The 2001 demonstration by Chan, Aksyuk, Kleiman, Bishop and Capasso that quantum vacuum fluctuations (the Casimir force) can actuate a micromechanical torsional device left several acknowledged limitations: the theory comparison used tabulated optical constants rather than the dielectric response of the specific evaporated and sputtered gold films, the ~30 nm rms surface roughness forced perturbative roughness corrections exceeding 50% of the force at the smallest gaps, and reversible, stiction-free operation was not achieved. The open problem is to establish a fundamental high-precision (sub-percent) test of the Casimir/Lifshitz interaction between metal surfaces in micromachined geometries with directly characterized film dielectric response and controlled roughness, and to make Casimir-based actuation reproducible in MEMS/NEMS by controlling residual electrostatic potentials and pull-in. Later micromechanical-oscillator experiments substantially improved precision and characterization, but the theory comparison is now entangled in the unresolved Drude-versus-plasma ('Casimir puzzle') controversy, so the original question remains open.

Background

The Casimir force is the attractive interaction between uncharged conducting bodies that arises from the zero-point (vacuum) fluctuations of the electromagnetic field; for two perfectly conducting parallel plates at separation z it scales as 1/z41/z^{4}. For real materials at finite temperature the relevant theory is the Lifshitz theory, which expresses the force as an integral over imaginary frequencies involving the complex dielectric function ε(iξ)\varepsilon(i\xi) of the interacting materials; the low-frequency behavior of ε(iξ)\varepsilon(i\xi) for metals (described either by the dissipative Drude model, which includes a finite relaxation parameter, or by the dissipationless plasma model) became a long-standing controversy. In experiments with a sphere facing a plate, the force is commonly computed using the proximity force approximation (PFA), which averages the parallel-plate result over the curved surface; finite-conductivity corrections (computed from tabulated optical data via the Lifshitz integral) and perturbative roughness corrections of the form F2(z)=F1(z)[1+6(Ar/z)2+15(Ar/z)4]F_{2}(z)=F_{1}(z)[1+6(A_{r}/z)^{2}+15(A_{r}/z)^{4}], with ArA_{r} the rms roughness amplitude, are then applied. Microelectromechanical systems (MEMS) are micromachined movable structures (plates, beams, torsional resonators) whose sub-micrometer gaps make such vacuum-fluctuation forces comparable to electrostatic and elastic forces; at even smaller scales one speaks of NEMS. A torsional MEMS device rotates about thin flexural rods, and its rotation angle is read out capacitively; electrostatic calibration (applying known voltages and fitting the residual potential V0V_{0} and a closest-approach offset z0z_{0}) converts rotation into absolute force. In the 2001 Bell Laboratories experiment, a gold-coated polysilicon torsional plate was tilted by the Casimir attraction from a gold-coated sphere (radius 100 μ\mum) at separations below ~300 nm, with agreement between measurement and a Lifshitz-based sphere-plane calculation reported at the smallest separations. The experiment also suffered irreversible snap-down (also called pull-in), the collapse that occurs when the attractive force grows faster than the elastic restoring force as the gap narrows, followed by stiction, the permanent adhesion of contacting microstructures; it was also affected by residual electrostatic potentials arising from work-function differences between the surfaces and spatially varying surface patch charges. The authors' acknowledged limitations — tabulated rather than measured optical constants of the actual films, roughness corrections exceeding 50% of the net force where Ar/z≈0.4A_{r}/z\approx 0.4, and uncontrolled stiction and residual potentials — define the open problem of turning this first MEMS Casimir demonstration into a fundamental, sub-percent-precision test of fluctuation-induced forces and a practical actuation mechanism.

Problem Statement

How precisely does the Casimir (Lifshitz) interaction between real, metallic surfaces behave in micromachined device geometries, and can it be both predicted and used at the level of fidelity required for a fundamental test and for engineering actuation? Specifically, the still-open program descended from the 2001 MEMS actuation experiment asks for: (1) a high-precision test of the Casimir force between metal-coated surfaces in a MEMS-scale geometry in which agreement between measurement and theory is established at the sub-percent level, with the dielectric function of the actual deposited films measured directly rather than taken from tabulated optical data, and with surface roughness either reduced well below the separation or corrected by a validated nonperturbative treatment; (2) a decidable comparison of the currently contradictory theory–experiment results, i.e., a determination, at a stated confidence level, of whether measured Casimir force data in the relevant separation range can discriminate the low-frequency dielectric-response predictions of the Drude and plasma models (the Drude-versus-plasma, or 'Casimir puzzle', question, including thermal corrections), so that the comparison identifies which of the two competing predictions the data favour, without requiring that the underlying controversy itself be settled; and (3) the reproducible, reversible operation of Casimir-based actuation in MEMS/NEMS — control of residual (patch) electrostatic potentials and of the Casimir-electrostatic pull-in/stiction instability at nanometer gaps — so that vacuum-fluctuation forces can be reliably exploited or avoided in device design. The single overarching objective is a quantitative, materials-faithful account of quantum vacuum forces in microdevices at the precision where both a fundamental test of Lifshitz theory and practical actuation become possible. The three components are posed as independent sub-questions of that objective: (1) a reported sub-percent-level theory–experiment comparison that uses the dielectric function measured directly on the actual deposited films and a roughness treatment validated for the surfaces employed, (2) a stated-confidence Drude-versus-plasma discrimination obtained from the data, and (3) a demonstrated reproducible, reversible, stiction-free actuation cycle in a MEMS/NEMS device.

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