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This paper presents the design and fabrication of a novel single-cell trapping dielectrophoretic (DEP) biochip, which consist of arrayed electrodes and 3D microstructures. The DEP biochips consist of ITO top electrodes, PDMS flow chambers, bottom electrode arrays, and SU-8 3D microstructure arrays. In order to achieve single-cell resolution, we fabricate a chess-type bottom electrode array and a bowl-type 3D microstructure array using excimer laser micromachining technique. The 3D structure not only yields a non-uniform electric field for DEP trapping but also enhances the positioning and immobilization of trapped cells. Theoretically, finite element method is applied to simulate the DEP forces. Experimentally, a new image processing method is developed to derive the flow dragging force on beads subjected to DEP force, and therefore estimate the magnitude of DEP force. It is shown that the chip can trap beads and cells in properly chosen media. We also fractionate beads of different sizes by bowl shaped microstructure. The proposed DEP chips have great potentials for measuring cell-membrane impedence and gene transfer in the future.