The energy associated with bosonic and fermionic pairs of topological spin defects in doped antiferromagnetic quantum spin- 1 ∕ 2 square lattice is estimated within a resonating valence bond scenario, as described by a t − t ′ − J -like model Hamiltonian, plus a t ⊥ , responsible of a three-dimensional screening of the electrostatic repulsion within the bosonic pairs. For parameters appropriate for monolayered high- T c superconductors, both fermionic and bosonic pairs show x 2 − y 2 symmetry. We find a critical value of doping such that the energy of the bosonic pairs goes below twice the energy of two fermionic pairs at their Fermi level. This finding could be related to the onset of high- T c superconductivity.