1. A fingerprint detection system formed on a single semiconductor chip, the system comprising: a rectangular scanning array defined by a first dimension and a second dimension wherein the first dimension is larger than the second dimension, the array comprising capacitive sensing cells arranged in rows and columns, the rows being aligned with the first dimension and the columns being aligned with the second dimension, the number of columns exceeding the number of rows; a horizontal scanning stage connected to the array for scanning the rows of capacitive sensing cells; a vertical scanning stage connected to the array for scanning the columns of capacitive sensing cells; a scan control unit connected to the scanning stages for operating the scanning stages to enable one capacitive sensing cell at a time according to a predetermined scanning pattern to scan the entire array at a frame rate of multiple frames per second; a thin protective layer disposed above the scanning array and providing a top surface for contact by a finger; an A/D converter connected to each capacitive sensing cell and having an output; and output logic connected to the output of the A/D converter for capturing successive images at the frame rate as a finger is moved over the scanning array in a direction parallel to the second dimension while in contact with the top surface of the thin protective layer, and for assembling the successive images into a complete fingerprint image; wherein each capacitive sensor cell comprises: adjacent first and second thin conductor plates, the conductor plates being closely spaced relative to each other and lying beneath the top surface of the protective layer; an inverting amplifier having an input and an output, the input being connected to the first conductor plate and the output being connected to the second conductor plate and to the A/D converter; and a reference voltage source connected to the input of the inverting amplifier.