  The quest for extremely high mobilities of 2d electron gases in MBE-grown
heterostructures is hampered by the available purity of the starting materials,
particularly of the gallium. Here we compare the role of different Ga lots
having nominally the highest possible quality on the mobility and the
photoluminescence (PL) of modulation doped single interface structures and find
significant differences. A weak exciton PL reveals that the purity of the Ga is
insufficient. No high mobility can be reached with such a lot with a reasonable
effort. On the other hand, a strong exciton PL indicates a high initial Ga
purity, allowing to reach mobilities of 15 million (single interface) or 28
million $cm^2/Vsec$ (doped quantum wells) in our MBE systems. We discuss
possible origins of the inconsistent Ga quality. Furthermore, we compare
samples grown in different MBE systems over a period of several years and find
that mobility and PL is correlated if similar structures and growth procedures
are used.
