  Observations of ionised carbon at 158 micron ([CII]) from luminous
star-forming galaxies at z~0 show that their ratios of [CII] to far infrared
(FIR) luminosity are systematically lower than those of more modestly
star-forming galaxies. In this paper, we provide a theory for the origin of
this so called "[CII] deficit" in galaxies. Our model treats the interstellar
medium as a collection of clouds with radially-stratified chemical and thermal
properties, which are dictated by the clouds' volume and surface densities, as
well as the interstellar radiation and cosmic ray fields to which they are
exposed. [CII] emission arises from the outer, HI dominated layers of clouds,
and from regions where the hydrogen is H2 but the carbon is predominantly C+.
In contrast, the most shielded regions of clouds are dominated by CO and
produce little [CII] emission. This provides a natural mechanism to explain the
observed [CII]-star formation relation: galaxies' star formation rates are
largely driven by the surface densities of their clouds. As this rises, so does
the fraction of gas in the CO-dominated phase that produces little [CII]
emission. Our model further suggests that the apparent offset in the [CII]-FIR
relation for high-z sources compared to those at present epoch may arise from
systematically larger gas masses at early times: a galaxy with a large gas mass
can sustain a high star formation rate even with relatively modest surface
density, allowing copious [CII] emission to coexist with rapid star formation.
