In-depth optical spectroscopic studies of single polar GaN/AlN quantum dots (QDs) grown by molecular beam epitaxy are carried out by means of low-temperature microphotoluminescence. Luminescence linewidths as low as 700 mu eV are obtained allowing thorough characterization of the QD electronic properties. Biexciton emission is observed for a wide range of dot size. It is shown that the binding energy (E-XX(b)) exhibits two regimes. The main one is governed by the dot height through the quantum confined Stark effect leading to a variation of E-XX(b) from +3 meV for the smallest dots to -11 meV for the largest ones. A secondary variation of opposite sign is demonstrated for dots having the same height but different lateral size.