Abstract
The fractional-dimensional approach, in which the real semiconductor heterostructure system is substituted by an effective isotropic environment with a fractional dimension, was used in the study of ground and excited excitonic states in GaAs-(Ga,Al)As quantum wells. The fractional-dimensional formalism was extended to include the possibility of dealing with excited states and varying effective masses across the heterostructure interfaces, with the fractional dimension chosen in a systematic way. Theoretical fractional-dimensional results for ground-state -like exciton states in GaAs-(Ga,Al)As quantum wells were shown to be in good agreement with previous detailed calculations and recent experimental measurements. Moreover, theoretical results within the fractional-dimensional scheme were found in excellent agreement with the recent experimental high-resolution spectroscopic studies on excited-exciton states of shallow quantum wells with Al concentration in the range of 1–4.5 %.
- Received 1 December 1997
DOI:https://doi.org/10.1103/PhysRevB.58.4072
©1998 American Physical Society