  We have searched for direct pair production of scalar top and scalar bottom
quarks in 88 pb$^{-1}$ of $p\bar{p}$ collisions at $\sqrt{s}=1.8$ TeV with the
CDF detector. We looked for events with a pair of heavy flavor jets and missing
energy, consistent with scalar top quark decays to a charm quark and a
neutralino, or scalar bottom quark decays to a bottom quark and a neutralino.
The numbers of events that pass our selection for each process show no
deviation from Standard Model expectations. We compare our results to
next-to-leading order calculations for the scalar quark production cross
sections to exclude regions in scalar quark-neutralino parameter space.
