We explore the impact of incorporating physically motivated ionisation and recombination rates on the history and topology of cosmic reionisation and the resulting 21-cm power spectrum , by incorporating inputs from small-volume hydrodynamic simulations into our semi-numerical code , SimFast21 , that evolves reionisation on large scales . We employ radiative hydrodynamic simulations to parameterize the ionisation rate { R _ { ion } } and recombination rate { R _ { rec } } as functions of halo mass , overdensity and redshift . We find that { R _ { ion } } scales super-linearly with halo mass ( { R _ { ion } } \propto M _ { h } ^ { 1.41 } ) , in contrast to previous assumptions . Implementing these scalings into SimFast21 , we tune our one free parameter , the escape fraction f _ { esc } , to simultaneously reproduce recent observations of the Thomson optical depth , ionizing emissivity , and volume-averaged neutral fraction by the end of reionisation . This yields f _ { esc } = 4 ^ { +7 } _ { -2 } \% averaged over our 0.375 h ^ { -1 } { Mpc } cells , independent of halo mass or redshift , increasing to 6 % if we also constrain to match the observed z = 7 star formation rate function . Introducing super-linear { R _ { ion } } increases the duration of reionisation and boosts small-scale 21-cm power by \times 2 - 3 at intermediate phases of reionisation , while inhomogeneous recombinations reduce ionised bubble sizes and suppress large-scale 21-cm power by \times 2 - 3 . Gas clumping on sub-cell scales has a minimal effect on the 21cm power . Super-linear { R _ { ion } } also significantly increases the median halo mass scale for ionising photon output to \sim 10 ^ { 10 } M _ { \odot } , making the majority of reionising sources more accessible to next-generation facilities . These results highlight the importance of accurately treating ionising sources and recombinations for modeling reionisation and its 21-cm power spectrum .