Introductory remarks

The wedge-shaped sensors were designed to provide robust phi overlap and strips pointing to the beam axis when placed at the radial positions they have in the TEC. With such radial positions, in the TID they do not provide hermeticity in eta. If the radial positions are changed, the phi overlap is modified (possibly lost, unless new detectors are added, increasing material and cost) and the pointing geometry is lost. The following considerations have to be kept in mind:

• The phi overlap has to do not only with the hermeticity, but also with the possibility of aligning the device. The overlap must be not only positive, but large enough that the porbability of failure due to bad strips anywhere along a ring be small.
• The pointing geometry is in principle a mild requirement, but in practice it can simplify and speed up the commissioning phase (esp. alignment) in a way that it is difficult to quantify at the moment.

For these reasons it is interesting to quantify the geometrical inefficiency obtained if the detectors are placed at the same radii as in the TEC, avoiding further design complications. Three layouts are studied:

1. Detectors are placed at the same radii as in the TEC (cfr. w6.result) in all disks, on each face of each ring. The only change compared to those figures is that the dimensions of ring 1 are reduced according to these documents (text, drawing) so that the inner radius of the active area becomes 235.1 and the inner radius of the physical area becomes 234.0. The outer radii are the same (320.2 for the active area, 321.3 for the physical surface). The width of the active area at the inner radius r=235.1 is 62.9. The z positions are taken from the drawings of F. Bosi (text, longitudinal view, detail).
2. The same as 1, but the z positions of rings 1 and 2 are swapped in each disk.
3. The same as 1, but detectors in ring 1 are redesigned. As there is more space on the wafer, the outer radius can be increased. In this case the inner radius is kept fixed (to the TEC value), and the outer radius is increaed as much as possible, using the conservative design rules adopted for the layout optimization in Spring 2000. The dimensions used are:
   Active:       r_in = 235.1 ; r_out = 342.1 ; L1 = 62.9 ; L2 = 91.5 ; H = 107.0
   Physical:   r_in = 234.0 ; r_out = 343.3 ; L1 = 64.6 ; L2 = 93.9 ; H = 109.3
4. The same as 3, but the outer radius (active) is reduced to 339.8; the dimensions used are:
   Active:       r_in = 235.1 ; r_out = 339.8 ; L1 = 62.9 ; L2 = 90.9 ; H = 104.7
   Physical:   r_in = 234.0 ; r_out = 340.0 ; L1 = 64.6 ; L2 = 93.2 ; H = 107.0
5. The same as 3, but the outer radius (active) is reduced to 338.1; the dimensions used are:
   Active:       r_in = 235.1 ; r_out = 338.1 ; L1 = 62.9 ; L2 = 90.5 ; H = 103.0
   Physical:   r_in = 234.0 ; r_out = 339.2 ; L1 = 64.6 ; L2 = 92.8 ; H = 105.3
6. The same as 5, but the inner radius (active) is reduced to 231.3; the dimensions used are:
   Active:       r_in = 231.3 ; r_out = 338.1 ; L1 = 62.1 ; L2 = 90.7 ; H = 106.8
   Physical:   r_in = 230.2 ; r_out = 339.2 ; L1 = 63.8 ; L2 = 93.0 ; H = 109.1

Results

Stiff tracks are shot with a flat distribution in rapidity and azimuthal angle. The rapidity range is larger than the TID acceptance. Tracks may be in the acceptance of 0/1/2/3 disks.

The number of hits actually collected in each disk is recorded (can be up to 4) for each track in the disk acceptance. A figure of efficiency is defined as the n of tracks collecting at least one hit over the total n of tracks in the acceptance.

The overall fraction of tracks missing 1/2/3 disks is shown, together with the fraction of tracks collecting from 0 up to (the theoretical) 12 hits, for tracks in the acceptance of 1, 2 or all the three disks.

The results are available on ascii files for layout 1, layout 2, layout 3, layout 4, layout 5 and layout 6.

Solutions 1 and 2 have pro and cons. The bottom line is that each disk is about 5% inefficient. As the gaps are rather anti-correlated, the probability of missing two disks is negligible. They are simple, provide good phi overlap, and make use of tha same detectors as the TEC.

Solutions 3 - 6 require a dedicated mask for detectors of TID ring 1.

Solution 3 is hermetic. Extending the outer radius to its maximal value is actually an overkill. There is an excess of r overlap between rings 1 and 2. The remaining tiny inefficiency is between rings 2 and 3.

Solution 4 has also maximal hermeticity, with a smaller outer radius for ring 1.

Solution 5 has a yet smaller outer radius for ring 1, with maximal hermeticity for disks 2 and 3, and a tiny increase of geometrical inefficiency for disk 1 (5x10^-4).

Solution 6 has (obviously) a larger acceptance. The acceptance of each disk increases by about 2%. The overall TID acceptance increases by 1.5%. The n of tracks in the acceptance of 1 or 2 disks is unchanged, the gain is in the number of tracks having hits in all three disks, which increases by 3.1%.

Additional remarks

If the decision was to go for a dedicated mask in the TID ring 1:

• It is probably pointless to extend the outer radius further than the value of Solutions 5-6.
• The inner radius of Solution 6 can be extended further inside, if it is allowed by the mechanical constraints: on the wafer there is space to extend the sensor by at least 4 mm.

D.A.