  The 133.5 nm lines are important observables for the NASA/SMEX mission
Interface Region Imaging Spectrograph (IRIS). To make 3D non-LTE radiative
transfer computationally feasible it is crucial to have a model atom with as
few levels as possible while retaining the main physical processes. We here
develop such a model atom and we study the general formation properties of the
C II lines. We find that a nine-level model atom of C I-C III with the
transitions treated assuming complete frequency redistribution (CRD) suffices
to describe the 133.5 nm lines. 3D scattering effects are important for the
intensity in the core of the line. The lines are formed in the optically thick
regime. The core intensity is formed in layers where the temperature is about
10kK at the base of the transition region. The lines are 1.2-4 times wider than
the atomic absorption profile due to the formation in the optically thick
regime. The smaller opacity broadening happens for single peak intensity
profiles where the chromospheric temperature is low with a steep source
function increase into the transition region, the larger broadening happens
when there is a temperature increase from the photosphere to the low
chromosphere leading to a local source function maximum and a double peak
intensity profile with a central reversal. Assuming optically thin formation
with the standard coronal approximation leads to several errors: Neglecting
photoionization severly underestimates the amount of C II at temperatures below
16kK, erroneously shifts the formation from 10kK to 25kK and leads to too low
intensities.
