  The exoplanet mass radius diagram reveals that super Earths display a wide
range of radii, and therefore mean densities, at a given mass. Using planet
population synthesis models, we explore the key physical factors that shape
this distribution: planets' solid core compositions, and their atmospheric
structure. For the former, we use equilibrium disk chemistry models to track
accreted minerals onto planetary cores throughout formation. For the latter, we
track gas accretion during formation, and consider photoevaporation-driven
atmospheric mass loss to determine what portion of accreted gas escapes after
the disk phase. We find that atmospheric stripping of Neptunes and sub-Saturns
at small orbital radii ($\lesssim$0.1AU) plays a key role in the formation of
short-period super Earths. Core compositions are strongly influenced by the
trap in which they formed. We also find a separation between Earth-like planet
compositions at small orbital radii $\lesssim$0.5AU and ice-rich planets (up to
50\% by mass) at larger orbits $\sim$1AU. This corresponds well with the
Earth-like mean densities inferred from the observed position of the low-mass
planet radius valley at small orbital periods. Our model produces planet radii
comparable to observations at masses $\sim$1-3M$_\oplus$. At larger masses,
planets' accreted gas significantly increases their radii to be larger than
most of the observed data. While photoevaporation, affecting planets at small
orbital radii $\lesssim$0.1AU, reduces a subset of these planets' radii and
improves our comparison, most planets in our computed populations are
unaffected due to low FUV fluxes as they form at larger separations.
