We explore an electrostatic mechanism for tuning the nonlinearity of nanomechanical resonators and increasing their dynamic range for sensor applications. We also demonstrate tuning the resonant frequency of resonators both upward and downward. A theoretical model is developed that qualitatively explains the experimental results and serves as a simple guide for design of tunable nanomechanical devices.
Nanomechanical resonators with high aspect ratio, such as nanotubes and nanowires are of interest due to their expected high sensitivity. However, a strongly nonlinear response combined with a high thermomechanical noise level limits the useful linear dynamic range of this type of device. We derive the equations governing this behavior and find a strong dependence ͓ϰd ͱ ͑d / L͒ 5 ͔ of the dynamic range on aspect ratio. © 2005 American Institute of Physics. ͓DOI: 10.1063/1.1929098͔The limits of mechanical detection with nanoelectromechanical systems ͑NEMS͒ are being actively pursued for sensing applications, such as the attainment of sub-attonewton force sensing for magnetic resonance force microscopy, 1 sub-attogram mass sensing, 2,3 mechanical single spin detection, 4 or the study of mechanical motion approaching the quantum regime. [5][6][7][8] Applications like these require both high responsivity and ultra-high-frequency operation. 9 Both can be attained simultaneously with small diameter, large aspect ratio doubly clamped resonators. Nanoscale materials such as carbon nanotubes or nanowires are a natural choice for these resonators due to their intrinsic small size. We recently reported a bottom-up nanomechanical resonator, a Pt nanowire, and found that it takes a very low driving power to bring this device into the nonlinear regime. 10 Here, we show how the onset of this nonlinear regime decreases with decreasing diameter, while the thermomechanical noise increases with aspect ratio. We conclude that the useful linear dynamic range of such devices is severely limited, with the result that many applications will involve operation in the nonlinear regime.A typical layout for a doubly clamped nanomechanical resonator is shown in Fig. 1. The resonator can be driven and detected in several ways, e.g., magnetomotively, 11 or optically. 12 The driving force f͑t͒ leads to a time dependent bending profile z͑x , t͒, which can be found by solving the differential equationwith boundary conditions z͑0͒ = z͑L͒ = z x ͑0͒ = z x ͑L͒ = 0. Here, A is the cross-sectional area, E is Young's modulus, is the density, and I is the moment of inertia about the longitudinal axis of the beam. The term in between brackets describes tension in the beam, and is a sum of residual tension T 0 and a bending-induced tension, respectively. Since Eq. ͑1͒ cannot be solved exactly we use the Galerkin discretization procedure, 13 representing the solution to Eq. ͑1͒ in terms of a linearly independent set of basis functions n ͑x͒ where each basis function satisfies the boundary conditions. The error associated with this approximation technique is ͑2͒The Galerkin procedure requires this error to be orthogonal to each basis function, or in other words, the error is a residual that cannot be expressed in terms of the given finite set of basis functions:We are interested in the response of the beam at resonance when the first mode is dominant, so it suffices to consider the case n = 1. For a doubly clamped beam, the simplest function that approximate...
The authors observed resonances from multiple vibrational modes of individual silicon-carbide-based nanomechanical resonators, covering a broad frequency range from several megahertz to over a gigahertz. The devices are actuated thermoelastically in vacuum at room temperature using localized Joule heating in a device-integrated metal loop. Their motion is detected piezoresistively using signal downmixing in a similarly integrated metal piezoresistor. The frequencies and amplitudes of the observed resonant peaks are in good agreement with the results from theoretical modeling and finite-element simulations. techniques provide a way to actuate and detect motion simultaneously. There are also stand-alone methods for both actuation, such as thermoelastic 8 and piezoshaker 9,10 actuation; and detection, such as piezoresistive 9-11 and optical, 3,8 as well as detection techniques based on motional changes in the electronic properties of single electron transistors 4,12 and nanotubes.13 Each of these techniques has advantages as well as limitations. For example, the magnetomotive technique typically requires large magnetic fields, whereas optical techniques require careful alignment of optical components.For the experiments reported here, we combine piezoresistive downmixing detection, developed earlier in Ref. 9, with thermoelastic actuation due to localized Joule heating of a metallic resistor. Figure 1͑a͒ shows one of the doubly clamped beam resonators used in the experiments. The beams were made from a single-crystal silicon carbon ͑3C-SiC͒ thin film by multiple aligned steps of e-beam lithography, thin film evaporation, lift-off, and reactive plasma etching.14 They had nominal lengths between 4 and 24 m, a width of 400 nm, and a thickness of 80 nm. Two different thin metal film loops were patterned near the two ends of the beam. The 80-nm-thick, 100-nm-wide loop was patterned from thermally evaporated gold and formed a part of the thermoelastic bilayer actuator ͓right inset of Fig. 1͑a͔͒. The thinner piezoresistor loop was patterned from a 30-nm-thick metal layer created by evaporating a 60%-40% gold palladium alloy ͓left inset of Fig. 1͑a͔͒. It consisted of 250-nm-long, 50-nm-wide legs connected by a larger pad ͓left inset of Fig. 1͑a͔͒. A 2-nm-thick chromium adhesion layer was used in both cases. Typical resistances of metal loops were 30 ⍀ for the actuation loop and 300 ⍀ for the detection loop.Thermoelastic actuation of bilayer structures has long been employed, for example, in thermostats, 15 and relies on the fact that the coefficient of linear thermal expansion varies for different materials. For gold and silicon carbide, ␣ Au Ϸ 12ϫ 10 −6 K −1 and ␣ SiC Ϸ 4.8ϫ 10 −6 K −1 , respectively. Local heating of the gold actuation loop in our devices therefore results in nonuniform expansion and thermal stresses that tend to flex the beam toward the substrate. If the temperature changes periodically at the resonance frequency of one of the mechanical modes of the resonator, the amplitude of deflection will be greatl...
We present an experiment that systematically probes the basins of attraction of two fixed points of a nonlinear nanomechanical resonator and maps them out with high resolution. We observe a separatrix which progressively alters shape for varying drive strength and changes the relative areas of the two basins of attraction. The observed separatrix is blurred due to ambient fluctuations, including residual noise in the drive system, which cause uncertainty in the preparation of an initial state close to the separatrix. We find a good agreement between the experimentally mapped and theoretically calculated basins of attraction. DOI: 10.1103/PhysRevLett.99.207201 PACS numbers: 85.85.+j, 05.45.ÿa In the last few years the dimensions of mechanical devices have been scaled deep into the submicrometer regime, which resulted in the increased detection sensitivity of extremely small physical quantities [1,2] and in an enhancement of the significance of nonlinear dynamics in such devices [3]. Deliberately operating the system in the nonlinear regime can improve precision of some experimental measurements on nanoscale. For example, a nonlinear resonator can be employed to suppress amplifier noise in an oscillator circuit [4], noise-induced switching between two stable states in a nonlinear beam resonator enables precision measurement of the resonant frequency [5], and the sensitivity of a resonator for mass detection can be improved when the resonator is driven into a region of nonlinear oscillations [6]. Finally, in a Josephson junction, which is dynamically similar to a mechanical resonator in the nonlinear regime, the bistable state of the nonlinear system can be used as a bifurcation amplifier to perform a nondissipative, low-backaction measurement of the phase across the junction [7]. When nanomechanical devices reach the quantum-limited regime [8], a nanomechanical version of such an amplifier could be used for a similar sensitive low-back-action measurement of the state of a quantum mechanical resonator. The nonlinear response of nanomechanical resonators could also be used to detect transition from the classical to quantum regime [9,10]. It is therefore important to understand nonlinear dynamics of these systems well, so that we can fully realize their potential in expanding our experimental capabilities.Although some work has been done with parametric systems [11,12], the majority of nonlinear nanoscale systems that have been studied are directly driven [5,13,14] and the dominant nonlinearity in the restoring force is cubic, also known as Duffing nonlinearity. When a system is driven strongly, the Duffing nonlinearity causes the resonance response curve to become asymmetric. When the resonance is pulled far enough to one side, hysteretic behavior is observed as two stable states appear in the system [15]. The stable states, known as ''attractors'' or ''fixed points'', correspond to the points in state space to which the system converges with time. For each attractor, a set of initial states that dynamically evo...
Along with increasing fossil-fuel consumption and greenhouse gas emissions, sustainable energy research has been a global topic for many years. Among all the renewable energy sources, solar energy has been attracting widespread attention because of its abundance, stability and environmental friendliness. Nowadays, more than 90% of the photovoltaic market is dominated by wafer-based silicon solar cells. The cost of this technique, which is dominated by the starting material, is diffi cult to reduce. [ 1 ] Thin fi lm silicon solar cells have an active layer of only several micrometers thick and are believed to be a promising candidate for further cost reduction while maintaining the advantages of bulk silicon. [ 2 ] However, the effi ciency of thin fi lm silicon solar cells critically depends on optical absorption in the silicon layer since silicon has low absorption coeffi cient in the red and near-infrared (IR) wavelength ranges due to its indirect bandgap nature. Therefore, an effective light trapping design is indispensable to achieve high effi ciency modules. To address this problem, several methods are used in current technology, for example, traditional schemes such as textured transparent conductive oxide (TCO) and metal refl ector. [ 3 ] These methods are diffi cult to precisely control and optimize the textured surface. In addition, some other issues should be considered such as enhanced surface recombination due to the roughness of silicon layer [ 4 ] and parasitic loss at the TCO/metal interface. [ 5 ] One, two and three dimensional photonic crystals have also been proposed to enhance the light trapping, [ 6 ] but this design is very diffi cult to be implemented experimentally. A practical approach for light trapping has been demonstrated using diffractive grating structures on the backside of a silicon cell. [ 7 ] However, interference lithography and high temperature processing were usually employed in fabricating this structure, limiting its scalability to large area applications. Previously, we reported fabrication of gratings using self-assembled porous alumina for light trapping in silicon solar cells. [ 8 ] However, the low refractive index of alumina ( n ∼ 1.7) has limited the diffraction effect. Furthermore, in production solar cells the electrolyte used in the anodization process reacts with the TCO resulting in device degradation. To achieve a stronger light trapping effect in production Si thin fi lm solar cell structures while exploiting a more controllable and reliable method for fabrication, here we design a backside photonic structure consisting of a high-index-contrast diffraction grating and a distributed Bragg Refl ector (DBR). We optimize the structure in a thin fi lm microcrystalline silicon ( μ c-Si) solar cell, and implement the design experimentally using a self-assembled mask to demonstrate signifi cantly enhanced cell effi ciency due to increased optical path length. The light trapping structures lead to a signifi cant increase of photon absorption in the red and near-infrared ...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.