We present an analysis of the structure of post-starburst (PSB) galaxies in the redshift range $0.5 < z < 2$, using a photometrically-selected sample identified in the Ultra Deep Survey (UDS) field. We examine the structure of $sim80$ of these transient galaxies using radial light $mu(r)$ profiles obtained from CANDELS $textit{Hubble Space Telescope}$ near-infrared/optical imaging, and compare to a large sample of $sim2000$ passive and star-forming galaxies. For each population, we determine their typical structural properties (effective radius $r_{rm e}$, Sersic index $n$) and find significant differences in PSB structure at different epochs. At high redshift ($z > 1$), PSBs are typically massive ($M_* > 10^{10}rm,M_{odot}$), very compact and exhibit high Sersic indices, with structures that differ significantly from their star-forming progenitors but are similar to massive passive galaxies. In contrast, at lower redshift ($0.5 < z < 1$), PSBs are generally of low mass ($M_* < 10^{10}rm,M_{odot}$) and exhibit compact but less concentrated profiles (i.e. lower Sersic indices), with structures similar to low-mass passive discs. Furthermore, for both epochs we find remarkably consistent PSB structure across the optical/near-infrared wavebands (which largely trace different stellar populations), suggesting that any preceding starburst and/or quenching in PSBs was not strongly centralized. Taken together, these results imply that PSBs at $z > 1$ have been recently quenched during a major disruptive event (e.g. merger or protogalactic collapse) which formed a compact remnant, while at $z < 1$ an alternative less disruptive process is primarily responsible. Our results suggest that high-$z$ PSBs are an intrinsically different population to those at lower redshifts, and indicate different quenching routes are active at different epochs.
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