Impact of GEM foil hole geometry on GEM detector gain

Detailed 3D imaging of Gas Electron Multiplier (GEM) foil hole geometry was realized. Scanning White Light Interferometry was used to examine six topological parameters of GEM foil holes from both sides of the foil. To study the effect of the hole geometry on detector gain, the ANSYS and Garfield ++ software were employed to simulate the GEM detector gain on the basis of SWLI data. In particular, the effective gain in a GEM foil with equally shaped holes was studied. The real GEM foil holes exhibited a 4% lower effective gain and 6% more electrons produced near the exit electrode of the GEM foil than the design anticipated. Our results indicate that the GEM foil hole geometry affects the gain performance of GEM detectors.


Introduction
Gas Electron Multiplier (GEM) detectors are radiation detectors [1] used in high-energy physics and in nuclear physics experiments. The active GEM element is a thin (approximately 50 ± 1 µm) polyimide foil with a 5 ± 1 µm copper/chromium coating on both sides [2]; see figure 1.

JINST 10 P12014
The foils have hourglass-shaped holes etched through them using lithography. Typically, their outer diameter D is 70 ± 5 µm, the inner diameter d is 50 ± 5 µm, and the hole pitch P is 140 µm [2]. Local variations in the size, shape [3], and rim roughness of the holes can alter the operational characteristics of the GEM foil. Consequently, these parameters should be uniform to achieve even performance across the active surface of the detector. There are approximately 6400 holes per cm 2 of GEM foil.
Several techniques are used for GEM quality assurance (QA). Most often a high-voltage test is applied -leakage current measurement of the GEM foil [4]. Optical/visual QA of GEM foils is less common. There are also ideas for X-ray-based GEM foil inspection.
Visual QA is necessary not only to examine the size and the shape of the hole, but also to catch foil defects, residuals, and dust. Visual inspection is the only way to confirm the hole parameters. Tardiness is the main disadvantage of visual QA compared to HV QA. Visual inspection usually takes hours, while the HV test is done in approximately 30 min. This drawback is pronounced since there is a need for large-area GEM foil detectors. The optical scanning system (OSS) for the quality assurance of GEM foils was developed in the Laboratory for Nuclear Science at the Massachusetts Institute of Technologies (U.S.A.) in 2006 [5,6]. The University of Helsinki (Finland) [7] and Temple University (Philadelphia, U.S.A.) [8] developed their own systems on the basis of the first one.
Previously, we have calibrated our large-area OSS for quality assurance of GEM foils by using a transfer standard specifically manufactured for this purpose [9,10]. The correlation between the GEM hole size distribution and the corresponding gain variation has also been studied [11].

Methods
The major advance represented by the current study is the use of a 3D reference device to reveal the GEM foil hole geometry; see figure 2. In addition to the parameters used nowadays, we introduce and study four new parameters -the shift (S) between the centers of the inner and outer diameters, the total foil thickness (T ), and metal (T m ) and polyimide (T p ) thickness -that we propose should be controlled during GEM foil manufacturing. The variations in the pitch and rim roughness parameters were not studied in this research.
A customized GEM foil sample allowed us to study the variation in hole size, as well as concentricity issues between the inner diameter d and outer diameter D of the holes. The ± 5 nm vertical resolution of our Scanning White Light Interferometer (SWLI) [12] permitted for the first time the study of variation in the foil thickness as a basis for detailed 3D QA analysis of the GEM foil hole geometry.
The effects of the six (d, D, S, T, T m , T p ) parameters were examined using the ANSYS [13] computer-aided engineering software and the Garfield++ [14] toolkit for detailed simulation of particle detectors. We used ANSYS to create a field calculation for the GEM foil hole, using topological parameter values obtained by SWLI. Garfield++ was then used to simulate the detector gain for the real geometry of the hole. 1000 avalanches in an ArCO 2 70/30% gas mixture with a penning factor r p = 0.7 and V GEM = 600 V were applied to the foil [3]. The probability r p that an excited Ar atom ionizes a CO 2 molecule through penning transfer was studied [15].

GEM foil sample preparation
A randomly chosen GEM foil was cut into 2.5 × 2.5 cm 2 pieces. Using the GEM foil-frame gluing technology [16], these pieces were cleaned and glued to a standard SF4 PCB (polychlorinated biphenyl) frame; see figure 3. This procedure took place in a class 1000 clean room.

Scanning White Light Interferometry
Our full-field-of-view non-contact SWLI device measures surface topography. On the basis of the reflection from the measured surface of a white light beam into an interferometric objective, this technique provides quantitative information across large areas with ± 5 nm vertical resolution [12].
-3 -Our device had a NIKON CF IC Epi Plan DI 50X 0.55NA objective lens with 25X (0.5X tube-lens NIKON) total magnification, a HAMAMTSU Orca Flash 2.8 camera, and a halogen bulb light source (Philips, type 77241, Amsterdam, The Netherlands).

SWLI measurements
The six main GEM foil hole parameters were examined with SWLI: d, D, S, T, T m , and T p . All 25 holes in our sample were scanned three times from the top and bottom of the sample without translating the hole between the images. Using the MountainsMap software [17], the GEM foil parameters for each hole were determined from the SWLI data.
The hole diameters d and D of the GEM foil sample were defined using a 'contour extraction' method (25 holes × 2 diameters × 2 sides × 3 times = 300 measurements). This method, shown in figure 4, employs the contour extraction feature of MMap. The top and bottom diameters d and D were then defined by multiplying the radii that had been obtained by two.
During the contour extraction procedure poor concentricity [18] between d and D was observed on both sides of the foil. Concentricity is the common center of cylindrical or spherical parts. We studied the relative shift (S) between d and D on the top and the bottom sides of the GEM foil sample when assuming the center of d to be the reference point for each side. The values were obtained using the distance measure feature of the MMap software; see figure 4 (right). Each value was formed as an average of three measurements (25 holes × 1 shift × 2 sides × 3 times = 150 measurements). Detailed 3D QA analysis of the GEM foil hole geometry was performed. The vertical resolution of the SWLI allowed us to examine the foil thickness (T ) for the first time and study its variation across the sample. Figure 5 shows the total thickness of the GEM foil around hole #8 scanned with SWLI. Figures 4 and 5 indicate the rim roughness R of the inner and outer diameter. The effect of this GEM foil parameter was not studied in the present study.
All T values were measured with SWLI and obtained using the step height ISO 5436 feature of the MMap software. The GEM foil sample was placed and gently pressed onto a flat reference surface (optically flat, with -0.07 µm out-of-flatness and 0.02 µm out-of-parallelism). Each value was calculated as an average of 4 step height profiles for the top and the bottom side of a single hole -4 -

JINST 10 P12014
(25 holes × 1 height × 4 profiles × 2 sides × 3 times= 600 measurements). The same technique was used to obtain the metal and polyimide thickness on both sides of the GEM foil sample; see figure 6. The sandwiched polyimide, close to the center of the holes, appears to be very thin and transparent to the SWLI, which left an unknown area in the image. Nevertheless, the measured total thickness (63.17 ± 0.07 µm) around hole #8 of our GEM foil sample was close to the nominal value for the GEM foil (60 ± 3 µm). Figure 7 shows a thickness reconstruction of GEM foil hole #8.

JINST 10 P12014
The uncertainty of all the measurements for each hole was defined as required by [19] and [20]. All the SWLI measurements were performed manually, using the same features of MMap. The precision and accuracy of the SWLI measurements depend on identifying the edges of the hole and on the granularity of the computer mouse movement.

Simulation methods
The ANSYS and Garfield ++ software were employed to study the effective gain as a function of hole parameters in a GEM foil with equally shaped holes. This simulation study focused on an hourglass-shaped hole with a nominal d and D (50 ± 5 µm and 70 ± 5 µm), T of 60 ± 3 µm, and P of 140 µm. We created and studied 70 different shape variations of the GEM foil hole. The five basic scenarios are shown in figure 8.
First, the nominal hourglass hole geometry (#1) was simulated and its effective gain was studied. After that the top part of the hole was kept static while the bottom part was moved from the center to the left and then from the center to the right with 1 µm steps in a total range of -5 to 5 µm (scenario #2 in figure 8). The same was done for scenario #3, but the bottom part of the hole was kept static. In the end, scenarios #4 and #5 were studied when both parts of the hole were moved in opposite directions with 1 µm steps in a total range of -5 to 5 µm.
A study of the effective gain as a function of the measured GEM foil hole shape was also performed. ANSYS was used to recreate the GEM foil on the basis of SWLI data from 10 holes in our GEM foil sample. These 10 holes were randomly chosen from the 25 holes examined with SWLI.  Next, the performance of the 10 replicated GEM foil holes simulated with Garfield ++ was evaluated against an hourglass-shaped hole (nominal result). The simulation results are reported in the results section.

ANSYS
ANSYS is a computer-aided engineering software program that we used to create a field calculation for a single GEM foil with equally shaped holes. For each simulated GEM hole category, a foil sandwich structure (thin polyimide foil with metal coating on both sides) surrounded by a gas mixture was created; see figure 10 (left). The hole shape -see figure 10 (middle) -was created from three polyimide layers and two layers of metal; see figure 7. All the volumes were then meshed to create a single body -see figure 10 (right) -which was later cut out of the initial sandwich structure to achieve the final GEM foil lookalike; see figure 11 (middle). V GEM = 600 V was applied to the simulated foil and a field calculation was performed for all 10 measured GEM foil holes and the 70 hole shaping scenarios.

Garfield ++
Garfield ++ is a toolkit for the detailed simulation of particle detectors. Garfield ++ was employed to simulate the detector gain using the ANSYS field calculations as input. For each of the 10 GEM holes and the 70 scenarios, a Garfield ++ simulation was performed for 1000 avalanches in an ArCO 2 70/30% gas mixture, a penning factor r p = 0.7, and V GEM = 600 V applied to the foil.  Figure 12 illustrates the GEM foil sample hole #8, scanned by SWLI and compared with the corresponding OSS image. A contour extraction method was used for both hole diameters, d and D; see figure 4. The extraction method confirmed the observed shift S between the centers of the top and bottom holes determined by SWLI; see figure 4 (right). It was, as expected, also possible to determine the -8 -total foil thickness T, as well as the thickness of the metal T m and polyimide layers T p . Table 1 presents the top and bottom parameters obtained for GEM foil sample hole #8. The results of the GEM foil sample that was examined indicated a probable mask misalignment during the fabrication.    The T values ranged from 62.30 to 65.60 µm. The thickness of the GEM foil close to most of the holes that were examined was 5.6 µm larger than the nominal thickness (60 ± 3 µm).

Comparison of multiple holes
This section focuses on the variation in the diameter of the holes located in one compact area of the GEM foil sample; see figure 3. This data was obtained by the contour extraction method ( figure 4).

JINST 10 P12014
value for the GEM foil, with a typical d of 50 ± 5 µm. However, the values obtained for D are much smaller (-7.5 µm for both the top and bottom sides) than the nominal value (70 ± 5 µm). All the data that was collected can be found in Supplementary_Material.doc (online resource 1). Figure 17 presents the variation in the effective gain studied with Garfield ++ for different shapes of a single hole in a GEM foil with equally shaped holes. A 7% drop in the effective gain was observed compared to the effective gain of the nominal hourglass-shaped hole. Figure 18 shows that the electrons produced near the exit electrode that do not contribute to the effective gain. A 7% maximum increase was observed in this region of the foil.

Simulations
During the GEM hole parameter extraction values different from the nominal ones were observed for the top and bottom sides of the foil. 10 of the 25 holes from our GEM foil sample were randomly chosen to be recreated, as a single foil, with ANSYS and their gain was studied with Garfield ++. Figure 19 illustrates the simulated effective gain (left) compared to that of the nominal hourglass-shaped hole foil and the electrons produced near the exit electrode for 10 real GEM foil hole geometries.
Several of the real GEM hole geometries exhibited a 4% lower effective gain compared to the nominal case. A close look at the hole geometry shows that the high slope from the center to the bottom of the foil might be the reason for this phenomenon. 6% more electrons were produced near the exit electrode of the GEM foil, compared to the nominal case.   Simulated results based on 10 SWLI measured GEM foil hole geometries. The magenta marker is for the hourglass-shaped hole and purple, cyan, and green are for the A (see figure 4), B, and C categories (see figure 9), respectively.

Discussion
There are no detailed studies in the literature on the shape and size of GEM foil holes. Hitherto the holes have been assumed to be perfectly hourglass-shaped [3] and only nominal hole shapes have been simulated [21]. There are papers reporting on both simulations and real measurements with regard to the optimal hole size for high gain [3,22], and [23]. In these cases all the holes were assumed to be identical. Most previous research on detector gain focuses on the gas mixture and pressure and the voltage applied rather than the actual hole shape [15,24], and [25].
- 12 -In the current study we used a calibration sample (to confirm the tool calibration) with a surface comparable to that of the GEM foil to obtain accurate values for the real-life GEM foil hole geometry. To guarantee accurate and traceable results we ensured that both individual holes and ensembles of holes were correctly imaged. This was done by collecting the data with a calibrated SWLI device. This kind of study has not been performed before. We also proposed a new approach to the 3D quality assurance analysis of GEM foil hole geometry. This method applied to a double masked GEM foil employs six parameters: inner (d) and outer (D) hole diameter, shift (S) between the centers of the two holes, and the total foil (T ), metal (T m ), and polyimide layer (T p ) thicknesses.
The S parameter is, however, a little tricky. How does one know which side has moved? The GEM foil fabrication process starts with etching from the top and then from the bottom to the center of the foil. Hence the top side pitch is the first parameter to be created. It is therefore possible to have misalignment of both top and bottom pitches. However, in this study we are observing a shift between D and d on both sides, which should be due to the etching process -the etchant does not create a perfectly centered cone. Consequently our approach of using the top hole center as our reference point should be solid.
To determine the effect of hole geometry on gain, the ANSYS and Garfield ++ softwares were employed to simulate the GEM detector gain performance on the basis of measured SWLI data. The effective gain in a single foil with equally shaped holes was also studied. Compared to predictions based on the ideal geometry, the hole based on the measured geometry featured 4% lower gain and 6% more produced electrons near the exit electrode of the GEM foil. Our results prove that the hole geometry affects the gain performance of the GEM detectors. The recorded effect, while small, may be important since the simulated cases are ideal -equally shaped holes along the GEM foil. As demonstrated in this study, the GEM foil contains holes of different shapes and sizes. Most papers report that GEM detectors are robust and can tolerate the radiation dose foreseen in 10 years of operation without loss in gain and energy resolution. For instance, LHCb published a paper in 2012 stating that 'as of today we don't observe classical aging effects on our GEM detectors' [26].
The simulations assumed a certain size and shape for all the holes in a GEM foil. For instance, each marker in figure 19 represents a foil with identical holes. A GEM detector gain evaluation on the device level could be performed for an assembly of differently shaped and sized holes over several GEM foil detectors. It is likely that the effective gain could significantly increase or decrease if a foil with different shapes and size holes is simulated. This is future work. The effect of the rim roughness also needs to be examined since asperities concentrate the electric field.
The proposed method is slow if used to examine a GEM foil sized 10 by 10 cm 2 . However, knowing the real hole geometry could help improve GEM fabrication, which could lead to better detector performance. Improving GEM foil fabrication is important because it is assumed on the basis of [3][4][5][6][7][8] that the characteristics of GEM foils strongly affect the behavior of the GEM foil detector.
The present work is important to the field of metrology, as well as for the QA and fabrication of GEM detectors. The study shows that the real GEM hole geometry differs from the designed geometry. It might also provide a deeper understanding of the processes inside the GEM detector during operation. We therefore recommend these parameters to be considered during further development, manufacturing, and performance simulations of GEM foils.

Conclusions
A GEM foil sample and high-resolution SWLI were used for a detailed examination of the geometry of GEM foil holes. Both sides of the sample were examined and six topological foil parameters were determined. On the basis of the measured data, ANSYS and Garfield ++ simulations were performed to study the effect of hole geometry on detector gain. Our results indicated that the real GEM foil holes exhibited a 4% lower effective gain and 6% more electrons produced near the exit electrode of the GEM foil than the design anticipated.