Assumptions and constraints

• The new "sector" mechanics, proposed by R. Siedling, is used.

• In the case of 4'', 5'' and 6'' wafers, respectively, the physical area of sensors is inscribed in a round of diameter:
  d₄ = 90 mm
  d₅ = 113 mm
  d₆ = 135 mm
  The physical surface of a sensor is made of the sensitive surface, surrounded by a "frame" for the guard ring, which is 0.80 mm wide in the case of thin detectors, and 1.15 wide for thick detectors, plus an additional insensitive area 0.34 mm wide along the strip direction and 0.20 mm wide orthogonal to the strip direction.
  In the case of detectors made out of two bonded sensors, there is an additional gap of 0.1 mm between the two sensors.

• For the phi overlap, at least 12 strips in overlap in the phi side, and at least 10 in the stereo side (when applicable), are required.

• For the radial overlap, for each transition between two adiacent rings the worst case is taken, considering the disk where that transition is most unfavourable, and the phi position on that disk where the z gap between detectors is largest. It is imposed that tracks coming from z = 0 see an overlap > 1.5 mm, and tracks coming from |z| < 10 cm see an overlap > 0.

• It is assumed that the mechanics of the inner endcap disks is identical to the mechanics of the forward disks, so for rings 1-3 the "worst case" is identified including the inner endcap disks as well.

• The number of detectors in phi is a multiple of 8 in each ring, a multiple of 16 in the last ring.

• The inner radius of the active area is taken to be 233 mm, obtained as follows:
  220 mm - pixel envelope (new value approved during the April Tracker Week)
  5 mm - clearance
  8 mm - inactive area (in present drawings it is 11, but it might be reduced to 8)

• The outer radius of the active area is 1095 mm (the present best guess).

• No pitch much larger than 200 micron is allowed (it seems that at 240 micron the breakdown voltage starts to become significantly lower, so this value should not be approached).

• In the outer three rings (thick modules) the detectors are optimized for 6" wafers. For the inner four (thin modules) different possibilities are studied.

Remark

• Compared to the previous one, the new mechanics provides radial coverage with larger efficiency when the same detector multiplicity is kept in two consecutive rings, or when for a given pair of adjacent rings, the phi coverage of detectors in the front panel is larger in the inner ring than in the outer ring.
  The efficiency is smaller otherwise.
  Actually it turns out to be more convenient, overall, to accept some additional inefficiency in the use of the silicon and try to avoid having too many "bad ring transitions" in the layout. In all solutions presented below, only one "bad transition" is present, between rings 5 and 6.

Here are the instructions to read all the following files.

Result: the layout chosen is described in this file.

All the options which were considered and studied are reported below.

1. w456.result: Inner four rings optimized simultaneously for 4'', 5"and 6'' wafers.
2. w6.result: Inner four rings optimized for 6'' wafers only.
   Compared to (1) this has 4.1% less APVs, 11.1% less thin 6" wafers, 19.4% less thin modules, and one mask less.
3. w45.result: Inner four rings optimized simultaneously for 4'' and 5'' wafers.
   Compared to (1) this has 1.6% less APVs, 3.7% less thin 5" wafers or 3.8% less thin 4" wafers, 3.5% less thin modules, and the same number of masks.
4. w5.result: Inner four rings optimized for 5'' wafers only.
   Compared to (1) this has 0.5% less APVs, 26.0% less thin 5" wafers, 16.7% less thin modules, and the same number of masks.
   Compared to (3) it has 1.1% more APVs, 23.2% less thin 5" wafers, 13.6% less thin modules, and the same number of masks.
   Compared to both (1) and (3) it has also the advantage that detectors of ring 2 are made out of one single wafer instead of 1.5 wafers.
5. w4.result: Inner four rings optimized for 4'' wafers only.
   Compared to (1) this has 1.6% less APVs, 3.8% less thin 4" wafers, 3.5% less thin modules, and the same number of masks.
   Compared to (3) there is no difference.

One single wedge for the three outer rings

The best configuration (in terms of number of modules) is obtained with modules optimized for the 5^th ring with a multiplicity of 48, and the strips chopped at a length of 170.5 mm. The number of modules and wafers needed for these three rings increases "only" by 11%. The number of APVs per detector must be the same everywhere, in order to reduce the n of masks from 6 to 2 (otherwise the reduction would be from 6 to 4, which is not worthwhile). The only plausible possibility is to have 4 APVs per detector, otherwise the number of channels becomes enormous. With 4 APVs per detectors, the n of APVs in these three rings is reduced by 6.25% and the pitches increase considerably in the 5^th and 7^th rings. This might have a visible effect on the momentum resolution.

The wedges in the 7^th ring stick out of the panel by 9 mm on each side at the top. That could be reduced to about 6 mm if needed, but not less.

The details can be found here (the inner four rings are identical to w6.result above).