Low-hydrogen-concentration a-Si:H grown by HW-CVD forms a continuous random network with no detectable free volume in the form of microvoids, and no evidence of a microcrystalline phase. Over a wide temperature range we observe a single positron state in the amorphous network with a temperature-independent lifetime of 322 ps. From the temperature dependence of the positron diffusion we show that this is a localized state and present direct observation of hopping diffusion of positrons. On anneal... »