The statistical equilibrium of neutral and ionised silicon in the solar photosphere is investigated. Line formation is discussed and the solar silicon abundance determined. High-resolution solar spectra were used to determine solar $log gfepsilon_{rm Si}$ values by comparison with Si line synthesis based on LTE and NLTE level populations. The results will be used in a forthcoming paper for differential abundance analyses of metal-poor stars. A detailed analysis of silicon line spectra leads to setting up realistic model atoms, which are exposed to interactions in plane-parallel solar atmospheric models. The resulting departure coefficients are entered into a line-by-line analysis of the visible and near-infrared solar silicon spectrum. The statistical equilibrium of ion{Si}{i} turns out to depend marginally on bound-free interaction processes, both radiative and collisional. Bound-bound interaction processes do not play a significant role either, except for hydrogen collisions, which have to be chosen adequately for fitting the cores of the near-infrared lines. Except for some near-infrared lines, the NLTE influence on the abundances is weak. Taking the deviations from LTE in silicon into account, it is possible to calculate the ionisation equilibrium from neutral and ionised lines. The solar abundance based on the experimental $f$-values of Garz corrected for the Becker et al.s measurement is $7.52 pm 0.05$. Combined with an extended line sample with selected NIST $f$-values, the solar abundance is $7.52 pm 0.06$, with a nearly perfect ionisation equilibrium of $Deltalogepsilon_odot(ion{Si}{ii}/ion{Si}{i}) = -0.01$.
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