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

Abstract

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.

Full text

Journal of Micromechanics and Microengineering
J. Micromech. Microeng. 33 (2023) 085006 (7pp) https://doi.org/10.1088/1361-6439/acdc32
Measurement and control of stiction
force in in-plane electrostatically
actuated Si nanoelectromechanical
cantilever relays with Pt contacts
Md Ataul Mamun, Bennett Smith, Benjamin Horstmann, Kai Ding,
Gary Atkinson, ¨
Umit Özgür and Vitaliy Avrutin∗
Department of Electrical and Computer Engineering, Virginia Commonwealth University, Richmond, VA
23284, United States of America
E-mail: vavrutin@vcu.edu
Received 17 February 2023, revised 22 May 2023
Accepted for publication 7 June 2023
Published 27 June 2023
Abstract
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 IDS vs VGS hysteresis curves, the
cantilever displacement information from nite 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 (Rc) and
drain-source current (IDS), 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.
Keywords: nanoelectromechanical system relays, stiction force, metallic bonding force,
NEMS/MEMS, electrostatically actuated relays, Pt contact, adhesion force
(Some gures may appear in colour only in the online journal)
1. 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 fur-
ther 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 [1–3] to logic
devices [4–6]. These relays exhibit a zero off-state leakage
current together with a steep subthreshold slope, and can oper-
ate at relatively high temperatures [1,7–9] while withstand-
ing radiation levels up to two orders of magnitude higher
when compared to complementary metal-oxide semicon-
ductor (CMOS) devices, leveraging them for high-efciency
and harsh-environment applications [9–11]. Despite these dis-
tinct 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
1361-6439/23/085006+7$33.00 Printed in the UK 1 © 2023 The Author(s). Published by IOP Publishing Ltd

J. Micromech. Microeng. 33 (2023) 085006 M A Mamun et al
of two electrodes [2,8,12–14]. Controlled stiction, however,
may be benecial for memory applications, such as in static
random access memory and eld programmable gate arrays
[1,15].
Fundamentally, an electrostatically actuated relay pos-
sesses three terminals, as shown in gure 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 con-
ventional switches based on eld-effect transistors. Generally,
Si-based relay electrodes contain a thin metal coating for
effective electrostatic actuation and enhanced current conduct-
ivity when the cantilever is actuated. When an electric eld
is applied between the gate and the source, the cantilever
bends towards the gate electrode due to electrostatic attrac-
tion force (Fes). A restoring/spring force (Frestore ) in the can-
tilever beam counteracts Fes, preventing the collapse of the
cantilever tip to the drain, and a new equilibrium position is
established. However, when the gate voltage VGequals a crit-
ical value, the pull-in voltage (Vpi), the cantilever tip contacts
the drain, closing the switch. Once the relay is pulled-in, a con-
tact adhesion/stiction force (Fstiction) develops on the contact
surface, which increases with increasing actual contact area
(e.g. when an overdrive is applied, VG>Vpi) (gure 1(b)).
The stiction/adhesion force is a combination of normal van der
Waals (vdW) forces, retarded vdW forces, and metallic bond-
ing forces [16]. With decreasing gate voltage, Fes reduces, and
once the combination of Fes and Fstiction falls below the Frestore,
i.e. when VGis below the pull-out voltage Vpo, the cantilever
separates from the drain. The following conditions thus apply
for the cantilever’s attachment to or detachment from the drain:
Attached: Fes +Fstiction >Frestore.(1)
Detached: Fes +Fstiction <Frestore.(2)
For relatively soft cantilevers (small restoring force), even
if the attracting electric eld is completely removed (i.eFes =
0 V), the cantilever tip may remain attached to the drain if the
surface adhesion force, Fstiction, overpowers the Frestore. This is
the failure mode, which can be mitigated by tuning the restor-
ing 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 deform-
ation, providing superior reliability to absorb electromechan-
ical shocks or stress, or both [17]. However, even with heavy
doping, the conductivity of Si is not sufcient 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 conduct-
ivity, stiction becomes a more prominent mode of failure [13]
for N/MEMS relays. It is thus necessary to know the strength
Figure 1. (a) A schematic diagram of a NEMS relay with three
terminals: a cantilever anchored in a source (S), a driving electrode
as the gate (G), and an output electrode as the drain (D). (b) An
electrostatically actuated relay with forces in effect. The
electrostatic force between G and S causes the cantilever to pull-in
to the drain. (c) The IDS vs VGS characteristics of the relay,
indicating pull-in and pull-out voltages. (d) A schematic of a
released and metallized cantilever relay. The inset in (d) shows the
cross-section SEM image of a metallized test sample to estimate the
sidewall to top metal deposition ratio for a gap of ∼300 nm.
of the stiction force for appropriate design and operation of
N/MEMS relays. Although Pt stiction force has been meas-
ured 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 measur-
ing 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 quantication 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 nite 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 metal-
lic bonding forces. Accordingly, the stiction force can be tuned
within a wide range by changing the current ow through the
contact.
2

J. Micromech. Microeng. 33 (2023) 085006 M A Mamun et al
2. 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-on-
insulator 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 SF6gas mixture. Then, a ∼500 nm thick posit-
ive 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 develop-
ment in xylenes, the sample was etched in the ICP RIE system
using a SF6and C4F8gas mixture. This was followed by resid-
ual e-beam resist removal in n,n-dimethylacetamide solution,
followed by additional cleaning in H2SO4/H2O2mixture (3:1).
To release the cantilevers, the sample was dipped into a 49%
HF solution for 2 min to remove the SiO2layer underneath. For
metallization, different thicknesses of Pt layers were deposited
via DC power sputtering using an AJA Orion 5 sputtering sys-
tem. 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 differ-
ent 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 determ-
ined to be 30% of that on the top surface, as shown in the
cross-sectional scanning electron microscopy (SEM) image in
gure 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 IDS – VGS 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 con-
trolled air ambient environment with a temperature of ∼24 ◦C
and relative humidity of ∼29%. To acquire a voltage hyster-
esis, both forward and reverse sweeps of I–V(primarily with
a 2 V resolution) were performed with or without a current
compliance.
An applied VGS 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 Fes and
its acting point for a given VGS using the following formula
Fes =ϵAV2
GS
2


δ+ (g−δ)ln(g−δ
g)
δ2(g−δ)

(3)
where ϵ, A,VGS,g, and δare the permittivity of the gap mater-
ial (air in this case, and the value is considered the same
as for vacuum), the electrostatic actuation area, the gate-to-
source 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 VGS
from COMSOL simulations using the actual electrode dimen-
sions of the relay (xed cantilever length of 11.65 µm and
cantilever thickness of 550 nm, but varying gap and cantilever
width). Then, using equation (3), the Fes at its acting point
(which is at 7.3 µm from the pivot point of the cantilever) is
calculated. Finally, the equivalent amount of Fes on the canti-
lever tip is determined using the lever rule. As stated earlier,
when a VGS is applied, the cantilever bends towards the gate
and parks at an equilibrium position, where the Fes becomes
equal to the Frestore. For any δ, the pivot model provides the
magnitude of a single equivalent Frestore and its acting point
using the following formula
Frestore =kδ(4)
where kis the stiffness or the spring constant of the cantilever
given by [20]
k=2
3Et(w
L)3
(5)
where E, t, w, and Lare the modulus of elasticity of Si, canti-
lever 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 pro-
duce cantilevers oriented in the <110>direction, which has an
elastic modulus of 169 GPa [21]. Using equations (4) and (5),
the Frestore at its acting point (which is at 6.2 µm from the pivot
point of the cantilever) is calculated. Finally, the equivalent
amount of Frestore on the cantilever tip is determined using the
lever rule.
3. Results and discussion
The stiction force can be estimated from the IDS vs VGS hys-
teresis curves using the cantilever displacement information
from simulations. For reliable assessment of an average stic-
tion force, we fabricate a range of relays with xed 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 hyster-
esis of ∼16 V with a pull-in voltage of 61 V, as presented in
gure 2(b). Under a drain bias of VDS =1 V, the drain cur-
rent (IDS) reaches its peak of 165 µA at a gate voltage (VGS)
of 80 V (i.e. 30% voltage overdrive). In the reverse sweep,
when the VGS is reduced, the drain current does not follow its
forward sweep trajectory due to the stiction force at the con-
tact point. The IDS value remains constant (∼165 µA) until the
pull-out occurs at ∼45 V.
As shown in gure 2(c), up to the pull-in voltage (61 V),
the extracted Fes and Frestore values are nearly equal, as expec-
ted for a balanced system. Just at the pull-in point, when the
cantilever contacts the drain, the force is ∼325 nN. Beyond
3

J. Micromech. Microeng. 33 (2023) 085006 M A Mamun et al
Figure 2. (a) An SEM image of a fabricated relay showing the dimensions of electrodes. (b) The measured I–Vresponse of the relay shown
in (a). No current compliance was set for the measurement, (c) Electrostatic force and restoring force at the cantilever tip as a function of the
gate-to-source voltage. The force plots (i.e. Fes and Frestore) in (c) are calculations using the pivot model and the COMSOL simulations with
the experimentally determined dimensions (shown in (a)) and experimental values of Vpi and Vpo (b).
Figure 3. (a) Stiction force correlation with contact resistance (RDS ) extracted from a range of cantilevers with various widths (spring
constants). Low contact resistance means a larger actual contact area, leading to higher stiction force. (b) The correlation of stiction force
with current conduction through the contact. A higher current ow leads to higher stiction force. The error bars show the standard deviation
of the stiction force for an IDS, measured over a number of samples with different widths and G–S gaps but with xed thickness and D–S
gaps.
Vpi,Fes increases with increasing VGS , but the Frestore remains
constant (at ∼325 nN) as the cantilever tip is in contact with
the drain and cannot move further. Note that any further bend-
ing of the cantilever beyond Vpi is neglected in this picture.
The increasing Fes is counteracted by the drain as it exerts an
opposing force (Fes – Fstiction ) to the cantilever tip. In reverse
sweep, if the VGS is gradually reduced to slightly below the
Vpi, the cantilever will pull-out in the absence of stiction [13].
However, the cantilever pulls out at ∼45 V. The Fes just before
the pull-out is 180 nN, whereas the Frestore remains at 325 nN
(as the cantilever is still in contact with the drain). As shown in
gure 2(c), the difference force (∼145 nN) between the Frestore
and Fes at the pull-out point is attributed to the minimum stic-
tion force, Fstiction.
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 separa-
tions 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 IDS,
and thus the contact resistance RDS, remain nearly constant, as
seen in the reverse sweep of gure 2(b).
As alluded to earlier, the total stiction force increases with
increasing contact area. The electrical contact resistance (RDS)
is a good representative measure of the actual contact area and
can be obtained from the measured IDS for a given VDS. As
shown in gure 3(a) for a variety of cantilevers with differ-
ent stiffnesses (different widths) and bias conditions, a clear
correlation between Fstiction and RDS 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 1KΩconsistently show
large voltage hysteresis, i.e. high Fstiction.
Figure 3(b) shows that Fstiction is also closely related to
the magnitude of IDS. In general, the higher the current ow,
the higher the stiction force is. A too high current (in the
4

J. Micromech. Microeng. 33 (2023) 085006 M A Mamun et al
Figure 4. Compared to the relay whose characteristics are shown in gure 2, we show the IDS vs VGS characteristics (upper panels) and
force curves (bottom panels) (a) for IDS ∼250 µA: hysteresis enlarged to 36 V, which corresponds to Fstiction ∼260 nN (no current
compliance was set for this test); and (b) for IDS =10µA: hysteresis shrinks to 8 V, which is equivalent to Fstiction ∼70 nN. For both (a) and
(b) the VDS was kept constant at 1.5 V, indicating that a low drain-to-source voltage has a negligible role in the hysteresis. The force curves
(i.e. Fes and Frestore) presented in the bottom panels are calculated using the pivot model and the COMSOL simulations using the
experimentally determined dimensions (shown in gure 2(a)) and experimental values of Vpi and Vpo (upper panel).
milliampere range and above), however, can cause a substan-
tial increase in contact temperature and eventually permanent
welding in the contact. In this work, we investigated Fstiction
vs IDS for relays with RDS values within the range of 0.5 kΩ
to 500 kΩ(gure 3(a)) by keeping VDS ⩽2 V, while ensuring
IDS <700 µA (gure 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 experi-
ments, we observe an increase in contact resistance and even-
tual 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 modication in con-
tact resistance, regardless of a higher or lower current pass; a
higher current should cause a rise in local temperature, which
may affect I–Vhysteresis. He et al [23] conducted an exper-
iment to nd out the potential effect of elevated temperat-
ure on NEMS relays’ electrical characteristics by raising the
relay ambient temperature. When an environmental temper-
ature is raised the contact temperature should also rise by
the same amount. However, as reported by He et al, no sig-
nicant effect is found for NEMS relays’ electrical charac-
teristics, 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 ow 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 ow through the relay contact (with varying CIMB)
the hysteresis, i.e. the Fstiction, can be tuned. As shown in
gure 4(a), a higher IDS (∼250 µA) for the same relay shown
in gure 2(a) increases the voltage hysteresis and Fstiction to
36 V and 260 nN, respectively (from 16 V and 145 nN). A
lower IDS (∼10 µA) to the same relay produces 8 V hysteresis
equivalent to Fstiction ∼70 nN (gure 4(b). This value is close
to the reported stiction force for Pt contact (Fstiction =50 nN)
in NEMS relays (for IDS 10 µA and RDS ∼10 kΩ), extrac-
ted using experimental I–Vhysteresis 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 lm to be 65 nN. However, the authors did not report
the stiction force dependence on the RDS and/or IDS.
The above-mentioned characteristics are for relatively stiff
cantilevers (width of ∼400 nm), which would require a
higher current ow 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 gure 2(a), the restoring force is much
smaller, Frestore =135 nN. Figure 5(a) shows the IDS -VGS
5

J. Micromech. Microeng. 33 (2023) 085006 M A Mamun et al
Figure 5. The I–Vdiagram (top panels) shows that the cantilever (a) is stuck after switching for IDS =10 µA, and (b) low hysteresis when
the IDS compliance was set to 1 µA. The inset in (b) shows the SEM image with the dimensions of the relay associated with the I–Vcurves
in (a) and (b). The measured dimensions are used in the corresponding simulations in COMSOL Multiphysics and the pivot model to
calculate the force plots. The bottom panel shows the electrostatic force and restoring force at the cantilever tip as a function of the
gate-to-source voltage for currents (a) 10 µA and (b) 1 µA.
characteristics and force curves at 10 µA current ow, which
reveals that the cantilever remains stuck to the drain, even
when the VGS is reduced to 0 V and the IDS remains at 10 µA.
This indicates an adhesion force of at least ∼135 nN. Upon
completion of the IDS –VGS sweep, the cantilever releases
itself, which was expected because of the absence of the
IDS and, therefore, the relay was ready for further cycling.
The same cantilever shows a low hysteresis of 6 V for an
IDS =1µA (gure 5(b)) with a corresponding stiction force
∼35 nN. This further conrms the dependence of the stiction
force on the contact current ow. However, when two metal-
lic surfaces are in contact, even if there is no apparent current
ow (through the contact), a metallic bonding force is still act-
ive 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. RDS 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 ow 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
(Fstiction –Frestore), i.e. application of a voltage equivalent to
Vpi 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 determ-
ine the actual contact area. Although the apparent surface area
of the source and drain contact is large in the cantilevers dis-
cussed here (550 nm ×650 nm), the actual contact area can be
quite small. As stated earlier, the electrical contact resistance
(RDS) is a good representative measure of the actual contact
area. For RDS =1 kΩ,the actual contact area can be calcu-
lated as 1.1 nm2from the following relation:
Aactual
Aapparent
=Rapparent
Ractual
where Rapparent is 3 mΩ(considering both the cantilever and the
drain sidewalls, each coated with ∼5 nm of Pt), and Aapparent
is the apparent overlap area of the cantilever and drain. From
gure 3(b) we can extract that, for an IDS of 0.01 −1µA,
the average stiction force is ∼60 nN. Therefore, the stiction
force per unit area is ∼55 N m2, which aligns reasonably well
with the theoretical stiction force per unit area (100 N m2) for
Pt reported by Pawashe et al, calculated from the Pt surface
energy (2.7 J m−2) [22].
4. Conclusion
In this work, we quantify the average stiction force using
in-plane electrostatically actuated Si NEMS cantilever relays
6

J. Micromech. Microeng. 33 (2023) 085006 M A Mamun et al
with Pt contacts. It is shown that the stiction force is inversely
and directly proportional to the contact resistance (Rc), which
is the measure of the contact area and drain-source current
(IDS), 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 0µA to 250 µA. We attribute the stiction force predomin-
antly to the metallic bonding force and show that the latter has
strong dependence on the contact current. The quantication
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 ndings of this study are included
within the article (and any supplementary les).
Acknowledgments
This research was funded by the Electric Power Research
Institute (EPRI). The relays were fabricated in the C Kenneth
and Dianne Harris Wright Virginia Microelectronics Center at
Virginia Commonwealth University.
ORCID iDs
Md Ataul Mamun https://orcid.org/0000-0003-2122-7709
Kai Ding https://orcid.org/0000-0003-4791-4742
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