I understand that the reason when you plot ionization energy against atomic number, you get peaks at the noble gases, is because they have full valence shells.
When I was trying to think this through, I wasn't sure why the outer electron is more tightly bound if the outer shell was full, as the more electrons in the outer shell, the more the nuclear charge is screened off and so the lower the potential energy of the electron being added, making it less bound? I know that my argument is flawed somewhere but I really only have a qualitative understanding of why full valence shells are most stable.
Can someone provide a more detailed explanation of this process?