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. 2024 Dec 28;14(1):30810.
doi: 10.1038/s41598-024-81346-6.

Numerical proceeding to calculate impurity states in 2D semiconductor heterostructures

Volodymyr Akimov  1   2 , Viktor Tulupenko  3   4 , Roman Demediuk  5 , Anton Tiutiunnyk  6 , Carlos A Duque  3 , Alvaro L Morales  3 , David Laroze  7 , Miguel Eduardo Mora-Ramos  8
Affiliations

Numerical proceeding to calculate impurity states in 2D semiconductor heterostructures

Volodymyr Akimov et al. Sci Rep. .

Abstract

The article provides and discusses details of numerical proceeding for the expansion method to calculate energy positions and wave functions of the localized and resonant electronic states emerging in quantum well-type semiconductor nanostructures because of perturbation of confined states by the Coulomb potential of the hydrogenic impurity center. Effective mass approximation is used. Several excited both resonant and non-resonant states are calculated and classified for the case of a simple rectangular GaAs/AlGaAs quantum well. Results are compared to the ones in literature.

Keywords: Expansion method; Hydrogenic impurity states; Semiconductor heterostructures.

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Conflict of interest statement

Declarations. Competing interests: The authors declare no competing interests.

Figures

Fig. 1
Fig. 1
Modified determinant DM of the matrix M for GaAs/AlGaAs 30 nm-wide rectangular quantum well with barrier height Vb=50Ry as a function of energy in Ry for different values of Rmax. s-levels (m = 0), Rmax=120 (orange squares), 180 (grey diamonds), 240 (light blue triangles), 480 (blue minuses) and 720 nm (green circles).
Fig. 2
Fig. 2
Modified determinant DM GaAs/AlGaAs 30 nm-wide rectangular quantum well with barrier height Vb=50Ry as a function of energy in Ry for different m: m=0 (s, orange squares), m=1 (p, blue triangles), m=2 (d, grey circles), Rmax=240 nm.
Fig. 3
Fig. 3
R-z plots and isosurfaces for squared wave functions of s11, s12, s21 and s22 impurity states. R and z are in nanometers.
Fig. 4
Fig. 4
R-z plots and isosurfaces for squared wave functions of p11, p12, p21 and p22 impurity states. R and z are in nanometers.
Fig. 5
Fig. 5
R-z plot of 18 impurity WFs, the scale in R is the same in all plots. z=−25.25 nm, R = 0.230 nm.
See this image and copyright information in PMC

References

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