Surface roughness effects on the frequency tuning performance of a nanoelectromechanical resonator
© Yoon et al.; licensee Springer. 2013
Received: 19 March 2013
Accepted: 27 May 2013
Published: 7 June 2013
Electrothermal heating is one of radio frequency tuning method in nanoelectromechanical resonators with magnetomotive transduction. This study confirmed that the surface roughness of the nanoresonator affects the electrothermal tuning performance under moderate conditions at room temperature. The effect of surface roughness on electrothermal tuning is complicated and involves interactions of mechanical and electrical properties. In addition, the electrothermal damping varied depending on the nanoscale molecular solid structure. These factors affect the signal-to-noise ratio, the effective stress of the beam, and the quality Q-factor of the nanoresonator.
KeywordsNanoelectromechanical resonator Electrothermal tuning Surface roughness
In nanoelectromechanical systems (NEMS), there are many demands such as a low power consumption, high signal-to-noise ratio (SNR), wide dynamic range, high critical value, and improved Q-factors. These issues are becoming increasingly important as resonators are developed for smaller devices in extremely sensitive applications including sub-atto-Newton force sensing, single-spin detection, and quantum experiments[4, 5]. Also, recent studies have reported the utilization of the photothermal effect to tune the frequency of a nanoresonator[6, 7]. Tremendous efforts have been exerted to improve the Q-factor of electromechanical resonators over the past few decades, especially at smaller scales such as in the nanometer range. Operating a nanoresonator with a high Q-factor is the most crucial prerequisite for their practical application, and the stiffness, damping factor, noise, and dissipation factors are very important to maintain high Q-factor[8, 9]. However, there are trade-offs with this approach. The diminishing device size effects provide higher sensitivity and frequency, whereas the Q-factor tends to decrease, and the resonance motion with higher Q-factor is easier to show nonlinear characteristic. Comparatively, high-quality performance has been observed under extreme conditions such as low temperatures, high field forces, and high vacuums. Recently, many efforts have been made to apply this technology in practical conditions[10, 12, 13]. However, it is difficult to maintain the Q-factor of the nanoelectromechanical resonator at a high level for radio frequency resonating because of mechanical and electrical damping effects experienced under moderate operating conditions.
Moreover, in the nanoscale structure, the surface roughness can be a significant issue for electron and phonon transmission or scattering[14, 15] since the surface-to-volume ratio increases. Electron and phonon scattering in the atomic solid state of the resonator is dominant with inter-atomic or inter-boundary structural changes due to thermally enhanced phonon–electron interactions by the electrothermal power. Therefore, in this study, Q-factor issues associated with the surface roughness of the resonator were analyzed under moderate conditions while performing frequency tuning.
After the nanomechanical resonator showed successful operation of the radio frequency (RF) resonance, deepening research topics of various working conditions have been investigated including frequency tuning, controlling the nonlinearity of resonating, and chemical vapor sensing[12, 18]. In our study, a doubly clamped nanoscale resonator using electromagnetomotive transduction was operated under a moderate vacuum (about 1 Torr) at room temperature with a B field of 0.9 T. Also, an RF tuning method was adopted in a magnetomotive transduction operation. It was previously demonstrated that linear tuning with an input power appears to be feasible at the application level with a low electrothermal power consumption of only a few microwatts. In addition to resonance frequency tuning, the Q-factor must be analyzed in order to maintain quality performance without degradation under moderate conditions.
The dissipation and damping effects which limit the performance of beam resonance are mainly induced from various causes such as physical defects from the beam structure, thermal elastic damping from the surroundings, clamping losses from supporting clamps on the substrate, signal loss due to electrical feedthrough, and phonon–electron couplings. Therefore, in our study, much effort was made to carefully construct and test the experimental conditions in order to minimize the dissipation factors except for the surface roughness of the resonator.
SiC provides superior material properties for high-frequency applications due to its high stiffness and low density, as well as its good tunability due to its higher thermal conductivity than other NEMS materials such as silicon and silicon nitride. Even though it has excellent mechanical properties including a high Young's modulus and low density, a drawback of SiC is its low electric conductivity. In this work, Al layers were applied to the surface of SiC to improve its conductance. This hybrid layer structure (Al/SiC) is a main loss factor but still results in comparable performance to other materials, which must be produced via careful fabrication processes.
The surface roughness of the resonators and their standard deviation values
Results and discussion
As presented in the equation, the beam stress is closely related to the resonance frequency and the Q-factor is also affected by changes of the beam stress via electrothermal stress due to critical parameters such as the thermal time constants and thermal conductivity. The resonant frequency is subject to variations despite the identical geometries and materials of the beams because of the different effective beam stresses. Predicting the resonant frequency is difficult due to the stress distributions over the beam structure, which is primarily caused by the different layer deposition conditions and the resulting molecular compositions.
The initial resonant frequencies, which are different for each beam, do not affect the frequency tuning ratio, as shown in Figure 4b,c. Furthermore, the stress of the beam is closely correlated to the quality factor during frequency tuning with the nanoelectromechanical resonator, which has a low surface roughness and a well-suspended beam. Actually, the amount of stress or changes of the Q-factor are caused by increased external force due to surface roughness.
The tuning performance is primarily decided by the effective beam stress of resonator, which controls not only the resonant frequency but also the resonant properties of the Q-factor, dynamic range, and SNR. The beam stress distributions may be critically determined by the surface roughness, especially at the nanoscale since the surface roughness suggests not only the defects on the surface but also the intermolecular binding condition beneath the surface in the very thin structure. There are two main issues regarding the effects of the surface roughness on the electrothermal tuning performance. One is that the electric conductivity and thermal conductivity are closely related to the tuning performance, which is induced from decreasing electron and phonon transfer through a conducting layer. The other factor is the mechanical stress distribution with thermal stress provided by the electrothermal power. Intermolecular expansion or subtraction interaction occur either regularly or irregularly, which is decided by isotropic or anisotropic molecular bindings. These mostly depend on the surface roughness and sub-layer structure, which affect the boundary between the SiC and Al composite layers. The Al layer tends to be affected by tensile stress whereas SiC is dominated by compression stress while undergoing electrothermal tuning. Those opposite stress distributions from composite layers, especially at the boundary layer, make the tuning effects clearly different from other various molecular structures.
Because the thermal damping effects on mechanical resonant motions over a megahertz resonant range are not trivial and many complicated effects exist regarding the thermal expansion among intermolecular bonding, the thermal stress over tight-binding solid structures is increased. These effects are mainly concentrated on the top metal layer of the composite resonator beam with a thickness of a few tens of nanometers, which is small enough to be sensitive to intermolecular stress changes induced by thermal stress. The nanoscale mechanical structure of a beam atomically deposited by chemical vapor deposition is highly related to the top layer surface roughness. From another point of view, the mechanical motion is primarily determined by a balanced weight distribution, especially in high frequency motion. Various unbalanced weight bumps distributed on the top of the surface increase the surface roughness, which strongly affects the resonant motions, contributing to Q-factor degradation. In the case of a nanoscaled beam, the roughness effects play a non-trivial role in RF motion.
We demonstrated that as the size of the NEMS beam decreases, the effect related to the beam surface roughness becomes the dominant characteristic due to a large surface-to-volume ratio. The frequency tuning performance was improved with less electrothermal power consumption by improving the surface roughness of the Al-SiC nanobeam. The surface roughness should be controlled in order to minimize the loss of the RF tuning performance. The surface roughness effects are related to not only electromechanical resonance performance but also to electrothermal conductance and dissipation, which are emphasized more in nanoscaled devices because electron and phonon interactions are complicated with scattering issues.
This research was partially supported by the Priority Research Centers Program (2012-8-1663), the Pioneer Research Center Program (2012–0000428), and the Basic Science Research Program (2012-8-0622) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (MEST) of the Korean government.
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