Ultralow Expansion Glass as Material for Advanced Micromechanical Systems

Ultralow expansion (ULE) glasses are of special interest for temperature stabilized systems for example in precision metrology. Nowadays, ULE materials are mainly used in macroscopic and less in micromechanical systems. Reasons for this are a lack of technologies for parallel fabricating high‐quality released microstructures with a high accuracy. As a result, there is a high demand in transferring these materials into miniaturized application examples, realistic system modeling, and the investigation of microscopic material properties. Herein, a technological base for fabricating released micromechanical structures and systems with a structure height above 100 μm in ULE 7972 glass is established. Herein, the main fabrication parameters that are important for the system design and contribute thus to the introduction of titanium silicate as material for glass‐based micromechanical systems are discussed. To study the mechanical properties in combination with respective simulation models, microcantilevers are used as basic mechanical elements to evaluate technological parameters and other impact factors. The implemented models allow to predict the micromechanical system properties with a deviation of only ±5% and can thus effectively support the micromechanical system design in an early stage of development.


Introduction
Glasses are certainly high-performance materials with adjustable properties in a wide range of parameters and offer countless application possibilities based on their optical, mechanical, electrical, chemical, and biological properties. The main fields of application in microsystems technology are in micro-optics, micro-fluidics, and biomedical engineering. [1][2][3] In addition, silicate materials with ultralow thermal expansion enable systems, which geometrically withstand temperature influences to an unimagined extent and thus, can act as reference structures in the field of high precision metrology. Notably, most applications of ultralow expansion (ULE) materials are so far still linked to macroscopic systems such as mirror substrates for astronomical applications, components of nanopositioning and nanomeasuring tools or as glass scales. [4][5][6] ULE materials, such as ULE glasses from Corning as well as the glass-ceramic Zerodur from Schott are hitherto rarely used for microscale applications, which originates mainly from a lack of capable manufacturing techniques that provide a superior patterning accuracy and reproducibility at the microscale. With our preliminary work on the reactive ion etching (RIE) of complex glasses and glass-ceramics, we established a technology for the fabrication of deep etched microstructures in glass with lithographic precision up to released micromechanical elements in the glass-ceramic Zerodur, with some restrictions in structure geometry and quality. [7,8] However, our latest results of ULE 7972 plasma structuring enabled the fabrication of high-quality structures with high etch rates and nearly vertical sidewalls. This paves the way to the fabrication of high-quality, free-standing 2.5D micromechanical systems in ULE glass with the possibility to integrate further functionalities. [9] To our knowledge, ULE glass was not used in micromechanical systems to date. Thus, there is a lack in research about the fabrication of released micromechanical structures in ULE titanium silicate glass, and the influence of the fabrication process on the material and its properties as well as in the system design of glass-based integrated microsystems.
The objective of this paper is to provide an according platform for the fabrication of released micromechanical elements in ULE glass and further, to determine the mechanical properties by using microcantilevers. Bending beam structures, so-called cantilevers, are widely used in microsystems technology and nanometrology. They constitute a platform for real-time, in situ physical, chemical, and biological sensors. This yields a wide range of applications starting from atomic force microscopy (AFM) with passive and active cantilever, [10,11] energy harvesting, biomedical application, environmental monitoring, or nanoparticle characterization. [12][13][14] Microcantilever are additionally suitable for the investigation of mechanical parameters such as Young's modulus by static or dynamic characterization. We discuss here different materials used for the fabrication of micromechanical elements in comparison to glasses and especially ULE glass in terms of temperature dependence, in terms of geometrical and mechanical properties, as well as for the integration of interdisciplinary functionalities. Suitable RIE protocols for the fabrication and characterization of released micromechanical elements are subsequently shown. Released microcantilevers are investigated by special metrology experiments concerning their mechanical properties and long-term stability. The experimental results are compared to analytical and numerical models including their influence parameters. Based on both, models and experiments, traceability of Young's modulus is investigated and compared to the given values by the glass manufacturer. The establishment of a suitable fabrication processes and the ability to predict the mechanical system behavior by numerical models pave the way toward an application of ULE glasses in micromechanical systems.

Micromechanical Materials in Comparison to Ultralow Expansion Glass
In micromechanical (cantilever) systems, a variety of materials are being currently used that show different mechanical properties as exemplified in Table 1 together with achievable characteristic structure sizes. A distinction can be made between bulk materials, thin and thick layers, and nanostructured materials. A qualitative overview of characteristic structural sizes and material classes related to cantilevers resembling bending beams are shown in Figure 1.
The currently preferred micromechanical materials for microfabrication comprise single-and poly-crystalline silicon, silicon oxide, silicon nitride, silicon carbide, as well as metal and polymer layers. [14][15][16] One possible fabrication method for a microcantilever is a sacrificial layer strategy to produce sufficiently thin cantilevers. [14] Therein addressed (ULE) glass as well as the glass-ceramic Zerodur are usually present as (macroscopic) bulk materials and thus represent a new class of micromechanical materials. The known mechanical material properties are based on macroscopic investigations and not on a characterization of micro-and nanomechanical systems, as available, for example, standard materials and thin films in microsystems technology.
Thus, glasses play so far, regardless of the type, only a minor role in micromechanical microsystems compared to standard materials such as silicon. Nevertheless, ultralow expansion glasses are also highly intriguing for microsystems technology and in particular for novel miniaturized high-precision force sensors with potential applications, for example, in medical technology/biology and pursue new approaches in glass structuring technology.
ULE glass combines superior mechanical properties with optical transparency rendering them thus as ideally suited for high-precision, miniaturized force measurement systems with integrated optical evaluation. The here addressed single-phase titanium silicate glass ULE 7972 from Corning is synthetically produced glass by hydrolysis, which consists of 93 wt% SiO 2 and 7 wt% TiO 2 , and can be therefore considered as a titaniumdoped fused silica. [17] The metrological properties of fused silica were already investigated in comparison to commonly used materials for load cells  www.advancedsciencenews.com www.aem-journal.com (e.g., aluminum, steel). [18] Fused silica exhibits a very low relative elastic aftereffect and thermoelastic strain. In a wide temperature range, fused silica continued to show no temperature dependence of the characteristic values. Nearly the same mechanical and thermal properties were found in the literature ULE glass. [19] In addition to its extremely low mean linear coefficient of thermal expansion (0 AE 30 ppb K À1 from 5 to 35°C), [20] ULE glass exhibits a long-term dimensional stability without any observable thermal hysteresis and delayed elasticity with a high thermal stability. [19,21,22] This makes this material more suitable for micromechanical applications than Zerodur with nearly identical thermal expansion properties.
The temperature dependence of the mechanical properties of glasses compared to the standard bulk material silicon with its different crystallite orientations is shown in Figure 2. Of interest are the thermal expansion and the temperature dependence of the Young's modulus, which vary for each material, but must be included in the system design. At this point, it should be mentioned that the benefit of glasses does not only rely on the mechanics, but also on the integration of optical, biological, and fluidic functionalities with a high resistance against harsh environmental conditions. Nevertheless, the introduction of complex glasses requires a parallel, high-precision fabrication as well as the predictability of the application-specific system properties, which are discussed in further more detail in the following.

Deep Etching and Releasing of Micromechanical Structures in ULE Glass
An RIE process in a fluorine-based plasma was used to fabricate released microcantilever structures in the ultralow expansion titanium silicate glass ULE 7972 from Corning. An optimized etching process based on the etching gases SF 6 /CHF 3 , and an inductively coupled plasma (ICP) power of 500 W as well as a platen power of 400 W, was used. This process provides a high etch rate of 380 nm min À1 with a selectivity of 26, allowing large etch depths above 100 μm with nearly vertical sidewalls. The average roughness Ra of the etched bottom was previously determined to be in the range of 14-30 nm and thus allows high-quality structures. [9] An overview covering the main fabrication steps for the fabrication of fully released structures are given in Figure 3. The process details of all fabrication steps are given in Experimental Section at the end of this article. The employed electroplated nickel hard mask with a thickness of more than 15 μm enables an etch depth of more than 100 μm and is thus suitable for bulk micromechanical systems as addressed here. The etching process itself is divided into three parts, which are first deep etching, second backside wafer thinning until a low residual thickness is achieved, and third releasing of the structures on a carrier wafer.
The first deep etching step can be done by the previously given process parameters with high etch rate without considering any issues of, for example, thermal heating and stress between substrate and hard mask. The etching depth itself is limited by the selectivity and mask erosion effects as shown in Figure 3c, which enables etch depths between 100 and 150 μm. After finishing the first step, all masking layers are removed by wet chemical etching as illustrated in Figure 3d to avoid high thermal stress during wafer thinning and structure releasing. The applied thin AlN layer (Figure 3e) acts as a protection against the plasma wrap and the attack of the etched structures during releasing step (Figure 3g-i). Afterward, all additional layer and residuals will be removed by wet chemical etching (Figure 3j). This includes the protective layer of AlN, the deposited plasma polymers, and accumulated nonvolatiles from the material itself (e.g., TiF 4 ) as well as redeposited surface contaminations (e.g., AlF 3 from the Al 2 O 3 clamping ring). The deposits are mainly found on the vertical sidewalls, where the physical removal is very low there. [9] Finally, monolithic and released bulk micromechanical structures can be achieved in high quality.
www.advancedsciencenews.com www.aem-journal.com microscopy (SEM) images of relevant locations at the cantilever clamping and tip site as well as some cross-sectional views of cantilevers are presented. As evidently shown, nearly vertical sidewalls in sufficient quality can be achieved, which yields nearly rectangular cross sections. Subsequently, the cantilevers were glued to a carrier substrate designed for the metrology experiments. This step is called assembly in the following and is described in detail in Experimental Section. The relevant geometrical parameters are identified to create numerical micromechanical simulation models based on the finite-element method (FEM).

Geometrical Characterization of RIE Etched Cantilever Structures
The geometrical values of the manufactured cantilevers, the roughness of the etched structure surfaces as well as the assembling were characterized because of their potential influence on the mechanical system behavior, which can thus cause significant deviations between the system design and the experiments. The consideration of experimental etching results in numerical models is expected to significantly improve the simulation quality and thus, the predictability of real system behavior as well as the traceability to mechanical material properties. A schematic illustration of a cantilever structure with the measured geometrical values in comparison to the design is shown in Figure 4. For this purpose, the width of the cantilever on the front and back side, the sidewall angle, and the bending beam thickness and its variation along the length and the rounding at the clamping to the base are influencing factors caused by the etching process itself. The assembling of the cantilever to the tailored carrier for static cantilever calibration can cause a protrusion of the cantilever base as well as angular errors in the horizontal in-plane direction, which can affect the bending line and thus stiffness measurement. Tilting in vertical direction can be determined directly during the measurement in the cantilever test bench by optical observations.
The acquisitions of the geometrical parameters were done by a calibrated light microscope with a measurement accuracy www.advancedsciencenews.com www.aem-journal.com AE0.1 μm, which was verified by reference scales. The measurement accuracy is quite high compared to the measured structure sizes in the range between 50 and 250 μm. Thus, each measured value shows a relative deviation between 2 Â 10 À3 and 4 Â 10 À4 . The measured dimensions of cantilevers used for metrological stiffness measurements in comparison to design parameters are as given in Table 2. A lateral structural widening results in sidewall angles α between 87°and 89°, which is in the expected range for the RIE process as discussed recently for the etching of this type of glass material. [9] A second major parameter is the height of the cantilever here denoted by h. Minor differences in the range between 1 and 5 μm (1-4% deviation in the thickness) are caused by differences in the etch rate distributed across the 100 mm wafer. Due to the relatively large cantilever sizes, differences must be even expected within the same cantilever. In addition, the slightly different etch rates can also cause minor differences in cantilever thickness when thinning the backside of the substrate and releasing the structures. However, it can be assumed that within a structure the deviations are relatively small, for the cumulative through-etched wafer thickness of 500 μm. The rounding at the clamping R between 2 and 3 μm is within the expected range for the employed UV-lithographic process by using the negative resist AZ 15nXT with a thickness of approx. 16 μm. The geometric rounding is subsequently also transferred into the etching mask. With growing etch depth, this rounding will increase due to the aforementioned sidewall angle formation.
Exemplary, the surface roughness Ra was determined for the released cantilever on the top surface and on the etched sidewall by the mean of white-light inference microscope. The glass areas on which the etch mask was applied shows a very low roughness Ra of only approximately 10 nm, as expected. The backside of the cantilever has a correspondingly higher roughness in the range of approx. 40 nm, since the thinning and the releasing of the structures was performed from this wafer side. In the future, this could be avoided by a one-sided through etching of thinner substrates (e.g., 150 μm substrate thickness). . Schematic drawing of the cantilever design I with the investigated parameters of cross section, rounding at the clamping position R, cantilever length l, surface roughness Ra, protruding G after assembling in comparison to the ideal (mask) design as well as the applied force F canti during the cantilever testing (left); manufactured cantilever on a carrier substrate for metrological characterization (right). The roughness of the etched sidewall was found to be in the range of 90-130 nm. The sidewall shows a rugged surface, which is caused by the roughness of mask and by the mask erosion during long etching times. With increasing depths, the roughness becomes more pronounced. This can be improved by optimizing the mask fabrication process through a more passivating etching regime (e.g., higher proportion of CHF 3 or C 4 F 8 ), which protects the sidewall and the mask more sufficiently.
The bulk protrusion G of cantilever base to the carrier is due to the manual assembling technique and depends mainly on the handling, the application, and curing of the adhesive. All the assembling steps are manually done by means of a micromounting device. A certain gap between the chip and the carrier can thus not be avoided, but needs to be appropriately considered based on its influence on the overall cantilever bending line.
In general, it can be confirmed that structures being well aligned with the intended system design can be fabricated by using a tailored RIE processes. Nevertheless, deviations from the ideal design exist and must be considered in numerical system models for an adequate prediction of the system behavior.

Metrological Investigation of Micromechanical Structures
The study of the mechanical properties of the fabricated structures is of distinct interest for future applications. For instance, if modern AFM would be targeted, the following cantilever parameters would be essential: stiffness, resonance frequencies, quality factor, radius of curvature of the probe, shape of the needle, and type of coating on the surface of the cantilever tip (magnetically sensitive layers, conductive layers, and dielectric and hard coatings). Static and dynamic measurements are used to investigate both, the stiffnesses and resonance frequencies of the structures. For the so-called contact mode of AFM, it is necessary to know the stiffness of the cantilever to accurately determine the topology of the measured surface in this mode. During contact scanning between the sample and the tip of the cantilever, on one side, repulsive forces are dominating, which increase exponentially with decreasing distance. On the side of the elastically deformed cantilever beam, the elastic force dominates and in the case of measurements in air, capillary forces (usually, the force of attraction). Since the metrological properties of the cantilevers strongly depend on the geometric parameters and can vary, for precision measurement a calibration respective the force-displacement characteristic of each cantilever needs to be determined.

Investigation of Cantilever Stiffness
As shown in Table 3, there are three global methods for determining the characteristics of the cantilever. The most accurate method of determination is the static method, in which the elastic force of the cantilever is directly measured. For the measurement, a unique setup for force-displacement measurements that was developed at TU Ilmenau was used. The system enables to determine the stiffness of micromechanical systems and is described in detail elsewhere. [23] The operating principle of the device is based on the concept of electromagnetic compensation, supplemented by an electrostatic actuator for calibrating small forces, which is described in Experimental Section. [24] To assess the stiffness of the sample, the measured signals of the compensation current and the displacement of the cantilever are required (Figure 5a,b). The red color represents the integrated data used for the calculation. Each cycle lasts 300 s. The total sample path in each cycle is 5 μm taken in 1 μm steps. At the beginning of the load, the cantilever is close to the load button, but not in contact with it. When the cantilever contacts and detaches from the load button, cohesive forces are generated, so the first step of the cantilever is not considered in the linear regression-based analysis.
The force-displacement characteristic is shown in Figure 5d. The differences between the measured forces and the regression line are less than 0.15 μN. This hysteresis is mostly dependent on creep effects in the load cell. Since measuring forces of over 1 μN are used, large loads are created. The hysteresis of the synthetically fused silica with a OH content of 800-1400 ppm was found to be 5.1-8 Â 10 À4 and relatively low compared to the loading cell (e.g., aluminum approx. 1 Â 10 À3 ). [18] The mean value of cantilever stiffness (cantilever (CL) design I-I, length 6,050 μm) was measured for 9 h, which corresponds to 105 measurement cycles (Figure 5c). There is no recognizable drift in the mean value of the stiffness, which thus is representative for long-term stability for the assembling technology as well as for the material properties itself.
For a more complete characterization of the cantilever stiffness, an eccentricity test and measurement of the cantilever stiffness along the length were additionally carried out (see Figure 6). Since the investigated cantilevers do not have upright tips unlike AFM probes, setting the position of the cantilever relative to the load button is more challenging. It is thus advisable to calibrate the cantilevers at several control points.
The cantilever I-I calibration starts at the zero point (X 0 , Y 0 ) and is moved relative to the load button by AE5 μm along the x and y axes. Each measurement consisted of three loading and unloading cycles. To measure the stiffness of the cantilever along the length, the touching point moves from the position X 0 , Y 0 to 80 μm along the x-axis in negative direction before the measurement consisting of three cycles is done. In the next step, the cantilever moves 20 μm along the x-axis in positive direction Table 3. Calibration methods for determination the stiffness coefficient with relative uncertainties. [ www.advancedsciencenews.com www.aem-journal.com and the measurement is repeated. Measurement end point is X 0 þ 80 μm. The resulting stiffness versus the moving distance is linear as shown in Figure 6 and in the measured values provided in Table S2, Supporting Information.

Investigation of Resonance Frequencies and Q-Factor
The determination of the cantilever resonance frequencies was done by using AFM (setup described in Experimental Section). For optical read-out purposes, an additional thin layer of 20 nm aluminum was vapor-deposited on the topside of the cantilever. The first and the third resonance frequencies were investigated because their out-of-plane oscillation direction and importance for AFM topography measurements (more information on the simulated vibrational modes and von Mises stress can be found in Figure S1, Supporting Information). In Figure 7, the measured vibration amplitudes, the identified resonance frequencies, and the Q-factors for different cantilever lengths or stiffnesses are shown.  www.advancedsciencenews.com www.aem-journal.com As shown in Figure 7, the resonance frequencies decrease with increasing cantilever length, which can be attributed to a reduced stiffness. The first resonance characteristic is asymmetric with a broad peak toward higher frequencies. This can have various reasons, as described later. Due to the measurement setup, the optical set point that was used to measure the vibration amplitude is approximately one third of the cantilever length. For the first resonant frequency and the direction of vibration, this results in relatively low vibration amplitudes that are more susceptible to disturbance. One influencing factor might be a superposition of oscillations from the first and the second resonance frequency, because numerical simulations showed that they are close to each other and may overlap in case of a small Q-factor. Furthermore, the surface roughness can influence the optical evaluation especially in the case of low cantilever deflections.
The third resonance frequency shows relatively sharp oscillation amplitudes that can be clearly assigned and exhibits a high Q-factor. With lower stiffness, the Q-factor decreases due to lower frequencies with similar peak width and parasitic oscillations. The minor deviations between the measured and the included simulated values are linked to fabrication-related influencing parameters and measurement conditions, which are described in detail in Section 3.5.

Micromechanical Systems Modeling
A crucial point for the system design is the predictability of the real mechanical system behavior based on determined manufacturing parameters. The analytical and numerical models should be able to sufficiently describe the experimental results, which simplifies the overall system design. In a first step, an analytical model of a simple cantilever structure was assumed with the geometrical parameter length l of 6,000 μm, width b of 150 μm, and thickness h of 100 μm. The axial moment of inertia I y for a rectangular cross section can be described as The maximum deflection z max at an applied force F z is calculated as a function of the Young's modulus E according to Equation (2) The stiffness is calculated according to Equation (3) For a cantilever with the aforementioned geometric parameters and an applied force F canti in the z-direction of 10 μN, the deflection is 0.85156 μm and the stiffness is c = 11.7426 N m À1 . The length l of 6,000 μm was chosen for simulation because it has higher stiffness at shorter lengths based on the analytical formula. The force of F canti = 10 μN and its point of attack is aligned with the force used in the metrological studies of Section 3.3.1. [23] For the cantilever modeling, numerical FEM simulations in COMSOL Multiphysics were carried out, allowing an efficient variation of both, geometrical and material parameters (more information given in Table S1, Supporting Information). At the beginning, the numerical models were compared with the analytical models to analyze the precision of the numerical discretization in comparison to the analytical solution. To achieve a high sensitivity in the bending direction (z-axis), the maximum element size was lowered for a higher number of volume elements and the scaling of the volume elements of the z-axis was adjusted (maximum element size: 25 μm and scale: 2 in z-direction). Using the same bending beam dimensions, an applied force of 10 μN and the material properties of ULE glass as specified by the manufacturer, an analytical bending stiffness www.advancedsciencenews.com www.aem-journal.com of c of 11.7396 N m À1 is obtained. With this, the deviation between the analytical and the numerical model is close to zero (0.026%). The customized mesh grid was used to compare spring stiffnesses data from a commercial cantilever manufacturer as reference with own models. The used cantilever benchmark was the Micro Cantilever OMCL/BL Series: OMCL-AC55TS-R3 from OLYMPUS. In the data sheet, a spring stiffness of c = 85 N m À1 is given. [25] Own simulations provide a value of c = 85.778 N m À1 , which is a very small deviation of 0.91% compared to the value given in the datasheet. Therefore, the used numerical modeling appears very well suited for the description of the mechanical cantilever properties and is used for stiffness and eigenfrequency simulations in the following.
The various fabricated ULE glass micromechanical cantilevers were first simulated using the ideal geometrical parameter as specified by the mask design. In addition, the models were extended with respect to fabrication-related parameter obtained from the structural characterization as discussed before and are subsequently defined realistic models. The included parameters as well as the differences between the design and the fabricated cantilevers and the finally assembled structures are shown in Figure 4 and quantitatively given in Table 2. The most important parameter used here for the calibration of the static bending beam is the stiffness.
Dynamic numerical simulations were also done in a comparable manner to determine the resonance frequency of the designed and fabricated cantilever. The simulations were performed assuming vacuum conditions and neglecting damping. The first and third resonance frequencies were used for the further investigations, because their main oscillation amplitudes are in the same direction as the optical measurement path.

Comparison between Model and Experimental Results
The comparison of the stiffnesses determined by numerical simulations based on the design parameters and the actually achieved geometries are given in Table 4. Here, simulated and measured cantilever stiffnesses for a length of 6,050, 7,050, and 8,050 μm are shown. As expected, the stiffness decreases with increasing length. The deviation between the realistic model and the measured value is within the range of approx. AE5% (I-I/6,050 μm length) and lower. Thus, the model based on the realistic geometry allows a relatively precise prediction of the mechanical system properties. In contrary, there is a higher deviation between models based on the ideal design and the experimental results. Here, homogeneous structures with vertical sidewalls (α = 90°), no curvatures (R = 0), constant cantilever thicknesses, and a protrusion G being zero are assumed.
The relative uncertainty in the measurement itself was determined to be 0.46% (k = 2), which exhibits thus a relatively small influence on the deviations between model and measurement. Therefore, the main influencing variables are in the model itself and in the integration of the fabrication-related parameters. On the one hand, the deviations between analytical and numerical values are minimal in the range of approx. 1% as mentioned before. On the other hand, it is not possible to integrate all Table 4. Simulated and measured stiffness for the cantilever design I-I, I-II, and I-III and the calculated deviation between simulations and measurements (above). Simulated and measured resonance frequencies for the cantilever design II-I, II-II, and II-III and the calculated deviation between simulations and measurements (below). (Design: simulation with ideal designed parameter, real: simulation with geometrical parameter from the characterization, measurement: static and dynamic measurement of the cantilever stiffness and resonance frequency]. fabrication-related parameters ideally in the models. In addition, only nearly vertical sidewalls are achieved thus yielding a slight tendency to trapezoidal cross sections, which affects the moment of inertia I y . Radii at the transition to the cantilever base can also influence the stiffness. However, the bulk protrusion to the carrier can be considered as a crucial point. Both, cantilevers I-I and I-III show a lower stiffness but a positive protruding (Table 2). This affects the bending line as well as the cantilever length, which translates into lower stiffness. In comparison, a negative protrusion of CL I-II results in increased stiffness as the cantilever length. However, by including these values in models, the deviation to the measured results can be significantly reduced. The bonding of the cantilever might also slightly influence the overall system stiffness between the ideal model and the measurement, but an appropriate consideration of this in numerical models requires far more sophisticated models.
Furthermore, the Youngs's modulus as provided by the manufacturer datasheet could also slightly differ in real. Gerlich et al. reported for ULE 7971 that their measured Young's modulus was 4.6% lower compared to the manufacturer datasheet, which is in the same order of magnitude of deviations between model and measurement found here. [26] ULE 7972 glass that is used here is not identical, so the values cannot be directly transferred. However, the findings may be indicative of other influencing variables originating from the material side.
In the dynamic case, deviations between model and measurement are higher (see Table 4). Therefore, the relative uncertainty of the dynamic calibration method with investigation of frequency, amplitude, and phase shift should be considered. The deviations between the measurement and the numerical models are in the same range as the relative uncertainty of the calibration method between 15% and 25% (Table 3). Further influencing factors are linked to the integration of fabrication-related geometries of the micro-mechanical structures. Minor differences in the structure width, the bending beam thickness, the surface roughness, and the clamping can cause deviations between models and experimental results.
The assembling technology can be mainly neglected because the cantilever was clamped directly to the piezo shaker without a carrier substrate in between. Since the measurement is carried out under ambient conditions, a higher damping and thus a reduction of the resonance frequency compared to the simulation models, assuming vacuum conditions as ambient, is visible in the experimental results. The top layer of 20 nm aluminum, acting as mirror surface, should only have a minor influence. The thickness of the coating is very small compared to the structure height of more than 100 μm and lower as the measurement uncertainty used for the structure characterization.
The determined stiffnesses from the measurement and models were used to trace back to the elastic modulus, which is an essential design parameter for micromechanical systems. Due to sidewall angles being smaller than 90°, the cross section represents a slight trapezoidal shape with impact on the moment of inertia, as mentioned already before. The more realistic area moment of inertia I y,real can be approximated by Equation (4) [27] This results in Equation (5) for the modulus of elasticity Since the models correspond relatively closely with the realistic geometric parameters, it can be assumed that the values determined for the Young's modulus do not differ significantly from the manufacturer's specifications.
With the given geometric quantities in Table S3, Supporting Information, and the stiffnesses from the realistic models (c real ) and the experimental investigations (c measurement ) in Table 4, the Young's modulus can be calculated. The deviations between calculated values based on the models and the measured values are low (realistic model: up to À4%, measurement: up to À9%). The deviation between the determined and the given Young's moduli are in the same order of magnitude as deviations between model and measurement and can also be attributed to this. As described before, not all geometric parameters can be considered in a model. Variations within the cantilever as well as roughness and influencing parameters from the assembling technology can play a crucial role. Furthermore, any deviations in the mechanical parameters should not be excluded, as described earlier.
With the discussed models, different parameters from manufacturing can be integrated to provide a more realistic description of the mechanical properties. With this, differences between the prediction models and the metrological investigations can be significantly reduced. Deviations in the range of AE5% for the static case and AE12% for the dynamic case are already adequate values for the micromechanical system design and fits to the relative uncertainty for the methods given in Table 3.
Certain production-related parameters can be considered in advance in the system design. This is, for instance, true for the sidewall angle (relative stability over the substrate). Avoiding the backside thinning of the wafer and the resulting thickness variation can also support further convergence of model and experimental results. This can be achieved, for instance, by using thinner substrates (e.g., 150 μm thickness) followed by a complete through etching. In this case, the structure height is determined by the substrate thickness and its homogeneity over the wafer. In addition, the surface roughness of the cantilever backside can be reduced by avoiding plasma backside thinning.
Differences between the numerical models assuming the material properties given by the manufacturer and the experimental investigations are within the expected range. These can be traced back to geometric parameters, their measurement uncertainty and integration into the models. Finally, micromechanical and released structures in ultralow expansion titanium silicate glasses can be accurately modeled and the mechanical parameters are close to the fabricated structures by RIE. This is a strong basis for the system design and realization of micromechanical elements and system.

Perspectives of ULE Glass for Interdisciplinary Microelectromechanical Systems
The presented cantilevers are so far just demonstrators that should pave the way for other and more complex glass-based (mechanical) systems. The combination of mechanical with micro-optical, micro-fluidical, and electrical functionalities using ULE titanium silicate glass is feasible and allows novel interdisciplinary system approaches. Some successfully implemented systems and their potential for unification in interdisciplinary glass-based applications are Figure 8 shown.
For the investigation, modeling and traceability to material properties, this paper mainly analyzed and discussed structures that can be well described. The next level involves more complex structures and systems. Some examples are already realized as gear wheels or parallel springs. For instance, parallel springs allow deflections without any lateral offset depending on the applied force direction. [28] In this case, the force would act on the etched sidewall, which requires vertical sidewalls in the etching process as well as a high etch depth (>100 μm). The implemented RIE process for ULE glass is more suitable and shows several advantages compared to more complex ULE glassceramics like Zerodur. Their limitations in processing are less steep sidewalls, lower etching depths due to limited selectivity, and higher surface roughness. [8] The etching process of ULE 7972 glass allows narrower trenches and thus small distances between released micromechanical structures and thus, a higher integration density. In applications itself, the almost rectangular cross section reduces parasitic torsional moments, which is also of potential interest for 2.5D flexible hinges and the integration in complex micromechanical systems. [29] Due to the UV/VIS-range transparency of glass, microoptical functionalities for example, read-out purposes can be integrated within a monolithic bulk-micromechanical system. First approaches in glass are shown in ref. [30]. The biocompatibility and inertness in combination with microfluidic functionalities open applications in miniaturized biotechnology and lab-on-a-chip systems, which can be combined with zero thermal expansion and thus thermally stable structure sizes, for example, reference systems.

Conclusion and Outlook
In this article, the use of ULE glass ULE 7972 for micromechanical applications was investigated. Free-standing cantilevers were realized as demonstrators and were metrologically investigated. We showed that with fabrication-related numerical models adequate predictions of the real micromechanical system, properties can be obtained with small deviations of AE5% for stiffness and AE12% for resonance frequency.
The achieved process parameters of the plasma etching process play an important role. The three-step tailored RIE process provides a high etch rate (380 nm min À1 ), selectivity of 26 and sidewall angle of approx. 88°. Thus, deep etched and freestanding bulk-micromechanical systems (e.g., also gear wheels, flexible hinges) with a structure height of 100 μm and above are possible and pave the way for (ULE) glass as alternative material to the mainly used silicon. Due to the nearly vertical sidewalls with low roughness and large height, the implantation of other functionalities such as in-plane micro-optics, micro-fluidic components, etc., enables novel interdisciplinary glass-based microsystems. In addition, the extremely low thermal expansion is particularly important for applications, which require temperature stable geometric, for example, for precision measurements.
With further optimization of the manufacturing process (e.g., reduction of sidewall roughness, complete etching through of thinner substrates), the quality and homogeneity of the geometric dimensions can be improved. www.advancedsciencenews.com www.aem-journal.com

Experimental Section
Substrate Preparation and Fabrication Released Cantilever in ULE Glass: In this work, double-sided polished ULE 7972 glass wafers from Corning with a thickness of 500 μm were used. First, the substrates were cleaned with anionic surfactants at 80°C followed by Caro's acid at 120°C. Subsequently, an adhesion promoter layer of 20 nm TiW followed by the electroplating start layer of 200 nm Au was sputtered. The structures were defined by means of UV lithography. The thick negative resist AZ 15nXT was used, which was chemically stable in the electroplating electrolyte and allowed sufficient resist thickness with vertical sidewalls. An exposure dose of 450 mJ cm À2 at a wavelength of 365 nm was suitable for achieving vertical sidewalls in the coating at a resolution of 4 μm in a 16 μm thick coating layer. The film was developed in AZ MIF-826 developer for 5 min. The stability of the resist film was further improved by a hard bake step at 130°C for 5 min. Electrodeposition of nickel was carried out in an electrolyte consisting of nickel sulfamate, boric acid, saccharin, and a wetting agent at a deposition temperature of 55°C at a current density of 7.7 A m À2 . The deposition time was selected so that growth of the nickel layer took place within the defined resist structures. A thickness of the etch masking of 15 μm was possible with the parameters listed here. Subsequently, the coating layer and the underlying layer of Au and TiW were removed by wet chemical means and the glass surface was released for etching. For plasma patterning, the process described in ref. [9] was used with an etch gas ratio of SF 6 /CHF 3 of 1:1 with ICP and bias power of 500 and 400 W, respectively, at 20°C electrode temperature.
After deep etching of the microstructures, the applied metal layers were removed by wet chemical means. Subsequently, a thin AlN layer was reactive sputtered onto the front surface, which served as an etch stop layer without insert significant thermal stresses (compared to, for example, thick electroplated Ni layer) during the releasing process. The structures were exposed from the backside of the substrate using a high-rate plasma etching process with the etch stop on the AlN layer. Thus, the geometry of the structures remained intact even during overetching and plasma envelope. This was possible since AlN thin films were stable enough to fabricate large-area membrane structures with diameters of several millimeters and in contrast stable in fluorine plasma. [31,32] Therefore, it was used as an etch mask for reactive etching of silicon and glass. [33] A mixture of H 3 PO 4 , H 2 O, and HNO 3 at 60°C for 20 min flowed by Caro's acid (H 2 SO 4 : H 2 O 2 = 5:1 @ 110°C for 10 min) were used to remove the remaining AlN as well as residuals (e.g., polymer layers and nonvolatile by-products) of the plasma etching process. [34,35] Assembling Technology: The exposed micromechanical bending beams were assembled to an adapter made of FR4 material with a thickness of 1.55 mm. The design was customized and adapted and allowed a complete integration in the cantilever measurement setup. The assembling was carried out with a micro-assembly device, while the fixing was done by the UV-curing adhesive Delo Katiobond LP655. This avoided thermal stress between the adapter and the cantilever base, which could mechanically influence the system behavior. The entire surface between cantilever base and adapter was glued to create a rigid structure (underfilling). The cantilever was aligned to the adapter in such a way that bending could take place at the micromachined clamping between the bending beam and the base. A certain amount of protrusion was therefore accepted, were measured, and considered in the subsequent modeling and simulation. The setup allowed direct installation in the cantilever measurement setup.
Geometrical Characterization of Fabricated Structures: SEM images were created in a Hitachi S4800 in a cross-sectional view or at a tilt angle of 45°f or improved 3D impression of the etched structures at constant magnification. The geometrical characterization of the etched micromechanical structures was performed using an optical microscope at an optical magnification of 200Â from different point of view. For lateral structure dimensions, the investigation from the top and bottom side was done. The measuring of the structure height was done at a tilt angle of 90°, which allowed also a direct measurement of the sidewall angle. The measurement uncertainty of the geometric values was determined by using reference scales and found to be in the range of AE0.1 μm for the used optical light microscope by this magnification. The surface roughness measurement of the structures (top/bottom areas as well as the sidewalls) was done by using a white-light interferometer microscope (Veeco Wyko NT9300).
Metrological Characterization of Micro-Mechanical Structures: Static Stiffness Measurement: The basic operating principle of the static stiffness measurement device was the principle of electromagnetic compensation, supplemented by an electrostatic actuator for calibrating small forces. [24] Figure 9 shows the functional principle of force-displacement measurement device. Based on the numerical models of cantilevers, the stiffness of the test samples was more than 1 N m À1 . The calibration of the cantilevers was carried out using the principle of electromagnetic force Figure 9. Test stand of the traceable force calibration: 1) slit aperture; 2) beam balance; 3) push button; 4) microcantilever; 5) joint; 6) permanent magnet; 7) coil; 8) deflection mirror; and 9) interferometer (adapted from ref. [23]). www.advancedsciencenews.com www.aem-journal.com compensation principle. When the cantilever acted on the load button, the balance deflected, and the deflection was detected by the slit aperture and the interferometer and transmitted to the controller, which regulated the compensation current on the coil attached to the balance. The coil was in a constant magnetic field and due to the Lorentz forces, the balance returned to the zero position. Thus, the force of the cantilever F canti was expressed by Equation (6) F canti ¼ B ⋅ l ⋅ r coil r canti ⋅ i coil (6) where B is the magnetic-flux density, l is the length of the coil, r coil is the distance from the balance hinge to the coil, and r canti is the distance from the balance hinge to the load button. The mounting of the cantilever to the holders must be stiff so as not to affect the measurement result. The assembled cantilever as described before was fixed on an aluminum holder and then installed in the measuring device. To position the cantilever relative to the conical load button, three linear platforms were used in the x, y, and z directions, respectively. For observation from above and from the side (Figure 10), a compact monochrome ThorLabs camera with a 12Â zoom lens was used. After positioning, the movement of the cantilever was carried out by a piezoelectric drive in the z direction. The cantilever displacement signal was detected by the differential interferometer (SIOS SP 2000 DI).
Metrological Characterization of Micro-Mechanical Structures: Investigation of Resonance Frequency and Q-Factor: The measurement of the eigenfrequencies for different cantilevers was done in the AFM Cypher/MFP 3D from Asylum Research. Therefore, the released structures were clamped directly to a piezo shaker, which can be actuated over a broad frequency range. The alignment could be done with a three-axis stage and could be observed optically. The measurement of the deflection amplitude as well as the eigenfrequency was done by a four-quadrant diode. Finally, the amplitude over the frequency could be exported and could be used for further analyses.

Supporting Information
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