A single-point diamond turning machine was used to make grooves on (111) p-type single-crystal silicon wafers at room temperature. Scratch tests have been performed with both sharp (Vickers and conical) diamond tools, and a spherical (Rockwell) diamond tool. Our results showed that material removal mechanisms differed between these tools. Pressure-induced metallization of Si allows the ductile regime mechanical micromachining of wafer surfaces. Raman microspectroscopy and electron microscopy were used to determine the machining parameters that do not introduce cracking or other types of damage. The surface of the groove, after machining, was covered by a mixture of metastable, high-pressure silicon phases and amorphous silicon. Further, these phases can be transformed into cubic silicon by annealing. The maximum depth of cut in the ductile regime has been determined for the given scratch test conditions and tools. The developed technique can be used to machine Ge, GaAs and other semiconductors. Applications drawing from this research are many. For example, channels for microfluidic devices can be engraved with a channel cross-section that is determined by the shape of the tool, which allows patterns that cannot be produced using etching. There are no limitations on the channel length or direction, and the channel width can vary from potentially a few nanometres to several micrometres.

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The dynamics of mechanical systems with distributed flexi bility are described by infinite-dimensional mathematical models. In order to design afinite-dimensional controller, a finite-dimensional model of the system is needed. The con trol problem of a flexible beam is a typical example. The general practice in obtaining a finite-dimensional model is to use modal approximation for distributed flexibility, retain a finite number of modes, and truncate the rest. In this approx imation, the appropriate selection of the mode shape func tions and the number of modes is not clearly known. Mostly standard pinned-free and clamped-free mode shapes are used for the flexible beam model, retaining only two or three modes and truncating the rest. The actual system, on the other hand, is infinite-dimensional, and the modes describing its flexible behavior under feedback control would be neither pinned-free nor clamped-free boundary condition modes. Rather, the mode shapes themselves are a function of the feedback control. The infinite-dimensional transcendental transfer functions for a flexible beam are formulated without any modal ap proximation. Finite-dimensional transfer functions with different shapes and numbers of modes are formulated. The closed-loop performance predictions of different models under the same colocated and noncolocated controllers, which attempt to achieve high closed-loop bandwidth, are compared. Results are surprisingly consistent in all cases; the predictions of clamped-free mode shape models are much more accurate than the predictions of the pinned-free mode shape models.

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