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

Shinichi Watanabe, Masahiro Yoshita, Shyun Koshiba, Hidefumi Akiyama

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)5924-5936
Number of pages13
JournalJapanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers
Volume41
Issue number10
Publication statusPublished - 2002 Oct
Externally publishedYes

Fingerprint

Semiconductor quantum wires
Optical transitions
Wave functions
quantum wires
optical transition
wave functions
Polarization
valence
orbitals
polarization
envelopes
Hamiltonians
ridges
Mirrors
mirrors
Electrons
symmetry

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

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title = "Polarization dependence of the optical interband transition defined by the spatial variation of the valence p-orbital Bloch functions in quantum wires",
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 Schr{\"o}dinger 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.",
keywords = "Finite element method, Heterostructure, III-V semiconductor, Luttinger Hamiltonian, Optical property, Polarization, Quantum wire, Transition matrix element",
author = "Shinichi Watanabe and Masahiro Yoshita and Shyun Koshiba and Hidefumi Akiyama",
year = "2002",
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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

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