Dynamic Characterization of Silicon Nitride Cantilevers

This thesis describes a series of experiments on dynamical characterization of silicon nitride cantilevers. These devices play an important role in micro-and nanoelectromechanical systems (MEMS and NEMS). They consist of a mechanical part, a sensor or actuator, and an electronic part for readout and control. The core of NEMS and MEMS, the so called mechanical part, exists in various shapes. Examples include disk resonators, doubly clamped beams, tuning forks and cantilevers. These mechanical sensors are good candidates for applications in e.g the medical world, and telecommunication. Examples of applications include micro-array biosensors and ultrasensitive mass sensors. On a fundamental level they can be utilized to explore phenomena like the Casimir force and quantum mechanical zero point motion. Mechanical resonators are fabricated through a top-down technique, making use of the bulk material and special micro-machining techniques. Experiments in this thesis are performed on cantilevers, which differ from each other in the clamping point due the release method, and in the accuracy in the pattern definition step. A short description of MEMS, NEMS and the fabrication is described in chapters 1 and 2. The cantilevers are dynamically characterized by measuring their eigenmodes, each with a specific resonance frequency and quality factor. From this information the effective Young's and shear modulus, and the dissipation mechanisms can be determined. The resonance frequency can be measured using an interferometric, capacitive or laser deflection technique. The latter is the most common technique and is used in atomic force microscopes (AFM). We have optimized this technique so that the cantilever deflection due to its thermal mechanical noise is probed. The output signal, the voltage difference generated by the reflected light focused on a two-segment diode, is measured using a spectrum analyser. The Fourier-transformed signal manifests itself as a Lorentzian peak, which contains the necessary information for the characterization. Amplitudes of the order of picometers can be detected with our setup. Details of the measurement technique are described in chapter 3. Chapter 4 describes the resonance frequency behavior as a function of cantilever dimensions. Two vibrational modes are distinguished; flexural and torsional modes, which are independently measured. Also higher order modes for each type of vibration are detected. Depending on the strength of the spring constant seven or more flexural modes and up to three torsional modes are observed. Furthermore we have investigated the dependence of the resonance frequency for different fabrication methods. For cantilevers with no undercut adding an additional length to the nominal length makes the resonance frequency behavior predictable by existing models. For resonance frequency behavior of cantilevers fabricated with no undercut such a correction is not necessary. Finite element simulations support the observations. The resonance frequency of the torsional modes as a function of dimensions is not properly described by commonly used models. It predicts lower frequencies. A different model describing torsional vibrations of airplane-wings, fits to our experimental data. Chapter 5 describes experiments on the behavior of the resonance frequency and quality-factor as a function of gas pressure. The experiments are performed in helium, argon, air and xenon environments. Three pressure regimes are distinguished in the pressure range between 10^{-5} mbar and atmospheric. Depending on the Knudsen number these regimes are known as 'intrinsic', 'molecular' and 'viscous'. Our experimental findings are well fitted by existing theories, for both the first and higher flexural modes. An unexpected slight increase in the resonance frequency in the viscous regime is observed, which is not predicted by the existing models. The increase is due to a slight stiffening of the cantilevers and might be caused by gas adsorption in the near surface. Measurements with higher laser power show a further increase in the anomalous resonance frequency shift. Its origin is not clear since a higher laser power is expected to further heat up the cantilever, and consequently decrease its resonance frequency. Chapter 6 discusses the behavior of Young's modulus as a function of decreasing thickness in the range of 20 to 680 nm. A significant decrease in the Young's modulus is observed for thicknesses below 150 nm, both in the first and second flexural modes. This decrease cannot be explained by neither a double layer and a sandwich model, in which case the extra layer(s) are considered to have a different Young's modulus. With a model including also a surface-elasticity term the experimental data can be understood. An infinitesimal thin layer with a certain surface elasticity, which is determined from a fit through the data, influences the Young's modulus. For thinner cantilevers this influence is even larger because at higher surface-to-volume ratios, surface-processes dominate the bulk properties. Finally chapter 7 describes measurements on the important application of cantilevers as ultrasensitive mass sensors. A cantilever can be considered as a harmonic oscillator so that the resonance frequency can be determined from its spring constant and the effective mass. By measuring the resonance frequency before and after mass loading, the amount of the added mass can be calculated, assuming the spring constant does not change. The first measurements are performed on cantilevers, with a homogeneously evaporated gold coating of 40 nm on top. A measured mass of 390 pg is calculated through resonance frequency shifts from both the first and the second mode. Mass of the gold layer calculated from the volume and mass density is 3 times higher. A possible explanation for this discrepancy is that the total Young's modulus due to the bilayer system is lower than that of bare silicon nitride. A lower effective Young's modulus decreases the resonance frequency and explains partially the mass difference. In a second measurement we performed mass sensing with smaller amounts of mass. For this purpose aminopropyltriethoxysilane (APTES) is selectively coated as a monolayer. These so-called functionalized cantilevers are good candidates for selective mass sensing purposes. As an example, an array of cantilevers, each functionalized with a different coating on a single chip, can be used to simultaneously detect different targets such as DNA, viruses and bacteria. Experimental results on the first three flexural modes and first torsional mode show the same amount of added mass of approximately 10 pg. In contrast to this value, the calculated mass of a monolayer coverage of APTES gives 5 pg. A possible explanation for this difference might be a variation in the spring constant, which was assumed to be constantKavli Institute of NanoscienceApplied Science

Size-dependent effective Young’s modulus of silicon nitride cantilevers

The effective Young’s modulus of silicon nitride cantilevers is determined for thicknesses in the range of 20–684 nm by measuring resonance frequencies from thermal noise spectra. A significant deviation from the bulk value is observed for cantilevers thinner than 150 nm. To explain the observations we have compared the thickness dependence of the effective Young’s modulus for the first and second flexural resonance mode and measured the static curvature profiles of the cantilevers. We conclude that surface stress cannot explain the observed behavior. A surface elasticity model fits the experimental data consistently.Kavli Institute of NanoscienceApplied Science