ¼ 3 1C for a fluence of 1 16 cm 2 (for R ¼ 5 cm this corresponds to 5 fb 1 ). Although the total thickness of the detector is 3 mm, due to the radiation-induced effective doping increase with the fluence, the depleted thickness can be less than the detector thickness in this range, both depending on radius and 1 A = 5x3 μm 2 - V = 6V 1 2x1 16 cm -2 2x1 15 cm -2 I [na] 1 1 I [na] 8 7 T = -3 C 6 φ = 1 16 cm R [cm] Temperature [ C] Fig. 7. Typical leakage current as a function of the temperature of a Si pixel with area 5 3 mm 2 operated at 6 V: at radius R ¼ 5 cm and 5 fb 1 ( cm 2 ) and R ¼ 7 cm, 25 fb 1 ( cm 2 ). The inset shows the dependence of the leakage current on the radius at T ¼ 3 1C for a fluence of 1 16 cm 2 (R ¼ 5 cm, 5 fb 1 ).

8 M. Bruzzi et al. / Nuclear Instruments and Methods in Physics Research A 579 (27) integrated luminosity. The plot of Fig. 7 shows that to get an upper limit of 1 na in the operational current, it will be necessary to operate at temperatures in the range p 3 1C. 7. Conclusions The unprecedented challenges for a semiconductor tracker at the LHC upgraded can be met by silicon detectors now under investigation. For the outer and mid-radius region, where the performance is much determined by the depletion characteristics, strip detectors based on p-type material (either FZ or MCz) will afford the advantage of electron collection and the safety margin of operating the detector under-depleted. For pixel detectors at small radii, trapping will be the limiting effect, almost independent of the detector material. Thus 3D silicon detectors, which offer short collection distances, seem to be the only solution to assure sufficient charge collection. Because of the strong temperature dependence of the silicon detector leakage current, careful thermal management of the entire tracker will be needed. With respect to silicon, diamond should present the advantage of trivial cooling and a reduced leakage current noise in the highest fluence range. In addition, the lower dielectric constant of diamond reduces the capacitance and thus the parallel noise in Eq. (8) when compared with Si. How this advantage can be used will depend on the ability to lower the threshold of the readout electronics to about 1 electrons. Scarce commercial availability and high cost of the material are nonetheless severe limitations to the future large-scale use of diamond sensors. References [1] F. Giannotti, et al., Physics potential and experimental challenges of the LHC luminosity upgrade, 22, /hep-ph/2487s. [2] The RD5 collaboration, CERN-LHCC-24-31, / cern.ch/rd5s. [3] W. Adam, et al. (The RD42 Collaboration), Development of diamond tracking detectors for high luminosity experiments at the LHC, CERN/LHCC 26-1 LHCC-RD-1, Status Report/ RD42, March 1, 26. [4] R. Horisberger, CMS workshop on detectors and electronics for SLHC, CERN, 24. [5] S. Baranov, M. Bosman, I. Dawson, V. Hedberg, A. Nisati, M. Shupe, Estimation of radiation background, impact on detectors, activation and shielding optimization in ATLAS atlas radiation background task force summary document, ATL-GEN-25-1, 13 January 25. [6] H.F.-W. Sadrozinski, A. Seiden, Nucl. Instr. and Meth. A 541 (25) 434. [7] F. Moscatelli, A. Scorzoni, A. Poggi, M. Bruzzi, S. Sciortino, S. Lagomarsino, G. Wagner, I. Mandic, R. Nipoti, IEEE Trans. Nucl. Sci. NS-53 (3) (25) [8] M. Bruzzi, IEEE Trans. Nucl. Sci. NS-48 (4) (21). [9] M. Bruzzi, S. Miglio, S. Pirollo, S. Sciortino, Diamond Relat. Mater. 1 (3 7) (21) 61. [1] The Rose Collaboration RD48, / [11] I. Pintilie, M. Buda, E. Fretwurst, G. Lindström, J. Stahl, Nucl. Instr. and Meth. A 556 (26) 197. [12] E. Tuovinen, J. Ha rko nen, P. Luukka, E. Tuominen, E. Verbitskaya, V. Eremin, I. Ilyashenko, A. Pirojenko, I. Riihimäkic, A. Virtanen, K. Leinonen, Nucl. Instr. and Meth. A 568 (1) (26) 83. [13] A. Candelori, Nucl. Instr. and Meth. A 56 (1) (26) 13. [14] D. Creanza, D. Bassignana, L. Borrello, M. Boscardin, M. Bruzzi, M. de Palma, E. Focardi, A. Macchiolo, N. Manna, D. Menichelli, A. Messineo, C. Piemonte, A. Pozza, V. Radicci, M. Scaringella, N. Zorzi, Nucl. Instr. and Meth. A, these proceedings, doi:1.116/j. nima [15] G. Casse, et al., Nucl. Instr. and Meth. A 535 (24) 362. [16] M. Bruzzi, D. Bisello, L. Borrello, E. Borchi, M. Boscardin, A. Candelori, D. Creanza, G.-F. Dalla Betta, M. DePalma, S. Dittongo, et al., Nucl. Instr. and Meth. A 552 (1&2) (25) 2. [17] M. Bruzzi, et al., J. Appl. Phys. 99 (26) [18] G. Kramberger, et al., in: Eighth RD5 Workshop, Prague, June 26. [19] M. Bruzzi, et al., Charge collection measurements in magnetic Czochralski n- and p-type Si microstrip and diode detectors, this conference. [2] C. DaVià, et al., 3D active edge silicon sensors: test results, this conference. [21] S.I. Parker, et al., Nucl. Instr. and Meth. A 395 (1997) 328. [22] M. Scaringella, et al., Charge collection in single-column 3D detectors, this conference. [23] V. Cindro, G. Kramberger, M. Lozano, I. Mandić, M. Mikuž, G. Pellegrini, J. Pulko, M. Ullan, M. Zavrtanik, Trapping of electrons and holes in p-type silicon irradiated with neutrons, in: IEEE Nuclear Science Symposium, San Diego, CA, USA, 3 October 26. [24] D. Creanza on behalf of the SMART project, in: Sixth RD5 Workshop, Helsinki, 2 4 June 25 / 6th-workshop/S; M. Lozano, et al., in: RD5 Workshop, 24. [25] J. Kaplon, et al., Fast CMOS binary front-end for silicon strip detectors at LHC experiments, in: IEEE NSS-MIC, Rome, 24. [26] H.F.-W. Sadrozinski, et al., Total dose dependence of oxide charge, interstrip capacitance and breakdown behavior of slhc prototype silicon strip detectors and test structures of the SMART collaboration, this conference.