  We present multi-wavelength characterization of 65 high mass X-ray binary
(HMXB) candidates in M33. We use the Chandra ACIS survey of M33 (ChASeM33)
catalog to select hard X-ray point sources that are spatially coincident with
UV-bright point source optical counterparts in the Panchromatic Hubble
Andromeda Treasury: Triangulum Extended Region (PHATTER) catalog, which covers
the inner disk of M33 at near infrared, optical, and near ultraviolet
wavelengths. We perform spectral energy distribution (SED) fitting on
multi-band photometry for each point source optical counterpart to measure its
physical properties including mass, temperature, luminosity, and radius. We
find that the majority of the HMXB companion star candidates are likely B-type
main sequence stars, suggesting that the HMXB population of M33 is dominated by
Be-XRBs, as is seen in other Local Group galaxies. We use spatially-resolved
recent star formation history (SFH) maps of M33 to measure the age distribution
of the HMXB candidate sample and the HMXB production rate for M33. We find a
bimodal distribution for the HMXB production rate over the last 80 Myr, with a
peak at $\sim$10 Myr and $\sim$40 Myr, which match theoretical formation
timescales for the most massive HMXBs and Be X-ray binaries (Be-XRBs),
respectively. We measure an HMXB production rate of 107$-$136
HMXBs/(M$_{\odot}$ yr$^{-1}$) over the last 50 Myr and 150$-$199
HMXBs/(M$_{\odot}$ yr$^{-1}$) over the last 80 Myr. For sources with compact
object classifications from overlapping NuSTAR observations, we find a
preference for giant/supergiant companion stars in BH-HMXBs and main sequence
companion stars in neutron star HMXBs (NS-HMXBs).
