Electron states in curved quantum structures with varying radius

The influence of size and shape is investigated for quantum-dot electronic states and intra-band oscillator strengths adapting a method originally due to Stevenson. The present work solves the one-band envelope-function problem for conduction-band eigenstates in the framework of k ⋅ p theory using general curved coordinates. The eigenstates found are subsequently employed to express intra-band oscillator strengths and emphasis is given to the dependence of oscillator strengths on quantum-dot size and shape. We finally provide four simple examples.