We explore here the decisive role of film thickness on Casimir and electrostatic forces from topological insulating Bi 2 Se 3 films. The forces were measured for the Au-Bi 2 Se 3 system under ambient conditions to simulate realistic applications. It is shown that the electrostatic forces associated with a nonzero contact potential of V o ∼ 200 mV played a dominant role, and could not be compensated for thinner films ( 20 nm thick). However, for thicker films the measured force, after voltage compensation, started to approach the genuine Casimir force in very good agreement with Lifshitz theory. Our results point out that any gradual deviation from theory for thinner films underlies the presence of strong electrostatic effects.
The sensitivity of nonequilibrium Casimir forces on material optical properties can have strong impact on the actuation of devices. For this purpose, we considered nonequilibrium Casimir interactions between good and poor conductors, for example, gold (Au) and highly doped silicon carbide (SiC), respectively. Indeed, for autonomous conservative systems, the bifurcation and phase portrait analysis have shown that the nonequilibrium Casimir forces can have signi cant impact on the stable and unstable operating regimes depending on the material optical properties. At a few micrometer separations, for systems with high conductivity materials, an increasing temperature di erence between the actuating components can enhance the stable operation range due to the reduction of the Casimir force, while for the poor conductive materials, the opposite takes place. For periodically driven dissipative systems, the Melnikov function and Poincare portrait analysis have shown that for poor conductive systems, the nonequilibrium Casimir forces lead to an increased possibility for chaotic behavior and stiction with an increasing temperature di erence between the actuating components. However, for good conducting systems, the thermal contribution to Casimir forces reduces the possibility for chaotic behavior with increasing temperature, as comparison with systems without thermal uctuations shows. Nevertheless, the positive bene t of good conductors toward increased actuation stability and reduced the chaotic behavior under nonequilibrium conditions can be easily compromised by any voltage application. Therefore, thermal, nonequilibrium Casimir forces can in uence the actuation of devices toward unstable and chaotic behavior in strong correlation with their optical properties, and associated conduction state, as well as applied electrostatic potentials.
Here, we investigate the sensitivity of nonequilibrium Casimir forces to optical properties at low frequencies via the Drude and plasma models and the associated effects on the actuation of microelectromechanical systems. The stability and chaotic motion for both autonomous conservative and nonconservative driven systems were explored assuming good, e.g., Au, and poor, e.g., doped SiC, interacting conductors having large static conductivity differences. For both material systems, we used the Drude and plasma methods to model the optical properties at low frequencies, where measurements are not feasible. In fact, for the conservative actuating system, bifurcation and phase space analysis show that the system motion is strongly influenced by the thermal nonequilibrium effects depending on the modeling of the optical properties at low frequencies, where also the presence of residual electrostatic forces can also drastically alter the actuating state of the system, depending strongly on the material conductivity. For nonconservative systems, the Melnikov function approach is used to explore the presence of chaotic motion rendering predictions of stable actuation or malfunction due to stiction on a long-term time scale rather impossible. In fact, the thermal effects produce the opposite effect for the emerging chaotic behavior for the Au-Au and SiC-SiC systems if the Drude model is used to model the low optical frequencies. However, using the plasma model, only for the poor conducting SiC-SiC system, the chance of chaotic motion is enhanced, while for the good conducting Au-Au system, the chaotic behavior will remain unaffected at relatively short separations (<2 µm).
In the current study, we explore the sensitivity of the actuation dynamics of electromechanical systems on novel materials, e.g., Bi2Se3, which is a well-known 3D Topological Insulator (TI), and compare their response to metallic conductors, e.g., Au, that are currently used in devices. Bifurcation and phase portraits analysis in conservative systems suggest that the strong difference between the conduction states of Bi2Se3 and Au yields sufficiently weaker Casimir force to enhance stable operation. Furthermore, for nonconservative driven systems, the Melnikov function and Poincare portrait analysis probed the occurrence of chaotic behavior leading to increased risk for stiction. It was found that the presence of the TI enhanced stable operation against chaotic behavior over a significantly wider range of operation conditions in comparison to typical metallic conductors. Therefore, the use of TIs can allow sufficient surface conductance to apply electrostatic compensation of residual contact potentials and, at the same time, to yield sufficiently weak Casimir forces favoring long-term stable actuation dynamics against chaotic behavior.
Comprehensive knowledge of Casimir forces and associated electrostatics from conductive SiC and Ru surfaces can be essential in diverse areas ranging from micro/nanodevice operation in harsh environments to multilayer coatings in advanced lithography technologies. Hence, the Casimir force was measured between an Au-coated microsphere and N-doped SiC samples with Si-and Cterminated faces, and the results were compared with the measurements using the same microsphere and a metallic Ruthenium surface. Electrostatic calibration showed that the Si-and Cfaces behave differently with a nearly ~0.6-0.7 V difference in the contact potentials V0 Si/C . We attribute this to a higher incorporation of N on the C-terminated face in the near surface region resulting in the formation of NOx and an increased work function compared to the Si-terminated surface which is in agreement with x-ray photoelectron spectroscopy data. Notably, the contact potential of the SiC-C face (V 0 C~ 0.1 V) was closer to the metallic Ru-Au system (V 0 Ru~0 .05 V).2 However, the measured optical properties of the SiC-Si/C terminated surfaces with ellipsometry did not show any substantial differences indicating that the effective depth of the Si/C terminating surface layers are significantly smaller than the photon penetration depth not leading to any differences in the calculated forces via Lifshitz theory. Nonetheless, the measured Casimir forces, after compensation of the electrostatics contributions, showed differences between the Si/C faces, whereas the comparison with the Lifshitz theory prediction shows better agreement for the SiC-Si face. Finally, comparison of the Casimir forces below 40 nm separations between the SiC-Si/C and Ru surfaces indicated that the short-range roughness effects on the Casimir force increase in magnitude with increasing metallic behavior of the plate surface. Therefore, not only the material optical properties but also the conductive state and roughness of the surface layers must be carefully taken into account in short range Casimir interactions between more complex dielectric materials. 3 I. Introduction Nowadays, the Casimir force that originates from the perturbation of electromagnetic vacuum fluctuations is still a topic of relentless research [1-21], though its proposition in 1948 by the Dutch physicist Hendrik Casimir almost dates back 70 years [1]. The interest stems from a multitude of research fields ranging from fundamental physics in search of new forces beyond the standard model to micro/nanodevices for technology applications [2-6]. Lifshitz and co-workers in the 1950s [7,8] considered the general case of flat dielectric plates by exploiting the fluctuationdissipation theorem, which relates the dissipative properties of the plates (due to optical absorption by many microscopic dipoles) and the resulting electromagnetic (EM) fluctuations. The theory describes the attractive interaction due to quantum fluctuations for all separations covering both the Casimir (long-range) and van der Waals (short-range) re...
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