  We use the large spectroscopic dataset of the MOSFIRE Deep Evolution Field
(MOSDEF) survey to investigate some of the key factors responsible for the
elevated ionization parameters (U) inferred for high-redshift galaxies,
focusing in particular on the role of star-formation-rate surface density
(Sigma_SFR). Using a sample of 317 galaxies with spectroscopic redshifts
z~1.9-3.7, we construct composite rest-frame optical spectra in bins of
Sigma_SFR and infer electron densities, n_e, using the ratio of the [OII] 3727,
3730 doublet. Our analysis suggests a significant (~3 sigma) correlation
between n_e and Sigma_SFR. We further find significant correlations between U
and Sigma_SFR for composite spectra of a subsample of 113 galaxies, and for a
smaller sample of 25 individual galaxies with inferences of U. The increase in
n_e -- and possibly also the volume filling factor of dense clumps in HII
regions -- with Sigma_SFR appear to be important factors in explaining the
relationship between U and Sigma_SFR. Further, the increase in n_e and SFR with
redshift at a fixed stellar mass can account for most of the redshift evolution
of U. These results suggest that the gas density, which sets n_e and the
overall level of star-formation activity, may play a more important role than
metallicity evolution in explaining the elevated ionization parameters of
high-redshift galaxies.
