A K-band electron-spin-resonance study of the appearance of the delocalized intrinsic EX center in dry thermal SiO2 was performed on (001) and (111) Si/SiO2. The defect is found in both structures in nearly identical spin densities, 1.2X10(12) cm(-2) being the maximum areal density. Variation of Si precleaning treatments showed the center's generation to depend on the initial surface condition of the c-Si substrate. For fixed initial surface conditions, however, systematic variation of the oxidation temperature (760-930 degrees C), oxidation time (a few min up to 24 h), and oxygen pressure (similar to 24 and similar to 110 kPa), in combination with stylus profilometry, revealed the EX areal density to be solely determined by the grown oxide thickness (d(ox)), EX being detectable from d(ox) approximate to 70 Angstrom onwards, with a maximum intensity at d(ox) approximate to 125 Angstrom. Etch back experiments showed the defects to reside in the top 45 Angstrom of the oxide layer, with the largest local volume density (similar to 3X10(18) cm(-3)) occurring near the ambient/SiO2 interface. With growing oxide thickness, the spatial profile remains largely unchanged, the mere effect being changes in the overall EX areal density. Alternated isochronal anneals in H-2 and vacuum revealed the defect's thermochemical properties to be dominated by the interaction with H-2, in a very similar fashion as for the P-b center at the (111)Si/SiO2 interface. Possible hints of these growth aspects as to the nature of the EX defect are discussed.