  We present results on the emission-line properties of 1.3<=z<=2.7 galaxies
drawn from the complete MOSFIRE Deep Evolution Field (MOSDEF) survey.
Specifically, we use observations of the emission-line diagnostic diagram of
[OIII]5007/Hb vs. [SII]6717,6731/Ha, i.e., the "[SII] BPT diagram," to gain
insight into the physical properties of high-redshift star-forming regions.
High-redshift MOSDEF galaxies are offset towards lower [SII]6717,6731/Ha at
fixed [OIII]5007/Hb, relative to local galaxies from the Sloan Digital Sky
Survey (SDSS). Furthermore, at fixed [OIII]5007/Hb, local SDSS galaxies follow
a trend of decreasing [SII]6717,6731/Ha as the surface density of star
formation (Sigma_SFR) increases. We explain this trend in terms of the
decreasing fractional contribution from diffuse ionized gas (f_DIG) as
Sigma_SFR increases in galaxies, which causes galaxy-integrated line ratios to
shift towards the locus of pure HII-region emission. The z~0 relationship
between f_DIG and Sigma_SFR implies that high-redshift galaxies have lower
f_DIG values than typical local systems, given their significantly higher
typical Sigma_SFR. When an appropriate low-redshift benchmark with zero or
minimal f_DIG is used, high-redshift MOSDEF galaxies appear offset towards
higher [SII]6717,6731/Ha and/or [OIII]5007/Hb. The joint shifts of
high-redshift galaxies in the [SII] and [NII] BPT diagrams are best explained
in terms of the harder spectra ionizing their star-forming regions at fixed
nebular oxygen abundance (expected for chemically-young galaxies), as opposed
to large variations in N/O ratios or higher ionization parameters. The evolving
mixture of HII regions and DIG is an essential ingredient to our description of
the ISM over cosmic time.
