摘要： Excitonic states of a many-electron system in phosphorene quantum dots (PQDs) are investigated theoretically by using a configuration interaction approach. For a triangular PQD in various dielectric environments, its exciton is found to obey two distinct scaling rules. When there is strong screening effect present in the nanodot, the exciton binding energy (?ex) is shown to be around ?150 meV as the long-range Coulomb interactions are totally suppressed and increases to about 100 meV when the effective dielectric constant (εr) decreases to 12.5. Over this range of εr, ?ex is found to be well fitted into a quadratic form of ε?1 r like the case of bulk three-dimensional semiconductors nor linearly with ε?1 r like the case previously reported for graphene nanostructures. When εr is reduced below 10.0, however, ?ex is shown to exhibit a perfect linear relation with ε?1 r, which behaves just like that of a two-dimensional graphene sheet. On the other hand, with the reduced εr, the quasiparticle gap is found to decrease instead of increase like in most of semiconductor nanostructures. As a result, it is revealed that the relationship of ?ex with the quasi-particle gap deviates largely from the linear one previously reported for graphene and many other two-dimensional materials.