Double-meander spring silicon piezoresistive sensors as microforce calibration standards

Abstract. A transferable force calibration standard based on a silicon microelectromechanical sensor has been designed, fabricated, and characterized for micrometrology applications. Two essential elements of double-meander springs and full piezoresistive etched p-silicon-on-insulator Wheatstone bridges (WBs) are integrated to the sensor for enhancing the device’s sensitivity and eliminating the current leakage during an active sensing operation, respectively. The design process is supported by three-dimensional finite element modeling to select the optimal proposed sensors as well as simulating their mechanical and electrical properties in the desired force range (≤1000  μN). To fabricate the microforce sensors, a bulk micromachining technology is used by frequently involving an inductively coupled plasma deep reactive ion etching at cryogenic temperature. Several optical and electrical characterization techniques have been utilized to ensure the quality of the fabricated WBs, where their measured offset voltage can be down to 0.03±0.071  mV/V. In terms of its linearity, the fabricated device exhibits a small nonlinearity of <3%, which leads this sensor to be appropriate for precise microforce standard.


Introduction
Trends toward miniaturization require not only suitable fabrication technology of the systems at microscale, but also reliable measurement techniques for its physical properties. In this context, measurement systems are expected to provide more precise values in smaller unit. Force-as one of the most important physical parameters-plays an enormous role in technological advances of humankind, both in fundamental research and applications. Moreover, to determine small force precisely, appropriate sensors are needed.
To date, several sensing mechanisms of sensors have been developed in recognizing small forces (e.g., changes of magnetic flux, capacitive, and piezoresistive). Mehrtash et al. 1 developed a system utilizing a magnetic field to determine the environmental forces in the microdevice for human drug delivery. Meanwhile, polydimethylsiloxane-based force sensors also have been introduced utilizing the overlap between two electrodes on their top and bottom sides, which can detect forces in normal and tangential directions through the change of capacitance values. 2 Hence, those flexible sensors were targeted for natural sensing mechanism with capability to measure weight and deflection of <10 mg and 8 μm, respectively. Nevertheless, transducing a mechanical into electrical signal by using the piezoresistive effect is still dominant in many sensing applications. Utilizing this effect, pressure sensors were fabricated and tested to determine sensitivity and linearity of different piezoresistive configurations at different temperatures. 3 In this context, sensor design made of parallel transverse resistors has better sensitivity and linearity than a single transverse resistor. In contrast, two longitudinal strain gauges were integrated into a cantilever-based microforce sensor. 4 The stress was applied on the free end of the beam structure with a length of 700 μm, a width of 20 μm, and a thickness of 12 μm, which could be used for measuring forces on a microgripper. After calibration, this type of sensor demonstrated stiffness and sensitivity of ∼130 N∕m and ∼5063 V∕N, respectively. Despite excellent sensitivity, the sensor was still too rigid, especially for applications in the fields of precision engineering (e.g., hardness measurement instruments, medical instruments, and micro-macro bilateral control).
Furthermore, another application of use for a microforce sensor is the nanoindentation, which is basically a technique allowing mechanical characterization of materials by applying defined load or deflection onto the sample, so that its hardness can be determined. 5 With the aim of broader force range and applications, depth sensing instruments have been successfully developed in the past to obtain a resolution of 1 nN and a displacement of <1 nm. However, to ensure the highest quality of indentation instruments, reliable calibration procedures are still required, especially for lower force range application (i.e., systems with haptic force-feedback in minimal invasive surgery). 6 Han et al. 7 developed piezoresistive ring-shaped axial sensors to predict forces during catheterization. This sensor was attached on the tip on the guidewire and its movements in z-direction led to deformation of the ring structure as well as the piezoresistive elements. Their thin resistors were fabricated on silicon-oninsulator (SOI) wafer, which showed a sensitivity value of ∼13.4 × 10 −3 μm −1 in z-direction.
In addition to this, precise measurement of small forces is also useful for applications in robotics (e.g., macro-microbilateral control). Transfers of real-world haptic information (i.e., force and position) from microenvironment (target object) into the macrosurrounding (operator) are important for further development of medical technology. 8 However, to realize this kind of operation control, the disturbances have to be taken into account. Mizutani and Katsura 9 compensated the disturbances of the control system by integrating the saving and loading system within closed-loop operation. Furthermore, since the disturbances were also usually scaled, scaling rate is very important to determine whether the effect of the disturbances within a system can be neglected or not. Therefore, precise measurements of environmental reactions are needed to obtain the highest possible transparency, which can only be performed by compensating the disturbances. 10,11 In this work, we proposed a stable microforce sensor based on double-layer (DL) SOI as transferable calibration standards. Unlike the similar calibration standard, our sensor was mainly fabricated employing an inductively coupled plasma (ICP) deep reactive ion etching (DRIE) process at cryogenic temperature. 12 Therefore, anisotropy of the process can be controlled and integration of meander structures into the device is feasible. On both clamped ends, two piezoresistive strain gauges are used as active sensing elements. Therefore, the sensors have direct force-reading capability. To evaluate their performances, static and dynamic properties of the devices were characterized showing promising results to broaden their industrial applications (e.g., mechanical feedback control and robotics).

Finite Element Modeling
In this initial effort, three different designs of SOI-based double-meander spring sensors were modeled, and an extensive micromechanical finite element modeling (FEM) was performed using COMSOL Multiphysics 4.3b. 13 However, the interest of this study was to determine the impact of different design configurations to sensor characteristics (i.e., stiffness, linearity, and sensitivity). Considering the real sensor geometry, a three-dimensional (3-D) model was constructed instead of a simplified two-dimensional model. In general, the sensor consists of three main components: contact area in the center (boss), double spring structures flanking to the boss, and piezoresistive Wheatstone bridges (WBs) clamped on both ends of the chip [Figs. 1(a)-1(c)]. While the sensor spring was varied into three designs, the main area of the device was kept to be identical (i.e., 20 mm × 2.2 mm). Several different mesh sizes were manually chosen for different 3-D structures to save computational time without compromising any reliability of the simulation results. 14 Moreover, single crystal anisotropic p-doped silicon was chosen from the COMSOL library. The models were either rotated 45 deg in the xy-plane or a rotated coordinate system was defined using z-x-z convention of Euler angle to perform simulation along 〈110〉 crystal orientation. 13,15,16 Therefore, comparable physical properties with a fabricated sensor can be determined.
Meanwhile, mechanical and electrical properties of the devices were computed with two physics interfaces from the MEMS module, i.e., solid mechanics (solid) and piezoresistivity, domain currents (pzrd). All exterior mechanical boundaries of the sensor spring were set to be free, excluding the bottom part of the sensor frame, which was set to be fixed during force loading on the center part of the boss. For the electrical boundaries, an electrical potential of 1 V was applied to one of the electrode contacts from the WB as a dc input voltage (V in ). Meanwhile, another contact electrode, which is diagonally aligned to the input electrode, was grounded. Thus, the offset voltages could be read from the other two diagonal nodes of the WB (V off ).
Three different sensor designs were differentiated by the shape of the spring structure close to the boss, although their total dimensions were kept equal (i.e., 750 μm in length and 1000 μm in width). Perpendicular to xy-plane, design 1 has deep and small gap meander structures [ Fig. 2(a)]. Compared to this, the spring design 2 has meander structures upright to the xy-plane or vertically aligned, which will require a more complex fabrication process to create such a rectangular corrugated surface profile [ Fig. 2(b)]. On the other hand, the spring design 3 uses only simple thin membranes instead of meander structures as its spring component [ Fig. 2(c)].

Simulation Results on Device Stiffness and Sensitivity
The numerical search of the optimal geometry configuration of the sensors is based on both mechanical and electrical properties (i.e., stiffness, nonlinearity, and sensitivity). The device models were assessed within the targeted application force range (i.e., between 0 and 1000 μN with a force increment of 100 μN). Deflection states of three different sensor designs under a force up to 1000 μN are shown in Fig. 4(a). Based on the assumption that the sensor elastically deforms and the origin of the coordinate system (x; y, and z) is located on the clamping area of the neutral layer [Figs. 3(a)-3(b)], a point load F applied on the boss structure induces a bending moment M b , which results in tensile stress σ L in h110i directions. The stress is distributed along the rectangular beam, which can be given as where z; x; l; w, and t are the distance from the neutral layer along the z-axis, a certain position on the x-axis, length, width, and thickness of the beam, respectively. 17 In this case, WB structures are placed on the location where the highest mechanical stress σ L;max is to be expected to occur, i.e., as far as possible from the applied force (x value should be minimum) and on the surface of the beam (z value should be t∕2). Depending on Young's modulus E, the elongation ε L may be expressed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 3 2 6 ; 6 9 7 Considering the same deflection value, the stress can be quantified through the bending radius r, which defines later the deformation of the WB structures and is accordingly determined as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 3 2 6 ; 6 1 5 The force needed to obtain the same deflection value depends on the material, geometry, and bending properties, which is defined as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 3 2 6 ; 5 4 1 and the stiffness k is defined by the ratio of the applied force to the outcome deflection.
E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 5 ; 3 2 6 ; 4 7 3 where ΔF and Δz are the applied load and boss deflection increments, respectively. Among the selected approaches, design 1 was evaluated to have the most compliant structure with a stiffness of 23.39 AE 9 × 10 −9 N∕m, which is around 4.5 times smaller than that of design 2 (i.e., 103.45 AE 1.6 × 10 −12 N∕m). As expected for a membrane spring, the structure of design 3 has resulted in the highest stiffness value of 6236.86 AE 2 × 10 −9 N∕m [ Fig. 4(b)]. In this case, the higher stiffness value indicates a more rigid behavior of the spring structure. Therefore, it can lead to better linearity of the force-deflection curves. Apart from the stiffness and linearity, another essential quality characteristic of the device is sensor sensitivity. Because the output signal of the device is read using a piezoresistive method, the sensitivity in this circumstance is related to the WB performance. As a result, the sensitivity of a microforce sensor is defined to be the change in the WB resistance values (ΔR∕R), which depends on the change of mechanical stress on the surface and the piezoresistive coefficient in longitudinal (σ L ; Π L ) and transverse directions (σ T ; Π T ). E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 3 2 6 ; 2 0 0 In the simulation, these piezoresistive effects are directly represented as output voltages with regard to the change in the applied force. 18 Moreover, doping concentrations on the WB and its electrical contact extensions are set to be 5 × 10 18 cm −3 and 1 × 10 19 cm −3 , respectively. Afterward, a supply voltage (V in ) of 1 V and the ground were applied through the diagonal opposite pads. Hence, the change of the output voltage (V off ) on the WB by different force loads can be measured, which is given as where R 1 ; R 2 ; R 3 , and R 4 are given resistor values corresponding to a full WB configuration. In Fig. 5(a), the distribution of voltage in the WB circuit under applied forces up to 1000 μN is presented. The sensitivity (S) is then calculated through the output voltage values (ΔV out ) of different sensor architectures by different force loads (ΔF ¼ 0 to 1000 μN) with an increment of 100 μN, which can be defined as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 8 ; 6 3 ; 2 5 3 S ¼ It is found that design 1 has the highest electromechanical sensitivity of 8.07 AE 0.004 V∕N, which is much higher than those of design 2 (i.e., 2.01 AE 3 × 10 −4 V∕N) and design 3 (i.e., 0.14 AE 8 × 10 −7 V∕N) by a factor of ∼4 and ∼57, correspondingly [ Fig. 5(b)]. Thus, design 1 can provide high sensor output voltages at relatively low applied forces. A comparison of the performed FEM of different sensor designs is shown in Table 1. These results suggest that design 1 with horizontal meander structures is superior to the other designs in terms of both stiffness and sensitivity with only relatively small standard deviation (<1%). Therefore, design 1 has been chosen for the device fabrication.

Fabrication Process Steps
After engineering the designs and analyzing the simulation results, microforce sensors were fabricated to match the geometry of design 1. For this purpose, commercial p-type DL-SOI    Table 2.
Sensor fabrication was conducted based on silicon bulk micromachining processes. The key fabrication steps are schematically shown in Fig. 6, which can be described in detail as follows: 1. Sensor fabrication started with cutting a 4-in. DL-SOI wafer into pieces with dimensions of 26 mm × 26 mm. After being diced, the sample was treated in a piranha cleaning (i.e., H 2 O 2 ∶H 2 SO 4 ¼ 1∶1) inside a quartz glass, which was subsequently boiled on a hot plate with a temperature of 90°C for 5 min to remove any organic residues on the sample during fabrication (e. g., before and after thermal oxidation and prior to photolithography).
2. To achieve higher quality contact formation to the etched p-WB, p þ -diffusion (boron) was applied on the device layer under a temperature of 1200°C within 30 min. Prior to this step, combination of dry and wet oxidation processes at 1100°C was used to create ∼300-nm-thick SiO 2 . 3. 3-μm-thick WB structures were created on the device layer using DRIE at cryogenic temperature (Sentech Instruments GmbH). A 1.7-μm-thick S1818 photoresist was used as an etching mask and two etch gases (i.e., O 2 and SF 6 ) were employed. Finally, a recipe of ICP source power of 500 W, a high-frequency power of 6 W, a process temperature of −80°C, an SF 6 flow of 129 sccm, and an O 2 gas flow of 7 sccm was used. 4. The oxide layer on the middle of the device (BOX1) was structured using buffered hydrofluoric acid (HF, 6 to 7%). Afterward, metal films (30/300-nm-thick Cr/ Au) were applied on the top of the device using ebeam evaporator. Lift-off process was then utilized to define the location of the metal layer. During this process, the metal marking in the middle of the boss structure was also created as a reference for the defined positioning of the stylus on the boss. 5. In the next step, photolithography and DRIE were performed for both the top and front sides of the device. By employing photoresist as an etching mask, the boss structure and the front side of the spring were defined. In this case, the 25-μm-thick silicon middle layer was etched with the same recipe as the WB structures within 12 to ∼15 min. Subsequently, the second buried oxide layer (BOX2) was removed by dipping the sample into buffered HF (6 to 7%). 6. The most challenging step during the device fabrication was the etching step of the meander structure from the backside of the device. A recipe with an ICP source power of 500 W, a high-frequency power of 7 W, a temperature of −75°C, and gas flow of 129 sccm (SF 6 ) and 6 sccm (O 2 ) was used for this etch process step to release the deep structure (300 μm) with small gaps (50 μm). Due to nonuniform temperature distribution during the etching process, parts of structures were overetched. Therefore, in terms of a fixed recipe, etch duration should be adjusted carefully (i.e., ∼1.5 h).

Fabricated Active Microforce Sensors
After being released from the fabrication batch, the 26 mm × 26 mm large samples were then diced into six single piezoresistive-based microforce sensing devices [i.e., each sensor has a dimension of 20 mm × 2.2 mm, see Fig. 7(a)] by taking the advantage of an annexed thin membrane located to one of the sensor frame sides. Thus, in this case, a tweezer can be used instead of a more complicated and expensive dicing blade tool to separate the sensors from the dies. The sensors were then taken to be examined optically in a scanning electron microscope (SEM). On both ends of the front side, WBs as active sensing elements were created to characterize mechanical tension during material deformation [ Fig. 7(b)]. These locations close to clamped ends are expected to have the maximum stress levels along the sensor beam length, which have been proven from FEM (i.e., ∼3 to 7 × 10 7 N∕m 2 for an applied force of 1 mN). The conversion of the material deformation into an electrical signal was carried out by the implemented piezoresistive mechanism. Moreover, the design of full p-type WBs may have better performance with regard to temperature effect cancellation compared to a half-bridge circuit. Meanwhile, for their vertical thickness, the fabricated resistors exhibit very high uniformity attributed to the predefined SOI-material thickness. This would be beneficial compared to the conventional diffused or implanted p-type resistors on n-type substrates for better designing and controlling the precise resistance values of the piezoresistors (i.e., in the range of kΩ). 19,20 Therefore, we could obtain well-defined perpendicularly arranged resistors [ Fig. 7(c)]. However, it should also be noted that the oxide areas surrounding the bridge had been extended compared to the former design (i.e., 40 μm) to avoid unwanted micro/nanoparticles shorting the active silicon regions. 21 This phenomenon could either occur during wire bonding or sensor characterization. In addition to the WB structures, we also characterized the fabricated spring structures on the device optically. Figure 8 (a) shows the boss and both clamped meander spring structures viewed from the bottom side. Although there were some imperfections of the overetched areas on the structures, which might be caused by nonuniform temperature distribution during the etch process, these meander structures were still expected to be able to improve the sensor performance [ Fig. 8(b)]. Another possible reason for this case was the used self-bias set by the high-frequency power. Nevertheless, this type of artifact could be reduced or  Optical Engineering 091409-6 September 2016 • Vol. 55 (9) even eliminated by better adjustment of the etch recipe. Hence, smoother trench sidewalls as well as more uniform silicon blocks could be obtained. 21,22 Furthermore, a 3-D laser microscope (LEXT OLS4000 3D Laser Measuring Microscope, OLYMPUS) was used to measure the meander actual geometry and its surface profile after fabrication. It can be obviously seen from the extracted 3-D micrograph [ Fig. 8(c)] that although the meander structures show good uniformity and perpendicular walls on their structure, their actual size has been shrunk to be smaller than designed and modeled geometry (i.e., from 50 to 35 μm), which may affect the performance of the sensors, especially for their stiffness.

Piezoresistive Wheatstone Bridges
The dimensions (i.e., width and thickness) of the fabricated WB structures are measured using SEM and a 3-D laser microscope. The full image of the WB and its magnification of several critical positions were captured and analyzed (s. Fig. 9). The measured width single resistor geometry exhibits very low deviation (∼1.3%) for the investigated WBs with an average value of 7.20 AE 0.10 μm. As a consequence, the offset voltage of the fabricated WBs was also low (i.e., expected to be V off < 10 mV∕V). Ideally, the offset voltage should be zero. However, due to imperfections of fabrication processing steps, such small values in practical situations can still be acceptable for signal processing of the piezoresistive sensors. Moreover, two neighboring WB structures, which are located next to each other at 90 deg angle, were measured by a 3-D laser microscope [Figs. 10(a)-10(c)]. The functional structure under line A is by 0.20 μm narrower than that under line B. In addition, the structure under line A has a height of ∼2.8 μm compared with the structure under line B of 2.7 μm, which are within the manufacturing tolerance of the DL-SOI device layer (i.e., 3 AE 1 μm). It should be noted that the measurements were also performed for the other three corners of the WB, which yielded similar results as the described one. These values demonstrate that the geometry deviation during the etching was relatively small with maximum values of 0.1 and 0.2 μm in vertical and horizontal directions, respectively. Therefore, the etch recipe can be used to reproducibly fabricate etched WBs with structure dimensions matching that of the employed lithography mask.
In this work, two different metallization forms were applied on the devices (i.e., full-and half-metal contacts). The full metal type covers the whole electrical path surfaces from the contact pads to the WB corners [ Fig. 11(a)]. For the half-metal contact, the Cr/Au layer was deposited only on the top of a defined area outside the membrane [ Fig. 11(b)]. This second metallization design was made considering the avoidance of an additional stress from full metal on the thin membrane area where the WB was located. However, the implementation of different metallization designs has consequences on the wire resistance values, which can be determined from the measured resistance values between contacts 2 and 3 as well as 5 and 6, i.e., R 23 and R 56 . In Table 3, the measured resistances R 13 ; R 14 ; R 16 ; R 34 ; R 36 , and R 46 are listed. As expected, higher values were observed with half-metal stripes owing to the higher wire resistance. However, the offset values of both options, which were reasonably low in both cases (i.e., <10 mV∕V), showed much lower values for the half-metal stripes (0.03 AE 0.001 mV∕V and 0.10 AE 0.051 mV∕V for left and right WBs, respectively) than the full-metal stripes. Therefore, regardless of the slight deviations of the fabricated WB geometries from an ideal cuboid shape, reliable output signals still can be expected in all cases.

Sensor Static Response
Following the optical and electrical characterizations of the WB, sensors were then further tested in force-loading Fig. 9 SEM images of the fabricated etched p-SOI WB with its magnified views on its middle and corner parts for quality inspection from optical measurements.
Optical Engineering 091409-7 September 2016 • Vol. 55 (9) measurements for investigating its mechanical properties and to confirm the benefits of the engineered meander springs, as it would be used as a microforce calibration standard. Moreover, to guarantee constant temperature, humidity, and pressure during the measurement as well as to eliminate measurement errors caused by environmental issues, the sample was placed inside a controlled chamber imitating normal laboratory conditions (T ¼ 24 AE 0.02°C, rH ¼ 37%). Figures 12(a) and 12(b) show the device under test, where the silicon microforce sensor was fixed on an aluminum block holder, which could be moved in 3-axis directions. Precise positioning of this part was secured by a nanopositioner with a resolution of 1 nm and a maximum displacement of 100 μm. 23 The applied forces were measured by a compensation balance through a ruby sphere with a diameter of 300 μm as the mechanical contact element. In this study, the force was limited to 70 μN to avoid overloading the structure. Meanwhile, the measured data acquisition was performed in every 400 nm steps of z-direction (i.e., parallel to the loading shaft). It is crucial to ensure linear beam behavior within the sensor operating range, because at a certain point too high applied forces may    cause nonlinear force-deflection curve as well as device fracture. Figure 12(c) exhibits a typical measured position-force curve of a microforce sensor and its first and second derivatives, which exhibit very good linearity with increasing force. The mechanical measurements were then repeated for 24 times to observe the sensor stability as well as to have quantitative measurement data. Hence, the device properties can be reliably extracted from the measured values. Moreover, to investigate its hysteresis behavior, the sensor monitoring was performed in both conditions of increasing and decreasing force loadings. The increasing loading started from the initial contact between the stylus ball and the boss, in which the shaft then further pushed the sensor toward its lower position. Similarly, the decreasing loading (i.e., unloading) was captured when the loading shaft had started to be pulled up toward its higher position. In these measurements, we determined three critical parameters, i.e., device stiffness, force sensitivity, and bending sensitivity. Figures 13(a) and 13(b) show the measured device stiffness in the force range from 1 to 70 μN during loading (i.e., 8.43 AE 0.02 N∕m) and unloading (i.e., 8.61 AE 0.02 N∕m) conditions, respectively. These measured stiffness values are almost three times lower than that of FEM (i.e., 23.39 N∕m), which can be attributed to the overetching of the meander springs leading to a stiffness reduction [ Fig. 8(c) 23 V∕m for loading and unloading conditions, respectively. All in all, the measurement values for those three parameters of the sensor mechanical properties have exhibited very small hysteresis (<3%), confirming the performance consistency and device stability on both loading and unloading characterizations.
Additionally, the performance of the fabricated doublemeander force sensors is evaluated by direct comparison of their experimental and simulation results (Table 4). For the stiffness, the final fabricated device has a lower mean value of 8.52 AE 0.02 N∕m, which is almost half that of the FEM. In contrast, the mean fabricated sensor sensitivity yields higher mean value than the FEM results (i.e., 15.01 AE 0.05 V∕N). Regardless of the required fabrication optimizations (e.g., improved etching process and spring designs), a combination of low stiffness and high sensitivity compared with the FEM solutions is beneficial for precise measurement procedures of very low forces.

Sensor Dynamic Response
In addition to the static response of the sensor, two real-time measurements (i.e., with constant and varied transverse loading speeds) were carried out to evaluate the dynamic response of the device, which is particularly exciting for robotics or automated systems based applications. In the first experiment, the signal of WB of the force sensor was monitored at the initial state, where there was no contact between the stylus and the device. Once the stylus had moved downward onto the sensor contact area and loaded the sensor with a defined velocity v s of 5000 μm∕s and a force of 305 μN, a maximum deflection Δz of 4.2 μm could be obtained. At this stage, the signal was measured within ∼1 s and its average value was calculated to investigate the stability of the sensor under loading condition [ Fig. 14(a)]. Afterward, the stylus was released to its initial position and reached its stable condition by experiencing an ∼0.5-s oscillation [ Fig. 14(b)]. The output voltage without and with contact loadings are 23.205 AE 0.092 and 24.548 AE 1.652 mV, respectively. After repeating the measurements three times, similar values of the output voltage during contact are obtained, confirming the reproducibility and reliability of the device. Furthermore, from the flexural frequency measurement, the device has a fundamental resonant frequency of 805 Hz [ Fig. 14(c)].
For the second dynamic loading measurement, the sensor was tested in different loading velocities to justify its rapid responses concerning the real applications, where the forces can be applied in various speeds. However, it should be noted that the system configuration and measurement method were kept identical as those of the first measurement. From Fig. 14  (d), the initial offset voltage value was 23.091 AE 0.092 mV in the condition of no contact. Under traverse speed of 50 μm∕s, the output voltage in loading position was 24.340 AE 0.116 mV. Although the indentation speed during Optical Engineering 091409-9 September 2016 • Vol. 55 (9) loading and unloading sequences had been increased sequentially (i.e., 500, 2500, and 5000 μm∕s), the output signal of the force sensor had shown similar behavior as the one measured at the lowest speed (i.e., 50 μm∕s). This could be seen from the calculated deviations of those four different output signals, which showed a very small value of <0.0008. Based on these results, the device can be considered to be potentially used to rapidly detect mechanical signal and transduce it directly into an electrical signal with stable and reliable performances.

Conclusion
Piezoresistive silicon microforce sensors as a transferable calibration standard have been developed by optimizing the mechanical (i.e., springs) and electrical readout elements (i.e., piezoresistors). The meander spring design was chosen among others for fabrication because of its superior properties (i.e., lower stiffness and higher sensitivity) obtained using FEM. A particular wafer of DL-SOI has been used instead of a bulk silicon wafer to ensure very well-defined dimensions of the boss, springs, and WBs. The experimental results showed that the fabricated sensors have very good stability and properties in repeated mechanical force measurements, although their values are slightly different from those predicted by FEM. Regardless of the shown promising  performance, some further experiments and optimizations are required to better justify the sensor functionality and obtain higher linearity and sensitivity.