We present a new concept and first results for a photoconducting detector exhibiting extremely high gain and extremely high detectivity. Previously we have demonstrated detectors and optical switches consisting of a n-i-p photodiode whose n-layer is depleted at sufficiently large reverse bias. Under illumination a photovoltage is induced by the photo-generated electrons and holes, accumulated in the n- and p-layer, respectively. We have shown that each photo-generated electron collected in the n-layer contributes about 10 nA to the photoconductive saturation current if the layer is covered with interdigitated `source' and `drain' contacts of about 1 micrometer separation. This signal persists until the photovoltage decays. For low-noise single- or few-electron detection the capacitance of the n-i-p diode has to be minimized. For this purpose we have fabricated n-i-p-structures consisting of crossed p- and n-doped stripes of a few micrometer width. First the (bottom) p-doped stripe is defined by focused Be-ion beam implantation directly into the semi-insulating substrate, followed by MBE-overgrowth with an i- and an n-doped layer. Narrow n-stripes are defined by wet-etching and n-contact fingers are deposited. Room temperature dark currents at a few volts reverse bias are in the low pA- and capacitances in the low fF-range and the expected large photoconductive gain is observed. The photoresponse is independent on the position of the illumination spot on the 50 X 50 micrometer mesa, although the area of crossing stripes is only a few micrometer wide.