Gap-fill methods comprise: (a) providing a semiconductor substrate having a relief image on a surface of the substrate, the relief image comprising a plurality of gaps to be filled; (b) applying a gap-fill composition over the relief image, wherein the gap-fill composition comprises a non-crosslinked crosslinkable polymer, an acid catalyst, a crosslinker and a solvent, wherein the crosslinkable polymer comprises a first unit of the following general formula (I): wherein: R1 is chosen from hydrogen, fluorine, C1-C3 alkyl and C1-C3 fluoroalkyl; and Ar1 is an optionally substituted aryl group that is free of crosslinkable groups; and a second unit of the following general formula (II): wherein: R3 is chosen from hydrogen, fluorine, C1-C3 alkyl and C1-C3 fluoroalkyl; and R4 is chosen from optionally substituted C1 to C12 linear, branched or cyclic alkyl, and optionally substituted C6 to C15 aryl, optionally containing heteroatoms, wherein at least one hydrogen atom is substituted with a functional group independently chosen from hydroxyl, carboxyl, thiol, amine, epoxy, alkoxy, amide and vinyl groups; and (c) heating the gap-fill composition at a temperature to cause the polymer to crosslink. The methods find particular applicability in the manufacture of semiconductor devices for the filling of high aspect ratio gaps.