Super Earths are the largest population of exoplanets and are seen to exhibit a rich diversity of compositions inferred through their mean densities. Here we present a model that aims to explain super Earth formation and the variety of compositions they can achieve. Our approach combines an equilibrium chemistry model of a protoplanetary disk with a core accretion model of Jovian planet formation. This allows us to track solids accreted onto a planet during its formation, such as ices, mantle and core materials. A key feature of these models is the trapped type-I migration regime that has been shown to reproduce the mass-period relation of Jovian exoplanets. The technique of population synthesis is employed to determine the key parameters, physical processes and associated timescales that lead to the formation of super Earths. In our picture, super Earth formation is linked to disk dispersal taking place prior to the planet undergoing rapid gas accretion. These planets form frequently in our population studies, at a ratio of roughly two super Earths for every formed Jupiter. Our model can explain the range of super Earth compositions, as the different locations of planet traps in the natal disk allows individual planets to form in vastly different chemical environments. As an example, we find that planets formed at the ice line achieve different compositions (~30% ice by mass) than planets formed within the dead zone trap, which lies interior to the ice line, and produces dry and rocky planets (~7% ice by mass).