Geometry optimization of uncoated silicon microcantilever-based gas density sensors

Abstract

In the absence of coating, the only way to improve the sensitivity of silicon microcantilever-based density sensors is to optimize the device geometry. Based on this idea, several microcantilevers with different shapes (rectangular-, U- and T-shaped microstructures) and dimensions have been fabricated and tested in the presence of hydrogen/nitrogen mixtures (H₂/N₂) of various concentrations ranging from 0.2% to 2%. In fact, it is demonstrated that wide and short rectangular cantilevers are more sensitive to gas density changes than U- and T-shaped devices of the same overall dimensions, and that the thickness does not affect the sensitivity despite the fact that it affects the resonant frequency. Moreover, because of the phase linearization method used for the natural frequency estimation, detection of a gas mass density change of 2 mg/l has been achieved with all three microstructures. In addition, noise measurements have been used to estimate a limit of detection of 0.11 mg/l for the gas mass density variation (corresponding to a concentration of 100 ppm of H₂ in N₂), which is much smaller than the current state of the art for uncoated mechanical resonators.

Introduction

In recent years microcantilever-based chemical, biological and physical sensors have attracted the interest of numerous researchers due to their high surface-to-volume ratio and their high performance in both gas and liquid phases [1], [2], [3], [4], [5], [6]. For chemical and biochemical sensing applications, the microcantilevers are usually coated with a sensitive layer whose purpose is to selectively sorb the analyte of interest, resulting in either a static deflection (bilayer effect) in the static mode or a shift in the resonant frequency (mass effect) in the dynamic flexural mode. Furthermore, it has been demonstrated that uncoated micro- or millimeter size cantilevers operated in the dynamic flexural mode exhibit good sensitivities to gas mass density [7], [8], liquid mass density [9] and/or viscosity [10], [11].

With a view toward chemical detection in gas media, the variation of the gas density can reflect the variation of a chemical species concentration in a gas mixture [8], [12], [13], [14]. The operating principle of an uncoated silicon microcantilever (USMC) used as a density or chemical sensor is based on the influence of the mass of the fluid moved by the vibrating cantilever on the resonant frequency. In fact, when the surrounding fluid mass density increases (decreases), the equivalent effective mass of the cantilever increases (decreases), thereby causing the resonant frequency to decrease (increase) [12].

The absence of a coating eliminates or significantly reduces several problems associated with microcantilever-based sensors such as long-time response, drift and aging effects. However, uncoated microcantilevers are non-selective and offer very low sensitivities, making it quite challenging to detect small concentration changes (small density changes). This last point serves as the motivation to increase the sensor sensitivity through geometry optimization.

In the literature geometry optimization has already been reported for other particular cases of chemical detectors. For example, in the static bending mode, Loui et al. [15] have studied the influence of the length-to-width aspect ratio on the sensitivity of rectangular cantilevers due to both surface stress and an end-force loading. They have found that structures with a low aspect ratio are better for surface-stress applications and structures with high aspect ratio are optimal for point-loading scenarios. In the case of dynamic mode operation, the cantilever mass sensitivity is proportional to its resonant frequency. The resonant frequency is proportional to the square root of the stiffness and inversely proportional to the square root of the effective mass. Therefore, the majority of the studies conducted in order to improve the mass sensitivity of cantilevers are focusing on increasing the stiffness (k) and/or decreasing the effective mass (m_eff) using different methods. Hocheng et al. [16] have demonstrated using different microcantilever shapes that the higher the structural stiffness is, the better the sensitivity is. Similarly, Subramanian et al. [17] suggested the use of a nonlinear width profile for V-shaped microcantilevers in order to increase the structural stiffness and subsequently the mass sensitivity. For bio-sensing applications and in order to improve the overall (static-mode and dynamic-mode) sensitivity of a microcantilever, as measured by the product of static deflection and resonant frequency, Ansari et al. [18] proposed using a non-uniform cantilever cross-section (giving increased k and decreased m_eff) and reducing the fixed-end area (increasing the static deflection). The authors suggested triangular or step cross-section profiles instead the conventional rectangular one. Another solution, proposed by Narducci et al. [19], consisted of reducing the microcantilever size (increasing k and reducing m_eff) and/or using higher-order modes. In the case of end-mass loading, Morshed et al. [20] have demonstrated via simulation studies that structures with high aspect ratio (length-to-width) are more sensitive to local end-mass variation; furthermore, they have suggested the use of a triangular microcantilever shape to enhance the stiffness and minimize the effective mass at the free-end of the structure. Furthermore, to enhance the capabilities of microcantilevers in liquid media, Beardslee et al. [21] have studied the influence of the beam geometry on both the quality factor and the resonant frequency in a liquid medium (water) in order to limit the viscous damping effect, thus improving the detection limit of chemical sensing. The authors reported that the use of the in-plane bending mode reduces the damping and the mass loading due to the surrounding fluid, and that beams that are wide, thin and short and operated in the in-plane mode are more suitable for liquid-phase chemical detection.

As reported above, the resonant frequency is a key parameter in determining the cantilever mass sensitivity and all researches are focusing on enhancing this parameter. The microcantilever operating in fluidic (gas or liquid) environments interacts with the surrounding fluid which causes a distributed mass depending on the fluid properties, frequency and cantilever width [22]. Thus, although the resonant frequency is an important parameter to mass density sensing, the structure's geometry and dimensions play an important role in the mass density sensitivity of microstructures. In the present work we study the effect of microcantilever shape (rectangular, U- and T-shaped microstructures) and geometrical dimensions on the gas mass density sensitivity (i.e., the ratio of resonant frequency variation to the density variation). To perform this study several uncoated silicon microcantilever shapes with different dimensions have been designed and fabricated. The structures have been tested at room conditions using different concentrations (0.2–2.0%) of hydrogen (H₂) in nitrogen (N₂). The density changes have been measured by monitoring the eigenfrequency (natural frequency) variation using the efficient phase linearization method [23].