Trapping ability on a biochip device is useful for systematic cell addressing and real-time observation of single cells analysis, however, precise control over the cell movements remains challenging. This thesis addresses the problem of controlling movement of single cells on a biochip platform by a technique called the Dielectrophoretic (DEP) force. Existing researches showed that the DEP force offers precise control of cell movements through various microelectrode designs which generate strong polarization effects i.e., DEP forces, but with the expense of damaging cell’s structure. The thesis contribute three new microelectrode designs for trapping single cells: the dipole, the quadrupole and the adaptive octupole, structured on a metal-insulator-metal (multilayer) biochip platform called the Sandwiched Insulator with Back Contact (SIBC) biochip. Cores of the study lie on the microelectrode designs that are capable of generating strong DEP holding forces, the back contact to enhance trapping of single cells and the fabrication process of creating a metal-insulator-metal structure. This thesis also presents details on the experimental setups of the trapping experiments and the numerical analysis of the microelectrode designs. The SIBC biochip comprises of the back contact on the first metal layer, the microcavity (cell trap) on the insulator layer and the three microelectrodes on the second metal layer. Together, the three microelectrodes and the back contact generate DEP forces that attract particles/single cells toward microcavities and maintain their positioning in the traps. Prior to the fabrication, profiles of the DEP force generated by the microelectrodes are studied using COMSOL3.5a software. Simulation results suggest that the DEP trapping region can be created surrounding the microcavity if the microelectrode and the back contact are connected with AC signals that have different phases. The strongest DEP force can be obtained by setting the back contact and the microelectrodes with AC signals that have 180 degree phase difference. Evaluations on the trapping functionality for the three microelectrodes were conducted using polystyrene microbeads and Ishikawa cancer cells line suspended in various medium. Trapping capability of the three microelectrodes was demonstrated through experiments with 22 percent of the Ishikawa cancer cells and 17 percent of the polystyrene microbeads were successfully trapped. With these promising results, the new microelectrode designs together with the SIBC biochip structure have huge potentials for biomedical applications particularly in the field of diagnosis and identification of diseases.