Numerical proceeding to calculate impurity states in 2D semiconductor heterostructures

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• Semiconductor nanostructures like quantum wells exhibit unique electronic properties.
• Perturbation by impurity centers significantly alters confined electronic states.
• Understanding these altered states is crucial for designing advanced electronic devices.

Purpose of the Study:

• To present a numerical expansion method for calculating electronic states in quantum wells.
• To investigate localized and resonant electronic states due to impurity potentials.
• To classify excited resonant and non-resonant states in a GaAs/AlGaAs quantum well.

Main Methods:

• Utilized the effective mass approximation.
• Employed a numerical expansion method to solve for energy positions and wave functions.
• Calculated and classified several excited states, including resonant and non-resonant ones.

Main Results:

• Successfully calculated energy positions and wave functions for perturbed electronic states.
• Identified and classified various excited resonant and non-resonant states.
• Provided detailed numerical proceeding for the expansion method.

Conclusions:

• The expansion method is effective for analyzing electronic states in quantum well nanostructures.
• Results align with existing literature, validating the numerical approach.
• The study contributes to the understanding of impurity effects on quantum well electronic properties.