Exciton binding energy in an infinite potential semiconductor quantum well-wire heterostructure

An interacting electron-hole pair in a quantum well-wire is studied within the framework of the effective-mass approximation. An expansion to a 1 dimensional, quantum well model is presented to include another confinement dimension for a quasi-2 dimensional, quasi-1 dimensional quantum well-wire heterostructure. The technique is applied to an infinite well-wire confining potential. The envelope function approximation is employed in the approach, involving a three parameter variational calculation in which the symmetry of the component of the wave function representing the relative motion is allowed to vary from the one- to the two- and three-dimensional limits. Results to such a numerical calculation are presented. Quantitative comparisons with previous calculations for quantum wells is made (in the wire limit where Lz → ∞) to find a good agreement between finite and infinite potential models up to a size of 100 Å.