Positron beam timing spectroscopy has been used to investigate positron dif
fusion in hydrogenated amorphous silicon between 85 and 350 K. The diffusiv
ity is determined from both the contribution of the surface, where the posi
trons have a different characteristic annihilation rate, and its effect on
the shape of the bulk annihilation rate distribution. We observe a single p
ositron state with a temperature independent lifetime of 322 ps. From the t
emperature dependence of the positron diffusion we show that this is a loca
lized state and present the first ever direct observation of hopping diffus
ion of positrons in solids. The migration enthalpy for positrons in this st
ate is found to be 17.7(3) meV.