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A Transient Current Technique (TCT) utilizing an IR laser with 100 ps pulse width and beam diameter of FWHM = 8 μm was used to evaluate non-irradiated and irradiated p-type silicon micro-strip detectors. The beam was parallel with the surface and perpendicular to the strips (Edge-TCT) so that the electron hole pairs were created at known depth in the detector. Induced current pulses were measured in one of the strips. The pulse shapes were analyzed in a new way, which does not require the knowledge of effective trapping times, to determine drift velocity, charge collection and electric field profiles in heavily irradiated silicon detectors. The profiles were studied at different laser beam positions (depth of carrier generation), voltages and fluences up to 5·1015 neutrons cm-2. A strong evidence for charge multiplication at high voltages was found with the detector irradiated to the highest fluence.