Controlling Casimir Forces in Mems and Nems
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CONTROLLING CASIMIR FORCES IN MEMS AND NEMS R. Esquivel-Sirvent, C. Villarreal Instituto de F´ısica, Universidad Nacional Aut´onoma de M´exico, Apartado Postal 20-364, D.F. 01000, M´exico ABSTRACT We present a theoretical study of vacuum effects in systems of length scales of micrometers and nanometers. In particular, we calculate the Casimir force between dielectric plates with different compositions. We show that by an appropriate choice and configurations of materials, the Casimir forces develop noticeable changes than could be used to inhibit or modulate the action of vacuum fluctuations in MEMS and NEMS. Introduction A macroscopic manifestation of quantum vacuum fluctuations in media are the Casimir forces. The best known example consists of two parallel plates made of an ideal conductor that attract each other with a force proportional to d−4 , where d is the separation between the plates. Even though Casimir predicted this effect in 1948 [1], it is only in recent years that experimental studies of Casimir forces have reached the necessary accuracy to test in detail theoretical predictions. The first measurements were done by Derjaguin etal. [2] in 1951 using dielectric materials. In the following decades, a number of experiments to measure Casimir interactions between dielectric or conducting materials were performed, however involving large relative errors in the measured forces [3]. It was until 1997 that Lamoreaux performed measurements with a precision of the order of 5 % [4] by using an electromechanical system based on a torsion balance. Other experiments were made taking advantage of the sensitivity of atomic force microscopes achieving precisions close to 1% [5][6]. Additional measurements have been made by Chan et al. [7] using a micro torsional balance. This experiment is representative of the effects that Casimir forces have in micromechanical systems as was theoretically shown by Serry and Maclay [8]. These experiments have boosted the study of Casmir forces in arbitrary materials [nos0,nos2] , as well as the influence due to rugosity and finite temperature. In this work we present a theoretical study of the magnitude of Casimir forces in systems with length scales of MEMS and NEMS and show how the dielectric properties of the materials and/or the introduction of ”dielectric buffers” can help to inhibit or modulate these forces. Theory and Results The theory of Casimir forces extends for several decades, however, the recent advances in instrumentation and experimental techniques has boosted the detailed theoretical study of Casimir forces in finite slabs made of materials with arbitrary dielectric properties. Consider two parallel slabs characterized by their thickness Li , and their dielectric function (ω)i . The subindex i = 1, 2 refers to either slab since the slabs need not to be made of the
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same material. The Casimir force between these slabs is [9] # " Z ∞ Z ˜ ˜ ~c k˜2 r1s r2s e2ikd r1p r2p e2ikd F (L) = A 2 dQQ dk Re + . ˜ ˜ 2π 0 q 1 − r1s r2s e2ikd 1 − r1p r2p e2ikd q≥
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