Why does ionisation energy increase across Period 3?

Ionisation energy is the energy required to remove the valence electron of an element/atom. The reason this increases is because, as we go across the period, the atomic number of the element increases. This means the effective nuclear charge (electrostatic attraction between valence electron and nucleus) increases. The reason is because electron and proton count both increase by one as atomic number increases by one. Negatively charged electrons increase repulsion and therefore increase shielding between valence e- and nucleus. However, a positive proton is also added to the nucleus. This extra proton heavily outweighs the extra shielding the electron added. Overall, as atomic number increases, the shielding between valence e- and nucleus decreases. This increases effective nuclear charge, and therefore more energy is required to separate the valence electron and atom.