Exciton binding energy in a quantum-well wire

Abstract

A model calculation is performed of the ground-state energy of an exciton confined to a quantum-well-wire system as a function of the well's width and depth, using a variational approach. The variational wave functions used in the calculation are taken as the product of the appropriate confining Bessel functions and a hydrogenic (exponential) function. For an infinite confining potential well, the binding energy diverges as the well width decreases, while for a finite confining potential well, the binding energy reaches some peak value and then decreases to its value in the bulk material surrounding the wire. It is also shown that the optical absorption coefficient for a quantum-well wire diverges with decreasing wire size when using an infinite-confining-well model. However, for the finite-well model the coefficient reaches a peak value with decreasing wire size, and then drops to its bulk material value.