Guard Ring Width Impact on Impact Parameter Performances and Structure Simulations

Transcription

1 LHCb , VELO Note 13th May 2003 Guard Ring Width Impact on Impact Parameter Performances and Structure Simulations authors A Gouldwell, C Parkes, M Rahman, R Bates, M Wemyss, G Murphy The University of Glasgow, University Avenue, Glasgow, UK, G12 8QQ P Turner, S Biagi The University of Liverpool, Liverpool, UK, L69 72E Abstract The 1 mm guard ring structure of the VELO sensors has been simulated. The performance of the baseline design is considered and a design which improves the electric field characteristics proposed. Designs which would permit a reduced guard ring width, to 0.5 mm or better, are also discussed and shown to also have similarly good electric field performances. The effect of implementing these designs on the impact parameter resolution of LHCb is found to be better than 5 %. This design is currently being fabricated. Finally, a very different structure, the trench guard ring, is considered which would then allow an impact parameter resolution improvement of approximately 7 %.

2 1 INTRODUCTION 1 1 Introduction This note describes possible alternatives to the wide non-sensitive region required by the 1120 micron guard ring for the VELO. Guard rings are required to prevent high surface electric field strengths in the biased sensor, which leads to avalanche breakdown 1. In the VELO there are currently nine n + floating implants at the edge of the bulk n sensor. The aim of these multiple guard rings is to distribute the bias potential as evenly as possible through this multiple structure without the breakdown electric field being exceeded at any point in the device. The distance of closest approach is defined as the impact parameter. The resolution of the impact parameter is proportional to the distance over which the track must be extrapolated and the extent of multiple scattering, resulting in a 1=p t dependence. The L1 trigger is interested in the tracks with a large impact parameter with respect to the primary vertex. A decrease in the guard ring width will overall move the sensitive silicon detector closer to the interaction point. This would come at a cost to the lifetime of the sensor due to increased radiation damage to the sensitive silicon, which would start closer to the beam. In section 2, the two opposing factors of sensor lifetime reduction, due to increased flux closer to the beam, and impact parameter resolution improvement will be evaluated for the various VELO sensor guard ring widths. Section 3 provides the expected guard ring performances for designs which will improve the VELO sensor impact parameter resolution. This will be achieved in the new designs by moving the sensitive silicon closer to the beam axis. The electric fields experienced in the guard region of the sensors will also be reduced in comparison to the baseline design. 2 Impact Parameter Resolution Studies 2.1 Software Brunel v14r0 was used for initial studies into the effect of guard ring widths on the impact parameter resolution. The alterations to the sensors were made in the core XML code (version 13r0). The jobs were run on ScotGRID, with the DST event files copied over to ScotGRID prior to the job submission. For each guard ring design studied, 4000 B! π + π events were submitted and analyzed in the initial studies. The four guard ring widths considered were: the VELO baseline design of 1 mm width; reduced 0.5 mm and 0.1 mm widths; and a design which was taken close to the maximum width 2 possible of 5 mm. Table 1 shows the geometrical parameters for the four designs used [1]. 2.2 Effect on the Impact Parameter Resolution The impact parameters of tracks were analysed as functions of the inverse transverse momentum of the particles. A Gaussian distribution was fitted to the impact parameter distribution in 1=p t bins. The sigma of this distribution was defined as the impact parameter resolution [2]. Figure 1 shows the distribution on this quantity for the four guard ring designs. It can be seen from Figure 1 that the impact parameter resolution degrades for larger guard ring widths. If the guard ring was to be increased to 5 mm in width then the degradation in the resolution of the impact parameters with respect to the 1mm baseline design in the range of p t between 600 MeV/c and 4.5 GeV/c would 1 Avalanche breakdown is when the electric field exceeds the point where the drift velocity in silicon saturates and the carriers have enough energy to collide with the lattice and release electrons (and a hole). These will gain energy due to the high electric field and then these electrons may collide with the lattice and release further electrons-hole pairs. 2 The maximum possible guard ring width is 5.7 mm. This is a purely geometrical limit due to fitting 640 strips at a pitch of minimum 40 µm and keeping the start and end points of the detector at 7 mm and 44 mm respectively.

3 2 IMPACT PARAMETER RESOLUTION STUDIES 2 Guard Ring [mm] R1 [mm] R2 [mm] R3 [mm] P1 [mm] P2[mm] Table 1: Parameters used for the 4 guard ring designs for the R silicon sensors. R1 is the inner radius for the sensitive silicon detector, R2 is the outer radius for the sensor and R3 is the transition radius between the region of silicon with a fixed pitch to a varying pitch. P1 is the pitch in the fixed pitch region and P2 is the outer most pitch. be 38.1±0.9 %. 3 This would obviously not be advisable since the resolution is of great importance to detecting displaced vertices in the VELO. The reduction in particle flux per year per cm 2 to the active regions of the silicon detector would be 44.4 %. This would mean that the VELO sensor would potentially survive the whole 10 year lifetime of the LHC experiments. Gaussian sigma (microns) Gaussian Fits to Impact Parameter log (1/Pt(GeV/c)) Figure 1: Impact parameter resolution for the four guard ring designs. The blue line with triangular markers is the 5 mm width, the red line with crosses is the 0.1 mm width, the green line with circles is the 0.5 mm line and the black line with squares is the current 1 mm guard ring design Upon reducing the baseline guard ring width to 0.1 mm or 0.5 mm, the percentage improvement in the impact parameter resolution can be seen in Figure 2. For the 0.1 mm width there is a 10.0±0.7 % improvement of the resolution. Due to the increased radiation flux of 27.7 % per year, the lifetime of the sensor would be reduced. The improvement in the resolution for a 0.5 mm guard ring width is 5.8±0.7 %. It would result in 14.1 % increase of the flux currently received at the 1 mm width. This is a less significant alteration for the VELO sensor lifetime. 3 This was calculated by fitting a constant to the percentage degradation with respect to the 1 mm baseline design plot where the χ 2 /NDF of the straight line fit was 0.74.

4 3 SIMULATIONS OF GUARD RING PERFORMANCE 3 Percentage Improvement log(1/pt(gev)) Figure 2: Straight line fits on the percentage improvements on the resolution of the impact parameters for the 0.1 mm (red crosses) and 0.5 mm (blue circles) guard ring widths. This is shown in the transverse momentum range between 600 MeV/c and 4.5 GeV/c. 2.3 First GEANT hits The GEANT package was used to simulate particle tracks intersecting with the silicon planes. The positions of the first GEANT hit on every track inside the sensitive silicon area of a sensor is plotted against the frequency of occurrence of that position in Figure 3. This was performed for a sensitive radius of 8.0 mm, corresponding to a guard ring width of 1 mm, Figure 3a. The same plot was repeated for a sensitive silicon radius of 7.5 mm, corresponding to a guard ring width of 0.5 mm and the results are shown in Figure 3b. When the sensitive silicon starts further away from the interaction point it would be expected to detect secondary or higher hits along the track as the first true hit may be in the dead guard ring area. Hence, it would be expected that the mean first GEANT hit radius would decrease on changing the 1 mm guard ring width to the 0.5 mm guard ring radius. This behaviour can be shown from Figures 3a and b. The mean position of the first GEANT hit decreases from 9.4 mm to 8.8 mm as a result of a 0.5 mm decrease in guard ring width. 3 Simulations of Guard Ring Performance 3.1 ISE Simulations of the baseline VELO, slightly altered baseline, 0.5 mm wide and a new trench guard ring structures were performed using the software package ISE 4. ISE solves the two dimensional Poisson equation (1) and the electron(e) and hole(p) continuity equations, (2) and (3), at each vertex on a mesh 4 Integrated Systems Engineering (version 7.0.9)

5 3 SIMULATIONS OF GUARD RING PERFORMANCE RFstPoint one_1d Entries Mean RMS Underflow 0 Overflow Radius of first GEANT hit (mm) RFstPoint half_1d Entries Mean 8.83 RMS Underflow 0 Overflow Radius of first GEANT hit (mm) Figure 3: The first GEANT hit of the track. (a) Sensitive silicon radius was 8.0 mm and the guard ring width was 1.0 mm. (b) Sensitive silicon radius was 7.5 mm and the guard ring width was 0.5 mm. that covers the simulated device ( V) = e(n D + p N A n) ε Si (1) e dn dt J n = e(g R) (2) e dp dt J p = e(g R) (3) where V is the potential, N D and N A are the donor and acceptor densities, ε Si is the permittivity of silicon, J n and J p are the electron and hole fluxes, and the generation and recombination rates of the carriers are G and R, respectively [3]. The simulated baseline design is shown in figure 4. The gap between each strip was 40 µm and each implant was 40 µm wide. Table 2 shows the dimensions simulated for the baseline, altered baseline and a modified 500 micron design. All of the nine R strips, p-spray and oxide thicknesses were simulated identically to the baseline design. All structures were 300 microns thick. For each

6 3 SIMULATIONS OF GUARD RING PERFORMANCE 5 Dimensions Baseline Altered Baseline 500 micron design GBias W G W G W G W G W G W G W G W G8extra Wextra Gextra G W Scribe GR width Table 2: All measurements in microns. GBiasX is the Gap between the Bias rail and the Xth guard rings. GXY is the Gap between the Xth and Yth guard rings. WX is the Width of the Xth guard ring. GRextra is only applicable to the altered baseline and is the extra guard ring between the 8th and 9th guard rings. Aspect BD1 BD2 BD3 BD4 BD5 Oxide Charge E FromEm id [ev] σ e [cm 2 ] 1.0e e e e e-14 - σ h [cm 2 ] 5.5e e e e e-15 - Conc non irradiated e11cm 2 Conc 3e14cm 2 4.5e14 6.6e e e13 4.5e14 2e12cm 2 Table 3: BD is the Bulk Defect introduced. The bottom row is the trap concentration introduced at a fluence of 3x10 14 n/cm 2 (neutron equivalence)

7 3 SIMULATIONS OF GUARD RING PERFORMANCE 6 Figure 4: Baseline guard ring structure simulated. The first nine R-sensor strips with the nine n + front guard rings and eight p+ back guard ring structures. The front of the device had a p-spray of 1.08x10 12 cm 2 concentration to approximately 1 micron depth simulated structure, fluence dependent bulk traps and fixed oxide charges were modelled. Parameters for the five bulk defects and the fixed positive oxide charge that were introduced are listed in table 3. All simulations were made using the package ISE. An increasing reverse bias was applied to the back p + implant, up to a maximum of -500 V. This bias was sufficient to deplete the sensors, even after irradiation. The bias rail was connected to ground and all the guard rings were left floating. The ISE output was analysed using two graphical packages; TecPlot and Inspect. 3.2 Baseline Simulation The electric potential and the electric field across the device and the guard ring potentials, while the diode was being biased up to -500 V, were plotted for each simulation performed on ISE. All of the simulations were performed at a fluence of roughly three years in the LHCb radiation environment of 3x10 14 n/cm 2. Simulations were run at higher and lower fluencies but no significant deviation from the following trends were observed. The three plots described have all been included for the baseline design to serve as example plots to determine relative success of further designs. The three plots may be seen in Figures 5, 6 and 7. The breakdown field in bulk silicon is 3 MV/cm and in the oxide layer it can reach 6 MV/cm, before avalanche breakdown occurs. It can be seen that the maximum electric field strength is located at the edges of the bias rail. However, the maximum value of around 250 kv/cm is well below the oxide critical field. The back guard rings do not have a significantly high field, see Figure 5. The guard ring potentials show an even distribution of potential in Figure 6. No single guard ring potential jump at -500 V exceeds around 80 V. The first guard ring, which is closest to the bias rail, has floated to only 12 V. Figure 7 confirms the findings of Figure 5, where there was found to be no significant electric field within the test structure. Both the front and back guard rings step through the potentials evenly. The oxide edge at the cleaved edge of the structure shows that there exists good conductive paths through the dangling oxide bonds at the interface.

8 3 SIMULATIONS OF GUARD RING PERFORMANCE 7 Figure 5: The electric fields strength in V/cm on the vertical z axis and the x-y plane shows the baseline design as laid out in the 2 dimensional x-y plane of Figure Altered Baseline and a 500 micron design As can be seen from table 2, the altered baseline guard ring has an extra floating guard ring but is the same width as the baseline. The same plots were repeated and the results were comparable with the baseline. The maximum electric field strength was shown to be lowered, see Figure 8. In all the simulations the maximum fields were consistently between the bias rail and the first guard ring. By inserting an extra implant the first guard ring in theory would be floating at a lower potential, hence lower the maximum field strength. This was what was found, with a reduction from 250 kv/cm to 170 kv/cm. Both of these fields are not at the critical level where breakdown occurs. The first guard ring floated to only 7 V. These two results showed that the amendments to the baseline design may yield improved performances. The electrostatic potential plots showed good sharing of the potentials, which can be seen in Figure 9. A new 500 micron wide guard ring design was also successful relative to the baseline design performance. This result was of greater significance as the reduced width would result in approximately 6 % improvement in the impact parameter resolution as well as a reduced maximum electric field.various 500 micron designs were simulated and the best design is shown here. The design followed the general guidelines for an optimized guard ring structure that were investigated previously [3]. The maximum field reduced from 250 kv/cm to 152 kv/cm, as can be seen in Figure 10. Due to the spatial constraints, it was necessary for a reduced number of guard rings, hence the first guard ring floated to 21 V. The design had a back guard ring jump of potential of around 50 V. This resulted in the undesirable back guard ring distribution that can be seen in Figure 9. The results for the simulations performed for the altered baseline and the 500 micron design can are summarized in Table 4. The baseline results are included for comparison. As an initial search into possible 500 micron guard ring widths, this design looks extremely promising for the next generation of LHCb sensors. However, if it is felt that the baseline guard ring width should be kept, at the expense of the impact parameter resolution, then the amended baseline design should be implemented. Due to the radiation environment and the nature of the tracking, the guard ring performance is critical for the LHCb VELO. Silicon test structures of both the amended

9 3 SIMULATIONS OF GUARD RING PERFORMANCE 8 Figure 6: The front guard ring potentials while a reverse bias of 500 V is being applied. Design V GR1 [V ] E max Front[kv=cm] E max Back[kv=cm] Baseline Altered Baseline micron Table 4: Comparison of 3 GR designs at -500 V and approximately 3 years in the LHCb radiation environment. Table shows for each design the voltage of the first front floating guard ring, maximum field strength on the front of the device and the maximum field on the back of the device, respectively. baseline and the 500 micron design are being fabricated so that data will be available to compare to the promising simulation results.

10 3 SIMULATIONS OF GUARD RING PERFORMANCE 9 Figure 7: The electric potential is shown on the z axis, while the x-y plane is the same as the 2 dimensional x-y plane in Figure 4. Figure 8: The electric field strength in V/cm for the altered baseline structure on the vertical z axis and the x-y plane shows the baseline design as laid out in the 2 dimensional x-y plane of Figure 4. The maximum electric field strength is 170 kv/cm, compared to 250 kv/cm for the baseline simulation. 3.4 Trench Guard Ring Design An alternative guard ring structure called a trench guard ring was simulated. The simulated device was surrounded by a vacuum and used p-stops, rather than the baseline p-spray. After the bias rail,

11 3 SIMULATIONS OF GUARD RING PERFORMANCE 10 Figure 9: 500 micron design. The electric potential is shown on the z axis, while the x-y plane is the same as the 2 dimensional x-y plane in Figure 4. Device at -500 V bias. Good distribution of the potential, with the exception of the first back guard ring jump. However, only gave rise to a field of 60,000 V/cm which is still a factor of 100 below the critical field. Figure 10: The electric field strength in V/cm for the new 500 micron structure on the vertical z axis and the x-y plane shows the baseline design as laid out in the 2 dimensional x-y plane of Figure 4. The maximum electric field strength is 152 kv/cm, compared to the baseline simulation where the maximum electric field strength was 250 kv/cm. a 200 micron deep and 50 micron wide trench was cut out of the 300 micron sensor and the last floating n+ guard ring was included. In total the dead space was 365 microns, which would lead to an improvement in the impact parameter resolution in the region of around 7 %. The increase in flux per year would be approximately 18 %. Varying trench depths were tried and did not deviate much from the following results. The trench guard rings aim to physically isolate the electric fields with an

12 4 CONCLUSIONS 11 empty space etched out of the silicon. The device was simulated up to 6x10 14 n/cm 2 and the electric field was shown to be less than 300 kv/cm. Compared to the baseline guard ring design under similar conditions of vacuum, p-stops and the same fluence, the trench design offered approximately 13 % improvement on the maximum electric field characteristics 5. The technology required to produce the trench is deep reactive ion etching. The process is readily available, however, not at our primary supplier, MICRON Semiconductors 6. 4 Conclusions A sensor that would demonstrably survive 10 years of radiation from LHC operation would require a sensitive inner radius of 12 mm. This sensor was shown to have a 38.1±0.9 % worse impact parameter resolution performance than the standard design. For an improved performance in the impact parameter resolution, two sensitive inner radii were considered, 7.1 mm and 7.5 mm. Compared to the baseline the improvements were 10.0±0.7 % and 5.8±0.7 %, respectively. For the 7.5 mm radius the increase in annual flux would be 14.1 % for the sensitive silicon. However, the guard ring silicon would receive a higher dose as it would cover the radial region of 7.0 mm to 7.5 mm. The mean radius of the first GEANT hit in active silicon sensor was evaluated for guard ring widths of 1.0 mm and 0.5 mm. The mean radial position decreases from 9.4 mm to 8.8 mm as a result of a 0.5 mm guard ring width decrease. Simulations of an altered baseline design, a 500 micron design and a trench guard ring design all showed improvements to the electric field characteristics. These simulations were performed at 500 V of reverse bias and after 3 years of LHC radiation damage. Plans have already been made to fabricate and test both the altered baseline and the new 500 micron design guard ring test structures. These results will follow. However, for an improvement to the impact parameter resolution the guard width must be reduced. Hence the most promising designs would be the 500 micron design and the 355 micron trench design. References [1] P. Turner. Private communication. [2] L.Wiggers et al. R-sensor sectorsand strippitch. LHCb Note, LHCb [3] K H Whyllie. The Design and Development of Radiation-Tolerant Silicon Microstrip Detectors for Tracking at the Future Large Hadron Collider. PhD thesis, King s College, The University of Cambridge, Trench guard ring maximum at 260 kv/cm compared to baseline 300 kv/cm, both at -500V and 6x10 14 n/cm 2 fluence 6 1 Royal Buildings, Marlborough Road, Lancing, Sussex, BN15 8UN, UK.