Controlling adhesion between multi-asperity contacting surfaces in MEMS devices by local heating

In this work, we have incorporated heaters in a MEMS device, which allow the in situ local heating of its contacting surfaces. This design offers a promising solution for MEMS devices with contacting components by preventing capillary-induced adhesion. The force of adhesion was assessed by optically measuring in-plane snap-off displacements. We were able to decrease adhesion from 500 nN to 200 nN with just one heated surface of which the temperature was set above 300 °C. The temperature should not be set too high: we observed increased adhesion due to a direct bonding process once the temperature was increased above 750 °C. Remarkably, adhesion increased by heating from room temperature to 75 °C, which is attributed to more water being transferred to the contact area due to faster kinetics. We observed the same effect in the cases where both surfaces were heated, although at slightly different temperatures. We demonstrated that heating only one surface to between 300 °C and 750 °C is sufficient to significantly lower adhesion, due to the removal of capillary menisci. The required heater is typically most easily implemented in a stationary part of the device.

For the past 30 years, the MEMS industry has managed to build many reliable devices by avoiding contacting surfaces. However, in some cases, a MEMS device may consist of microstructures that are intentionally forced to contact the substrate or other microstructures. Such components involve scanning MEMS mirrors [8], deformable grating light modulators [9], and impact microactuators [10], as well as micro gears and turbines. After repetitive contact, the surfaces in these structures are often observed to adhere permanently to each other. In some other cases, stiction occurs accidentally, especially when suspended elements are involved. In addition, the surface properties can be particularly unpredictable when the environmental conditions are not tightly controlled. Thus, devices that include cantilevers, suspended proof masses, gyroscopes, RF resonators and oscillators are likely to exhibit stiction phenomena. It is therefore of paramount importance to address and overcome the adhesion-related issues.
Traditionally, the research and development conducted to minimize adhesion between contacting surfaces in MEMS devices can be classified in two categories. One category involves the mechanical modification of surfaces in order to minimize the real contact area, for example, through the increase of surface roughness [11] or by applying microdimples [12]. The other focuses on the chemical modification of the contacting surfaces. This is realized by hydrogen termination [13], chemical vapour deposition of anti-stiction coatings such as self-assembled monolayers (SAMs) [14], deposition of hard coatings like diamond-like carbon (DLC) [15], or even by using a completely different structural material, like ultrananocrystalline diamond [16]. The approaches involving the mechanical modification of surface topography solve the problem of adhesion only partially, and they are mainly used to tackle release stiction that may occur during the drying process in microfabrication [17]. Hydrogen termination provides an unstable interface [18]. SAMs, as the term indicates, are limited to a single monolayer. This monolayer can be non-uniform, prone to wear and unable to tolerate high temperatures [19]. Finally, DLC coatings often suffer from delamination from the structural elements of the MEMS device and typically introduce high stress gradients in the structural elements [20]. Thus, much work remains to be done to find (in)organic, tough coatings that can be used as lubricating layers and also as adhesion prevention in MEMS contacting surfaces.
In this work, we propose the use of a new third approach, where high temperatures are generated locally at the contacting surfaces of a MEMS device. The subsequent evaporation of water will decrease capillary condensation and hence decrease adhesion. This approach mimics experiments by Greiner et al, in which they explore the dependence of nanoscale friction on contact temperature [21]. In their work, a heated atomic force microscope (AFM) tip was slid against a silicon oxide substrate in a humid environment. It was shown that for tip temperatures of 75 °C friction increases to a maximum, an effect ascribed to more fully developed capillary menisci between the tip and the substrate at this temperature. Furthermore, friction decreases significantly and remains low above 100 °C, due to the evaporation of water from the contact. Pull-off experiments performed with the same tip to study adhesion demonstrated similar behaviour.
For our study, we have developed a new concept of a MEMS device with integrated micro-heaters that allow the in situ selective increase of temperature only where contact occurs and locally remove condensed water. Contrary to the case of Greiner et al, in our study we are dealing with a multiasperity contact, which is more relevant to the MEMS scale than the investigation of a single-or few-asperity contact of an AFM. Adhesion in MEMS devices is best studied with a MEMS test device. It is our goal to obtain an understanding of adhesion on the microscale and, based on this knowledge, to reduce and eventually solve the stiction problems that currently hamper the MEMS industry.

Device design and actuation
To carry out our study, we have designed an adhesion sensor that is based on the 'nano-battering ram' by van Spengen  et al [22]. It is manufactured in a three-layer polycrystalline silicon multi-user MEMS process by MEMSCAP Inc., commercially known as PolyMUMPs ™ . Figure 1 shows a scanning electron microscope (SEM) micrograph of the adhesion sensor and figure 2 illustrates a close-up of the contacting parts. The device consists of a comb-drive actuator and a 'ram' that can move over a distance of 2 μm before it touches a counter-surface. When the actuator voltage is increased, the ram moves forward until its head makes contact with the counter-surface (snap-in) and temporarily adheres to it. When the voltage is reduced again, the head of the ram remains stuck until the restoring spring forces are large enough to pull it from the counter-surface (snap-off). The displacement of the ram after snap-off is a measure for the adhesion force. By passing an electrical current through the thin parts of the ram and the countersurface, the device is heated in situ at the area where contact occurs.
To measure the force of adhesion, we use an optical method for detecting in-plane displacements with sub-nm resolution developed by Kokorian et al [23]. For each voltage applied on the comb-drive actuators, an image of  two beams, one stationary and one attached to the moving ram, is captured by a standard optical microscope, and the displacement is determined through an algorithm based on curve-fitting. Figure 3 demonstrates a measurement of the displacement of the ram as a function of the voltage applied to the comb-drive actuators connected to it. The adhesion force is equal to the difference between the restoring spring force just before the ram's snap-off from the counter-surface and the restoring spring force after snap-off. Adhesion can be calculated from the voltage-displacement curve by multiplying the snap-off jump length with the spring constant of the support springs.
The spring constant of the ram was computed numerically via finite element analysis (FEA) using COMSOL Multiphysics 4.3b (figure 4). A 2D solid mechanics model was developed to calculate the maximum displacement of the moving component, from which it was possible to extract the stiffness of the support springs connected to it. A 10 μN load was applied onto the ram in the x-axis direction. The material properties of polycrystalline silicon used in the computation were a Young's Modulus of 169 GPa and Poisson's ratio of 0.22 [24]. The resulting displacement was 2.76 μm, which corresponds to a spring constant of 3.6 N m −1 .

Calibration between heater voltage and heater temperature
The contact area between the ram and the counter-surface is heated in situ by applying a voltage to their heating elements. The heaters subsequently convert the corresponding electrical power to heat, which relates to a certain temperature. It is possible to determine this temperature very locally using micro-Raman spectroscopy.
Micro-Raman spectroscopy offers the possibility of assessing the local temperature with μm resolution, limited by the spot size of the focused laser light that is used to excite the material. Higher temperatures increase the lattice spacing due to thermal expansion, and they increase the vibrational mode frequencies of the silicon lattice [25]. By observing the Raman peak position while changing the temperature of the polycrystalline silicon, we are able to obtain the relation between heater voltage and the temperature of the heated parts and locally map the temperature of the contact area.
The Raman spectra were obtained on a HORIBA Scientific LabRam HR spectrometer with excitation from an Argon-ion laser with a 514 nm wavelength, and a 50× objective lens with a numerical aperture of 0.5. We first placed the device on a heating stage to set the sample temper ature and obtain the Raman peak position of polycrystalline silicon for a range of temperatures. In figure 5, the spectra that correspond to room temperature, 300 °C and 550 °C are plotted. The Raman peak positions of each sample temper ature, interpolated by a linear curve fit, are shown in figure 6. Afterwards, we applied a range of voltages to the heating element of the counter-surface. Because of the small lateral dimension of the counter-surface, we observed two peaks in the Raman spectra, one of which corresponds to the Raman signal of the substrate (figure 7). The Raman peak position of the substrate does not shift with the increase of the heater voltage, therefore we are able to distinguish the Raman signal of the substrate from the one of the device layer. The Raman peak position of the device layer is the one we use in our calibration. Having determined all Raman peak positions for the range of heater voltages, we were able, through figure 6, to relate the heater voltage to the local heater temperature of the counter-surface (figure 8). A quartic (fourth-degree) polynomial curve fit was used to interpolate the data points. The calibration between heater voltage and temperature for the heating element of the ram was performed in the same way as for the counter-surface ( figure 9).
Furthermore, we have investigated whether the heating of either the ram or the counter-surface would cause heating of the other component through thermal conduction. We measured the temperature of the counter-surface while in contact with the ram, when the latter was set to a T ram,set of room temperature, 30 °C and 50 °C. These temperatures correspond to the temperatures the ram would have had if it had been out of contact from the counter-surface, set to room temper ature. The heater temperature of the counter-surface was swept from room temperature to 955 °C. We observed that the heater temperature of ram, T ram,set , has very little influence on the temperature of the counter-surface. On the contrary, the heater temperature of the counter-surface, which we will simply refer to as temperature of the counter-surface, greatly influences the temperature of the ram, regardless of the ram heater temperature, T ram,set . This is due to the fact that the thermal resistance to the substrate is much smaller for the counter-surface than for the ram, as the latter has long springs connected to it. The temperature of the ram for a given temperature of the countersurface, for example 400 °C, is 330 °C, 365 °C and 380 °C, for each of the three different T ram,set . In figure 10, we show the temperature of the ram as a function of the temperature of the counter-surface.

Experiments
We have studied the influence of local temperature on adhesion by performing ten consecutive cycles per temperature of one heating element, and the opposite element is either at room temperature or set to a certain temperature. In table 1, we classify the different types of experiments that are conducted in this paper. We first started with the temperature of the counter-surface swept from room temperature to 855 °C, with the temperature of the ram sweeping from room temperature to 715 °C. This experiment has a 'twin', in which the temperature of the counter-surface started at 855 °C and was swept back  Raman spectrum of the counter-surface at a heater voltage of 5 V. Observe the two Raman signals that originate from both the substrate and the device layer. In our calibration, we use the Raman peak position that corresponds to the device layer.
to room temperature. We carried out such an experiment because we are also interested in investigating whether elevated temperatures from the beginning of the experiment trigger different effects between the contact area and hence result in different adhesion values.
We observed that, when the temperature of the countersurface was set above 400 °C, the adhesion values were very low. Therefore, we performed another experiment in which we swept the heater temperature of the ram from room temperature to 60 °C, while the temperature of the counter-surface was set to 400 °C. In fact, the temperature of the ram ranged from 25 °C to 70 °C when not in contact with the countersurface, and, once in contact, the temperature ranged from 330 °C to 385 °C. Above 385 °C, the ram was seen to behave erratically: the support springs buckle due to the unintended thermal expansion and push it into the substrate. This leads to a stick-slip motion that prevents us from measuring adhesion. Therefore, the temperature of the ram had to be kept below 385 °C. This experiment was sufficient to reveal two contact temperatures of the ram, 365 °C and 380 °C, at which adhesion increased and decreased respectively. These two temperatures correspond to ram heater temperatures of 30 °C and 50 °C, with the counter-surface kept at room temper ature, and subsequently reached temperatures of 725 °C and 740 °C when the temperature of the countersurface was set to 855 °C. These temperatures were used for two twin experiments, with the temperature of the countersurface starting from room temperature to 855 °C, and from 855 °C to room temperature.
In the following figures, we plot the force of adhesion as a function of temperature of the heating element of which the temperature was swept. The resulting adhesion force was calculated from the spring constant of the ram multiplied by the displacement measured from ten consecutive cycles. The error bars that appear in the following figures do not indicate measurement errors, but the standard deviation of the ten measured adhesion forces. This is a measure for the cycle-to-cycle variability of the adhesion force.    The temperatures of the ram given in this table are the temperatures the ram would have had if it had been in contact with the counter-surface, which is set to certain heater temperatures. Figure 11. Adhesion evolution in experiment A1 for temperatures of the counter-surface that increased from room temperature to 855 °C. The ram was set to room temperature, but it reached a temperature of 715 °C upon contact due to the temperature of the counter-surface. The ambient temperature was between 20 °C and 21 °C, while the relative humidity was between 37.5% and 39%.

Results
For experiment A1, we swept the temperature of the countersurface from room temperature to 855 °C. The temperature of the ram was then ranged from room temperature to 715 °C. Figure 11 shows the evolution of adhesion as a function of the temperature of the counter-surface. Adhesion reached a maximum between room temperature and 130 °C, with the highest value appearing at 75 °C. Afterwards, adhesion is seen to decrease and stabilize. It is observed that, between 300 °C and 750 °C, the adhesion force is one third of its initial value at room temperature. However, at elevated temperatures between 750 °C and 855 °C, adhesion starts to increase again. In experiment A2, we swept the temperature of the counter-surface from 855 °C back to room temperature ( figure 12). In the beginning, adhesion is very high, and gradually decreases with the decrease of the temperature of the counter-surface. This behaviour is followed by consecutive regimes, in each of which adhesion goes through a local maximum, first between 230 °C and 115 °C and The temperature of the ram upon contact reached 715 °C at the start of the experiment due to the temperature of the counter-surface, and it decreased back to room temperature together with the counter-surface. The ambient temperature was between 21 °C and 22 °C, while the relative humidity was between 38% and 40%. Figure 13. Adhesion evolution in experiment B for temperatures of the ram that increased from 330 °C to 385 °C, while the temperature of the counter-surface was kept at 400 °C. At the start of every ten adhesion cycles, the ram is 2 μm away from the hot counter-surface. The temperatures of the ram on the top x-axis will increase once it starts approaching the counter-surface. The temperatures on the bottom x-axis represent those the ram will reach once in contact with the counter-surface. The temperature of the ram when not in contact with the counter-surface does not have a linear relation with that of the ram when in contact with the counter-surface. The ambient temperature and the relative humidity are not known. then between 105 °C and 70 °C. From 55 °C down to room temper ature, adhesion remains relatively stable.
For experiment B, we set the temperature of the countersurface to 400 °C and swept that of the ram from 330 °C to 385 °C ( figure 13). The adhesion values began relatively low, however they increased until a certain plateau for temper atures of the ram between 360 °C and 370 °C. This plateau is at a lower adhesion value than when only one surface was heated as in experiment A1, but it is still very significant. Moreover, once the temper ature of the ram reached higher temperatures, adhesion decreased and became lower than when the ram was at room temperature. For temperatures of the ram between 380 °C and 385 °C, adhesion increased slightly. The temperatures of the ram on the top x-axis represent those the ram has at the beginning of each ten adhesion cycles, when it is 2 μm away from the hot counter-surface.
Because in experiment B we observed a maximum of adhesion when the temperature of the ram was at 365 °C, we carried out experiment C1 with the heater temperature of the ram set to 30 °C and the temperature of the counter-surface swept from room temperature to 855 °C ( figure 14). The actual temper ature of the ram was therefore ranged from 30 °C to 725 °C accordingly. Adhesion appears to increase between 50 °C and 200 °C, while, with the increase of the temperature of the counter-surface, it decreases until 520 °C, followed by a rather sudden increase of its values. Adhesion evolution in experiment C1 for temperatures of the counter-surface that increased from room temperature to 855 °C. The ram was set to 30 °C, but it reached a maximum temperature of 725 °C due to the temperature of the counter-surface. The ambient temperature was between 20 °C and 20.5 °C, while the relative humidity was between 35% and 36.5%. Figure 15. Adhesion evolution in experiment C2 for temperatures of the counter-surface that decreased from 855 °C to room temperature. The temperature of the ram reached 725 °C due to the temperature of the counter-surface and decreased with it to 30 °C. The ambient temperature was at 20.5 °C, while the relative humidity was between 36.5% and 42.5%.
For experiment C2, we kept the heater temperature of the ram at 30 °C, while the temperature of the counter-surface started at 855 °C, and then it was gradually set back to room temper ature ( figure 15). The adhesion values were particularly high in the beginning and, with the decreasing temper ature of the counter-surface, they appear to stabilize between 595 °C and 400 °C. Afterwards, there is a further decrease from 350 °C to 80 °C and, from this point to room temperature, adhesion appears to obtain its lowest values.
In experiment B, the lowest value of the adhesion force was observed when the temperature of the ram was at 380 °C. Therefore, for experiment D1, we set the heater temper ature of the ram to 50 °C and repeated the ten-cycle adhesion measurements by sweeping the temperature of the counter-surface from room temperature to 855 °C ( figure 16).
The actual temperature of the ram therefore ranged from 50 °C to 740 °C. Adhesion demonstrates a maximum between 50 °C and 155 °C. Between 155 °C and 350 °C, adhesion decreases again. From 350 °C to 855 °C, adhesion increases considerably, to about four times its value at the start of the experiment.
In experiment D2, we swept the temperature of the counter-surface from 855 °C back to room temperature, while the heater temperature of the ram was kept at 50 °C ( figure 17). Adhesion was relatively high in the beginning and, with decreasing temperature of the counter-surface, it stabilized between 455 °C and 230 °C. Afterwards, there is a further decrease between 200 °C and 85 °C. From this point onwards, the mean value of adhesion seems to decrease, although it becomes highly variable from cycle to cycle. Figure 16. Adhesion evolution in experiment D1 for temperatures of the counter-surface that increased from room temperature to 855 °C. The ram was set to 50 °C, however it reached a maximum temperature of 740 °C due to the temperature of the counter-surface. The ambient temperature was between 20.5 °C and 21 °C, while the relative humidity was between 47.5% and 51.5%. Figure 17. Adhesion evolution in experiment D2 for temperatures of the counter-surface that decreased from 855 °C to room temperature. The temperature of the ram reached 740 °C due to the temperature of the counter-surface and decreased with it to 50 °C. The ambient temperature was between 20.5 °C and 21 °C, while the relative humidity was between 39% and 41.5%.

Discussion
From experiments A1, C1 and D1 we are able to conclude that adhesion is low for temperatures of the counter-surface above 300 °C. This is logical due to the absence of capillary menisci, which obeys the thermodynamics of evaporation. However, it is not a priori clear why a local maximum in the adhesion occurs at 75 °C, 110 °C and 120 °C in each experiment respectively. This maximum can be dangerous for actual MEMS devices used at slightly elevated temperatures. For simplicity, we introduce a variable called T peak to indicate all three temper atures where the local maximum is present. In addition, for temperatures of the counter-surface above 750 °C, 520 °C and 350 °C, an even higher maximum was observed. We will use the name T high to represent the temperatures where very high adhesion occurs in all three experiments.
At high temperatures, thermodynamics predicts the dominance of the gas phase over the liquid phase due to the higher entropy of a gas. This explains the decrease of adhesion from T peak to 300 °C. However, it does not explain the increase from room temperature to T peak . We argue that this increase is due to a kinetic effect: the limited transport of water either in the adsorbed layer on the substrate or in the gas phase. With the increase in temperature, the water molecules are moving fast enough and increase their density at the contact area, which leads to larger menisci. T peak is the crossover from the kineticsdominated regime to the thermodynamics-dominated regime and will depend on the exact temperatures in the experiment, hence the different temperatures at which the peak occurs in experiments A1, C1 and D1.
The kinetics of the condensate is complicated due to the fact that the meniscus nucleation time does not only depend on the temperature but also on the transport time of the water molecules to the location where the capillary meniscus is being formed. A single voltage-displacement curve takes about 90 s to record, while the ram and counter-surface are in contact for slightly less than half of the duration of a single measurement. The contact time is then about 40 s. This time is much longer than a typical meniscus nucleation time, which is of the order of microseconds [26]. When two low-roughness multiasperity surfaces are in contact, with the standard deviation of the height distribution of the asperities being tens of nanometers [27], they form a confined system. The path for the water to reach the contact area is smaller than the mean free path of the water vapour molecules, and the kinetics enters into a molecular flow regime. Thus, because the water molecules need time to travel to the location of the nucleating meniscus, more time is needed for an equilibrium state to be reached. This time is available only if the surfaces are in contact much longer than the normal meniscus nucleation time.
The capillary force is affected by the contact area of the condensate. The contact area can be estimated with a simple plastic flow contact mechanics model based on the bearing area concept [28]. The contact area A contact is expressed as the ratio of the contact force F contact and the effective hardness H eff of the polycrystalline silicon surface. To obtain the effective hardness, all the properties of the two contacting surfaces are transferred to a single surface, while the other surface is defined to be perfectly flat and infinitely hard. The effective hardness of polycrystalline silicon is calculated as [29] The hardness H surface was taken to be 11.0 GPa, the mean value of 10.5 GPa and 11.5 GPa, which are the hardnesses measured by nanoindentation at two different loads and two different indentation depths [30]. The contact force F contact can be extracted from the voltage-displacement curve. This is done by calculating how much further the ram would have moved in the absence of the counter-surface at the maximum actuator voltage. This distance multiplied by the spring constant yields a contact force of 360 nN. The contact area A contact is then: Our preliminary explanation of the high-temperature behaviour of the adhesion evolution is as follows: for temperatures of the counter-surface above T high , both surfaces have been rendered sufficiently flat after repetitive contact [31]. Blunted asperities in combination with high local temperature and pressure while in intimate contact may lead to a situation known as direct bonding. The surfaces become more adhesive and the native oxide that covers them becomes more fluid-like and exhibits glassy flow. This effect is thermally activated; it is illustrative that elevated temperatures are used as a treatment step in wafer bonding processes. The temperature of both surfaces determines the starting point of this process, therefore T high shifts accordingly to a lowest temperature in experiment D1, where the heater temperature of the ram is set to 50 °C.
For experiments A2, C2 and D2, in which the temperature of the counter-surface was swept from 855 °C down to room temperature, we observe higher adhesion which is indicative of the silicon-oxide bonding process as described above. The bonding process takes effect from 855 °C to T high , which is equal to 265 °C, 350 °C and 455 °C for experiments A2, C2 and D2, respectively. At this moment, the two opposite surfaces form bonds with each other, and may become flatter due to the increased contact pressure. However, with the decrease of the temperature to T water that corresponds to 105 °C, 90 °C and 80 °C for the three experiments, the chances of forming chemical bonds decrease significantly and so does the real contact area. The existing bonds are breaking, the surface roughness becomes higher and, in the absence of water, adhesion is mainly caused by van der Waals forces. With further decrease of the temperature from T water to room temperature, water returns to the contact and forms capillary menisci which contribute to the total adhesion.
In experiments A1, C1 and D1, the absolute adhesion values vary per experiment, due to different devices being used in each experiment that all have slightly different surface roughnesses. Such differences between nominally identical devices have recently been extensively addressed theoretically [32]. Furthermore, we observe that the peak attributed to capillary condensation is shifting towards higher temperatures of the counter-surface with higher temperatures of the ram. The reason behind this is that the temperature of the ram influences the temperature of the interface between the counter-surface and itself. We expect the temperature of the interface to be somewhere between that of the countersurface and the ram. The way in which heat is conducted away from the heating elements once they are in contact may also influence the interface temperature. For the same temper ature of the counter-surface, we observe that the temperature of the interface is lower when the ram was at room temperature, then it increases with the heater temperature of the ram at 30 °C and it goes even higher when the ram was set to 50 °C. For the regime when the direct bonding takes place, which is when higher adhesion is observed in all three experiments, the temper ature is also seen to shift accordingly, and the same occurs for the twin experiments A2, C2 and D2.
For experiment B, where the temperature of the countersurface was set to 400 °C and that of the ram was swept from 330 °C to 385 °C, a local maximum appears between 360 °C and 370 °C, probably caused by capillary condensation. However, the temperatures of the ram before it makes contact with the counter-surface are between 30 °C and 45 °C. We suggest that, while the ram is approaching the hot counter-surface, water is being evaporated from its surface just before contact occurs. The temperature shifts from 30 °C to 360 °C and from 45 °C to 370 °C, so the contact experiences the 'dangerous' temperature range where kinetic effects are more pervasive. Because two multi-asperity contacting surfaces compose a confined system, the water, which starts to evaporate once the surfaces are approaching one another, remains trapped and forms menisci at the contact area. The probability for the water to exist in the liquid state is temperature-dependent and therefore it seems that a capillary meniscus is still energetically favourable. In addition, the maximum between 360 °C and 370 °C is shifted above the boiling point of water, which was also observed in experiments C1 and D1. Therefore, the shift in temperature is consistent in all experiments where two hot contacting surfaces are involved.

Conclusions
In this work we have demonstrated the reduction of adhesion in MEMS devices by locally heating the contacting surfaces. The incorporated heaters allow in situ Joule heating of the contacting MEMS sidewalls which leads to the evaporation of adsorbed water. As revealed in our study, the optimum temperature is slightly above 100 °C. Between room temperature and 100 °C, the kinetics of water prominently increase adhesion. Care should be taken that the temperature is not set too high (above 750 °C), as there is a risk of thermally activated direct bonding of the native oxides that cover most silicon-based MEMS devices. Local heating is recommended to mitigate stiction problems in hydrophilic MEMS surfaces to keep the adhesion low and stable. However, the temperature increase should be between well-defined limits; heating only one surface to between 300 °C and 750 °C appears to be ideal. In actual MEMS designs, incorporating a heater to the stationary surface only appears to be sufficient, and is much easier to implement than designing a heater within a moving structure.