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Signal-to-Noise and Resolution Analysis of Alternately Bonded Silicon Microstrip Detectors. By Chris McGuinness. CMS Project and UCSB’s Involvement. LHC Arial View. ~5 miles. CMS Detector. CMS Tracker. TOB Module. TOB & TEC Modules. Rods and Petals. Silicon Microstrip Detectors.
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Signal-to-Noise and Resolution Analysis of Alternately Bonded Silicon Microstrip Detectors By Chris McGuinness
LHC Arial View ~5 miles
Silicon Lattice • Silicon atoms have four valence electrons • Causes silicon atoms to preferentially form bonds with four other silicon atoms in order to fill the valence band • Crystal structures like the one above are the result
Silicon lattice doped with atoms with 5 valence electrons Silicon Doping N-doped Silicon P-doped Silicon Silicon lattice doped with atoms with 3 valence electrons
P-N Junction A diode is formed by bringing p-doped silicon in contact with n-doped silicon Electrons from the n-doped silicon will diffuse into the p-doped silicon, filling the holes introduced by the p dopants. A depletion region, free of charge carriers, forms between the two types of silicon. This creates an electric field between the p-doped side, which now carries a larger number of electrons, and the n-doped side, which is left lacking some of its initial electrons.
Reverse Biasing The depletion region can be expanded by applying a voltage across the diode. This is called reverse biasing when the edge of the n-doped silicon is at a higher potential than that of the p-doped silicon. As illustrated above our sensors have a large region of weakly n-doped silicon, sandwiched by small regions of strongly doped p-doped and n-doped silicon. The weakly n-doped region becomes fully depleted after biasing.
Silicon Detector This image represents a cutaway of our silicon sensors. The p-type silicon is implanted in thin channels along the n-type bulk. A layer of insulating silicon-oxide is placed between the p-type implants and aluminum strips which are used to readout signals. As a charged particle passes through the silicon it ionizes electron-hole pairs which react to the electric field created by the reverse biased silicon. Holes drift towards the p-doped implants and create image charges on the aluminum strip electrodes, which are readout by the APVs.
Hypothesis Can this method of charge readout be improved or made more efficient?
Alternating Strips • What if the signal from only alternating strips is read? • Strips not being directly read could still capacitively transfer charge to their neighboring strips, which are being read
Benefits • This would reduce the amount of electronics needed to readout signals by half • Saves money directly in cost of electronics • Saves cooling required to keep electronics at sub-zero temperatures
Potential Drawbacks • Signal-to-Noise • Signal-to-noise may decrease on strips not being directly readout due to capacitive transfer • This effect is enhanced due to an additional coupling to the backplane of the silicon • Resolution • The resolution may be diminished due to the lack of direct charge readout in cells corresponding to the unbonded strips • Might be able to be compensated by using charge-weighted positioning • These characteristics must be compared between normally bonded and alternately bonded sensor configurations. This is the focus of my experiment.
Test Particles How does one go about testing a modified module?
Cosmic Rays • Consist of primarily protons traveling at relativistic speeds throughout space • Exact origin is unknown, but are assumed to come from exotic galactic/stellar events which are not well understood • When protons collide with particles in our atmosphere they undergo nuclear reactions similar to those observed in particle accelerators • Numerous types of particles are created in these interactions, but many have very short lifetimes (pion ~2.6x10-8 sec) and do not reach us on the surface of the earth before they decay • The lifetime of a muon is slightly longer than the majority of these particles and is the primary component of cosmic rays measured from the surface of the earth
Muons • Muons are charged particles similar to electrons, but with much larger mass • Provide a large source of particles which could be detected by the modules we produce • They travel with very high momentum and thus follow very straight paths, making them a perfect source of test particles
CRAMT Stand Cosmic Ray Module Test Stand
CRAMT Stand Scintillators Modules Electonic Readout Hardware
Module Box • The box which housed the five modules was machined to align each module to within ± 50m of the others. This precision was necessary for accurate resolution measurements.
Scintillators Scintillator Photomultiplier • Scintillators consist of a plastic material which emits photons as charged particles pass through • Photomultipliers convert and amplify the photon signal into an analog signal which can be interpreted by our electronics
Triggering • External triggers are required to tell the electronics when an important event has taken place • The APVs are consistently storing the charge information from the sensors. All this data would overwhelm the computer, so we must discriminate which frames are important • Scintillators accomplish this by sending a signal to the readout electronics when a charged particle passes through • By using two scintillator paddles, one on top and one on bottom of the stack of modules, we restrict the number of events saved to those where the charged particle is likely to have passed through all the sensors
Event Discrimination • Once an event has been triggered, one must determine whether that particular event can be used for the measurement at hand • Histograms can be filled and plotted for each triggered event representing the charge on all the strips for these events • Clear distinctions must be made on what is classified as a signal and what is discarded as noise
Noise Weighted Signal • By subtracting out the average charge on each strip, referred to as the pedestal, and dividing by the noise of each strip, defined to be the standard deviation of the charge, one is left with a much clearer signal lending itself to more efficient analysis.
Clusters • A cluster is defined to be a group of strips which pass the cuts for a signal. • In my analysis I required a strip to have a signal-to-noise of 6, and added the neighboring strips if their signal-to-noise was above 3
Cluster Position • The hit position for a given cluster was determined using a charge weighted positioning algorithm defined below
Line Fit • By requiring events with exactly one cluster per module, I was able to limit the events used in the analysis to those which a charged particle had passed through all five sensors. • This allowed me to take the raw data shown on the left, and interpret it into specific tracks shown on the right.
Signal-to-Noise • I performed the signal-to-noise measurement by including data from only the strips involved in a cluster. • This garanteed that I was incoorporating all events with an actual signal, and neglecting those from noise • In order to determine a total signal-to-noise for a given cluster I added the signal-to-noise ratio for each strip involved in that cluster. • This value would vary depending on the path length of the particle through the silicon, the charge, mass and momentum of the particle, and fundamental quantum fluctuations of the interaction of the particle with the silicon atoms.
Path Length Correction • The ionization of a charged particle passing through silicon varies proportionally to the path length of the particle • In order to correct for this effect one must multiply the charge by the cosine of the angle of the passing particle • This would effectively correct for any additional charge deposited due to particles passing through the detectors at a wider angle relative to the normal
Signal-to-Noise Distribution • The resulting values for the signal-to-noise still vary due to other quantum fluctuations • The signal, or amount of charge ionized in the silicon, will vary according to the Bethe-Bloch equation, which describes the energy loss of a charged particle passing through a medium • For the case of a thin material, of which our silicon sensors apply, the signal will follow a Landau distribution • The noise in the electronics will also contribute by smearing the Landau distribution with a Gaussian distribution
Landau-Gaussian Convolution • A Landau-Gaussian Convolution Distribution will result, plotted below
SN vs. Region • In order to futher verify the loss of signal-to-noise being due to poor capacitance between the bonded and unbonded strips, I made of plot of the signal-to-noise as a function of distance away from a bonded strip • It is clear that signal-to-noise decreases as the hit position approaches the unbonded strips mp=31.9±0.29 mp=28.86±0.38 mp=22.46±0.36 mp=20.68±0.21
dx P Theoretical Resolution Calculation • The resolution for a one strip cluster can be roughly predicted through a direct probability distribution analysis • Assume the region corresponding to a strip, with a length P, were sliced up into a large number of sub-regions, with length dx • The probability that a particle which has passed through the strip region in question, will pass through one of the sub-regions, dx, is dx/P
Theoretical Resolution Calculation • The variance, or the square of the standard deviation, , for this probability distribution is • If we take the origin, <x>, to be at the center of the region, it becomes 0 and drops out of the equation • After integrating becomes: • This is neglecting effects of the diffusion of electrons and holes near the edges of strip boundaries, angular path lengths, and two strip clusters, which will all affect the resolution.
Line Fit Method • Cross section view of the five modules with the silicon thickness and cell width blown up. • The ratio of 500 m for the silicon thickness to 180 m for the cell width is roughly proportional. • As a particle passes through the array of modules particular strips yield signals. • A line is fit using the coordinates of the clusters on the outer four modules. • One can extrapolate the expected hit position on the middle module • The resolution of the middle module is determined by comparing the actual cluster position on the middle module with the extrapolated line fit position x y -z
Method of Least Squares • The line fit was done using the method of least squares, sometimes referred to as 2 • This is done by minimizing the sum of the square of the difference between the measured value and the value of the function at each point
Method of Least Squares • After some mathematical manipulation one is left with an equation for the value of m and c • These values are plugged in along with the x-coordinate for the middle module to yield the y-coordinate position for the extrapolated line fit
Misalignment Effects • Despite the highly precisioned alignment of the modules relative to each other, slight mechanical deviations are to be expected. • This is not a problem in the z direction (parallel to the strip lengths) because measurements were not performed in this direction and thus would not cause any noticeable effect • Deviations in the y direction (perpendicular to the strip lengths) will distort the line fit however • One can compensate for these deviations by calculating residuals prior to performing the analysis • Any angular deviations cannot be compensated for using this method and will increase the error of the measurement. This error can only be estimated using a simulation
Biased Residuals • Biased residuals are found by fitting a line to the hit position on all five modules, and subtracting the line fit position from the actual position measured on each module. • If this is done for a large number of events a gaussian distribution will result. The peak of the gaussian will be offset from zero. • The peak of the gaussian distribution is the residual or calibration constant • One can artificially align the modules by subtracting this value from each measurement taken
