Measurement and control of stiction force in in-plane electrostatically actuated Si nanoelectromechanical cantilever relays with Pt contacts

We measure the stiction force using in-plane electrostatically actuated Si nanoelectromechanical cantilever relays with Pt contacts. The average current-dependent values of the stiction force, ranging from 60 nN to 265 nN, were extracted using the I DS vs V GS hysteresis curves, the cantilever displacement information from finite element method (Comsol Multiphysics) simulations, and the force distribution determined using an analytical model. It is shown that the stiction force is inversely and directly proportional to the contact resistance (R c) and drain-source current (I DS), respectively. Using the dependence of the stiction force on the contact current, we demonstrate the tuning of the voltage hysteresis for the same relay from 8 V to 36 V (equivalent to a stiction force of 70 nN to 260 nN, respectively). We attribute the stiction force primarily to the metallic bonding force, which shows a strong dependence on the contact current.


Introduction
Since their inception, electrostatically actuated relays based on nano/micro electromechanical systems (N/MEMS), mostly based on single crystalline or polycrystalline Si, have gathered considerable attention due to their compact design, relative * Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. ease of fabrication process, and many potential applications, ranging from accelerometers and sensors [1][2][3] to logic devices [4][5][6]. These relays exhibit a zero off-state leakage current together with a steep subthreshold slope, and can operate at relatively high temperatures [1,[7][8][9] while withstanding radiation levels up to two orders of magnitude higher when compared to complementary metal-oxide semiconductor (CMOS) devices, leveraging them for high-efficiency and harsh-environment applications [9][10][11]. Despite these distinct characteristics, the poor reliability due to contact failures in the NEMS relays remains a major concern. Due to the large surface area-to-volume ratio of these relays, one of the major modes of failure is the stiction that occurs at the contact area of two electrodes [2,8,[12][13][14]. Controlled stiction, however, may be beneficial for memory applications, such as in static random access memory and field programmable gate arrays [1,15].
Fundamentally, an electrostatically actuated relay possesses three terminals, as shown in figure 1(a): a cantilever as the source (S), a driving electrode as the gate (G), and an input/output electrode as the drain (D) in analogy to the conventional switches based on field-effect transistors. Generally, Si-based relay electrodes contain a thin metal coating for effective electrostatic actuation and enhanced current conductivity when the cantilever is actuated. When an electric field is applied between the gate and the source, the cantilever bends towards the gate electrode due to electrostatic attraction force (F es ). A restoring/spring force (F restore ) in the cantilever beam counteracts F es , preventing the collapse of the cantilever tip to the drain, and a new equilibrium position is established. However, when the gate voltage V G equals a critical value, the pull-in voltage (V pi ), the cantilever tip contacts the drain, closing the switch. Once the relay is pulled-in, a contact adhesion/stiction force (F stiction ) develops on the contact surface, which increases with increasing actual contact area (e.g. when an overdrive is applied, V G > V pi ) ( figure 1(b)). The stiction/adhesion force is a combination of normal van der Waals (vdW) forces, retarded vdW forces, and metallic bonding forces [16]. With decreasing gate voltage, F es reduces, and once the combination of F es and F stiction falls below the F restore , i.e. when V G is below the pull-out voltage V po , the cantilever separates from the drain. The following conditions thus apply for the cantilever's attachment to or detachment from the drain: (1) For relatively soft cantilevers (small restoring force), even if the attracting electric field is completely removed (i.e F es = 0 V), the cantilever tip may remain attached to the drain if the surface adhesion force, F stiction , overpowers the F restore . This is the failure mode, which can be mitigated by tuning the restoring force and the stiction force, or by changing the operation mode, which will be discussed later.
Compared to other approaches, the processing of NEMS/MEMS devices using Si technology is desirable as it is well established, and single-crystal Si is well known to be extremely resistive to material fatigue and creep deformation, providing superior reliability to absorb electromechanical shocks or stress, or both [17]. However, even with heavy doping, the conductivity of Si is not sufficient for a reliable contact [5]. As a solution, the Si-based device is coated with a thin conductive material, such as Pt, which has shown an outstanding performance due to its high current conductivity, mechanical robustness, and high chemical resistance, even in harsh ambient environments [1,18]. With increased conductivity, stiction becomes a more prominent mode of failure [13] for N/MEMS relays. It is thus necessary to know the strength of the stiction force for appropriate design and operation of N/MEMS relays. Although Pt stiction force has been measured using atomic force microscopy (AFM) [19], it is not entirely applicable to NEMS/MEMS relays since an AFM tip surface guarantees maximum contact with the measuring surface, unlike a source-drain contact in a NEMS/MEMS cantilever relay, where only a few asperities are in actual contact [6,7,13]. Additionally, contributions from retarded vdW forces and metallic bonding forces may not be properly accounted for during stiction force determination using an AFM tip. Also note that the AFM tip material and relay contact material are often different, as evident from past experiments [15]. Therefore, direct quantification of the stiction force in actual NEMS/MEMS relays would provide the much-needed design rules.
In this work, stiction is evaluated in laterally actuated Si NEMS cantilever relays with Pt contacts. The stiction force is determined using the actuation voltage hysteresis curves, the cantilever displacement from finite element method (FEM) simulations, and force distribution obtained from an analytical model. The drain current and contact resistance are shown to strongly impact stiction, which is primarily attributed to metallic bonding forces. Accordingly, the stiction force can be tuned within a wide range by changing the current flow through the contact.

Experimental methods
The gate-voltage-dependent tip displacement and pull-in voltage values of cantilevers with different dimensions were simulated using FEM COMSOL Multiphysics 5.4 software, and the design dimensions were determined for the desired operational voltage range. For fabrication, a silicon-oninsulator wafer with a 2.8 µm thick device layer and 2 µm thick buried-oxide layer was utilized. First, the device layer was thinned by an inductively coupled plasma reactive ion etching (ICP RIE) system (SAMCO RIE-101iPH) down to ∼550 nm using an Ar and SF 6 gas mixture. Then, a ∼500 nm thick positive e-beam resist (ZEP-520A ZEON CO.) was spin-coated on the device layer, followed by patterning using a Raith Voyager 50 KV electron-beam lithography system. After 75 s development in xylenes, the sample was etched in the ICP RIE system using a SF 6 and C 4 F 8 gas mixture. This was followed by residual e-beam resist removal in n,n-dimethylacetamide solution, followed by additional cleaning in H 2 SO 4 /H 2 O 2 mixture (3:1). To release the cantilevers, the sample was dipped into a 49% HF solution for 2 min to remove the SiO 2 layer underneath. For metallization, different thicknesses of Pt layers were deposited via DC power sputtering using an AJA Orion 5 sputtering system. To achieve a relatively uniform coating on both sidewalls of the cantilever electrode, the sample was rotated with the holder inside the sputtering chamber. Figure 1(d) shows the schematic of a released and metallized cantilever.
For stiction force measurements, a number of relays of different cantilever widths (300-500 nm) were fabricated. Although the cantilever widths were different (i.e. of different spring constants) the cantilever-to-drain gap was kept at a narrow range of 300-325 nm. Based on measurements on test samples, for a typical cantilever-to-drain separation of ∼300 nm, the metal thickness on the sidewalls was determined to be 30% of that on the top surface, as shown in the cross-sectional scanning electron microscopy (SEM) image in figure 1(d) inset. The actual devices were then sputtered with Pt for various time durations to obtain different Pt thicknesses (2 nm to 7 nm) on the cantilever sidewalls and drain.
The I DS -V GS characteristics of the relays were measured using a Keithley 4200 SCS system connected to a Karl Suss probe station. The measurements were performed in a controlled air ambient environment with a temperature of ∼24 • C and relative humidity of ∼29%. To acquire a voltage hysteresis, both forward and reverse sweeps of I-V (primarily with a 2 V resolution) were performed with or without a current compliance.
An applied V GS exerts a distributed force on the cantilever which, as a result, bends towards the drain. A cantilever pivot model [20] provides the amount of resultant effective F es and its acting point for a given V GS using the following formula where ϵ, A, V GS , g, and δ are the permittivity of the gap material (air in this case, and the value is considered the same as for vacuum), the electrostatic actuation area, the gate-tosource voltage, the gap between the source and the gate, and cantilever displacement at the gate tip, respectively. We acquire the cantilever displacement (δ) dependence on V GS from COMSOL simulations using the actual electrode dimensions of the relay (fixed cantilever length of 11.65 µm and cantilever thickness of 550 nm, but varying gap and cantilever width). Then, using equation (3), the F es at its acting point (which is at 7.3 µm from the pivot point of the cantilever) is calculated. Finally, the equivalent amount of F es on the cantilever tip is determined using the lever rule. As stated earlier, when a V GS is applied, the cantilever bends towards the gate and parks at an equilibrium position, where the F es becomes equal to the F restore . For any δ, the pivot model provides the magnitude of a single equivalent F restore and its acting point using the following formula where k is the stiffness or the spring constant of the cantilever given by [20] where E, t, w, and L are the modulus of elasticity of Si, cantilever thickness, width, and length, respectively. Single-crystal Si has an elastic modulus that varies with the direction of the applied force. For our work, we selected (100) Si to produce cantilevers oriented in the <110> direction, which has an elastic modulus of 169 GPa [21]. Using equations (4) and (5), the F restore at its acting point (which is at 6.2 µm from the pivot point of the cantilever) is calculated. Finally, the equivalent amount of F restore on the cantilever tip is determined using the lever rule.

Results and discussion
The stiction force can be estimated from the I DS vs V GS hysteresis curves using the cantilever displacement information from simulations. For reliable assessment of an average stiction force, we fabricate a range of relays with fixed cantilever length (11.65 µm) and thickness (550 nm) but with varying cantilever widths and varying S-G gaps. Figure 2(a) presents the SEM image of a relay with a cantilever width of ∼390 nm with a D-S gap of ∼300 nm. This relay exhibits a hysteresis of ∼16 V with a pull-in voltage of 61 V, as presented in figure 2(b). Under a drain bias of V DS = 1 V, the drain current (I DS ) reaches its peak of 165 µA at a gate voltage (V GS ) of 80 V (i.e. 30% voltage overdrive). In the reverse sweep, when the V GS is reduced, the drain current does not follow its forward sweep trajectory due to the stiction force at the contact point. The I DS value remains constant (∼165 µA) until the pull-out occurs at ∼45 V. As shown in figure 2(c), up to the pull-in voltage (61 V), the extracted F es and F restore values are nearly equal, as expected for a balanced system. Just at the pull-in point, when the cantilever contacts the drain, the force is ∼325 nN. Beyond  V pi , F es increases with increasing V GS , but the F restore remains constant (at ∼325 nN) as the cantilever tip is in contact with the drain and cannot move further. Note that any further bending of the cantilever beyond V pi is neglected in this picture. The increasing F es is counteracted by the drain as it exerts an opposing force (F es -F stiction ) to the cantilever tip. In reverse sweep, if the V GS is gradually reduced to slightly below the V pi , the cantilever will pull-out in the absence of stiction [13]. However, the cantilever pulls out at ∼45 V. The F es just before the pull-out is 180 nN, whereas the F restore remains at 325 nN (as the cantilever is still in contact with the drain). As shown in figure 2(c), the difference force (∼145 nN) between the F restore and F es at the pull-out point is attributed to the minimum stiction force, F stiction .
When two surfaces of any material(s) are in contact, vdW forces are active. For small separations (<∼5 nm), normal vdW forces are prominent whereas, for larger separations (>5 nm), retarded vdW forces dominate [12,16]. However, the attractive forces between 'metallic' surfaces at separations below 0.5 nm also involve the metallic bonding force, which arises due to short-range electron exchange interactions between the surfaces [16,22]. This type of force is partially responsible for retaining contact, even when the gate voltage is reduced well below the pull-in voltage. As a result, the I DS , and thus the contact resistance R DS , remain nearly constant, as seen in the reverse sweep of figure 2(b).
As alluded to earlier, the total stiction force increases with increasing contact area. The electrical contact resistance (R DS ) is a good representative measure of the actual contact area and can be obtained from the measured I DS for a given V DS . As shown in figure 3(a) for a variety of cantilevers with different stiffnesses (different widths) and bias conditions, a clear correlation between F stiction and R DS is evident. The stiction force is inversely proportional to the contact resistance, i.e. it decreases with decreasing contact area. Accordingly, relays with low contact resistance below 1KΩ consistently show large voltage hysteresis, i.e. high F stiction . Figure 3(b) shows that F stiction is also closely related to the magnitude of I DS . In general, the higher the current flow, the higher the stiction force is. A too high current (in the milliampere range and above), however, can cause a substantial increase in contact temperature and eventually permanent welding in the contact. In this work, we investigated F stiction vs I DS for relays with R DS values within the range of 0.5 kΩ to 500 kΩ (figure 3(a)) by keeping V DS ⩽ 2 V, while ensuring I DS < 700 µA ( figure 3(b)), resulting in the power released in contacts not exceeding 0.375 mW. In this operation window, we did not observe any noticeable effect of joule heating due to the contact current in our experiments. In separate experiments, we observe an increase in contact resistance and eventual contact welding at powers exceeding 1.2 mW.
Although within our operation range (i.e. maximum power ⩽0.375 mW), we did not observe any modification in contact resistance, regardless of a higher or lower current pass; a higher current should cause a rise in local temperature, which may affect I-V hysteresis. He et al [23] conducted an experiment to find out the potential effect of elevated temperature on NEMS relays' electrical characteristics by raising the relay ambient temperature. When an environmental temperature is raised the contact temperature should also rise by the same amount. However, as reported by He et al, no significant effect is found for NEMS relays' electrical characteristics, even when the temperature is elevated to ∼500 • C [23]. For all-metal electrostatic relays, Sushil et al [14] report a 12% increase in hysteresis when the ambient temperature is raised from room temperature to 150 • C; however, they also report a decrease in hysteresis (∼6%) when the ambient temperature increased from 150 • C to 300 • C. Figure 3(b) shows a clear boost in the stiction force from ∼60-65 nN to ∼200-265 nN when the current flow is increased from 0.01 to 1 µA to 500-1000 µA. We attribute this extra force to the current-induced metallic bonding (CIMB). Thus, by changing the current flow through the relay contact (with varying CIMB) the hysteresis, i.e. the F stiction , can be tuned. As shown in figure 4(a), a higher I DS (∼250 µA) for the same relay shown in figure 2(a) increases the voltage hysteresis and F stiction to 36 V and 260 nN, respectively (from 16 V and 145 nN). A lower I DS (∼10 µA) to the same relay produces 8 V hysteresis equivalent to F stiction ∼70 nN ( figure 4(b). This value is close to the reported stiction force for Pt contact (F stiction = 50 nN) in NEMS relays (for I DS 10 µA and R DS ∼ 10 kΩ), extracted using experimental I-V hysteresis in electromechanical simulations [24]. Our results also agree with the data reported by Tabib-Azar et al [19], who measured the Pt stiction force between a Pt-coated tip in an atomic force microscope and a Pt thin film to be 65 nN. However, the authors did not report the stiction force dependence on the R DS and/or I DS .
The above-mentioned characteristics are for relatively stiff cantilevers (width of ∼400 nm), which would require a higher current flow for stiction failure compared to softer (thinner) cantilevers. For cantilevers with a reduced width of ∼300 nm but the other dimensions kept the same as those shown in figure 2(a), the restoring force is much smaller, F restore = 135 nN. Figure 5 characteristics and force curves at 10 µA current flow, which reveals that the cantilever remains stuck to the drain, even when the V GS is reduced to 0 V and the I DS remains at 10 µA. This indicates an adhesion force of at least ∼135 nN. Upon completion of the I DS -V GS sweep, the cantilever releases itself, which was expected because of the absence of the I DS and, therefore, the relay was ready for further cycling. The same cantilever shows a low hysteresis of 6 V for an I DS = 1 µA (figure 5(b)) with a corresponding stiction force ∼35 nN. This further confirms the dependence of the stiction force on the contact current flow. However, when two metallic surfaces are in contact, even if there is no apparent current flow (through the contact), a metallic bonding force is still active in addition to vdW forces because of short-range electron exchange among the adjacent atoms on the contact asperities [16]. If the actual contact area is large (i.e. R DS is low), this force can be large enough for a soft cantilever (i.e. a cantilever of narrow width), and the cantilever can be permanently stuck, even without any contact current flow after actuation.
To completely eliminate stiction, the mode of cantilever operation can be changed to electrostatic repulsion rather than attraction. When the same voltage is applied to S and G of a relay, because of the like charges, the electrodes will repel each other. When a cantilever is stuck, its spring force is already in effect. Thus, to release it, the required extra force is equal to (F stiction -F restore ), i.e. application of a voltage equivalent to V pi to both S and G terminals will result in detachment of the cantilever from the drain.
Finally, the determination of stiction force per unit area can be a useful parameter as it can be universally used. To calculate the stiction force per area, it is essential to determine the actual contact area. Although the apparent surface area of the source and drain contact is large in the cantilevers discussed here (550 nm × 650 nm), the actual contact area can be quite small. As stated earlier, the electrical contact resistance (R DS ) is a good representative measure of the actual contact area. For R DS = 1 kΩ, the actual contact area can be calculated as 1.1 nm 2 from the following relation: where R apparent is 3 mΩ (considering both the cantilever and the drain sidewalls, each coated with ∼5 nm of Pt), and A apparent is the apparent overlap area of the cantilever and drain. From figure 3(b) we can extract that, for an I DS of 0.01 −1 µA, the average stiction force is ∼60 nN. Therefore, the stiction force per unit area is ∼55 N m 2 , which aligns reasonably well with the theoretical stiction force per unit area (100 N m 2 ) for Pt reported by Pawashe et al, calculated from the Pt surface energy (2.7 J m −2 ) [22].

Conclusion
In this work, we quantify the average stiction force using in-plane electrostatically actuated Si NEMS cantilever relays with Pt contacts. It is shown that the stiction force is inversely and directly proportional to the contact resistance (R c ), which is the measure of the contact area and drain-source current (I DS ), respectively. Using the dependence of the stiction force on the contact current, we tune the voltage hysteresis from 8 V to 36 V, which is equivalent to a stiction force of 70 nN to 260 nN, respectively, by increasing the drain current from 1 0 µA to 250 µA. We attribute the stiction force predominantly to the metallic bonding force and show that the latter has strong dependence on the contact current. The quantification of the stiction force provides the means to tune it either by designing the parameters or operating conditions of a relay, and makes it possible to eliminate or mitigate stiction-related contact failure in such cantilever designs.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).