We present an analysis of the mid-infrared emission lines for a sample of 12 low metallicity Blue Compact Dwarf (BCD) galaxies based on high resolution observations obtained with Infrared Spectrograph on board the {rm Spitzer} Space Telescope. We compare our sample with a local sample of typical starburst galaxies and active galactic nuclei (AGNs), to study the ionization field of starbursts over a broad range of physical parameters and examine its difference from the one produced by AGN. The high-ionization line [OIV]25.89$mu$m is detected in most of the BCDs, starbursts, and AGNs in our sample. We propose a diagnostic diagram of the line ratios [OIV]25.89$mu$m/[SIII]33.48$mu$m as a function of [NeIII]15.56$mu$m/[NeII]12.81$mu$m which can be useful in identifying the principal excitation mechanism in a galaxy. Galaxies in this diagram split naturally into two branches. Classic AGNs as well as starburst galaxies with an AGN component populate the upper branch, with stronger AGNs displaying higher [NeIII]/[NeII] ratios. BCDs and pure starbursts are located in the lower branch. We find that overall the placement of galaxies on this diagram correlates well with their corresponding locations in the log([NII]/H$alpha$) vs. log([OIII]/H$beta$) diagnostic diagram, which has been widely used in the optical. The two diagrams provide consistent classifications of the excitation mechanism in a galaxy. On the other hand, the diagram of [NeIII]15.56$mu$m/[NeII]12.81$mu$m vs. [SIV]10.51$mu$m/[SIII]18.71$mu$m is not as efficient in separating AGNs from BCDs and pure starbursts. (abridged)
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