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

doi:10.1143/jjap.41.5924

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 journal › Article › peer-review

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 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
DOIs	https://doi.org/10.1143/jjap.41.5924
Publication status	Published - 2002 Oct
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

General Engineering
General Physics and Astronomy

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10.1143/jjap.41.5924

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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 et al.
In: Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers, Vol. 41, No. 10, 10.2002, p. 5924-5936.

Research output: Contribution to journal › Article › peer-review

Watanabe, S, Yoshita, M, Koshiba, S & Akiyama, H 2002, 'Polarization dependence of the optical interband transition defined by the spatial variation of the valence p-orbital Bloch functions in quantum wires', Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers, vol. 41, no. 10, pp. 5924-5936. https://doi.org/10.1143/jjap.41.5924

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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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AU - Yoshita, Masahiro

AU - Koshiba, Shyun

AU - Akiyama, Hidefumi

PY - 2002/10

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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

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KW - Luttinger Hamiltonian

KW - Optical property

KW - Polarization

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KW - Transition matrix element

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

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Keywords

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