  The sub-gap density of states of amorphous indium gallium zinc oxide
($a$-IGZO) is obtained using the ultrabroadband photoconduction (UBPC) response
of thin-film transistors (TFTs). Density functional theory simulations classify
the origin of the measured sub-gap density of states peaks as a series of
donor-like oxygen vacancy states and acceptor-like Zn vacancy states. Donor
peaks are found both near the conduction band and deep in the sub-gap, with
peak densities of $10^{17}-10^{18}$ cm$^{-3}$eV$^{-1}$. Two deep acceptor-like
metal vacancy peaks with peak densities in the range of $10^{18}$
cm$^{-3}$eV$^{-1}$ and lie adjacent to the valance band Urbach tail region at
2.0 to 2.5 eV below the conduction band edge. By applying detailed charge
balance, we show increasing the density of metal vacancy deep-acceptors
strongly shifts the $a$-IGZO TFT threshold voltage to more positive values.
Photoionization (h$\nu$ > 2.0 eV) of metal vacancy acceptors is one cause of
transfer curve hysteresis in $a$-IGZO TFTs owing to longer recombination
lifetimes as they get captured into acceptor-like vacancies.
