Chaotic behavior in Casimir oscillators: A case study for phase-change materials

Abstract

Casimir forces between material surfaces at close proximity of less than 200 nm can lead to increased chaotic behavior of actuating devices depending on the strength of the Casimir interaction. We investigate these phenomena for phase change materials in torsional oscillators, where the amorphous to crystalline phase transitions lead to transitions between high and low Casimir force and torque states respectively, without material compositions. For a conservative system bifurcation curve and Poincare maps analysis show the absence of chaotic behavior but with the crystalline phase (high force/torque state) favoring more unstable behavior and stiction.However, for a non-conservative system chaotic behavior can occur introducing significant risk for stiction, which is again more pronounced for the crystalline phase. The latter illustrates the more general scenario that stronger Casimir forces and torques increase the possibility for chaotic behavior. The latter is making impossible to predict whether stiction or stable actuation 2 will occur on a long term basis, and it is setting limitations in the design of micro/nano devices operating at short range nanoscale separations.

Dependence of chaotic behavior on optical properties and electrostatic effects in double-beam torsional Casimir actuation

“…The occurrence of transversal intersections can be inferred from the presence of zeroes of the so-called Melnikov [30,35]. If we φ het C (T) and φ hom C (T) denote the heteroclinic and homoclinic solutions, respectively, of the conservative system then the Melnikov functions for the torsional system are given by [11,33,34,44] M het (T 0 ) = 1 Q ∫ ( However, for parameter values below the curve, the transversal intersections of stable and unstable manifolds causes chaotic motion. Clearly for systems with higher conductivity, which lead to stronger Casimir torques, chaotic motion is more likely to occur as is manifested by the larger area below the threshold curves.…”

“…By shrinking the size of these devices an unavoidable problem could be the occurrence of chaotic motion leading to device malfunction. This phenomenon causes abrupt change in the dynamical behavior and eventually leads to stiction hampering long term device predictability [11,33,34]. Therefore, in this paper we will investigate the actuation dynamic of a torsional double beam actuating under the influence of electrostatic and Casimir torques, with electrodes made from materials with a wide and diverse range of optical properties including gold (Au), phase change materials (PCMs), and conductive silicon carbide (SiC).…”

Sensitivity of chaotic behavior to low optical frequencies of a double-beam torsional actuator

“…Nowadays advances in microfabrication techniques have pushed microelectromechanical systems (MEMS) to enter the submicron length scales, and simultaneously unravel the significant role of Casimir forces in nanoengineering [1][2][3][4][5][6]. Unlike electrostatic forces, which can be switched on and off by applying a potential, the Casimir force is always omnipresent and can set fundamental limitations on the design of micronanodevices [2,3,7,8]. This is because at separations less than 200 nm [9] the ratio of surface area to distance in MEMS components is large enough for the Casimir force to play a significant role, and pull components together leading to their permanent adhesion, which is a phenomenon known as stiction [1,2,10,11].…”

“…So far several investigations have been conducted to study the actuation dynamics of torsional actuators under the influence of Casimir and electrostatic forces for a wide range of material optical properties [8,20,21]. From these studies it has emerged that chaotic behavior is unavoidable during actuation dynamics, which leads to increased possibility for stiction and consequently limiting the long term prediction of devices to perform stable operation.…”

Dependence of chaotic actuation dynamics of Casimir oscillators on optical properties and electrostatic effects

“…One of the most prominent methods of device actuation is electrostatic, where inevitably Casimir forces and torques could play a role [3,[10][11][12][13][14]. Although the electrostatic forces can be switched off when no potential is applied, the Casimir forces are omnipresent and a e-mail: g.palasantzas@rug.nl can influence the actuation dynamics of devices.…”