Exciton localization on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>p</mml:mi><mml:mo>−</mml:mo><mml:mi>i</mml:mi><mml:mo>−</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:math> junctions in two-dimensional crystals

We consider a neutral exciton localized on model p-i-n junction defined in two-dimensional crystal: MoSe$_2$ and phosphorene, using variational approach to the effective mass Hamiltonian. The non-homogeneous electric field at prevents separation of center mass. solution provides density real space accounts for kinetic energy due localization. For low values potential step across junction, occupies an area which is much larger than nominal range remains essentially insensitive value step. Localization within accompanied by appearance dipole moment induced local field. becomes linear function only when sufficiently large. In consequence, dependence non-parabolic. demonstrate that gets not exactly but side more energetically favourable heavier carrier: electron or hole.