Bending silicon nitrides

The minimum detectable signal for cantilever bending depends on the geometry and the material properties of the cantilever. For a silicon nitride cantilever of 200 pm long and 0.5 pm thick, with E = 8.5 x 1010 N/m2 and v = 0.27, a surface stress of 0.2 mJ/m2 will result in a deflection of 1 nm at the end. Because a cantilever s deflection strongly depends on geometry, the surface stress change, which is directly related to molecular adsorption on the cantilever surface, is a more convenient quantity of the reactions for comparison of various measurements. 

The piezoresistive readout technique has several advantages over commonly used optical beam deflection methods. For example, optical beam deflection probes the bending of the free end of the cantilever. It is assumed that the bending is uniform along the length of the cantilever. The piezoresistive method, however, measures the integrated bending of the cantilever. Piezoresistive cantilevers can be encapsulated in silicon nitride... 

The cantilevers can be fabricated of any shape and from substantially any material utilized in microelectronics industry, i.e. crystalline or poly-silicon, silicon nitride, silicon oxide, polymer materials (see Note 2). The rectangular shape beams are the most frequently used in biological research. In biological sensors based on the bending method, it is important to have the cantilevers flat and in plane with the base surface. Initial offset or curvature of the beams complicates adjustment of the experimental setup, especially, if working with arrays of cantilever. For this reason, the most common material for cantilevers fabrication nowadays is single crystalline silicon. A large variety of biomolecular interactions have been detected with silicon microcantilevers. 

In order to improve the sensor response time, a thin hydrogel layer was directly deposited onto the backside of the bending plate covered with a 220 nm thick PECVD silicon nitride film and with a 17 run thick adhesion promoter layer (Fig. 2c). The final thickness of the dried and then cross-linked hydrogel layer was 4... 50 pm. 

In the following these ideas are applied to describe bending test results of a commercial silicon nitride ceramic. 

Fig. 1 a) Strength data of a silicon nitride ceramic tested in four point bending (4PB) in a Weibull plot and b) the relative frequency distribution of flaw sizes. The data points were determined by fracture experiments. 

Nakabeppu et al. [58] describe the use of composite cantilevers made from tin or gold deposited on conventional silicon nitride AFM probes to detect spatial variations in temperature across an indium/tin oxide heater. Differential thermal expansion of the bimetallic elements causes the beam to bend. This movement is monitored using the AFM optical lever deflection detection system. In order to separate thermal deflection of the beam from displacement of the cantilever caused by the sample topography, an intermittent contact mode of operation is employed. Measurements were made under vacuum so as to minimize heat loss. A more practical use of this technology is in the form of miniature chemical and thermal sensors [59]. This approach has been used to perform thermal analysis on picolitre volumes of materisd deposited on the end of a bimetallic cantilever [60]. Arrays of such devices have applications as highly sensitive electronic noses . 

The strength of a brittle material is proportional to the fracture toughness and indirectly proportional to the square root of the defect size. The defect size of the materials can be reduced by optimised processing. [55,82], The highest measured mean three-point-bending strength for silicon nitride was 2000 MPa [85]. This corresponds to a defect size of about 5 pm. Materials with a strength level of 1400 to 1500 MPa usually have a defect size of 10 pm [55,83], i.e. these materials have... 

Figure 12.7 Fracture origins, (a) In a silicon nitride bending test specimen (b) In a barium titanate (PTC ceramic) bending test specimen (c) In an alumina bending test specimen. The origins are an agglomeration of coarse.

Figure 12.8 Bending strength test results for a silicon nitride ceramic. Plotted is the probability of failure versus the strength. The straight lines represent Weibull distributions. The measured Weibull distribution has a mod ulus of m = 15.5, and the characteristic strength is 844 MPa. Also...

Figure 16.13 Relationship between thermal conductivity and four-point bending strength of various types of high-thermal conductivity Si3N4 fabricated by different routes. GPSN = gas-pressure-sintered silicon nitride SRBSN = sintered reaction-bonded silicon nitride [62].

Keywords Fretting fatigue, alumina, silicon nitride, cyclic fatigue, four-point-bending... 

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