2.1.

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., $20\mathrm{mm}\times 2.2\mathrm{mm}$). 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.

Fig. 1

3-D finite element model of (a) the proposed silicon microforce sensor comprising (b) two identical etched WBs located close to the clamped ends and (c) the double-meander springs flanking to the boss.

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 ($V_{\text{in}}$). 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 ($V_{\text{off}}$).

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., $750\mu \mathrm{m}$ in length and $1000\mu \mathrm{m}$ 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)].

Fig. 2

Three spring modifications of the enhanced microforce sensors showing (a) design 1 with horizontal meander structures on a flat surface profile, (b) design 2 with vertical meander structures on a rectangular corrugated surface profile, and (c) design 3 with flat rectangular plates fixed on the bottom of the boss.

2.2.

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 $1000\mu \mathrm{N}$ with a force increment of $100\mu \mathrm{N}$). Deflection states of three different sensor designs under a force up to $1000\mu \mathrm{N}$ 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 ${\sigma }_L$ in $\langle 110\rangle$ directions. The stress is distributed along the rectangular beam, which can be given as

Fig. 3

Bending mechanism of microforce sensor: (a) before and (b) after beam deformation.

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

The force needed to obtain the same deflection value depends on the material, geometry, and bending properties, which is defined as

Fig. 4

(a) 3-D FEM results showing the conditions of three different designed microforce sensors under a force loading up to $1000\mu \mathrm{N}$. The color legend describes the device displacement in micrometer scale. (b) Maximum displacements of their boss structure as a function of applied vertical force on its center position. Design 1 exhibits the most compliant structure among them.

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 ($\mathrm{\Delta }R/R$), which depends on the change of mechanical stress on the surface and the piezoresistive coefficient in longitudinal (${\sigma }_L,{\mathrm{\Pi }}_L$) and transverse directions (${\sigma }_T,{\mathrm{\Pi }}_T$).

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 $5\times {10}^{18}{\mathrm{cm}}^{-3}$ and $1\times {10}^{19}{\mathrm{cm}}^{-3}$, respectively. Afterward, a supply voltage ($V_{\text{in}}$) of 1 V and the ground were applied through the diagonal opposite pads. Hence, the change of the output voltage ($V_{\text{off}}$) on the WB by different force loads can be measured, which is given as

Fig. 5

(a) 3-D FEM results demonstrating the etched silicon piezoresistors designed in a full WB circuit under a force loading up to $1000\mu \mathrm{N}$. The color legend describes the voltage distributed on the device structure in V-unit. (b) Sensor sensitivity of the sensors as a function of applied vertical force on its center position.

It is found that design 1 has the highest electromechanical sensitivity of $8.07\pm 0.004\mathrm{V}/\mathrm{N}$, which is much higher than those of design 2 (i.e., $2.01\pm 3\times {10}^{-4}\mathrm{V}/\mathrm{N}$) and design 3 (i.e., $0.14\pm 8\times {10}^{-7}\mathrm{V}/\mathrm{N}$) by a factor of $\sim 4$ and $\sim 57$, 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.

Table 1

Simulation results of the microforce sensors with three different spring designs observed in the force range of 0 to 1000  μN.

3.1.

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 wafers with $\langle 100\rangle$ orientation and a resistivity of the top layer of 0.01 to $0.02\mathrm{\Omega }\mathrm{cm}$ were used (Active Business Company GmbH, Germany). According to the manufacturer, the device, middle, and handle layers have thicknesses of $(3\pm 1)\mu \mathrm{m}$, $(25\pm 0.5)\mu \mathrm{m}$, and $(350\pm 15)\mu \mathrm{m}$, respectively. Between those silicon layers, two isolation layers of buried oxides (i.e., BOX1 and BOX2), which are located on the upper and lower positions, possess thicknesses of $(0.2\pm 0.01)\mu \mathrm{m}$ and $(0.5\pm 0.025)\mu \mathrm{m}$, respectively. The physical parameters of the wafer are summarized in Table 2.

Table 2

Material specification of the DL-SOI used for meander spring microforce sensors.

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:

Fig. 6

Schematics of the process flow for the fabrication of the double-meander spring microforce sensors, including (a) wafer preparation, (b) boron diffusion with a thermal oxide mask, (c) WB etching, (d) metallization, (e) topside spring dry etching, and (f) backside meander spring release.

3.2.

Fabricated Active Microforce Sensors

After being released from the fabrication batch, the $26\mathrm{mm}\times 26\mathrm{mm}$ large samples were then diced into six single piezoresistive-based microforce sensing devices [i.e., each sensor has a dimension of $20\mathrm{mm}\times 2.2\mathrm{mm}$, 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., $\sim 3$ to $7\times {10}^7\mathrm{N}/{\mathrm{m}}^2$ 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 $\mathrm{k}\mathrm{\Omega }$).^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., $40\mu \mathrm{m}$) to avoid unwanted micro/nanoparticles shorting the active silicon regions.²¹ This phenomenon could either occur during wire bonding or sensor characterization.

Fig. 7

(a) Optical and (b) scanning electron microphotographs of the fabricated active silicon microforce sensors showing (c) the etched piezoresistive WB structures at the sensor clamped end.

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 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 $35\mu \mathrm{m}$), which may affect the performance of the sensors, especially for their stiffness.

Fig. 8

SEM images of (a) the middle part of the active microforce sensor showing its meander springs flanking over the boss structure. (b) Some undercut areas on the meander structures viewed from the bottom side. (c) 3-D surface profile of meander springs measured with 3-D laser microscopy.

3.3.

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 ($\sim 1.3\%$) for the investigated WBs with an average value of $7.20\pm 0.10\mu \mathrm{m}$. As a consequence, the offset voltage of the fabricated WBs was also low (i.e., expected to be $V_{\text{off}}<10\mathrm{mV}/\mathrm{V}$). 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.

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.

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 $0.20\mu \mathrm{m}$ narrower than that under line B. In addition, the structure under line A has a height of $\sim 2.8\mu \mathrm{m}$ compared with the structure under line B of $2.7\mu \mathrm{m}$, which are within the manufacturing tolerance of the DL-SOI device layer (i.e., $3\pm 1\mu \mathrm{m}$). 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 $0.2\mu \mathrm{m}$ 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.

Fig. 10

(a) One corner of the etched WB under test in 3-D laser microscope showing two cross section lines (i.e., lines A and B) to characterize (b) the width and (c) the height of the piezoresistor structures.

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., $<10\mathrm{mV}/\mathrm{V}$), showed much lower values for the half-metal stripes ($0.03\pm 0.001\mathrm{mV}/\mathrm{V}$ and $0.10\pm 0.051\mathrm{mV}/\mathrm{V}$ 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.

Fig. 11

Optical micrographs of the piezoresistive etched WBs with (a) full- and (b) half-metal contacts.

Table 3

Electrical properties different metallization type.

4.1.

Sensor Static Response

Following the optical and electrical characterizations of the WB, sensors were then further tested in force-loading 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 ($T=24\pm 0.02°\mathrm{C}$, $rH=37\%$). 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 $100\mu \mathrm{m}$.²³ The applied forces were measured by a compensation balance through a ruby sphere with a diameter of $300\mu \mathrm{m}$ as the mechanical contact element. In this study, the force was limited to $70\mu \mathrm{N}$ 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.

Fig. 12

Photographs of (a) the microforce sensor under test using (b) a microshaft attached with a stylus ball for applying force on the center of the boss. (c) Measurement results in the force range of 0 to $70\mu \mathrm{N}$ showing linear profile.

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 $70\mu \mathrm{N}$ during loading (i.e., $8.43\pm 0.02\mathrm{N}/\mathrm{m}$) and unloading (i.e., $8.61\pm 0.02\mathrm{N}/\mathrm{m}$) conditions, respectively. These measured stiffness values are almost three times lower than that of FEM (i.e., $23.39\mathrm{N}/\mathrm{m}$), which can be attributed to the overetching of the meander springs leading to a stiffness reduction [Fig. 8(c)]. Furthermore, some parts of the meander structures were not completely released, causing a reduction of the stiffness. On the other hand, the measured sensitivity values of the sensor with respect to the bending forces are $15.19\pm 0.05\mathrm{V}/\mathrm{N}$ and $14.82\pm 0.04\mathrm{V}/\mathrm{N}$ during loading and unloading of the shaft, respectively [Figs. 13(c) and 13(d)]. It is also interesting to determine the bending sensitivity. From Figs. 13(e) and 13(f), it is found that their measured values are in the ranges of $128.54\pm 0.19$ and $128.16\pm 0.23\mathrm{V}/\mathrm{m}$ 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.

Fig. 13

Repeated measurements at one loading position on the center of the boss showing the small differences of [(a) and (b)] stiffness, [(c) and (d)] force sensitivity, and [(e) and (f)] bending sensitivity in loading and unloading conditions, respectively.

Additionally, the performance of the fabricated double-meander 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 $8.52\pm 0.02\mathrm{N}/\mathrm{m}$, 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., $15.01\pm 0.05\mathrm{V}/\mathrm{N}$). 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.

Table 4

Comparison of device properties (numerical analysis versus fabricated device).

4.2.

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 $5000\mu \mathrm{m}/\mathrm{s}$ and a force of $305\mu \mathrm{N}$, a maximum deflection $\mathrm{\Delta }z$ of $4.2\mu \mathrm{m}$ could be obtained. At this stage, the signal was measured within $\sim 1\mathrm{s}$ 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 $\sim 0.5\text{-}\mathrm{s}$ oscillation [Fig. 14(b)]. The output voltage without and with contact loadings are $23.205\pm 0.092$ and $24.548\pm 1.652\mathrm{mV}$, 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)].

Fig. 14

Repeated dynamic measurements of microforce sensor to determine at [(a) and (b)] constant loading speed, (c) fundamental resonance, and (d) sequentially increasing loading velocity.

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 $23.091\pm 0.092\mathrm{mV}$ in the condition of no contact. Under traverse speed of $50\mu \mathrm{m}/\mathrm{s}$, the output voltage in loading position was $24.340\pm 0.116\mathrm{mV}$. Although the indentation speed during loading and unloading sequences had been increased sequentially (i.e., 500, 2500, and $5000\mu \mathrm{m}/\mathrm{s}$), the output signal of the force sensor had shown similar behavior as the one measured at the lowest speed (i.e., $50\mu \mathrm{m}/\mathrm{s}$). 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.