The enormous progress in silicon semiconductor technology allows one to construct one- and two-dimensional position-sensitive detectors for neutrons with large area Si diodes and thin 6LiF converter layers. Such detectors promise to have extreme low gamma sensitivity, a spatial resolution in the wide range from 10 to 0.1 mm, and operate in varying magnetic fields as those present in spin-echo experiments. The first position sensitive neutron detector of this kind was built with a strip diode. Its spatial resolution was 1.25 mm and its gamma sensitivity less than 10 -6. Sufficiently large detection efficiency for thermal and subthermal neutrons can be obtained by applying various methods: (1) by processing deep grooves filled with 6LiF in the diodes via anisotropic etching with KOH or sawing with diamond blades, (2) by inclining semiconductor/converter/semiconductor sandwiches with respect to the neutron beam direction, and (3) by stacking such sandwiches. Some investigations towards higher detector efficiency have started.