### Abstract

We developed a method to express wave functions of hole states in semiconductor quantum wire (QWR) structures based on spatial variation of the valence p-orbital Bloch functions, to show how envelope wave functions relate to polarization-dependent interband transition. A wave function of a hole state is obtained solving the Schrödinger equation based on the 4 × 4 Luttinger Hamiltonian, and then recomposed by means of six bases of three p-orbital Bloch functions with two spin components. As a result, the hole wave function is expressed by six envelope wave functions for the six bases. Then, interband optical transition matrix elements with x-, y-, and z-polarizations are separately given by overlap integrals between envelope wave functions of holes for p_{x}, p_{y}, and p_{z} orbitals and those of electrons. We also calculate the wave functions for a modeled ridge QWR structure with mirror symmetry as well as for an asymmetric structure, and discuss the polarization dependence of the optical transition.

Original language | English |
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Pages (from-to) | 5924-5936 |

Number of pages | 13 |

Journal | Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers |

Volume | 41 |

Issue number | 10 |

Publication status | Published - 2002 Oct 1 |

Externally published | Yes |

### Keywords

- Finite element method
- Heterostructure
- III-V semiconductor
- Luttinger Hamiltonian
- Optical property
- Polarization
- Quantum wire
- Transition matrix element

### ASJC Scopus subject areas

- Engineering(all)
- Physics and Astronomy(all)

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## Cite this

*Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers*,

*41*(10), 5924-5936.