TABLE 2.

Calculated defect formation energies (E^f) together with the electronic band gap values (E_g, estimated from singe particle Kohn-Sham eigenvalues) of sulphur and zinc vacancies present in the bulk as well as (220) surface of ZnS. The up (down) arrows represent spin up (down) states. All formation energies correspond to neutral defects and were obtained using HSE06.

Defect	Ef (eV)		Eg (eV)
	Zn-rich/S-poor	Zn-poor/S-rich
$V_S^{bulk}$	2.06	4.37	3.79
$V_{Zn}^{bulk}$	5.84	3.53	3.55
$V_S^{surf}\left(top\right)$	1.19	3.50	3.22
$V_{Zn}^{surf}\left(top\right)$	4.17	1.87	2.33 ( $\uparrow$ )/3.92 ( $\downarrow$ )
$V_S^{surf}\left(sub\right)$	1.64	3.95	3.56
$V_S^{surf}\left(mid\right)$	1.70	4.01	3.45
$V_{S-double}^{surf}\left(top\right)$	2.13	6.74	3.19