I incorporate an Al-AlO_x-Al single-electron transistor (SET) as the gate of a narrow (~ 100 nm) metal-oxide-semiconductor field-effect transistor (MOSFET). Near the MOSFET channel conductance threshold, Coulomb blockade oscillations are observed at about 20 millikelvin, revealing the formation of a Si SET at the Si/SiO₂ interface. Based on a simple electrostatic model, the two SET islands are demonstrated to be closely aligned, with an inter-island capacitance approximately equal to 1/3 of the total capacitance of the Si transistor island, indicating that the Si transistor is strongly coupled to the Al transistor. This vertically-aligned Al and Si SET system is used to characterize the background charges in a MOS structure at low temperature, which may also be sources of decoherence for Si quantum computation. A single charge defect, probably either a single charge trap at the Si/SiO₂ interface or a single donor in the Si substrate, is detected and the properties of the defect are studied in this dissertation.