Dependence of the polaron binding energy and effective mass in a crystal layer on its thickness

The effective mass and module of the binding energy of a strong-coupling large polaron in a crystal layer are calculated as functions of the layer thickness. It is shown that these values may considerably exceed the corresponding quantities for an infinite crystal at a layer thickness of the order of the polaron radius already. The dependence of the binding energy module on the thickness is not monotonous: with the increase of the thickness the binding energy module first increases and then decreases up to the value of an infinite crystal.