We now turn to motion detection techniques or displacement sensors. Again, we have arbitrarily divided our review into optical techniques and techniques not involving light. Furthermore, we try to differentiate between integrated and free-space optical techniques—even though some transducers combine the two and are thus difficult to categorize as either. As before, the emphasis will be on the scalability of the techniques discussed.
3.1. Techniques Based on Free-Space Optics
The mainstay free-space optical approach for transducing the mechanical motion of miniaturized mechanical systems has been optical interferometry. With stable laser sources, and fast and sensitive photodetectors, interferometry provides a very high displacement sensitivity and a large measurement bandwidth, and is suitable for room-temperature applications. In a simple Michelson type interferometer, one interferes the optical beam reflecting from the surface of the miniaturized resonator with a reference beam. A Fabry–Perot type interferometer, shown in
Figure 8a, uses multiple reflections of the same optical beam and tends to increase the sensitivity. Optical interferometry has served the MEMS and NEMS communities well in early and ongoing works [
97,
98,
99,
100,
101,
102,
103]. Recently, interferometry has been further exploited to read out the motion of an array of NEMS resonators [
37]. This adaptive full-field interferometer successfully mapped out the photothermally-induced individual mechanical resonances of multiple doubly-clamped beam resonators—about 40 beam resonators—within a ∼ 100
m × 100
m area, as shown in
Figure 1. In another recent work, the oscillations of Si nanowire resonators with widths between 100–200 nm were detected by monitoring the interference between the leaky optical resonance modes around the wires and the surrounding electromagnetic field from the substrate within a Fabry–Perot-like cavity formed by the nanowires and the substrate underneath [
104].
In interferometry, light is typically tightly focused on the device using an objective lens, and one cannot achieve an optical spot size below the diffraction limit. This significantly degrades the displacement sensitivity as the linear dimensions of a NEMS device becomes smaller than the diameter of the optical spot, which is typically around a few micrometers. Second, the motion of the device must be along the optical path (in the out-of-plane direction) since this motion generates a change in the optical path length required for interferometry. These factors complicate optical interferometry (as well as other optical techniques) that are based on free-space optics.
Under certain circumstances, one might need to detect degrees of freedom of mechanical motion other than those moving along the optical path. For instance, if one actuates a mechanical structure in the in-plane direction, interferometric techniques tend to become insensitive to the mechanical motion. Recently demonstrated transduction techniques suitable for such motions are primarily based on optical scattering: optical knife-edge technique [
105,
106,
107], and scattering enhanced with near-field optical probes and/or approaches [
59,
63,
108,
109,
110,
111,
112,
113,
114].
The optical knife-edge technique for in-plane motion of NEMS [
105] is in principle similar to the optical deflection detection method for a microcantilever using a sectioned photodiode or a knife-edge placed in front of a regular photodiode [
34,
115]. In the optical knife-edge technique, the device to be probed works as a knife-edge, and its motion modulates the optical signal reflecting toward the photodetector, as shown in
Figure 8b. The displacement sensitivity of this approach for a doubly-clamped beam resonator can be estimated by carefully scanning the optical spot along the width of the beam and monitoring the resulting reflected optical signal at each step, as long as the beam length is sufficiently long so that the bending of the beam within the optical spot is negligible. The demonstrated displacement sensitivity at sub-mW power levels is around 1 pm/Hz
for a subwavelength doubly-clamped beam resonator. In addition to the optical power, the detection sensitivity depends on the relative sizes of the optical spot (focused by an objective lens) and the nanobeam, and is limited by diffraction—as in free-space optical interferometric approaches.
In the near-field adaptation of this technique, one exploits the interaction between the NEMS to be probed and an evanescent optical wave localized in the vicinity of the NEMS; the scattered optical power is detected by a photodetector in the far field [
114]. The coupling of the evanescent wave to the NEMS resonator may be accomplished by using a variety of structures, such as a waveguide, an optical cavity, a fiber taper, a sharp metallic tip or a similar plasmonic structure. While integrated optical detection exploits on-chip components, such as a waveguide, an optical cavity or a fiber taper (see
Section 2.1 and
Section 3.2), free-space near-field optical motion detection employs a metallic tip or a plasmonic structure—which is the subject of this section.
The coupling of surface plasmons to suspended NEMS resonators has been achieved by plasmonic structures, such as surface plasmon-supporting metal films [
110], nanoantennas [
111], and prisms [
112]. These plasmonic elements are embedded into the NEMS resonator or are fabricated in the vicinity of it, and form a dielectric gap with a metallic surface. The metallic surface can be in the form of a metal-coated substrate or another freestanding metallic resonator. In this way, the motion of the resonator can be directly coupled to optical modes, as shown in
Figure 8c. The nanomechanical motion of the resonator changes the effective refractive index of the volume with which the optical modes interact, and the resulting optical response through the dispersive nature of the plasmonic resonance is monitored by transmission or reflection measurements at the far field. This approach has been extended to detect the motion of an array of beam resonators by using an expanded optical spot covering multiple beams separated by 20-nm-wide ion-beam-milled slits [
116]. The strong spatial concentration of plasmons within the dielectric gap between the metallic surfaces, scaling with the size of the resonating device, ensures that the optomechanical coupling strength—defined as optical frequency shift per unit displacement—is above 1 THz/nm, leading to a displacement sensitivity as high as 6 fm/Hz
.
In the scanning probe microscopy (SPM)-based near-field method demonstrated by Ahn et al. [
113], a sharp metallic tip on a microcantilever with a line-grating serves both as a local probe and a local source (
Figure 8d). Localized surface plasmons are generated and confined at the tip, by tightly focusing the light onto the tip. The interaction between the tip and the moving device surface scatters the localized plasmons, which are then measured at the far-field with a photodetector. Because the intensity of the optical interaction varies significantly with the distance between the tip and the surface as in apertureless scattering-type near-field optical microscopy [
117], the scattered light collected at the far-field carries information on the oscillations of the mechanical resonator. The reported sensitivity of this technique is about 0.45 pm/Hz
.
In these near-field approaches, the confinement of surface plasmons scales with the physical dimensions of the plasmonic structures: for the nanoantenna, the footprint is 485 nm × 50 nm; for the prism, it is 350 nm × 165 nm; and in the SPM-based approach, it is the tip radius, which is about 20 nm. This results in a detection technique which scales below the conventional diffraction limit. In some of these techniques, one can also detect the in-plane oscillations since the optical interactions only depend on the separation between the the plasmonic element on the resonator and the metallic surface or the separation between the resonator surface and the tip. For example, in the SPM-based technique, this can be done by carefully placing the tip near the side of the resonator. This capability of motion detection in both the in-plane and out-of-plane directions can provide flexibility in NEMS resonator design and fabrication. Another interesting aspect of the SPM-based method is the mechanical double-frequency demodulation. The double-frequency demodulation is performed by monitoring the optical signal at the difference frequency between the well-separated resonance frequencies of the tip-mounted microcantilever, which is typically about a few hundred kHz, and the nanoscale resonator, which is well above a few MHz. Furthermore, this can suppress the unwanted optical background noise.
3.2. Integrated Optical Techniques
As hinted above, near-field (evanescent) optical interactions provide an attractive avenue for nanomechanical motion transduction. Near-field optical interactions have been well explored in MEMS-scale structures [
118,
119]. Furthermore, they fit the length scale of NEMS well and can provide sensitivity beyond the diffraction limit. They can be used in both interferometric and non-interferometric approaches, as in free-space optical techniques. Several key elements for integrated optical motion detection, such as suspended optical waveguides and miniaturized optical cavities, have already been discussed above in optical actuation in
Section 2.1; other aspects, such as use of optical scattering, are similar to far-field or free-space optical approaches that have been discussed in
Section 3.1. Here, we will review some scalable approaches.
We first turn to an integrated interferometric approach [
60] in which the phase of light propagating through a photonic circuit is modulated by the motion of a nanomechanical beam. Here, two on-chip waveguides are configured in a Mach–Zehnder interferometer [
120]. A portion of one of the waveguides is suspended to form the nanomechanical beam resonator (
Figure 3). When the waveguide (i.e., the nanomechanical beam) moves toward the substrate, the local optical index and hence the total optical path length changes. This optical path length change (phase shift) is detected in the Mach–Zender interferometer. This scheme has provided a displacement sensitivity ≤0.1 pm/
at mW-level optical powers. More recently, a similar on-chip interferometric approach has been applied to detect the motion of nanocantilevers [
121]. Other possibilities to generate interferometric signals, for instance, from the strain-optic (photo-elastic) effect in a flexing nanostructure, also exist but have not yet been fully explored.
Non-interferometric approaches come with less stringent coherence and stability requirements for the light. Here, one of the approaches successfully demonstrated is based on the scattering of evanescent waves in a waveguide due to nanomechanical motion [
59,
61,
62,
108,
122,
123,
124]. In the implementation by Basarir et al. [
62,
125], a tapered fiber waveguide is brought in the vicinity of a NEMS resonator such that the NEMS structure interacts with the evanescent tail of the optical wave propagating through the waveguide. As the NEMS-waveguide gap is modulated due to the NEMS motion, the optical power transmitted through the waveguide is modulated due to optical scattering by the NEMS resonator. This is a simple but sensitive technique and has allowed for motion detection in arrays of NEMS resonators [
63]. The demonstrated sensitivity approaches ∼0.1 pm/Hz
at optical power levels ≤100
.
The detection signals in integrated optical devices described here can further be enhanced by using optical cavities or optical resonators [
65,
126], as in the case of optical actuation discussed in
Section 2.1. By re-inspecting the device in
Figure 3c, we can explain the enhancement in an intuitive manner. As the nanomechanical beam moves toward the microdisk resonator, its motion changes the local optical index of the microdisk and hence the optical path length around the microdisk, resulting in a modulation of the optical field in the microdisk. Given that the microdisk stores a large amount of optical energy at steady state, one can again naïvely assume that a small mechanical perturbation will result in a large optical response. Enhancement using a variety of cavities has commonly allowed for displacement sensitivities approaching and even below
for different types of nanomechanical structures at mW–
W level input powers.
Finally, one of the technological challenges in developing integrated optical devices is the coupling of light into and out of the device. A commonly used technique is the direct or “butt” coupling of light [
127]. In this technique, two single-mode fibers are directly aligned to the waveguides on the chip to couple the light into and out of the chip. Improvements on this straightforward technique have been achieved by using tapered couplers, lensed fibers, fiber focusers, 3D couplers, and inverse nanotapers [
128]. A detailed review of some of these methods is given in [
127,
129,
130,
131]. Another approach is based on the use of grating couplers [
108]; while somewhat inefficient, grating couplers are easier to implement and may be preferable in some applications.
3.3. Electronic and Other Approaches
The widespread electronic displacement detection techniques of the MEMS domain, e.g., capacitive detection, do not scale into the NEMS domain in a straightforward manner (see below). As with electronic actuation, electronic detection of nanoscale mechanical motion in NEMS was first accomplished by the magnetomotive transduction technique. Here, the detection loop containing the nanoscale structure is placed in a magnetic field. As the structure resonates, the magnetic flux through the detection loop gets modulated due to the motional area change. By picking up the electromotive force (EMF) generated due to the varying flux, one can measure the motion of the NEMS [
8]. The electronic background can be greatly reduced by using an on-chip bridge structure [
132]. As discussed above in
Section 2.2, however, the requirement of high magnetic fields limits the applicability of this technique.
Initial experiments that pushed the limits of electronic displacement sensitivity were motivated by a desire to observe quantum effects on mechanical motion. Researchers engineered displacement detection schemes suitable for cryogenic temperatures. For instance, a DC-biased nanomechanical structure was electrostatically coupled to the island portion of a single-electron transistor (SET), where mechanical motion modulated the impedance of the SET [
78,
133]. In both these experiments, displacement sensitivities ≤5
were achieved at low temperatures ≤50 mK. Nanomechanical motion of a miniaturized mechanical device can also be detected by monitoring the current through an atomic point contact or a tunnel junction formed between a sharp tip and the device in question, either on the same chip [
134,
135] or off board [
136,
137]. Coupling mechanical devices to superconducting quantum interference devices (SQUID) likewise has enabled extremely precise measurement of mechanical motion, e.g., with a sensitivity of
[
138].
Piezoresistive effect—the change of electrical resistance due to mechanical strain—offers possibilities for robust, integrated and room-temperature transducers for motion detection. Piezoresistivity is quantified by the dimensionless gauge factor defined as the ratio of the change in normalized resistance over the strain. Here, one needs to make a distinction between two different mechanisms that generate piezoresistivity: the geometric effect and the resistivity () change. Deformation of an electrode causes a purely geometric effect: for instance, axial elongation together with the accompanying reduction in cross-section (for a positive Poisson ratio) causes the resistance R to increase since , where is the resistivity, L is the length and A is the cross-sectional area of the resistor. This geometric effect is relevant for metals which typically have gauge factors between 1 and 2. The other mechanism, the resistivity change, originates from a change in the electronic band configuration of the material due to applied strain. This is usually the dominant effect in piezoresistive semiconductors, in which gauge factors of a few hundred are possible.
For NEMS applications, both types of the piezoresistive effect have been exploited. Using metallic electrodes, which utilize only the geometric effect, it is easier to obtain resistances close to
. This is not only important for matching to 50-
RF lines, but also for avoiding signal reduction due to parasitic capacitances. Parasitic capacitances in the system (between cables/printed circuit board (PCB) traces/wirebonds carrying the signal and any ground plane nearby) give rise to a low-pass filter with a cut-off frequency at
, where
C is the total capacitance from the signal path to the ground and
R is the resistance of the device. Thus, the small electrode (source) resistance
R is an important advantage of metallic piezoresistive detection. In contrast, silicon based piezoresistive electrodes have resistances of at least a few
and typically a few tens of
. Therefore, it is difficult to directly measure signals from silicon-based piezoresistors due to the
cut-off (for a 1-
sensor resistance and 1 pF cable capacitance,
cut-off frequency is 160 kHz). It becomes feasible, however, to obtain an unattenuated output signal by shifting the measurement frequency to smaller values by using a mix-down technique [
82,
139]. In this important technique, the resistance of the output electrode is biased by an AC voltage, which has a frequency set very close to but slightly different from the mechanical actuation frequency (
Figure 9). Mathematically, the resistance of the electrode has both a constant and a dynamical term:
. When this resistance is biased with a voltage of the form
, the output current contains a term
at the mix-down frequency
, which can be set to be a low value (typically 10–100 kHz for a lock-in amplifier based detection). By working at
, the
cut-off due to parasitic capacitances is avoided (
Figure 9c,d). Therefore, the mix-down technique allows for piezoresistive detection with semiconductor electrodes, which have gauge factors a few orders-of-magnitude larger and conductances significantly smaller than metallic electrodes.
Piezoresistive detection utilizing the geometric effect at the nanoscale was first demonstrated by Li et al. [
140]. In this work, 30-nm thick gold detection electrodes were fabricated on 70-nm thick silicon carbide u-shaped cantilevers. A displacement sensitivity of
was reported. A piezoceramic shaker under the NEMS chip was used to actuate the device. Since low-resistance metallic electrodes were used, mechanical resonances were measured directly with a low-noise amplifier/network analyzer chain without the need for mix-down detection. Metallic piezoresistive detection was also used in tandem with thermo-elastic actuation [
75] by placing u-shaped metallic electrodes on both ends of a doubly-clamped beam as shown in
Figure 4. While one can optimize the thermo-elastic drive and the piezoresistive detection by fabricating the two electrodes from different materials and with different geometries, it is also possible to use identical electrodes from the same material (e.g., gold) in order to simplify the fabrication process.
An early example of semiconductor-based piezoresistive detection was the work of He et al. [
141]. In this work, a bottom-up silicon nanowire was grown between electrically-accessible microtrenches. Although the material exhibits piezoresistivity, it is not straightforward to harness this property for detection, since the total strain over a flexural mode shape is zero to first order (i.e., the top surface extends whereas the bottom surface compresses). However, there is a second order effect: the total elongation of the structure as it vibrates. Since maximal elongation happens twice during one cycle of oscillation, this effect appears at twice the frequency of the nanowire motion (the
term). For this reason, this effect is quadratic with respect to the oscillation amplitude. Using a circuitry capable of actuating the wire at
(with an off-chip piezoelectric shaker) and detecting the output voltage at
, the authors were able to measure resonances in the very high frequency (VHF) range. To facilitate detection, a mix-down technique was used.
In an interesting variant of this technique, efficient piezoresistive detection through an entire nanowire was accomplished by inducing a static deflection and exciting the structure at resonance [
142], as shown in
Figure 10. Here, the authors realized that an initial static displacement profile on the structure,
, would generate a linear (at frequency
) piezoresistive response when a dynamical motion was induced. In this study, the static displacement originated from the fabrication process. When the deflected beam was excited dynamically at the
mode, the total displacement profile was given by
, where
is the amplitude and
is the frequency of the mode with eigenfunction
. As before, piezoresistive signal is proportional to the strain in the beam, which can be calculated as
. From this expression, two distinct terms arise: a term at
proportional to
—this term is identical to the term measured in [
141]. The second term, which is due to the static deflection, occurs at frequency
and is proportional to both the static deflection
and
. The
term dominates the
term as long as
. Therefore, inducing a large initial deflection on the structure facilitates efficient detection of mechanical motion using piezoresistive detection at the resonance frequency of the structure.
The studies mentioned above [
141,
142] solved the problem of detecting piezoresistive changes through an entire nanowire. Thus, they were able to extend the technique to very small mechanical structures. There is another option though: to embed semiconductor piezo gauges of desired shapes onto the mechanical structure. One of the first examples of this approach accomplished piezoresistive detection of in-plane motion [
80]. Here, degenerately doped silicon structures are fabricated on SOI wafers. Typical device geometry is similar to that shown in
Figure 4, where a nearby gate drives the mechanical motion of the entire structure. Piezoresistive transduction occurs at the two small nano-bridges connecting the suspended structure to the side anchors: as the structure moves in plane, one of these bridges experiences compression and the other extension. Consequently, their resistance changes have opposite signs and the mechanical motion can be conveniently read out using a differential measurement. As the source resistances are large, mix down detection is used. This work was also significant because devices were fabricated in a foundry at the wafer scale. This technique was used in several sensing applications, such as single-molecule [
29] and single-particle [
81] detection, as well as for gas sensing with arrays composed of u-shaped silicon cantilevers [
143]. Complementary metal–oxide–semiconductor (CMOS) integration of this device architecture has also been demonstrated [
144].
An interesting detection technique, in some ways similar to piezoresistive detection, is employed in carbon nanotube [
82] and graphene nanomechanical [
6] devices. Here, as the device oscillates back and forth near a gate electrode, the number of charge carriers in the structure gets modulated by electrical gating—which cause the conductance across the device to change. Although this mechanism is different from piezoresistivity, the end result is the same: the dynamic resistance change across the suspended nanostructure enables motion detection. This technique also necessitates the use of mix-down detection since device resistances are in the
range.
Piezoelectric detection was used in combination with piezoelectric actuation (under parametric amplification to avoid cross-talk) [
94] as mentioned above in
Section 2.2. In a room temperature variant of this technique, piezoelectrically actuated resonators were detected through a capacitively coupled silicon field effect transistor [
145] with a displacement sensitivity of
. Recent experiments with nanoscale resonators with embedded 2-dimensional electron gas (2-DEG) structures also used the piezoelectric effect in order to detect nanomechanical vibrations [
146]. To verify the piezoelectric mechanism—which arises due to the underlying crystal structure rather than a mere change in electronic density—the authors fabricated two cantilevers along perpendicular crystal orientations: the readout signals had opposite signs indicating a dependence on the crystal orientation, an anisotropy which signifies piezoelectricity. The experiments were performed at 4.2 K using GaAs/AlGaAs heterostructures and employed electrostatic actuation [
147].
The actuation technique based on dielectric gradient force can be reversed to detect the mechanical motion of polarizable resonators [
85]. This technique has already been discussed in detail in
Section 2.2.
Capacitive detection can also be used in an elaborate way for detecting nanoscale motion of doubly-clamped beam resonators [
77]. The main challenge for this technique is that the motional change in capacitance is extremely small, in the atto-Farad range, which is much smaller than parasitic capacitances in the detection circuit. To remedy the situation, the NEMS beam is biased with a DC voltage; when the nanobeam oscillates, its electromechanical impedance can be modeled as an
circuit in series with the static coupling capacitance. The total impedance of the system varies significantly between off-resonance and on-resonance states. To read the impedance change due to mechanical motion, one still needs to match the impedance close to the
impedance of the RF circuit. A simple
impedance transformation circuit with off-chip components can be used for impedance matching purposes. With this improvement, sufficient electrical contrast is obtained to clearly detect the mechanical resonances in frequency sweeps. Moreover, the technique enables the measurement of many resonators in parallel. Here, each of the many resonators are connected to the external impedance matching circuit through their own coupling capacitances. Individual resonator frequencies are slightly different but close enough such that all resonators can be matched using the same
tank circuit. In this way, an array of 10 resonators was measured through the same RF line [
77]. Capacitive detection with impedance transformation was also used at milliKelvin temperatures for nanoresonator-based read-out of a superconducting charge qubit [
148]. Another elaborate way to use capacitive detection for nanoscale motion is to integrate the CMOS readout circuitry monolithically with the NEMS device [
149,
150,
151]. By fabricating the amplifier next to the resonator, the issue of parasitic capacitance is virtually eliminated and an entire measurement system with extremely small device area is obtained. Using this technique, a self oscillating NEMS + CMOS system at 7.8 MHz was demonstrated [
150].
As discussed in the optical actuation and detection sections (
Section 2.1,
Section 3.1 and
Section 3.2), coupling between optical cavities and mechanical resonators opens up novel ways to detect as well as dampen (cooling via red-detuning) and drive (amplification via blue-detuning) mechanical motion [
42,
43,
44,
152,
153,
154,
155]. These techniques can also be implemented using electromagnetic waves at microwave frequencies rather than at optical frequencies. Instead of optical cavities, microwave resonators in the form of coplanar waveguides or microstriplines can be used. Low-noise microwave generators replace tunable lasers. Since microwave components can be readily integrated and require no geometric alignment, microwave approaches offer practical benefits. There are important drawbacks, however: the momentum of a microwave photon is much smaller than a photon at optical frequencies, hence radiation pressure effect (per photon) is much smaller [
156]. Moreover, it is difficult to obtain microwave resonators with high
Q factors at room temperature due to resistive and dielectric losses. Therefore much of the work in this area has been done at low temperatures using superconducting circuit elements. In typical experiments, a movable electrode (i.e., the nanomechanical resonator) modulates the frequency of the microwave resonator by changing the effective capacitance [
157,
158,
159,
160,
161,
162]. The resulting sidebands of mechanical origin can then be mixed down with the same signal driving the microwave resonator to obtain the mechanical resonance signals. Detailed information on the use of microwave based optomechanics for observing quantum mechanical effects can be found in [
156]. In addition to sensitive motion detection, microwave-based cavity mechanics coupled with an optomechanical transducer has allowed for bidirectional conversion between optical and microwave photons, with possible applications in quantum computing and information processing [
163,
164,
165].
Nanomechanical detection has recently been accomplished by using a room-temperature (electrical) microwave resonator. In one of the first examples [
166], researchers used a
microwave resonator, in which input and output ports were coupled inductively through nearby traces on a PCB. A room-temperature
Q factor of 70 was obtained for the microwave resonator. To couple this microwave resonator to mechanics, a wirebond was used to connect the anti-node region of the microstripline to a gate electrode in close proximity of the dielectric NEMS device. The fringing electric field of the gate electrode samples the space around; the relative permittivity of the NEMS increases the total capacitance of the microwave resonator (
Figure 6). With this scheme, a displacement sensitivity of
was reported at room-temperature; moreover, cavity induced damping and oscillation were demonstrated. It is also possible to detect both in-plane and out-of-plane motion [
87] since the effective capacitance of the microwave resonator changes for both motion directions. Mechanical actuation based on dielectric gradient force can be combined effectively with microwave based detection, by using a bypass capacitor to decouple the GHz range microwave signal from the MHz range mechanical drive signal, as shown in
Figure 6d. In a different implementation, the tip of a
coaxial microwave resonator is exposed, sharpened and placed near a microcantilever [
167]. The evanescent field from the resonator probes the motion of cantilever. Mechanical motion modulates the capacitance, produces sidebands in the microwave resonance frequency and is detected by homodyne detection.
An extension of the tunnel-current-based displacement detection is one that relies on the interaction forces between two surfaces in close proximity. Various AFM modalities have been used to detect the motion of micro- and nanomechanical resonators. In these experiments, a resonant mode of the small device under study is excited by an actuator. An AFM cantilever is brought in close proximity of the resonator to probe the oscillations. Both contact mode [
7] and non-contact mode AFM [
168] have been employed for probing. In some of these experiments, especially in the non-contact mode ones, the strong inherent nonlinearity of the interaction forces between two surfaces in close proximity may offer some advantages from a device perspective [
168].