Ab initio simulations were used to determine electron affinity, work function, and ionization energy of AlN, GaN, and InN polar surfaces. The work function depends weakly on the doping in the bulk for the nitrides due to pinning of Fermi level at all polar surfaces. At the metal surface, it is smaller, equal to 3.87, 4.06, and 2.99 eV for AlN, GaN, and InN, respectively, while at the nitrogen side, it is much higher: 9.14, 9.02, and 8.24 eV. It was shown that the electron affinity and ionization potential do not obey the bandgap rule because of the quantum overlap repulsion of the surface and band states: conduction at the metal, and valence at the nitrogen side. The shift is substantial, even more than 1 eV, which may explain the first measured InN identified bandgap of 1.9 eV and the later much lower value of 0.7 eV. Cesium at both polar GaN surfaces does not create bonding states, nevertheless initially decreases electron affinity by charge transfer to surface states reducing electric dipole layer so that at some point the electron affinity becomes negative. At the Ga side, the positively charged Cs ions reduce the energy of Cs 6s states down to the Fermi level at about 0.3 monolayer (ML) coverage, the ionization of additional Cs adatoms is terminated, the electron affinity increases to saturate at 0.75 ML coverage. At the N-side, the Fermi level is pinned by N-broken bond states located close to the valence band maximum. At 0.75 ML Cs coverage, the nitrogen states are all filled, the additional Cs adatoms have to keep their electrons, and the Fermi level jumps from the N-state to the Cs 6s state in the bandgap, which drastically changes the work function. Additional Cs adatoms are not ionized; therefore, the electron affinity is steeply increasing.
