The present invention provides a semiconductor structure having at least one CMOS device in which the Miller capacitances, i.e., overlap capacitances, are reduced and the drive current is improved. The inventive structure includes a semiconductor substrate having at least one overlaying gate conductor, each of the at least one overlaying gate conductors has vertical edges; a first gate oxide located beneath the at least one overlaying gate conductor, the first gate oxide not extending beyond the vertical edges of the at least overlaying gate conductor; and a second gate oxide located beneath at least a portion of the at one overlaying gate conductor. In accordance with the present invention, the first gate oxide and the second gate oxide are selected from high k oxide-containing materials and low k oxide-containing materials, with the proviso that when the first gate oxide is high k, than the second gate oxide is low k, or when the first gate oxide is low k, than the second gate oxide is high k.