Vertex Detector Conceptual Design

The conceptual design of the vertex detector was based on two concentric, approximately cylindrical, barrels of single-sided 300 thick silicon strips with 100 pitch². Fig. 1 shows schematic views. Half of the strips in each barrel are oriented parallel to z (the beam direction) and half orthogonal to z. The parallel and perpendicular strips are sometimes called "r- " and "z" strips, respectively.

Figure 1: The conceptual design of the vertex detector. The bottom part shows the view along the beam line. The top part shows a 3D perspective view.

The inner and outer detectors should not move relative to one another; details of these constraints are discussed in a later section. The detector should be constructed from "ladders" which maintain accurate relative positioning of the inner and outer detector wafers in each azimuthal segment. Each ladder will be constructed from Rohacell foam⁴, which is a very light (reduces multiple scattering) but rigid foam whose coefficient of thermal expansion is close to that of Si. Using a ladder-like structure, rather than a solid piece of foam, further reduces the mass of the support structure and permits better airflow for cooling. Based on the expected power dissipation of the chips, preamps, and transmitters, the assembly will be air-cooled.

The ladders fit into a graphite/epoxy mechanical structure with a small coefficient of thermal expansion. The thermal expansion of the different pieces of the detector must be considered to maintain position accuracy. A large mismatch in the coefficients of thermal expansion of the detector wafers and the support structure could also result in severe damage to the detector. The modular construction of the detector allows some azimuthal segments to be removed if necessary.

A series of simulations of the detector were performed, using a nearly realistic model. The model was a pair of cylinders, whereas the "real" detectors² have a hexagonal cross-section. The "real" detector has dead areas around the edges of the chips, but in the simulations, the chips are assumed to be active even at their edges. Table 1 summarizes the number of channels assumed in the simulations of the vertex detector. For the chips containing strips parallel to the beam, there are some further differences between the simulations and a realistic design. The simulations assume 150 pitch for parallel strips in the outer barrel, with 100 pitch in the rest of the detector. This assumption is convenient because it means that the parallel strips in the inner and outer barrel each occupy the same .

barrel	strip type	R (mm)	Wafer size (mm x mm)	segments	# of wafers	strips/wafer	total strips
inner		61.1	64 x 50	3	20	640	38400
inner		61.1	32 x 50	3	40	480	57600
outer		91.7	96 x 50	3	40	320	38400
outer		91.7	48 x 50	3	40	480	57600
Totals					140		192000

Table 1: Summary of the number of channels in the simulation of the vertex detector. The shape is approximated by a cylinder, whose radius is given. Pitch=100 except parallel strips in the outer barrel, where 150 is assumed.

The total number of channels per barrel shown in table 1 is about a factor of two larger than the estimate in the introduction. This was necessary because the distribution of particles along the length of the detector is not uniform, and because single particles can hit more than one strip --- a serious problem for strips perpendicular to the beam.

The particle distributions in the simulations all come from Fritiof³. These simulations were done for p+p, p+Au, and Au+Au collisions assuming 100GeV/nucleon beams. The average charged particle multiplicities from these calculations are shown in table 2. The vertex position was assumed to always be on the central axis of the vertex detector. The z position was varied assuming a Gaussian distribution whose tails were cut off so that all interactions were assumed to take place within 50cm of the center of the vertex detector. The Gaussian distributions assumed⁵ =20, 16, and 5.7cm, for Au+Au, p+Au, and p+p collisions, respectively.

Table 2: The average fraction of the particles which hit both layers of the vertex detector and the average total number of charged particles produced. Based on Fritiof³ for 100GeV/nucleon beams.

Each charged particle produced in the simulation was tested to see if it would hit the vertex detector; uncharged particles were ignored. If a particle entered the vertex detector, the program calculated which parallel and perpendicular strips would be hit. Multiple scattering of charged particles in the inner barrel of the vertex detector was included. To approximately account for the support structure and electronics, the multiple scattering calculation assumed that the inner barrel of the vertex detector was twice its real thickness. Particles were allowed to hit more than one strip. When a particle hit a detector barrel, the program calculated how much silicon a particle would pass through in each strip of the detector. A minimum-ionizing particle (mip) will lose an average of 116 keV in 300 of Si. The result of this was an array giving the amount of Si (approximately equivalent to the energy loss) that particles passed through in a strip.

Figure 2: Assumed efficiency as a function of of Si traversed in a cell.

The array giving the amount of Si traversed in each strip is used to generate a pattern of "hits" in the strips. This is done using the efficiency function shown in fig. 2, which shows the efficiency as a function of the amount of Si traversed in a strip. The maximum efficiency⁶ was assumed to be 95%. A "threshold", corresponding to (or 75 of Si here) was assumed. A noise level, which was varied from 0.1% to 0.01% was included in the efficiency function --- this means that a strip which was not hit has a small probability (P_noise) to be "on". If a strip was "on" then each of the adjacent strips were assumed to have a 10% probability to be "on" too --- introducing some charge sharing effects into the simulation. This final array holds the pattern of strips that were "on" or "off" --- no analog information is used in the analysis of the events. The array was then used as input to algorithms to find the vertex, , and the multiplicity.

The inner barrel has a "radius" of R₁ = 6.1cm, constrained by the beam pipe radius of 5 cm. If is to be measured out to 3, the length of the detector must be R₁/tan(6) = 58cm. A length of 50 cm has been chosen. The variation in the vertex position means that for some events the coverage will extend above (below) = 3 in the forward direction with a compensating decrease (increase) in the coverage around = -3. The "radius" of the outer barrel is R₂ = 1.5 x R₁ = 9.2cm.

In the following sections some discussion of the loss in performance expected from a modified design has been included along with the discussion of the detector described above. In these discussions, the conceptual design described here is compared to the vertex detector described in the Tales/Sparhc Letter of Intent⁷, which covers only 1/3 of the azimuthal angle with strips perpendicular to the beam and is 64cm long instead of 100cm.