### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

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

*41*(10), 5924-5936.

**Polarization dependence of the optical interband transition defined by the spatial variation of the valence p-orbital Bloch functions in quantum wires.** / Watanabe, Shinichi; Yoshita, Masahiro; Koshiba, Shyun; Akiyama, Hidefumi.

Research output: Contribution to journal › Article

*Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers*, vol. 41, no. 10, pp. 5924-5936.

}

TY - JOUR

T1 - Polarization dependence of the optical interband transition defined by the spatial variation of the valence p-orbital Bloch functions in quantum wires

AU - Watanabe, Shinichi

AU - Yoshita, Masahiro

AU - Koshiba, Shyun

AU - Akiyama, Hidefumi

PY - 2002/10

Y1 - 2002/10

N2 - 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 px, py, and pz 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.

AB - 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 px, py, and pz 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.

KW - Finite element method

KW - Heterostructure

KW - III-V semiconductor

KW - Luttinger Hamiltonian

KW - Optical property

KW - Polarization

KW - Quantum wire

KW - Transition matrix element

UR - http://www.scopus.com/inward/record.url?scp=0036819286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036819286&partnerID=8YFLogxK

M3 - Article

VL - 41

SP - 5924

EP - 5936

JO - Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes

JF - Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes

SN - 0021-4922

IS - 10

ER -