**FVTX configuration**

Hubert van Hecke

Los Alamos National Laboratory

May 18 2006ecke

Different configurations of the FVTX have been studied, and results are
presented here. The aim is to settle two choices: cone-shaped versus
flat silicon planes, and the width of the ministrips.

**A - Cones versus flat silicon planes**

One half of each of the two configurations are shown in figure 1. In
both cases, 24 panels

of silicon detectors form each of the four cones or planes. In the plots
below, simulation results are shown for the plane closest to the
interaction point, since the highest occupancies occur there.

![](media/image1.png){width="5.995138888888889in"
height="2.698611111111111in"}

Figure 1: cone and flat configurations

**I - Track distribution**

Figure 2 shows the distribution of tracks along one column of strips on
the innermost FVTX detector cone or disk. Each is made up of 24 support
panels, and each panel has two silicon detectors on it, one on the front
and one on the back, such that we can have slight overlaps. This ensures
coverage with no dead spaces. Each silicon detector has two columns of
strips, with the (5) readout chips straddling the centerline. Thus there
are 96 radial columns of ministrips around the circle.

The inner-radius silicon is a trapezoid 6.6 cm tall, and divided into 75
um strips, for a total of 880 strips.

![](media/image2.png){width="5.9944444444444445in"
height="3.1777777777777776in"}

Figure 2: tracks per strip

The slope reflects the rapidity distribution of tracks in a central AuAu
event, and the small difference in the slopes is due to the difference
in the angles of the planes wrt the beam axis.

**II -- Strip clusters**

The silicon is 300 um thick, and in this simulation the strip width is
75 um. Therefore tracks that hit at an angle will deposit energy in a
cluster of adjacent strips. Figure 3 shows the cluster size distribution
for the cone and flat configuration.

![](media/image3.png){width="5.997916666666667in"
height="3.1993055555555556in"}

Figure 3: cluster size distributions

The mean is 1.6 for the cones, which on average is perpendicular to
incoming tracks, and 2.6 for the flat configuration. The insets show the
same plots on a log scale, where you can see that there are rare
occurrences where clusters are very large.

![](media/image4.png){width="5.992361111111111in"
height="3.2805555555555554in"}

Figure 4: cluster size vs. strip number

Figure 4 shows the cluster size vs strip location. On the left can be
seen that tracks around strip 600 come in normal to the silicon, causing
single hits, while tracks above and below that tend to hit 2 strips. On
the right one sees a monotonic increase of cluster size with strip
number, as expected for the flat planes.

**III-- Hit distributions**

The strip hit distributions are shown in figure 5. For the tilted planes
(left), the dip around 600 corresponds to normally incident tracks. For
the tilted planes (right), it is clear that the falling track density is
compensated by the increasing cluster size, leading to a much flatter
distribution. The maximum hit density is roughly the same for both
cases.

![](media/image5.png){width="5.99375in" height="3.2465277777777777in"}

Figure 5: strip hit distributions

**IV-- Occupancy**

![](media/image6.png){width="5.996527777777778in"
height="3.328472222222222in"}

Figure 6

In Figure 6, the number of strip hits per column of ministrips for 9
events (96 columns × 9 = 855 entries) is shown. From this, we derive
mean occupancies of 1.8% and 2.8%, for the cones or flat planes,
respectively. As expected the occupancy is higher for the flat planes.

Figure 7 shows the number of clusters per ministrip column. Typically
there are 10 clusters distributed over 880 strips, which is a 1.1%
cluster density (\~= track density), and this number is the same for
both configurations.

In a central AuAu event there are about 1000 tracks (10.44× 96) hitting
the first plane/cone.

![](media/image7.png){width="5.995833333333334in"
height="3.2416666666666667in"}

Figure 7: number of hit clusters per strip column

**IV-- Overlaps**

Hits that are too closely spaced can cause problems for pattern
recognition. Figure 8 shows the space (as the number of empty strips)
between adjacent clusters.

![](media/image8.png){width="5.999305555555556in"
height="3.2333333333333334in"}

Figure 8: distribution of number of unhit strips between adjacent
clusters

An (extrapolated) separation of 0 strips means we have merging or
overlapping clusters. The probability of such merging clusters is
80/8005 = 1%, or 110/7985 = 1.4%, a low figure for both configurations.

The pattern recognition software will have to deal with these (rare)
overlap occurrences.

Since we have (limited) pulseheight readout, some of the overlapping
clusters may still be disentangled.

**IV-- Signal and thresholds**

For each track traversing the silicon, PISA gives the total energy
deposited, properly Landau-distributed. I scale this to the number of
electrons, taking 24K electrons for the mean number deposited in 300 um
of silicon. This distribution peaks at 22K electrons. I simple partition
this over the number of strips hit, proportional to the path length.
Figure 9 shows the distribution of the number of electrons per strip in
the cone and flat configuration.

![](media/image9.png){width="5.999305555555556in"
height="3.1847222222222222in"}

Figure 9: number of electrons per strip

The peaks are at 17K and 12K electrons for the cones and flats,
respectively. This reflects the differences in the angles of incidence.
The blue lines mark the maximum, and 14 of this value. Our expected
readout threshold is a few k electrons, well below these values.

**B -- Strip width**

Historically, the strip width was set to 50 um. Increasing the strip
width would reduce the channel count, bump or wire bond density etc.

We estimate the z-vertex resolution by throwing 5 GeV muons from a
z-vertex position uniformly spread from z = -10 to +10 cm, in a wide
cone towards the North endcap, and do a simple track reconstruction:
requiring hits in at least 3 planes, placing the radial coordinate in
the middle of a cluster of hit strips, and drawing a line towards the
vertex through these two radial coordinates.

Figure 10 shows that the z-vertex resolution only has a weak dependence
on the strip width. Note that the actual resolution, using pulse height
information, can derive a better estimate of a track coordinate then was
done here, and the curve will be flatter than in figure 10. What we have
so far is an upper limit.

![](media/image10.png){width="3.501388888888889in"
height="3.2881944444444446in"}

Figure 10: z-vertex resolution versus silicon strip width

**C - Conclusions**

In section A I showed that there are no compelling reasons to stay with
the cone configuration.

On the side of the conical configuration we have:

\- angle of incidence roughly normal \> this minimizes thickness

\- strip cluster size \~1 \> smaller data volume

On the side of the flat planes we have:

\- easier, cheaper construction

\- angle of incidence not normal \> strip cluster size \>1.

This improves tracking resolution

The thickness issue is an 8% effect. Currently the material budget is
dominated by the carbon panels that support the silicon. The data volume
issue can be addressed by having enough readout lines. The simplified
mechanical construction is the overriding argument for choosing the flat
configuration.

On the strip width issue, there is a tradeoff between a 9% worse
resolution (this is an upper limit) and a 33% reduction in readout
channels. In addition, increased bond spacing makes for simpler
construction.