Geometry-induced localization phenomena in semiconductor quantum-dot heterostructures

Conduction-band electrons of semiconductor heterostructures described using the k⇒·p⇒ theory obey, for wide-bandgap semiconductors, the one-band effective-mass equation. We present, based on the one-band effective-mass equation, electron-state solutions for a quantum-dot heterostructure composed of two material layers (A and B) and identify localization properties of the groundstate. In particular, we show that the groundstate of two-material layer cylindrical quantum-dot systems can be localized in either material A or B depending on the dimensions of the nanostructure. A structure which is axially stacked (configuration A-B-A) has a certain critical radius below which the electron becomes localized in material A if the total axial length is big enough (A is assumed to be the material with the highest conduction-band edge). Similarly, a structure which is radially stacked (configuration B-A) has a certain critical (axial) length below which the electron becomes localized in the high conduction-band edge material A if the radius is big enough. Although results are presented for cylindrical-shaped heterostructure semiconductors, similar localization inversion of the groundstate may occur in other geometries such as rectangular-shaped quantum-dot heterostructures.