### Abstract

A new, explicit, efficient, and meshfree multi-domain spectral method (MDSM) is presented to calculate the eigenstates of arbitrary semiconductor quantum wells (QW). The method is functional expansion based where the quantized energy states are approximated using efficient basis sets and the boundaries are considered using Tau approach. For bounded domains, Chebyshev polynomials and power series are used as the basis sets, while non-orthogonal predefined exponential basis sets are used for the half bounded domains. Many QW structures were studied and the results are compared with published results for validation. The comparisons exhibit the accuracy and efficiency of the presented method. For QWs that can be analyzed analytically, the relative errors in the calculated quantized energy levels are in the order of 10^{- 12} with very small number of bases in few ms.

Original language | English |
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Pages (from-to) | 2501-2505 |

Number of pages | 5 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 374 |

Issue number | 25 |

DOIs | |

Publication status | Published - 31 May 2010 |

Externally published | Yes |

### Fingerprint

### Keywords

- Arbitrary quantum well
- Meshfree method
- Multi-domain spectral method
- Non-orthogonal predefined exponential basis set
- Spectral methods

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Meshfree eigenstate calculation of arbitrary quantum well structures.** / Alharbi, Fahhad.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Meshfree eigenstate calculation of arbitrary quantum well structures

AU - Alharbi, Fahhad

PY - 2010/5/31

Y1 - 2010/5/31

N2 - A new, explicit, efficient, and meshfree multi-domain spectral method (MDSM) is presented to calculate the eigenstates of arbitrary semiconductor quantum wells (QW). The method is functional expansion based where the quantized energy states are approximated using efficient basis sets and the boundaries are considered using Tau approach. For bounded domains, Chebyshev polynomials and power series are used as the basis sets, while non-orthogonal predefined exponential basis sets are used for the half bounded domains. Many QW structures were studied and the results are compared with published results for validation. The comparisons exhibit the accuracy and efficiency of the presented method. For QWs that can be analyzed analytically, the relative errors in the calculated quantized energy levels are in the order of 10- 12 with very small number of bases in few ms.

AB - A new, explicit, efficient, and meshfree multi-domain spectral method (MDSM) is presented to calculate the eigenstates of arbitrary semiconductor quantum wells (QW). The method is functional expansion based where the quantized energy states are approximated using efficient basis sets and the boundaries are considered using Tau approach. For bounded domains, Chebyshev polynomials and power series are used as the basis sets, while non-orthogonal predefined exponential basis sets are used for the half bounded domains. Many QW structures were studied and the results are compared with published results for validation. The comparisons exhibit the accuracy and efficiency of the presented method. For QWs that can be analyzed analytically, the relative errors in the calculated quantized energy levels are in the order of 10- 12 with very small number of bases in few ms.

KW - Arbitrary quantum well

KW - Meshfree method

KW - Multi-domain spectral method

KW - Non-orthogonal predefined exponential basis set

KW - Spectral methods

UR - http://www.scopus.com/inward/record.url?scp=77953293877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953293877&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2010.04.030

DO - 10.1016/j.physleta.2010.04.030

M3 - Article

VL - 374

SP - 2501

EP - 2505

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 25

ER -