Micromanipulation transfer of membrane resonators for circuit optomechanics

A capacitive coupling between mechanical resonator and a microwave cavity enables readout and manipulation of the vibrations. We present a set-up to carry out such experiments with aluminum membranes fabricated as stamps and transferred in place with micromanipulation. The membrane is held in place by van der Waals forces, and is supported by three microscopic points. We measure the lowest mechanical modes, and conclude the membrane vibrates as an essentially free–free resonator. Sliding clamping conditions are identified via a softening Duffing nonlinearity. The method will enable reduction of clamping losses, while maintaining a narrow vacuum gap for strong capacitive coupling. (Some figures may appear in colour only in the online journal) Micromechanical resonators are widely used everywhere in technology. A growing motivation for their basic study is the fact that thus far micromechanical vibrations serve as the only model system for the quantum nature of motion. These works can take advantage of coupling the mechanical degree of freedom to electrical resonances in the microwave frequency regime. The electrical systems, often in the form of on-chip microwave resonators dubbed as cavities, act in a dual role of both detecting and manipulating the motion [1, 2]. For studies near the quantum limit, the vibrating object should be strongly coupled to the electrical mode, which necessitates a narrow vacuum gap between a metallic resonator and a gate to maximize the capacitive coupling. Second, the mechanical quality factor should be as high as possible. Clamped–clamped beam resonators are the most commonly used concept. The strongest capacitive coupling with beams is realized by focused ion beam cutting of a 10 nm vacuum gap [3, 4]. Recently, the best results in studies near the quantum limit have been obtained not with beam geometry 4 These authors contributed equally to this work. 5 Present address: Korea Research Institute of Standards and Science, Daejeon 305-340, Korea. but using a drumhead, which maximizes the participation of the volume to the movable capacitance [5]. In order to realize the vibrating objects, the suspended structures are defined through a selective chemical etching of a sacrificial layer. However, etching is limited to specific materials because of the requirement of chemical compatibility with the rest of the structure. Here, we introduce a scheme to realize a membrane or bridge resonator by assembling a metallic ‘stamp’ into a measurement platform patterned on a Si chip. The method can flexibly adapt various conducting or non-conducting [6] materials, as well as be combined with numerous other processes because etching compatibility is irrelevant. Our approach is a promising way towards achieving strong capacitive coupling, and reduction of mechanical losses by minimizing acoustic radiation into the supports [7, 8], as clamps are essentially eliminated in our design. The fabrication process is related to our previous work on micromanipulation transfer of graphene mechanical resonators [9]. The whole set of the process, see figure 1, is divided into three steps; aluminum (Al) sheet fabrication, building up the metallic gate and support structure for coupling to the microwave resonator, and piecing these parts together. 0960-1317/13/125024+05$33.00 1 © 2013 IOP Publishing Ltd Printed in the UK & the USA M. Berdova, S. U. Cho, J.-M. Pirkkalainen, J. Sulkko, X. Song, P. J. Hakonen, and M. A. Sillanpää. Micromanipulation transfer of membrane resonators for circuit optomechanics. Journal of Micromechanics and Microengineering 23, 125024 (2013). DOI: 10.1088/0960-1317/23/12/125024. © 2013 Institute of Physics Publishing. Reprinted by permission of Institute of Physics Publishing.