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Characterization of non-uniformly irradiated silicon micro-strip sensors
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 571 (2007) 636–643 www.elsevier.com/locate/nima
Characterization of non-uniformly irradiated silicon micro-strip sensors M.E. Dinardoa,, G. Alimontib, G. Chiodinic, P. d’Angelob, L. Moronib, S. Salab a
INFN and Universita` degli Studi di Milano, Italy b INFN Milano, Italy c INFN Lecce, Italy
Received 3 May 2006; received in revised form 7 November 2006; accepted 7 November 2006 Available online 5 December 2006
Abstract We describe a method we used to characterize micro-strip sensors, which were non-uniformly irradiated up to a fluence of 1014 1 MeV equivalent neutrons per cm2 . The method allows for a complete bidimensional mapping of the sensor characteristics over the entire active area. Information is gathered through the Q–V characteristic, measured scanning the sensor with an infra-red laser source. Q–V characteristics are then fitted to a simple analytical model, which returns local full-depletion voltages, carrier lifetimes, etc. With the present method one can even obtain the profile of the absorbed fluence. The development and tuning of the present method have been done in the context of the R&D programs for the micro-strip forward tracker of the BTeV experiment at the Tevatron. r 2006 Elsevier B.V. All rights reserved. PACS: 29.40.Gx Keywords: Laser; Radiation hardness; Sensor characterization; Silicon micro-strip
1. Introduction One of the main issues in employing silicon detectors in HEP experiments is to certify through dedicated measurements their radiation tolerance [1]. This is particularly crucial for detectors which are going to be used at hadron colliders, where the total fluence after 10 years of operation can reach values well in excess of 1014 1 MeV equivalent neutrons per cm2 . The picture is even more complicated in the presence of highly non-uniform irradiation since the performance of the sensors can dramatically vary over the active area. In these cases, a point to point characterization of the sensors is required. To this extent we developed a simple analytical model, which was employed to fit the local Q–V characteristics measured on several points of a silicon micro-strip sensor previously irradiated up to a fluence of 1014 200 MeV protons per cm2 and hence extract the main physical parameters. The local Q–V characteristic was measured by illuminating the sensor with an infra-red laser source. We were able to perform a full Corresponding author.
E-mail address: [email protected] (M.E. Dinardo). 0168-9002/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2006.11.038
bidimensional characterization of the sensor over its entire active area. In each point we measured the local fulldepletion voltage and the local carriers trapping-time. As expected, we observed a smooth transition from the original n-type to the inverted type bulk behaviour moving along the strips toward the most irradiated zone. From the measurement of the carriers trapping-time we were able to reconstruct the absorbed dose profile and compare it with the actual one measured by the irradiation facility. All arguments reported in this article are extensively detailed in Ref. [2]. 2. Collected charge model In this model we approximate the sensor with a simple p/n diode with infinite plane electrodes. To the extent of describing the total collected charge by all the strips, the validity of this approximation is only limited by the different electric field configuration in a small region [3] near the p-implant, which could in principle affect the evaluation of the collected charge in case of very short carrier trapping-times, as those typical for highly irradiated sensors. It turns out that even in these cases this effect is
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completely negligible because of other much more important distortions of the electric field caused by the radiation damage. We will discuss this issue in the next section, when we introduce the extensions of this model. For non-irradiated sensors, i.e., for long carrier trappingtimes, our model reproduces the data with excellent accuracy, as shown in Fig. 3. This means that the development of the depleted region with the bias voltage is well reproduced even in proximity of the p-implant. This also demonstrates that the assumption we made of an uniform density of charge generated by the laser in the bulk of the sensor is correct. The main advantage of the present approach is that applying a very simple approximation is possible to obtain an analytical expression for the total collected charge, which is extremely advantageous for these kinds of applications. We begin by describing the transport of the charge carriers during their migration toward the electrodes and we will then exploit the Ramo theorem to calculate the total induced charge. 2.1. Transport In the case of a p/n diode with infinite plane electrodes, the problem one has to deal with becomes monodimensional, the only surviving coordinate being x along the electric field lines. The mean free path, lðxÞ, for trapping is given by lðxÞ ¼ tvðEðxÞÞ
(1)
with t ¼ svth1N t . E is the electric field, v the drift velocity, t the carrier trapping-time, s the trapping cross-section, vth the thermal velocity and N t the effective trap concentration. While t is independent on the electric field, the drift velocity depends on it through the relation [4]: vðEÞ ¼
m0 E 1 þ ðm0 =vs ÞE
(2)
m0 is the mobility and vs is the saturation velocity (88 mm ns1 for holes and 116 mm ns1 for electrons). The mobilities we used were rescaled from the quoted values at 300 K (507 cm2 V1 s1 for holes and 1590 cm2 V1 s1 for electrons) according to the well-known relations: mh / T 2:2 and me / T 2:4 [5]. There is no evidence that the mobilities and saturation velocities change with irradiation [6]. The solution of the Poisson equation for a constant fixed charge density is a linear electric field: ( Ax if V b pV d ; EðxÞ ¼ (3) Ax þ B if V b 4V d : The x coordinate is defined only within the depleted region and is zero on the side where the electric field vanish. It is possible to express the electric field in terms of the bias voltage V b , the full-depletion voltage V d and the bulk d width w. In this case A and B can be written as A ¼ 2V and w2 d B ¼ V b V . w
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The residual charge density, rðx1 ; x2 Þ, either electrons or holes, for a charge density, rðx1 Þ, generated by ionization at x1 and reaching x2 subject to trapping, is R x2 dx=lðxÞ rðx1 ; x2 Þ ¼ rðx1 Þe x1 . (4) Eq. (4) can be explicitly calculated by using Eqs. (1) and (2). In order to obtain an analytical expression for the collected charge, we approximated at first order the exponential term in the equation, obtaining: Eðx2 Þ 1=tm0 A x2 x1 rðx1 ; x2 Þ ¼ rðx1 Þ 1 . (5) Eðx1 Þ tvs This approximation is justified as long as ðx2 x1 Þ5ðtvs Þ, which is satisfied for tb5 ns, since the highest value that x2 x1 can assume is the bulk thickness, 320 mm, and the lowest saturation velocity is 88 mm ns1 for holes. 2.2. Induction By applying the Ramo theorem one can obtain the total charge induced at the electrodes: Z XZ X 1 QI ¼ rðx; x0 ÞEðxÞ dx dx0 (6) V b 0 x0 qffiffiffiffiffi b where X ¼ w V V d is the depth of the depleted region. Integrating explicitly Eq. (6), the expressions for the charge signal induced by holes, QIh , and electrons, QIe , can be obtained r0 2 Rh QIh ¼ EðX Þ3 3ð1 þ Rh Þ V b A2 ð2 Rh Þ EðxÞ3 EðX Þ X ð1 þ Rh Þth vsh Að2 þ Rh Þ EðX Þ2Rh B1þRh B B3 þ 1 þ Að2 þ Rh Þth vsh 1 þ Rh 3 3 r0 EðX Þ EðX Þ X þ V b A2 ð2 Rh Þth vsh 1 þ Rh 4A EðX Þ2Rh B1þRh EðX Þ B4 X þ Að3 Rh Þ 1 þ Rh 4Að3 Rh Þ ð7Þ r0 EðX Þ3 EðX Þ1Re B2þRe QIe ¼ 3 1 Re V b A2 ð2 þ Re Þ 1 EðX Þ 1þ X te vse Að2 Re Þ B4 2 þ Re þ þ B3 ð1 Re Þð2 Re Þte vse 3ð1 Re Þ r0 EðX Þ4 þ 2 4Að3 þ Re Þ V b A ð2 þ Re Þte vse 1Re 3þRe EðX Þ B B4 þ Að1 Re Þð3 þ Re Þ 4Að1 Re Þ
ð8Þ
ARTICLE IN PRESS M.E. Dinardo et al. / Nuclear Instruments and Methods in Physics Research A 571 (2007) 636–643
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ReðhÞ is defined as ReðhÞ ¼ teðhÞ1 m
eðhÞ A
. It is worth noting that in
doing these calculations we had tacitly assumed a constant free charge density, r0 , generated by the laser pulse through the whole depleted region [7,8]. Our data seem to confirm this assumption. So far this model has four free parameters: r0 , the initial free charge density in the bulk, generated by the laser pulse; te , the electron trapping-time; th , the hole trapping-time; V d , the full-depletion voltage. The number of free parameters can be reduced to three using the empirical relation [9]: 1 teðhÞ
¼
MeV geðhÞ F1eq:n:
(9)
which relates the trapping-times of electrons and holes to the radiation fluence. The coefficients geðhÞ are known from literature and are in units of ns1 ð1014 1 MeV eq:n:=cm2 Þ1 , and do not depend on the sensor type. For instance, at 10 C, ge ¼ 0:042 0:003 for electrons and gh ¼ 0:061 0:003 for holes [10]. Thus g (10) th ¼ e te . gh This model can be easily extended to accommodate effects due to non-linearities of the electric field which are typically observed on irradiated sensors [11–14]. To this extent we allow for an additional fit parameter, V off . This defines a kind of effective bias voltage, V 0b ¼ V b V off , which should replace V b in our previous equations. In the case of an excess of charge close to the p-implant, which is typically caused by positive charge trapped in the oxide layer, V off acts as an initial offset voltage, which saturates the charge excess; for V b values higher than V off , the sensor quickly reaches the canonical asymptotic behaviour in V 0b . This requires that the first measurement points, up to voltages of the order of V off , should be eliminated from the fit. In an analogous way, V off is even able to allow for huge deviations from linearity of the electric field, as those encountered at very high absorbed doses, which could be explained by trapping of generation currents in acceptor and donor traps [15]. At the end, this model has four free parameters, namely: r0 , te , V 0d and V off . We studied in detail the systematics that the assumption of linear electric field inside the bulk and the first-order approximation in the transport equation, Eq. (5), might introduce in the extraction of the main physical parameters, fitting with our model different sets of Q–V characteristics, which were accurately simulated. We also estimated the effects introduced by the fact that the geðhÞ coefficients are not well known. To do this we run the simulation with the coefficient ratio of Eq. (10) displaced from its central value by s, where s is the error on the ge =gh ratio measurement. From these studies and many others, performed for different field configurations and absorbed doses (for a detailed description of these studies cf. Ref. [2]), we can conservatively estimate the systematics on the fit parameters as reported in Table 1.
Table 1 Estimation of the systematics on the fit parameters Fit parameters
Systematics (%)
Electron trapping-time (te ) Full-depletion voltage (V d ¼ V 0d þ V off ) Initial charge density (r0 )
6 6 2
3. Sensors and readout electronics features The silicon micro-strip sensors, which have been studied in this paper, are the same as those produced by Hamamatsu for the second layer of the Inner Barrel (IB2) of the CMS experiment. The sensors are made in standard FZ silicon with p-implant micro-strips on an ntype bulk, 320 mm thick, with crystal orientation h1 0 0i and resistivity 2:5 kO cm1 (i.e., 150 V initial full-depletion voltage). They have 512 strips, 116 mm long and with a 120 mm pitch. Each strip has a pþ implant width of 30 mm, AC-coupled to an aluminum metallization 40 mm wide. The readout chip employed is the TAA1 produced by Ideas [16] in 0:8 mm CMOS technology. Each chip has 128 channels and from each channel the analog signal can be readout. The main characteristics of the TAA1 chips are the 3 ms shaping time, that guarantees a very low noise of 150 e per channel, and the possibility to readout either positive or negative input signals. The data acquisition system is the VA–DAQ, comprising of a LabVIEW readout software and a board to interface the PC to the TAA1 chips, provided by Ideas [17] as well. One of the main features of the VA–DAQ board is to digitize, in two’s complement with a 14 bit ADC, the analog signal coming from the TAA1 chips; moreover it provides an internal pulser used to characterize each single channel of the chips. 4. Irradiation and global behaviour We irradiated the sensors at Indiana University Cyclotron Facility (IUCF) [18] with a proton beam of 200 MeV energy. The beam shape, measured with a wire scanner technique, was quasi-Gaussian with sx ¼ sy ’ 19 mm and was approximately centered on the edge of the sensor opposite to the readout electronics, as shown in Fig. 1. We irradiated the sensor up to a peak fluence of 0:8 1014 1 MeV equivalent neutrons per cm2 . Since 200 MeV energy protons cause approximately the same damage as 1 MeV energy neutrons, we used a hardness factor k ¼ 1 for fluence rescaling [19] in the usual conversion formula, MeV MeV F1eq:n: ¼ kF200 . The sensor, after irradiation, was p: always kept at a temperature lower than 12 C in order to prevent any annealing. The first plot of Fig. 2 reports the I–V characteristics measured at different fluences during irradiation. On the second plot of Fig. 2 we compare the measured leakage current at VRbias ¼ 400 V, with the MeV empirical formula I leak ¼ a w F1eq:n: ðx; yÞ dx dy for several values of the fluence. Since the irradiation was
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non-uniform, we calculated the total absorbed dose by integrating the two-dimensional Gaussian shape of the MeV proton beam, F1eq:n: ðx; yÞ, over the sensor surface 7 (a ¼ 4:56 10 A cm1 was taken from literature [20]). The expected behaviour of the leakage current with the fluence is confirmed by our measurements. We also measured the noise on strips before and after irradiation. We observed an appreciable increase of its value due to the irradiation from 985 to 1200 e . 5. Laser setup and measurements An infra-red laser source of 1064 nm wavelength [21] was used to locally generate electron–hole pairs in the bulk of
Fig. 1. Irradiation geometry. Shown are the proton beam Gaussian shape and the approximated position of the beam peak which was centered on the edge of the sensor, opposite to the readout electronics.
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the sensor. In order to perform a bidimensional scan of the sensor, we placed the detector on an X –Y moving table and the laser beam focusing lens directly on the fixed Z-axis of the table. The sensor was kept at 12 C by a water–glycol refrigeration system. The atmosphere around the detector was filled with nitrogen to prevent condensation. We illuminated the sensor on the strip side. In this situation, only the fraction of the laser light impinging on the sensor between adjacent strip metallizations could reach the bulk of the sensor. To reduce to a negligible level the dependence of the quantity of absorbed light on the source position, we illuminated a wide region, 20 strips, by placing the sensor out of the focal plane of the lens. Given the ratio of metallization to pitch, 40 mm=120 mm, only 23 of the laser light penetrated the bulk. For each position of the laser beam and for different bias voltages, we sent 1000 laser pulses and we measured the collected charge. The total collected charge was obtained by summing up all the signals of the illuminated strips, once equalized and common-mode subtracted. Fig. 3 shows two typical sets of measurements with superimposed the fit with our model. Empty triangles and circles represent the two contributions, due to electrons and holes, respectively, to the total signal. For n-type bulk, holes are the carriers that give the highest contribution. This fact is explained reminding that, for non-irradiated sensors, holes drift toward higher electric field magnitude, thus, the integral of the work done by the electric field on this type of carrier is greater than the work done on electrons. In case of moderate irradiation, before type inversion, the carriers trapping-time is decreased and both electrons and holes might be trapped before reaching the electrodes. In this situation, due to the higher mobility of electrons, the electron contribution rises and becomes dominant even before type inversion. In case of high irradiation the bulk
Fig. 2. First plot: I–V characteristics measured during irradiation. In the inset, in the upper right corner, is shown the I–V characteristic before irradiation. Second plot: leakage current, measured biasing the sensors at 400 V, as a function of the fluence. The straight line is the expected empirical curve taken from literature. All the measurements were performed at room temperature.
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×103
×103 1000
1000
800 Q [ e-]
Q [ e-]
800 600 400
Data Fit Holes Electrons
200 0
600 400 Data Fit Electrons Holes
200 0
0
100
200 300 Bias [V]
400
500
0
100
200
300 Bias [V]
400
500
Strip 77 0
160 140 120 100 80 60 40 20 0
20 40 60 80 100 Coord. Along Strips [mm]
Full-depletion Voltage [V]
160 140 120 100 80 60 40 20 0
Full-depletion Voltage [V]
Full-depletion Voltage [V]
Fig. 3. Q–V characteristic with superimposed the fit obtained from the model. First plot: data from the lowly irradiated region. Second plot: data from the highly irradiated region.
Strip 281 0
160 140 120 100 80 60 40 20 0
20 40 60 80 100 Coord. Along Strips [mm]
Strip 470 0
20 40 60 80 100 Coord. Along Strips [mm]
Fig. 4. Full-depletion voltage along strips: strip 281 shows a minimum at 90 mm from chip side, as expected for intrinsic silicon. The errors reported are those returned by the fit. An error of 6%, coming from the systematics of the model, should be added.
300
250 200 150 100 50
75 80 85 90 95 100 105 110 115 Coord. Along Strips [mm]
250
Strip 281
200 150 100 50 75 80 85 90 95 100 105 110 115 Coord. Along Strips [mm]
Trapping-time [ns]
300 Strip 77
Trapping-time [ns]
Trapping-time [ns]
300
250
Strip 470
200 150 100 50 75 80 85 90 95 100 105 110 115 Coord. Along Strips [mm]
Fig. 5. Trapping-time along strips: strip 281 shows the lowest trapping-time value, where the irradiation beam was centered. The errors reported are those returned by the fit. An error of 6%, coming from the systematics of the model, should be added.
becomes of p-type and the junction moves toward the back-plane. In this case, the electrons drift toward the higher electric field region and always give the highest contribution to the total signal. 6. Results and discussion In our case the statistical measurement error of our Q–V characteristics is negligible with respect to the systematic error due to the relative instability of the employed setup,
which can be a priori estimated around 1% taking into account the laser system stability and temperature fluctuations. Actually, we cross-checked this guess by estimating the systematic error required to obtain an average w2 value equal to the number of degrees of freedom for the fits to the data taken in the non-irradiated region of the sensor, where our model is expected to closely reproduce the measurements. The required systematic error turned out to be 1:2%. This is the value we used for our measurements.
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6.1. Results on full-depletion voltage and carriers trappingtime We performed a detailed map of the sensor active area by measuring Q–V characteristics in 45 different points. We will now discuss the evolution of full-depletion voltage and carriers trapping-time along the strips, considering three significant examples: two lateral strips, 77 and 470, and a central strip, 281. Fig. 4 reports the full-depletion voltage along the three strips. All strips show a big drop of the measured fulldepletion voltage corresponding to highest irradiated region. For the central strip the full-depletion voltage reaches a minimum at 90 mm from chip side, then it starts raising again. Fig. 5 shows the carriers trapping-time along the three considered strips. The trapping-time diminishes going toward the highest irradiated side and reaches a value above 50 ns on the two lateral strips and 20 ns on the central strip. These measurements are fully consistent with the picture where the radiation beam was centered approximately on the edge of the sensor opposite to the
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readout electronics. In Tables 2–4 we summarize the result of our measurements. We do not report the same table for the r0 parameter since all values are consistent with 3300 e within 2%. 6.2. From trapping-time to fluence From the carriers trapping-time we easily recovered the radiation fluence through the empirical relation expressed Table 4 Additional measurement points in the highest irradiated region for strips 110, 174 and 311, at 110 mm with respect to the non-irradiated side V d and t for strips 77, 110 and 174 at 110 mm Parameter
# strip
Vd t
110
174
311
16:1 1:3 45:5 2:2
19:8 1:7 30:3 1:2
31:5 1:7 26:2 1:3
The errors reported are those returned by the fit. An error of 6%, coming from the bias of the model, should be added as reported in Table 1.
Table 2 Fit results on full-depletion voltage Full-depletion voltage D (mm)
10 40 60 80 90 100 110
# strip 77
145
208
281
344
470
98:4 1:6 123:9 1:6 124 2:0 145:8 2:6 102:5 3:9 39:6 3:0 25:5 1:2
103:9 1:5 128:0 1:7 117:0 1:8 106:6 3:9 75:2 3:9 23:0 1:3 21:7 1:5
100:9 1:4 120:3 1:6 140:5 2:9 80:5 3:6 38:0 7:5 22:6 1:4 31:3 1:5
107:4 1:5 123:5 1:6 115:2 3:3 86:8 5:2 15:0 7:1 24:1 1:5 41:7 1:7
102:2 1:4 111:7 1:4 134:7 1:7 102:0 3:7 50:5 2:9 21:0 1:2 30:8 1:4
101:0 1:4 131:2 1:6 150:4 1:2 149:0 2:4 109:2 3:8 58:9 2:7 28:6 4:8
The data reported are the sum of the effective full-depletion voltage, V 0d , and the V off parameter. The errors reported are the sum in quadrature of the errors returned by the fit on the two parameters. An error of 6%, coming from the bias of the model, should be added as reported in Table 1. D: distance from chip side.
Table 3 Fit results on trapping-time Trapping-time D (mm)
10 40 60 80 90 100 110
# strip 77
145
208
281
344
470
1000 1000 1058 1282 242 98 84:3 18:4 67:4 6:5 50:8 2:7
1000 1000 1962 3157 162 84 72:3 14:0 40:1 1:6 35:7 1:5
1000 1000 1237 681 74 10 59:8 6:1 38:0 1:6 29:3 1:4
1000 1000 930 579 68 11 67:6 4:3 37:6 1:6 25:5 1:5
1000 1000 2768 3404 70 13 62:7 7:5 44:2 1:9 29:2 1:3
1000 1000 800 688 1665 1555 77:1 14:6 70:3 9:0 61:3 5:0
The errors reported are those returned by the fit. An error of 6%, coming from the bias of the model, should be added as reported in Table 1. D: distance from chip side. For the first 12 measurement points, which belong to the non-irradiated side, the carrier trapping-time parameter was fixed to 1000 ns.
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Coord. Transv. Strips [mm]
by Eq. (9). The sensor fluence-map was fitted with a 2DGaussian shape giving the radiation beam profile shown in Fig. 6. Reconstructed fluence profiles at 80 mm, (A), and 110 mm, (B), are shown in Fig. 7. Our measurements are in good agreement with the beam measurements provided by Indiana University Cyclotron Facility, reported in Table 5 and obtained with a completely different technique. The consistency w2 and the corresponding CL, in the worst case scenario of Indiana measurements with negligible errors, are 4% and 26%, respectively. This is an important cross-check for the reliability of our model. It demonstrates that our extraction/measurement of the carrier trappingtimes at different doses are consistent with data and, indirectly, it confirms the measurements of the geðhÞ coefficients by the ROSE collaboration [10]. It is also important to notice that the lowest full-depletion voltage for the central strip in Fig. 4 is measured at a radiation fluence of 0:35 1014 1 MeV equivalent neutrons per cm2 , in agreement with the expected fluence needed to obtain type inversion for this kind of sensors [1].
(A)
80
7. Conclusions With a very simple method based on an analytical model for the Q–V characteristics we were able to extract the main physical information required to assess the radiation tolerance of silicon sensors to be used in HEP experiments. The method allows for a point to point characterization of Table 5 Radiation beam properties Beam properties
IUCF measurement
Our measurement
Peak (1 MeV eq.n. per cm2) Width (mm)
0:8 1014
ð1:01 0:12Þ 1014
sx ¼ sy ’ 19
sx ¼ 21:9 3:0 sy ¼ 19:0 0:8
Consistency w2 : 4 ðCL26%Þ Comparison between irradiation profile gathered through our model and the beam characteristics measured at IUCF with the wire scanner technique.
1
(B)
0.8
60 40
0.6
20
0.4
0
0.2
-20 0 0
20
40
60
80
100
120
140
160
180
200
220
Coord. Along Strips [mm]
χ2 / ndf Coef Mean Sigma
1 0.8
5.294 / 3 0.3769 ± 0.0408 29.61 ± 1.10 11.76 ± 0.74
0.6 0.4 0.2 0
Fluence [1014 1MeV eq.n.] [cm]-2
Fluence [1014 1MeV eq.n.] [cm]-2
Fig. 6. Contour plot of the fluence profile (colour scale is in unit of 1014 1 MeV equivalent neutrons per cm2 ). The fit parameters are: ð1:01 0:12Þ 1014 1 MeV equivalent neutrons per cm2 , mean along strips 120 6 mm, sx along strips 21:9 3:0 mm, mean transverse to strips 33:4 1:5 mm, sy transverse to strips 19:0 0:8 mm. Dashed line: sensor position. (A) and (B) refer to the fluence profile reported in Fig. 7.
1 0.8 0.6 2.053 / 6 χ2 / ndf Coef 0.9098 ± 0.0390 Mean 32.32 ± 0.77 18.69 ± 1.02 Sigma
0.4 0.2 0
0
10
20
30
40
Coord. Transv. Strips [mm]
50
60
0
10
20
30
40
50
60
Coord. Transv. Strips [mm]
Fig. 7. Reconstructed fluence profiles. First plot: 80 mm from chip side; cf. (A) in Fig. 6. Second plot: 110 mm from chip side, corresponding to the highest irradiated region; cf. (B) in Fig. 6.
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the sensor, which is particularly important in case of a highly non-uniform irradiation. The analytical model has four free parameters only and it is capable to extract reliable information even in the case of highly radiationdamaged sensors. This method has also been proven to provide a very good estimate of the dose locally absorbed by the sensor. References [1] ROSE Collaboration, Nucl. Instr. and Meth. A 466 (2001) 308. [2] M.E. Dinardo, Ph.D. Thesis, FERMILAB-THESIS-2005-66, December 2005, 158pp, on hhttp://lss.fnal.gov/archive/thesis/fermilab-thesis2005-66.shtmli. [3] G. Kramberger, V. Cindro, I. Mandic´, M. Mikuzˇ, M. Zavrtanik, IEEE Trans. Nucl. Sci. NS-49 (4) (2002) 1717. [4] S.M. Sze, Physics of Semiconductor Devices, second ed., Wiley, Singapore, 1981. [5] V. Eremin, Z. Li, Nucl. Instr. and Meth. A 362 (1995) 338. [6] T.J. Brodbeck, A. Chilingarov, T. Sloan, E. Fretwurst, M. Kuhnke, G. Lindstroem, Nucl. Instr. and Meth. A 477 (2002) 287. [7] S. Gadomski, M. Turala, E. Barberis, N. Cartiglia, J. Leslie, H.F.-W. Sadrozinski, Nucl. Instr. and Meth. A 326 (1993) 239.
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[8] I. Abt, S. Masciocchi, B. Moshous, T. Perschke, R.H. Richter, K. Riechmann, W. Wagner, Nucl. Instr. and Meth. A 423 (1999) 303. [9] G. Kramberger, V. Cindro, I. Mandic´, M. Mikuzˇ, M. Zavrtanik, Nucl. Instr. and Meth. A 476 (2002) 645. [10] ROSE/TN/2001-01 January 2001 on hhttp://cern.ch/rd48i. [11] G. Casse, M. Glaser, E. Grigoriev, Nucl. Instr. and Meth. A 426 (1999) 140. [12] Type inversion in irradiated silicon: half truth, arXiv: physics/ 0409049 v2, 13 September, 2004. [13] V. Chiochia, M. Swartz, D. Bortoletto, L. Cremaldi, S. Cucciarelli, A. Dorokhov, C. Ho¨rmann, D. Kim, M. Konecki, D. Kotlinski, K. Prokofiev, C. Regenfus, T. Rohe, D.A. Sanders, S. Son, T. Speer, IEEE Trans. Nucl. Sci. NS-52 (4) (2005) 1067. [14] A. Dorokhov, et al., Nucl. Instr. and Meth. A 560 (2006) 112. [15] V. Eremin, E. Verbidskaya, Z. Li, Nucl. Instr. and Meth. A 476 (2002) 556. [16] Ideas readout chip web site: hhttp://www.ideas.no/products/ASICs/ pdf/TAA1.pdfi. [17] Ideas DAQ web site: hwww.hep.princeton.edu/tziegler/svd/vadaq/ VADAQ_UserManual.pdfi. [18] Indiana University Cyclotron Facility home page: hhttp://www. iucf.indiana.edui. [19] ROSE/TN/2000-02 June 2000 on hhttp://cern.ch/rd48i. [20] ROSE Collaboration, Nucl. Instr. and Meth. A 479 (2002) 487. [21] Document Fermilab-TM-1849 on hhttp://lss.fnal.gov/ird/index.htmli.
Nuclear Instruments and Methods in Physics Research A 571 (2007) 636–643 www.elsevier.com/locate/nima
Characterization of non-uniformly irradiated silicon micro-strip sensors M.E. Dinardoa,, G. Alimontib, G. Chiodinic, P. d’Angelob, L. Moronib, S. Salab a
INFN and Universita` degli Studi di Milano, Italy b INFN Milano, Italy c INFN Lecce, Italy
Received 3 May 2006; received in revised form 7 November 2006; accepted 7 November 2006 Available online 5 December 2006
Abstract We describe a method we used to characterize micro-strip sensors, which were non-uniformly irradiated up to a fluence of 1014 1 MeV equivalent neutrons per cm2 . The method allows for a complete bidimensional mapping of the sensor characteristics over the entire active area. Information is gathered through the Q–V characteristic, measured scanning the sensor with an infra-red laser source. Q–V characteristics are then fitted to a simple analytical model, which returns local full-depletion voltages, carrier lifetimes, etc. With the present method one can even obtain the profile of the absorbed fluence. The development and tuning of the present method have been done in the context of the R&D programs for the micro-strip forward tracker of the BTeV experiment at the Tevatron. r 2006 Elsevier B.V. All rights reserved. PACS: 29.40.Gx Keywords: Laser; Radiation hardness; Sensor characterization; Silicon micro-strip
1. Introduction One of the main issues in employing silicon detectors in HEP experiments is to certify through dedicated measurements their radiation tolerance [1]. This is particularly crucial for detectors which are going to be used at hadron colliders, where the total fluence after 10 years of operation can reach values well in excess of 1014 1 MeV equivalent neutrons per cm2 . The picture is even more complicated in the presence of highly non-uniform irradiation since the performance of the sensors can dramatically vary over the active area. In these cases, a point to point characterization of the sensors is required. To this extent we developed a simple analytical model, which was employed to fit the local Q–V characteristics measured on several points of a silicon micro-strip sensor previously irradiated up to a fluence of 1014 200 MeV protons per cm2 and hence extract the main physical parameters. The local Q–V characteristic was measured by illuminating the sensor with an infra-red laser source. We were able to perform a full Corresponding author.
E-mail address: [email protected] (M.E. Dinardo). 0168-9002/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2006.11.038
bidimensional characterization of the sensor over its entire active area. In each point we measured the local fulldepletion voltage and the local carriers trapping-time. As expected, we observed a smooth transition from the original n-type to the inverted type bulk behaviour moving along the strips toward the most irradiated zone. From the measurement of the carriers trapping-time we were able to reconstruct the absorbed dose profile and compare it with the actual one measured by the irradiation facility. All arguments reported in this article are extensively detailed in Ref. [2]. 2. Collected charge model In this model we approximate the sensor with a simple p/n diode with infinite plane electrodes. To the extent of describing the total collected charge by all the strips, the validity of this approximation is only limited by the different electric field configuration in a small region [3] near the p-implant, which could in principle affect the evaluation of the collected charge in case of very short carrier trapping-times, as those typical for highly irradiated sensors. It turns out that even in these cases this effect is
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completely negligible because of other much more important distortions of the electric field caused by the radiation damage. We will discuss this issue in the next section, when we introduce the extensions of this model. For non-irradiated sensors, i.e., for long carrier trappingtimes, our model reproduces the data with excellent accuracy, as shown in Fig. 3. This means that the development of the depleted region with the bias voltage is well reproduced even in proximity of the p-implant. This also demonstrates that the assumption we made of an uniform density of charge generated by the laser in the bulk of the sensor is correct. The main advantage of the present approach is that applying a very simple approximation is possible to obtain an analytical expression for the total collected charge, which is extremely advantageous for these kinds of applications. We begin by describing the transport of the charge carriers during their migration toward the electrodes and we will then exploit the Ramo theorem to calculate the total induced charge. 2.1. Transport In the case of a p/n diode with infinite plane electrodes, the problem one has to deal with becomes monodimensional, the only surviving coordinate being x along the electric field lines. The mean free path, lðxÞ, for trapping is given by lðxÞ ¼ tvðEðxÞÞ
(1)
with t ¼ svth1N t . E is the electric field, v the drift velocity, t the carrier trapping-time, s the trapping cross-section, vth the thermal velocity and N t the effective trap concentration. While t is independent on the electric field, the drift velocity depends on it through the relation [4]: vðEÞ ¼
m0 E 1 þ ðm0 =vs ÞE
(2)
m0 is the mobility and vs is the saturation velocity (88 mm ns1 for holes and 116 mm ns1 for electrons). The mobilities we used were rescaled from the quoted values at 300 K (507 cm2 V1 s1 for holes and 1590 cm2 V1 s1 for electrons) according to the well-known relations: mh / T 2:2 and me / T 2:4 [5]. There is no evidence that the mobilities and saturation velocities change with irradiation [6]. The solution of the Poisson equation for a constant fixed charge density is a linear electric field: ( Ax if V b pV d ; EðxÞ ¼ (3) Ax þ B if V b 4V d : The x coordinate is defined only within the depleted region and is zero on the side where the electric field vanish. It is possible to express the electric field in terms of the bias voltage V b , the full-depletion voltage V d and the bulk d width w. In this case A and B can be written as A ¼ 2V and w2 d B ¼ V b V . w
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The residual charge density, rðx1 ; x2 Þ, either electrons or holes, for a charge density, rðx1 Þ, generated by ionization at x1 and reaching x2 subject to trapping, is R x2 dx=lðxÞ rðx1 ; x2 Þ ¼ rðx1 Þe x1 . (4) Eq. (4) can be explicitly calculated by using Eqs. (1) and (2). In order to obtain an analytical expression for the collected charge, we approximated at first order the exponential term in the equation, obtaining: Eðx2 Þ 1=tm0 A x2 x1 rðx1 ; x2 Þ ¼ rðx1 Þ 1 . (5) Eðx1 Þ tvs This approximation is justified as long as ðx2 x1 Þ5ðtvs Þ, which is satisfied for tb5 ns, since the highest value that x2 x1 can assume is the bulk thickness, 320 mm, and the lowest saturation velocity is 88 mm ns1 for holes. 2.2. Induction By applying the Ramo theorem one can obtain the total charge induced at the electrodes: Z XZ X 1 QI ¼ rðx; x0 ÞEðxÞ dx dx0 (6) V b 0 x0 qffiffiffiffiffi b where X ¼ w V V d is the depth of the depleted region. Integrating explicitly Eq. (6), the expressions for the charge signal induced by holes, QIh , and electrons, QIe , can be obtained r0 2 Rh QIh ¼ EðX Þ3 3ð1 þ Rh Þ V b A2 ð2 Rh Þ EðxÞ3 EðX Þ X ð1 þ Rh Þth vsh Að2 þ Rh Þ EðX Þ2Rh B1þRh B B3 þ 1 þ Að2 þ Rh Þth vsh 1 þ Rh 3 3 r0 EðX Þ EðX Þ X þ V b A2 ð2 Rh Þth vsh 1 þ Rh 4A EðX Þ2Rh B1þRh EðX Þ B4 X þ Að3 Rh Þ 1 þ Rh 4Að3 Rh Þ ð7Þ r0 EðX Þ3 EðX Þ1Re B2þRe QIe ¼ 3 1 Re V b A2 ð2 þ Re Þ 1 EðX Þ 1þ X te vse Að2 Re Þ B4 2 þ Re þ þ B3 ð1 Re Þð2 Re Þte vse 3ð1 Re Þ r0 EðX Þ4 þ 2 4Að3 þ Re Þ V b A ð2 þ Re Þte vse 1Re 3þRe EðX Þ B B4 þ Að1 Re Þð3 þ Re Þ 4Að1 Re Þ
ð8Þ
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ReðhÞ is defined as ReðhÞ ¼ teðhÞ1 m
eðhÞ A
. It is worth noting that in
doing these calculations we had tacitly assumed a constant free charge density, r0 , generated by the laser pulse through the whole depleted region [7,8]. Our data seem to confirm this assumption. So far this model has four free parameters: r0 , the initial free charge density in the bulk, generated by the laser pulse; te , the electron trapping-time; th , the hole trapping-time; V d , the full-depletion voltage. The number of free parameters can be reduced to three using the empirical relation [9]: 1 teðhÞ
¼
MeV geðhÞ F1eq:n:
(9)
which relates the trapping-times of electrons and holes to the radiation fluence. The coefficients geðhÞ are known from literature and are in units of ns1 ð1014 1 MeV eq:n:=cm2 Þ1 , and do not depend on the sensor type. For instance, at 10 C, ge ¼ 0:042 0:003 for electrons and gh ¼ 0:061 0:003 for holes [10]. Thus g (10) th ¼ e te . gh This model can be easily extended to accommodate effects due to non-linearities of the electric field which are typically observed on irradiated sensors [11–14]. To this extent we allow for an additional fit parameter, V off . This defines a kind of effective bias voltage, V 0b ¼ V b V off , which should replace V b in our previous equations. In the case of an excess of charge close to the p-implant, which is typically caused by positive charge trapped in the oxide layer, V off acts as an initial offset voltage, which saturates the charge excess; for V b values higher than V off , the sensor quickly reaches the canonical asymptotic behaviour in V 0b . This requires that the first measurement points, up to voltages of the order of V off , should be eliminated from the fit. In an analogous way, V off is even able to allow for huge deviations from linearity of the electric field, as those encountered at very high absorbed doses, which could be explained by trapping of generation currents in acceptor and donor traps [15]. At the end, this model has four free parameters, namely: r0 , te , V 0d and V off . We studied in detail the systematics that the assumption of linear electric field inside the bulk and the first-order approximation in the transport equation, Eq. (5), might introduce in the extraction of the main physical parameters, fitting with our model different sets of Q–V characteristics, which were accurately simulated. We also estimated the effects introduced by the fact that the geðhÞ coefficients are not well known. To do this we run the simulation with the coefficient ratio of Eq. (10) displaced from its central value by s, where s is the error on the ge =gh ratio measurement. From these studies and many others, performed for different field configurations and absorbed doses (for a detailed description of these studies cf. Ref. [2]), we can conservatively estimate the systematics on the fit parameters as reported in Table 1.
Table 1 Estimation of the systematics on the fit parameters Fit parameters
Systematics (%)
Electron trapping-time (te ) Full-depletion voltage (V d ¼ V 0d þ V off ) Initial charge density (r0 )
6 6 2
3. Sensors and readout electronics features The silicon micro-strip sensors, which have been studied in this paper, are the same as those produced by Hamamatsu for the second layer of the Inner Barrel (IB2) of the CMS experiment. The sensors are made in standard FZ silicon with p-implant micro-strips on an ntype bulk, 320 mm thick, with crystal orientation h1 0 0i and resistivity 2:5 kO cm1 (i.e., 150 V initial full-depletion voltage). They have 512 strips, 116 mm long and with a 120 mm pitch. Each strip has a pþ implant width of 30 mm, AC-coupled to an aluminum metallization 40 mm wide. The readout chip employed is the TAA1 produced by Ideas [16] in 0:8 mm CMOS technology. Each chip has 128 channels and from each channel the analog signal can be readout. The main characteristics of the TAA1 chips are the 3 ms shaping time, that guarantees a very low noise of 150 e per channel, and the possibility to readout either positive or negative input signals. The data acquisition system is the VA–DAQ, comprising of a LabVIEW readout software and a board to interface the PC to the TAA1 chips, provided by Ideas [17] as well. One of the main features of the VA–DAQ board is to digitize, in two’s complement with a 14 bit ADC, the analog signal coming from the TAA1 chips; moreover it provides an internal pulser used to characterize each single channel of the chips. 4. Irradiation and global behaviour We irradiated the sensors at Indiana University Cyclotron Facility (IUCF) [18] with a proton beam of 200 MeV energy. The beam shape, measured with a wire scanner technique, was quasi-Gaussian with sx ¼ sy ’ 19 mm and was approximately centered on the edge of the sensor opposite to the readout electronics, as shown in Fig. 1. We irradiated the sensor up to a peak fluence of 0:8 1014 1 MeV equivalent neutrons per cm2 . Since 200 MeV energy protons cause approximately the same damage as 1 MeV energy neutrons, we used a hardness factor k ¼ 1 for fluence rescaling [19] in the usual conversion formula, MeV MeV F1eq:n: ¼ kF200 . The sensor, after irradiation, was p: always kept at a temperature lower than 12 C in order to prevent any annealing. The first plot of Fig. 2 reports the I–V characteristics measured at different fluences during irradiation. On the second plot of Fig. 2 we compare the measured leakage current at VRbias ¼ 400 V, with the MeV empirical formula I leak ¼ a w F1eq:n: ðx; yÞ dx dy for several values of the fluence. Since the irradiation was
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non-uniform, we calculated the total absorbed dose by integrating the two-dimensional Gaussian shape of the MeV proton beam, F1eq:n: ðx; yÞ, over the sensor surface 7 (a ¼ 4:56 10 A cm1 was taken from literature [20]). The expected behaviour of the leakage current with the fluence is confirmed by our measurements. We also measured the noise on strips before and after irradiation. We observed an appreciable increase of its value due to the irradiation from 985 to 1200 e . 5. Laser setup and measurements An infra-red laser source of 1064 nm wavelength [21] was used to locally generate electron–hole pairs in the bulk of
Fig. 1. Irradiation geometry. Shown are the proton beam Gaussian shape and the approximated position of the beam peak which was centered on the edge of the sensor, opposite to the readout electronics.
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the sensor. In order to perform a bidimensional scan of the sensor, we placed the detector on an X –Y moving table and the laser beam focusing lens directly on the fixed Z-axis of the table. The sensor was kept at 12 C by a water–glycol refrigeration system. The atmosphere around the detector was filled with nitrogen to prevent condensation. We illuminated the sensor on the strip side. In this situation, only the fraction of the laser light impinging on the sensor between adjacent strip metallizations could reach the bulk of the sensor. To reduce to a negligible level the dependence of the quantity of absorbed light on the source position, we illuminated a wide region, 20 strips, by placing the sensor out of the focal plane of the lens. Given the ratio of metallization to pitch, 40 mm=120 mm, only 23 of the laser light penetrated the bulk. For each position of the laser beam and for different bias voltages, we sent 1000 laser pulses and we measured the collected charge. The total collected charge was obtained by summing up all the signals of the illuminated strips, once equalized and common-mode subtracted. Fig. 3 shows two typical sets of measurements with superimposed the fit with our model. Empty triangles and circles represent the two contributions, due to electrons and holes, respectively, to the total signal. For n-type bulk, holes are the carriers that give the highest contribution. This fact is explained reminding that, for non-irradiated sensors, holes drift toward higher electric field magnitude, thus, the integral of the work done by the electric field on this type of carrier is greater than the work done on electrons. In case of moderate irradiation, before type inversion, the carriers trapping-time is decreased and both electrons and holes might be trapped before reaching the electrodes. In this situation, due to the higher mobility of electrons, the electron contribution rises and becomes dominant even before type inversion. In case of high irradiation the bulk
Fig. 2. First plot: I–V characteristics measured during irradiation. In the inset, in the upper right corner, is shown the I–V characteristic before irradiation. Second plot: leakage current, measured biasing the sensors at 400 V, as a function of the fluence. The straight line is the expected empirical curve taken from literature. All the measurements were performed at room temperature.
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×103
×103 1000
1000
800 Q [ e-]
Q [ e-]
800 600 400
Data Fit Holes Electrons
200 0
600 400 Data Fit Electrons Holes
200 0
0
100
200 300 Bias [V]
400
500
0
100
200
300 Bias [V]
400
500
Strip 77 0
160 140 120 100 80 60 40 20 0
20 40 60 80 100 Coord. Along Strips [mm]
Full-depletion Voltage [V]
160 140 120 100 80 60 40 20 0
Full-depletion Voltage [V]
Full-depletion Voltage [V]
Fig. 3. Q–V characteristic with superimposed the fit obtained from the model. First plot: data from the lowly irradiated region. Second plot: data from the highly irradiated region.
Strip 281 0
160 140 120 100 80 60 40 20 0
20 40 60 80 100 Coord. Along Strips [mm]
Strip 470 0
20 40 60 80 100 Coord. Along Strips [mm]
Fig. 4. Full-depletion voltage along strips: strip 281 shows a minimum at 90 mm from chip side, as expected for intrinsic silicon. The errors reported are those returned by the fit. An error of 6%, coming from the systematics of the model, should be added.
300
250 200 150 100 50
75 80 85 90 95 100 105 110 115 Coord. Along Strips [mm]
250
Strip 281
200 150 100 50 75 80 85 90 95 100 105 110 115 Coord. Along Strips [mm]
Trapping-time [ns]
300 Strip 77
Trapping-time [ns]
Trapping-time [ns]
300
250
Strip 470
200 150 100 50 75 80 85 90 95 100 105 110 115 Coord. Along Strips [mm]
Fig. 5. Trapping-time along strips: strip 281 shows the lowest trapping-time value, where the irradiation beam was centered. The errors reported are those returned by the fit. An error of 6%, coming from the systematics of the model, should be added.
becomes of p-type and the junction moves toward the back-plane. In this case, the electrons drift toward the higher electric field region and always give the highest contribution to the total signal. 6. Results and discussion In our case the statistical measurement error of our Q–V characteristics is negligible with respect to the systematic error due to the relative instability of the employed setup,
which can be a priori estimated around 1% taking into account the laser system stability and temperature fluctuations. Actually, we cross-checked this guess by estimating the systematic error required to obtain an average w2 value equal to the number of degrees of freedom for the fits to the data taken in the non-irradiated region of the sensor, where our model is expected to closely reproduce the measurements. The required systematic error turned out to be 1:2%. This is the value we used for our measurements.
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6.1. Results on full-depletion voltage and carriers trappingtime We performed a detailed map of the sensor active area by measuring Q–V characteristics in 45 different points. We will now discuss the evolution of full-depletion voltage and carriers trapping-time along the strips, considering three significant examples: two lateral strips, 77 and 470, and a central strip, 281. Fig. 4 reports the full-depletion voltage along the three strips. All strips show a big drop of the measured fulldepletion voltage corresponding to highest irradiated region. For the central strip the full-depletion voltage reaches a minimum at 90 mm from chip side, then it starts raising again. Fig. 5 shows the carriers trapping-time along the three considered strips. The trapping-time diminishes going toward the highest irradiated side and reaches a value above 50 ns on the two lateral strips and 20 ns on the central strip. These measurements are fully consistent with the picture where the radiation beam was centered approximately on the edge of the sensor opposite to the
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readout electronics. In Tables 2–4 we summarize the result of our measurements. We do not report the same table for the r0 parameter since all values are consistent with 3300 e within 2%. 6.2. From trapping-time to fluence From the carriers trapping-time we easily recovered the radiation fluence through the empirical relation expressed Table 4 Additional measurement points in the highest irradiated region for strips 110, 174 and 311, at 110 mm with respect to the non-irradiated side V d and t for strips 77, 110 and 174 at 110 mm Parameter
# strip
Vd t
110
174
311
16:1 1:3 45:5 2:2
19:8 1:7 30:3 1:2
31:5 1:7 26:2 1:3
The errors reported are those returned by the fit. An error of 6%, coming from the bias of the model, should be added as reported in Table 1.
Table 2 Fit results on full-depletion voltage Full-depletion voltage D (mm)
10 40 60 80 90 100 110
# strip 77
145
208
281
344
470
98:4 1:6 123:9 1:6 124 2:0 145:8 2:6 102:5 3:9 39:6 3:0 25:5 1:2
103:9 1:5 128:0 1:7 117:0 1:8 106:6 3:9 75:2 3:9 23:0 1:3 21:7 1:5
100:9 1:4 120:3 1:6 140:5 2:9 80:5 3:6 38:0 7:5 22:6 1:4 31:3 1:5
107:4 1:5 123:5 1:6 115:2 3:3 86:8 5:2 15:0 7:1 24:1 1:5 41:7 1:7
102:2 1:4 111:7 1:4 134:7 1:7 102:0 3:7 50:5 2:9 21:0 1:2 30:8 1:4
101:0 1:4 131:2 1:6 150:4 1:2 149:0 2:4 109:2 3:8 58:9 2:7 28:6 4:8
The data reported are the sum of the effective full-depletion voltage, V 0d , and the V off parameter. The errors reported are the sum in quadrature of the errors returned by the fit on the two parameters. An error of 6%, coming from the bias of the model, should be added as reported in Table 1. D: distance from chip side.
Table 3 Fit results on trapping-time Trapping-time D (mm)
10 40 60 80 90 100 110
# strip 77
145
208
281
344
470
1000 1000 1058 1282 242 98 84:3 18:4 67:4 6:5 50:8 2:7
1000 1000 1962 3157 162 84 72:3 14:0 40:1 1:6 35:7 1:5
1000 1000 1237 681 74 10 59:8 6:1 38:0 1:6 29:3 1:4
1000 1000 930 579 68 11 67:6 4:3 37:6 1:6 25:5 1:5
1000 1000 2768 3404 70 13 62:7 7:5 44:2 1:9 29:2 1:3
1000 1000 800 688 1665 1555 77:1 14:6 70:3 9:0 61:3 5:0
The errors reported are those returned by the fit. An error of 6%, coming from the bias of the model, should be added as reported in Table 1. D: distance from chip side. For the first 12 measurement points, which belong to the non-irradiated side, the carrier trapping-time parameter was fixed to 1000 ns.
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Coord. Transv. Strips [mm]
by Eq. (9). The sensor fluence-map was fitted with a 2DGaussian shape giving the radiation beam profile shown in Fig. 6. Reconstructed fluence profiles at 80 mm, (A), and 110 mm, (B), are shown in Fig. 7. Our measurements are in good agreement with the beam measurements provided by Indiana University Cyclotron Facility, reported in Table 5 and obtained with a completely different technique. The consistency w2 and the corresponding CL, in the worst case scenario of Indiana measurements with negligible errors, are 4% and 26%, respectively. This is an important cross-check for the reliability of our model. It demonstrates that our extraction/measurement of the carrier trappingtimes at different doses are consistent with data and, indirectly, it confirms the measurements of the geðhÞ coefficients by the ROSE collaboration [10]. It is also important to notice that the lowest full-depletion voltage for the central strip in Fig. 4 is measured at a radiation fluence of 0:35 1014 1 MeV equivalent neutrons per cm2 , in agreement with the expected fluence needed to obtain type inversion for this kind of sensors [1].
(A)
80
7. Conclusions With a very simple method based on an analytical model for the Q–V characteristics we were able to extract the main physical information required to assess the radiation tolerance of silicon sensors to be used in HEP experiments. The method allows for a point to point characterization of Table 5 Radiation beam properties Beam properties
IUCF measurement
Our measurement
Peak (1 MeV eq.n. per cm2) Width (mm)
0:8 1014
ð1:01 0:12Þ 1014
sx ¼ sy ’ 19
sx ¼ 21:9 3:0 sy ¼ 19:0 0:8
Consistency w2 : 4 ðCL26%Þ Comparison between irradiation profile gathered through our model and the beam characteristics measured at IUCF with the wire scanner technique.
1
(B)
0.8
60 40
0.6
20
0.4
0
0.2
-20 0 0
20
40
60
80
100
120
140
160
180
200
220
Coord. Along Strips [mm]
χ2 / ndf Coef Mean Sigma
1 0.8
5.294 / 3 0.3769 ± 0.0408 29.61 ± 1.10 11.76 ± 0.74
0.6 0.4 0.2 0
Fluence [1014 1MeV eq.n.] [cm]-2
Fluence [1014 1MeV eq.n.] [cm]-2
Fig. 6. Contour plot of the fluence profile (colour scale is in unit of 1014 1 MeV equivalent neutrons per cm2 ). The fit parameters are: ð1:01 0:12Þ 1014 1 MeV equivalent neutrons per cm2 , mean along strips 120 6 mm, sx along strips 21:9 3:0 mm, mean transverse to strips 33:4 1:5 mm, sy transverse to strips 19:0 0:8 mm. Dashed line: sensor position. (A) and (B) refer to the fluence profile reported in Fig. 7.
1 0.8 0.6 2.053 / 6 χ2 / ndf Coef 0.9098 ± 0.0390 Mean 32.32 ± 0.77 18.69 ± 1.02 Sigma
0.4 0.2 0
0
10
20
30
40
Coord. Transv. Strips [mm]
50
60
0
10
20
30
40
50
60
Coord. Transv. Strips [mm]
Fig. 7. Reconstructed fluence profiles. First plot: 80 mm from chip side; cf. (A) in Fig. 6. Second plot: 110 mm from chip side, corresponding to the highest irradiated region; cf. (B) in Fig. 6.
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