C*-diagonals with Cantor spectrum in Cuntz algebras

We prove that there exists a C*-diagonal with Cantor spectrum in the Cuntz algebra ${\mathcal{O}}_k$ for $2\le k<\mathrm{\infty }$. Our method generalises to an uncountable family of UCT Kirchberg algebras with distinct K-theory. Moreover, we construct principal étale groupoid models for these Cuntz algebras and UCT Kirchberg algebras.