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$ u$ > 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.
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