Quality Control of Mass-Produced GEM Detectors
for the CMS GE1/1 Muon Upgrade¹¹1Manuscript prepared by S. D. Butalla (FIT), M. Hohlmann (FIT), J. Merlin (UoS), R. Venditti (Bari) on behalf of the CMS Muon GEM Collaboration.

While the impedance check helps to identify major problems with a GEM foil, it might not be sufficiently sensitive to minor issues or hidden defects that can affect the long-term stability of the chamber. Specifically, some GEM foils could reach their nominal voltages with high impedances, while simultaneously experiencing discharges at high frequency (e.g., several per hour). These discharges can seriously and permanently damage the GEM foils, and they can also prevent stable operation of the detector, once in continuous run mode. Consequently, it is essential to monitor the leakage current and discharge rate of all the GEM foils for several hours before the detectors are assembled.

The total leakage current of a GEM foil mainly depends on the resistivity of the biconical holes of the polyimide layer between the two copper layers of the foil. This resistivity can vary with the ambient humidity or because of contaminants. For a precise measurement of the leakage current, the foil needs to be operated at the maximum stable voltage, i.e. just below the breakdown voltage of the gas. As the Paschen curves in Fig. 9 indicate that the breakdown voltage in pure nitrogen is close to 660 V for a GEM foil where the two copper layers are separated by 50 $\mu$m, an appropriate voltage for testing GEM foil stability is 600 V in pure nitrogen. In such conditions, and with a relative gas humidity below 10%, we require that the leakage current of a GE1/1-sized foil not exceed 1 nA, with a maximum discharge rate below 3 discharges per 5 hours.

Before performing this quality control step, both sides of the foils are mechanically cleaned using an anti-static silicone roller to remove dust and contaminants. The GEM foils are enclosed in a plexiglass box filled with pure nitrogen flowing at a rate of 30-40 L/hr. The box, which can accommodate up to 8 foils, is placed in a cleanroom and covered to prevent ambient light from reaching the foils. This is done because electrons can be released from the GEM copper as a consequence of a photoelectric effect induced by UV photons emitted from fluorescent lighting. We observed that when the foils operate at the maximum voltage of 600 V, these photo-electrons can get sufficiently amplified by the GEM to generate a leakage current of the order of 2–3 nA, which can bias the test results for the intrinsic leakage current measurement.

The foils are powered by an 8-channel CAEN R1471HETD power supply, which has a current monitoring resolution down to 50 pA. The power supply is controlled by a LabView interface that is programmed to run the test automatically. A picture of the QC2b test setup is shown in Fig. 10.

The test procedure consists of three main steps: the initial ramp-up phase, a power cycling phase, and the final stability phase. During the ramp-up phase, the voltage is increased from 0 to 500 V in steps of 100 V, and then from 500 V to 600 V in smaller steps, typically in increments of 50 V. After a desired voltage is reached, it is maintained for 15 seconds before moving to the next step. During the cycling phase, the voltage is quickly ramped up and down between 600 V and 100 V within ten seconds in order to stress the foil and to lift potential solid contaminants off the foil via the oscillating electric field. During the stability phase, the foil is maintained at the maximum voltage of 600 V for 6–8 hours. This final step is designed to verify the long-term behavior and the stability of the foil during continuous operation. At any phase of the test, if the leakage current exceeds a limit of 20 $\mu$A (a typical magnitude of a discharge current), the system trips and automatically restarts at the same phase. If the system records more than three trips in the same phase, it automatically goes back to the previous phase. Three phase failures result in aborting the test and automatic rejection of the foil from chamber production.

Figure 11 shows typical QC2b data for a “good” GEM foil, that is fully validated and approved for detector assembly. All three phases are completed and it is demonstrated that the foil can safely operate long-term at 600 V without high voltage (HV) trips and with an average leakage current below 0.5 nA.

Conversely, Fig. 12 shows the typical QC2b data of a “bad” GEM foil that suffers from instabilities. The plot shows multiple trips that force the system to go back from the stability phase to the cycling phase. The repetition of the trips and the measurement of a high leakage current prematurely abort the test. Such a foil would require an additional, in-depth cleaning at the manufacturer’s facility before going back through the entire QC protocol from the beginning.

Over the course of the GE1/1 detector mass production, on average, about one to two foils per batch of 15 foils were rejected by the QC2 tests and sent back to the manufacturer. After additional, in-depth cleaning at the manufacturer’s facility, those foils were tested again and most of them could be validated for assembly. Overall, only one foil out of 485 had to be completely rejected without any possibility for recovery.

Detector gas-tightness is crucial to avoid gas leaks and to reduce the possibility of contamination by external pollutants. The presence of undesired gas molecules, e.g. those found in air, particularly oxygen and other electronegative elements, can deteriorate the charge amplification and electron transfer process, which will affect the detector performance during operation. Additionally, dust particles could enter the gas volume and jeopardize the foil integrity. Such effects can have a significant impact on the HV stability and the long-term behavior of the chamber. Given the design of the GE1/1 detectors, where a large number of screws are employed, the leak test is the first verification performed after the assembly.

To maintain high gas purity, the maximum acceptable leak rate for a single detector is set to 1% of the total incoming gas flow rate. For GE1/1, this rate is initially set to 2.5 L/hr with a maximum internal over-pressure of 25 mbar. Directly measuring a leak rate as little as 0.025 L/hr is challenging and would require a specific and expensive tooling, which is not necessarily available at all production sites. The leak rate, however, can also be derived from the measurement of the internal pressure loss when the chamber input and output are both closed. Such a measurement is much easier and more reliable with standard laboratory equipment.

Assuming that the detector volume remains constant during the test, the time evolution of the internal pressure can be expressed as a simple exponential:

Consequently, we can calculate the detector leak rate from the measurement of the pressure-loss time constant $\tau$. Figure 13 shows the gas leak rate as a function of the time constant for different values of internal over-pressure $P_{0}$ during operation. Figure 14 shows the gas leak rate as a function of the internal over-pressure for different time constants $\tau$. To ensure that the leak rate will remain below 1% of the total incoming flow rate, the time constant for each GE1/1 chamber should be greater than 3.04 hours.

The leak test aims to quantify the gas leak rate of a GE1/1 detector by monitoring the drop of the internal over-pressure as a function of time. A pressure sensor connected to an Arduino-Mega micro-controller allows the monitoring of the over-pressure in the detector and the gas system. The ambient temperature and pressure are also monitored via sensors connected to the Arduino board during this quality control procedure. The top schematic in Fig. 15 shows a basic diagram of the data acquisition (DAQ) and gas system setup for this test.

Before the leak test is conducted, the DAQ system is calibrated to ensure accurate measurement of the leak rate (see the bottom diagram of Fig. 15). After calibration of the system, a chamber is connected to the gas system with its outflow gas line plugged. The chamber is then pressurized to about 25 mbar, and the over-pressure is monitored every minute over the course of one hour.

The pressure drop is modeled by the function $P(t)=P_{0}\ e^{-t/\tau}$ discussed above, where $P_{0}$ is a constant representing the initial over-pressure of the detector (set to about 25 mbar at all the production sites and for each detector) and the time constant $\tau$ quantifies how fast the over-pressure inside the detector decreases as a function of time.

Results of the leak tests for two different chambers measured at two different sites (serial numbers: GE1/1-X-L-CERN-0018 and GE1/1-X-S-FIT-0004) are displayed in Fig. 16. The expected exponential behavior is exhibited by GE1/1-X-L-CERN-0018 (green data points with a blue fitted exponential curve), and shows a time constant of $\tau=(21.6\pm 0.14)$ hr, which is well above the acceptance criterion for a gas-tight chamber ($\tau\geq 3.04$ hr). In some cases, we observe chambers that initially do not follow an exponential leak profile. This can be attributed due to the bulging of the readout and drift PCBs after the initial pressurization of the chamber to 25 mbar. Once the PCBs return from the deformed shape to their planar shape, the gas volume returns to its nominal, constant shape, and the gas escaping from the closed chamber exhibits the theoretically predicted exponential leak behavior. Consequently, the time constant determined from the fit for GE1/1-X-S-FIT-0004 (black data points with a red fitted exponential curve) has the first few points excluded. Note that this chamber exhibits a time constant of $\tau=(33.27\pm 0.41)$ hr, which is also well above the acceptance criterion. Out of the 161 fully assembled chambers, 158 chambers could be tested in this QC step; three chambers were eliminated due to failures in earlier QC steps and were not tested for leak tightness. As shown in Fig. 17, all 158 GE1/1 detectors are found to be gas-tight except two built with a pre-series internal frame. These two detectors with excessive leak rates are not installed in CMS.

The goal of this test is to check the on-detector circuitry that distributes the high voltage to the detector electrodes. The proper functioning of this circuitry is important for the operational stability of the GE1/1 detector with respect to the applied HV, both for guaranteeing a stable effective gas gain and for avoiding discharges that could damage the surface of the GEM foils or the readout electronics. This need is particularly crucial for GE1/1 detectors because of the large size of the GEM foils. Even with the foils being segmented into 40 HV sectors (with the sensitive sector areas ranging from dozens to a hundred cm²), the foils still have large total capacitances—on the order of tens of nF—and store considerable charge.

During the detector production and test phase, a simple ceramic voltage divider, directly soldered onto the drift board, is used to divide the voltage from a single high voltage input line [9]. This ceramic divider comprises a small network of ohmic resistors (see the bottom of Fig. 18 for the circuit diagram) with resistances $R_{i}$ (see the top right of Fig. 18 for the values of the resistors). This HV divider has an equivalent resistance of $R_{\mathrm{divider}}=4.7$ M$\Omega$. The current $I_{d}$ through this network produces voltage drops $V_{i}=R_{i}\times I_{d}$ across the various resistors that are used to create the appropriate electric potentials needed to power the different electrodes $i$ of the detector. A custom low-pass protection filter (with equivalent resistance $R_{\mathrm{filter}}=0.3$ M$\Omega$) connects the detector to the power supply to eliminate the high frequency noise (see the top of Fig. 18 for the circuit diagram). The total equivalent resistance of the ceramic divider and low-pass filter is 5.0 M$\Omega$. The HV stability is quantified by monitoring two quantities: the deviation of the measured total resistance of the powering circuit with respect to the one predicted by Ohm’s law, and the noise induced on the bottom of the third GEM foil in a gas with high ionization energy.

For each HV step, the current through the powering circuit is recorded, as shown in Fig. 19. The measured resistance of the powering circuit $R_{m}$ is then obtained by computing the average of all the values recorded in each step. This value is compared with the nominal resistance $R_{n}$ of the powering circuit measured with a standard multimeter (at a few volts) before soldering the divider onto the detector, and the resistance deviation is computed. The deviation of the resistance of the powering circuit with respect to Ohm’s law, labeled $D_{R}$ in the following discussion, is defined in Eq. (4) as the relative deviation of the measured resistance, $R_{m}$, with respect to the nominal value, $R_{n}$:

The value of the resistance deviation includes the tolerances on the resistors in the HV divider and HV filters used for biasing the GE1/1 detector. Ten resistors are employed in total in this powering circuit, each of them rated with a 1% tolerance. Summing all of the involved tolerances in quadrature shows that a deviation $D_{R}$ of up to 3% can be tolerated. Consequently, GE1/1 detectors exhibiting resistance deviation greater than this value are rejected or undergo further investigation.

A commercial power supply able to provide up to 1 mA current with 1 $\mu$A monitoring resolution is used to ramp the HV applied to the filter and divider (connected to the detector) up to 5 kV in steps of 100 V, and also used to monitor the current. The detector is flushed with pure CO₂ gas with a flow rate of 5 L/h.

To characterize the biasing circuit, the slope from the linear fit on the points of a plot of the applied voltage as a function of divider current is obtained (see Fig. 19), and then the resistance deviation is computed using equation 4. The distribution of the resistance deviations for all of the GE1/1 detectors is displayed in Fig. 20. The HV biasing circuits for all detectors were found to have a resistance deviation $D_{R}$ better than the 3% tolerance.

Micro-pattern gaseous detectors are known to suffer from spurious discharges, particularly when operating at very high counting rates or at exceptionally high gas gains [16]. These glow discharges, which are not induced by the direct detection of any ionizing particles, can produce spurious signals and must therefore be reduced to an acceptably low rate. The test described in this section is designed to quantify the intrinsic noise rate of the detectors due to those spurious signals. To perform this measurement, the detectors are put into a safe mode by flushing them with a gas that has a high ionization energy, such as pure CO₂, which suppresses signals from cosmic rays. The rate of spurious signals as a function of the applied high voltage is then observed. This procedure serves to disentangle effects related to the detection of actual radiation from those induced solely by the application of high voltage.

Figure 21 shows the number of spurious signals recorded by each strip in the eta sector next to the narrow base of the trapezoid for a prototype of the GE1/1 detector. In this reference measurement, the detector is operated with Ar/CO₂ (70:30) with an average effective gas gain of only $\sim$300 to reduce the detection efficiency for cosmic ray muons to a few percent. It is found that the discharges that create the spurious signals here are induced mainly in strips near the screws used to stretch the GEM foils. Similar results are found for the eta partition next to the long base of the trapezoid while measurements performed in the remaining sectors showed no substantial contribution to the spurious signal rate. We conclude that the origin of the spurious signals in the GE1/1 detectors under these conditions is a coronal discharge from the active area of the GEM along the internal frame (which holds the GEM foils inside the gas volume) to ground through the anode strips where the signal is read out.

The rate of intrinsic noise signals produced by coronal discharges across the full 3500 – 4000 cm² surface area of a normally operating GE1/1 detector is found to not exceed $\mathcal{O}(10^{-2})$ Hz/cm². Consequently, the detector is accepted if the intrinsic noise rate for the full detector does not exceed 100 Hz. This value is negligible when compared to the 4.5 kHz/cm² background rate [9] expected in the CMS experiment during standard operating conditions.

A grounding plate is attached to the backside of the detector readout board and connected to the ground pad of the drift PCB to reduce environmental RF noise pick-up. The readout sectors are grounded via Panasonic-to-LEMO adapters with 50 $\Omega$ termination. To measure the intrinsic noise rate, signals are read from the contiguous bottom of the third GEM foil through a decoupling CR differentiator circuit soldered onto the drift board of the GE1/1 detector. The signals are then processed with a readout chain (Fig. 22) that comprises a charge-sensitive preamplifier, an amplifier, and a discriminator with the threshold set to suppress the environmental noise (140 mV). The resulting digital pulses go through a dual timer and then to a counting unit for the rate measurement. A linear fan-in fan-out module is placed between the shaper and the discriminator to allow simultaneous monitoring of the intrinsic noise signals on the scope.

The rate of intrinsic noise signals induced on the bottom of the third GEM foil is measured as a function of applied HV for each detector as shown in Fig. 23. The maximum measured value of the intrinsic noise rate at 4.9 kV is taken as a final result. All GE1/1 detectors show a noise rate that is well below the 100 Hz acceptance threshold, as displayed in Fig. 24.

The effective gas gain is a crucial parameter for operating a gaseous detector in proportional mode. It is a combination of two main components: the amplification factor given by each GEM foil and the transparency factor which depends on the fraction of the electrons that get lost because they recombine with the gas ions or attach to gas molecules or get absorbed by one of the GEM electrodes. It governs the detection performance such as efficiency and time resolution, which are key parameters for successfully reconstructing detector hits associated with charged particles that traverse the active detector volume.

The effective gas gain is determined experimentally by comparing the primary current induced in the drift gap by an incident, ionizing radiation quantum, with the output current provided by the amplification structure of the detector, i.e. the three GEM foils, with the signal induced on the readout electrode. The effective gas gain primarily depends on the operating gas and the electric field configuration inside the detector. For a triple-GEM detector, the effective gas gain is also a function of the electron multiplication factor in the GEM holes and the electron transparency of the GEM foils.

To successfully detect muon hits used by the CMS trigger and offline reconstruction, a time resolution below 8 ns and at least a 97% detection efficiency are necessary. Previous test beam campaigns showed that such performance can be obtained using GE1/1 detectors operating with an effective gas gain around $2\times 10^{4}$. The gain performances of all detectors should fall within $\pm$37% of this nominal effective gas gain value to ensure a detection system with sufficiently uniform gain [17]. The typical HV range for obtaining such gain values is 3290-3390 V applied on the drift electrode for GE1/1 detectors. Previous studies [18] show that this operational regime is far from the breakdown voltage that would trigger discharges towards the readout electrode with non-negligible probability.

The effective gas gain of a GE1/1 detector is measured in the central readout sector as a function of the current through the HV divider. To perform the test, we use an X-ray generator with an emission cone size of 120 degrees that makes it possible to irradiate the entirety of the chamber simultaneously. The X-ray generator uses an electron gun with electrons incident on a silver target. The X-rays emitted from the silver consist mainly of K_α and K_β emission lines, centered on energies of 22.5 and 25 keV, on top of a Bremsstrahlung continuum. The X-ray photons are absorbed by the copper atoms that constitute the drift electrode which in turn emit 8 keV photons by fluorescence. These 8 keV photons are then converted to electrons via the photoelectric effect in the gas atoms in the detector volume – in particular in the drift gap. The primary current induced in the drift gap is given by the product of the rate $R$ of electrons converted from the photoelectric effect from the incident photons, multiplied by the elementary charge $e$ and the number of primary electrons $N_{p}$ produced by the incident photoelectron in the Ar/CO₂ (70:30) gas mixture. To measure the rate of incident photoelectrons, the readout electrode in the sector under test is connected to the signal processing chain in Fig. 25.

The current $I_{RO}$ induced on the readout electrode is measured separately with a pico-ammeter connected to the sector under test (Fig. 25). For each measurement, the thermal noise current and noise rate are also measured and treated as pedestals to be subtracted from the readout current and the photoelectron rate, respectively, that are measured when irradiating the detector with the X-ray beam. The effective gas gain $G$ is given by:

For determining the experimental error on the gain values, Poissonian uncertainty is assumed on the number of recorded photoelectrons for the determination of $R$. For the determination of the readout current, a sample of 300 measurements is taken and the standard deviation of the mean is taken as the uncertainty on $I_{RO}$.

A dedicated calibration procedure is performed to measure the mean number of primary electrons $N_{p}$ created by an incident X-ray photon in a GE1/1 detector filled with the Ar/CO₂ (70:30) gas mixture. The energy spectrum of the resulting photoelectrons is recorded by a GE1/1 detector with a multi channel analyzer for several detector operating points, each corresponding to a particular value of the effective gas gain. The peak position of each energy spectrum, which is extracted with a fit procedure assuming a Gaussian model for the peaks and a polynomial distribution for the underlying continuum, is taken as the measured value of the amplified charge recorded by the GE1/1 detector for an incident photoelectron from copper fluorescence with an energy of 8 keV. By assuming that the effective gas gain of the operating detector is precisely known, the number of primary electrons can be obtained. The mean number of primary electron induced by an 8 keV X-ray photon in an Ar/CO₂ (70:30) gas mixture in the GE1/1 detector is found to be $N_{p}=346\pm 3$ from this measurement.

As a cross-check, this procedure is performed with two more X-ray sources (⁵⁵Fe, ¹⁰⁹Cd) with the same detector under the same conditions. These same X-ray sources are then used to measure the effective gain calibration curve of the detector. It is found that the resulting respective gain curves, obtained with the same detector under irradiation by different sources, agree with each other within the uncertainties.

Examples of typical effective gas gain curves for GE1/1 production detectors, measured as a function of the HV applied to the drift electrode and the current in the HV divider, are shown in Fig. 26. The blue and red curves refer to GE1/1 detectors produced and tested at different production sites. The difference in the measured effective gain is due to the different environmental conditions at the two production sites. Given the dependence of the effective gas gain on the exponential of the Townsend coefficient, which in turn depends on the ratio between environmental temperature and pressure, the gain curves are normalized to a predefined reference pressure and temperature. The reference values correspond to the average pressure and temperature at the location of the GE1/1 station in the CMS apparatus observed over one year, with $P_{0}=964$ mbar and $T_{0}=297$ K. Rather than correcting the gain values, the value of the applied drift voltage $V_{\textrm{drift}}$ (or the current running through the divider), for a given production site $X$, is corrected by the relation

The impact of the normalization procedure is clearly evident in Fig. 27, where the two curves are shown after applying the pressure and temperature correction. While this particular correction was used during the QC process described here, we note that an empirical correction was developed subsequently to improve the description of the gain dependence on environmental temperature and pressure [19].

The gain measurement performed in a central readout sector of each GE1/1 detector sets the absolute gain scale of the detector as a function of HV. To find the gain across the entire detector and to quantify its variation, the relative response is measured for all readout strips.

The drift electrode is irradiated with a wide X-ray beam from the X-ray generator described in Sec. 3.7.3. The charge induced on the readout strips is amplified by analog pipeline voltage 25 (APV25) analog readout chips [20], digitized by analog-to-digital converters (ADCs), and recorded by front-end concentrator cards (FECs), which are components of the RD51 Scalable Readout System (SRS) [21]. Figure 28 gives a schematic of this test setup.

During data taking, one would ideally want to trigger on the signal from the contiguous bottom electrode of the third GEM foil, which is the mirror image of the signals collected on all the readout strips. However, because of the large capacitance of this electrode relative to the anode strips, the electronic noise is typically too high to reliably trigger the APV system, in particular for the lower range of the energy distribution of the interacting particles. Consequently, the APV25 is operated in random trigger mode. Given the rate from the X-ray gun, which is on the order of several MHz over the entire chamber, and the size of the APV25 acquisition time window (up to 750 $\mu$s), it is basically guaranteed that at least one event is recorded for each random trigger.

As the APV25 ASICs were initially designed for detection of minimum-ionizing particles with silicon-based detectors [20], the amplifiers tend to saturate when operating with X-rays in gaseous detectors at full nominal gain. This saturation typically prevents the proper reconstruction of the collected charge and diminishes the data quality. To overcome this issue, the GEM chambers under test are operated at a reduced gas gain (typically between 500 and 600), below the saturation level. Figure 29 demonstrates that at lower operating voltages, i.e. at lower total effective gains, the response uniformity measured across all readout sectors of the chamber is very similar to that measured at higher voltages and gains. This is an important result as it allows flexibility when setting the operating point of the chamber. A broad range of drift voltages can be used without compromising the uniform response of the detector.

In the data analysis, the readout of the GE1/1 detector is divided into 768 slices with each slice comprising four readout strips that are adjacent in the $i\phi$ coordinate. For each detector slice, the position of the main peak in the spectrum—the copper fluorescence photopeak—is determined from fitting a Cauchy distribution to the ADC spectrum of the total measured strip-cluster charges. Here, the total charge in each X-ray conversion is obtained by summing the ADC counts over the strips in the strip cluster. To model the background, a fifth-order polynomial is fit to the data. Figure 30 shows a typical example of this strip-cluster charge ADC spectrum for one slice of a production GE1/1 detector.

As discussed in Sec. 3.7, the effective gas gain is a combination of the amplification factor given by each GEM foil and the transparency factor. The uniformity of the amplification factor is mostly driven by the consistency of the GEM hole geometry across the foil since the applied voltage is usually constant. Past measurements [22] show that the main variations in the GEM geometry are the thickness of the polyimide layer and the inner and outer diameters of the biconical holes. From the manufacturer’s specifications, the polyimide thickness is typically $(50.0\pm 0.1)\,\mu$m. The corresponding uncertainty on the electric field propagates into a gain variation of 2.4% for a single GEM and 4.2% for a triple-GEM stack. Similarly, the effect of the uncertainty on the hole diameter can be translated in terms of gain variations. Based on the measurements shown in Fig. 31 [22], we estimate that with a typical outer GEM hole diameter of $(70.0\pm 5.0)\,\mu$m, the corresponding gain uncertainty is on the order of 15% for a single foil, and 26% for a triple-GEM stack.

The transparency factor is mostly affected by the variations of the electric field across the detector volume. While the input voltage is unique for each entire electrode, the variation of the gaps between the electrodes impacts the electric field uniformity. In the particular case of the GE1/1 detector, the gaps between the foils are defined by the thickness of the internal frame pieces and the foil stretching applied from the periphery of the GEM stack. The corresponding variation of the gap sizes is below 1% and introduces only negligible gain variations. However, the drift and readout boards are large PCBs with uneven copper deposits on one side, and both are subject to significant mechanical tensions when they are fixed to the foil pull-outs. As a result, those boards can slightly bend, causing variations in gap thickness, especially near the center of the trapezoid. In addition, the boards can bulge in the center due to the applied gas pressure. Consequently, the typical dimension and variation of the drift gap is $(3.0\pm 0.6)$ mm and $(1.0\pm 0.4)$ mm for the readout gap. The corresponding relative errors on the electric fields are 20% for the drift field and 40% for the induction field in the readout gap. Figures 32 and 33 show the influence of these electric field variations on the effective gain. From these values, we estimate the gain variations arising from the deformations of the PCBs to be 7.5% on the drift side and 25% on the induction side. The impact of the various effects are summarized in table 2.

The position of the copper fluorescence photopeak in the ADC spectrum of the total strip-cluster charges is a good measure of the local gain across the chamber. A typical distribution of the fitted positions of these photopeaks across all 768 slices in a chamber is plotted in Fig. 34. This distribution is fitted with a Gaussian to extract the mean ($\mu$) and the standard deviation ($\sigma$) of the distribution.

The standard deviation is a measure of the response uniformity of the detector. Specifically, the relative response uniformity of a GE1/1 detector, quoted as a percent, is defined as $\frac{\sigma}{\mu}\cdot 100\%$, which characterizes the gain variation across the whole detector area. Figure 35 shows two examples for the absolute azimuthal gain variations across a chamber for each $i\eta$ sector, and Fig. 36 gives an example of the relative gain variation across a chamber. In general, we observe a continuous, “u”-shaped curve that peaks at the edges of the detector and attains a minimum at the center of the detector (Fig. 35, bottom). This phenomenon can be attributed to the bending of the readout and drift electrodes previously discussed. We also observe chambers with less variation along the azimuthal direction ($i\phi$), e.g.  Fig. 35 (top), which results from more planar drift and readout PCBs. As Fig. 37 shows, all tested GE1/1 detectors exhibit gain variations below 30%. This value is well below the threshold (37%) that was described in the previous section and consequently all detectors pass this final QC step.