The performance of a novel instrument, the Scanning Charge-Transient Microscope, is demonstrated by analysis of defect states in thin-film transistors fabricated in location-controlled single-grain crystallised amorphous silicon. In the instrument, the principle of Isothermal Charge-Transient Spectroscopy is implemented. Its heart is a sensitive charge-to-voltage converter. It integrates the minute charge emitted from traps, periodically filled by voltage pulses. The sensitivity of the converter is in the attocoulomb range. The frequency of filling pulses is swept from a few hundred kHz to tens of Hz and the charge transients are transformed into a spectrum by suitable sampling and integration. In contrast to earlier investigations of defects in micron-sized field effect transistors, the sensitivity of the instrument makes it possible to investigate the defects in simple capacitors without the need to make use of the gain of the transistor. Thus, it can be combined with a scanning force or tunnelling microscope and perform local analysis of selected areas of the sample.