### Abstract

A quantum mechanical method based on the Kramers-Heisenberg dispersion relation is used to evaluate the dielectric response of small metal particles, and thereby to determine the influence of particle size on the widths of the plasmon resonance line shapes. Several different particle shapes are considered (sphere, cylinder, rectangular prism, spherical shell, and cylindrical shell) and for each shape a free electron Schrödinger equation is used to determine conduction band energies and dipole matrix elements. The main emphasis in this work is on particle sizes large enough that only the first order deviations from the infinite size limit are important, and for such sizes we find that the size dependent contribution to the width can be expressed in terms of an effective length L_{eff}. This effective length is found to depend on the direction of the external field relative to the particle symmetry axes, and on the shape of the particle. For compact shapes, L_{eff} is accurately approximated by 0.65 L_{av} along each principal axis, where L_{av} is the ratio of particle volume to its projected area along the relevant axis. Comparison with previous classical and semiclassical calculations is considered, and for spherical particles, we find good agreement with the classical surface scattering model, differing by about 16%. More significant differences are found for other shapes, most notably because the classical theory ignores the dependence of resonance width on the orientation of the field relative to the particle.

Original language | English |
---|---|

Pages (from-to) | 6130-6139 |

Number of pages | 10 |

Journal | Journal of Chemical Physics |

Volume | 79 |

Issue number | 12 |

Publication status | Published - 1983 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*79*(12), 6130-6139.

**Plasmon resonance broadening in small metal particles.** / Kraus, W. A.; Schatz, George C.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 79, no. 12, pp. 6130-6139.

}

TY - JOUR

T1 - Plasmon resonance broadening in small metal particles

AU - Kraus, W. A.

AU - Schatz, George C

PY - 1983

Y1 - 1983

N2 - A quantum mechanical method based on the Kramers-Heisenberg dispersion relation is used to evaluate the dielectric response of small metal particles, and thereby to determine the influence of particle size on the widths of the plasmon resonance line shapes. Several different particle shapes are considered (sphere, cylinder, rectangular prism, spherical shell, and cylindrical shell) and for each shape a free electron Schrödinger equation is used to determine conduction band energies and dipole matrix elements. The main emphasis in this work is on particle sizes large enough that only the first order deviations from the infinite size limit are important, and for such sizes we find that the size dependent contribution to the width can be expressed in terms of an effective length Leff. This effective length is found to depend on the direction of the external field relative to the particle symmetry axes, and on the shape of the particle. For compact shapes, Leff is accurately approximated by 0.65 Lav along each principal axis, where Lav is the ratio of particle volume to its projected area along the relevant axis. Comparison with previous classical and semiclassical calculations is considered, and for spherical particles, we find good agreement with the classical surface scattering model, differing by about 16%. More significant differences are found for other shapes, most notably because the classical theory ignores the dependence of resonance width on the orientation of the field relative to the particle.

AB - A quantum mechanical method based on the Kramers-Heisenberg dispersion relation is used to evaluate the dielectric response of small metal particles, and thereby to determine the influence of particle size on the widths of the plasmon resonance line shapes. Several different particle shapes are considered (sphere, cylinder, rectangular prism, spherical shell, and cylindrical shell) and for each shape a free electron Schrödinger equation is used to determine conduction band energies and dipole matrix elements. The main emphasis in this work is on particle sizes large enough that only the first order deviations from the infinite size limit are important, and for such sizes we find that the size dependent contribution to the width can be expressed in terms of an effective length Leff. This effective length is found to depend on the direction of the external field relative to the particle symmetry axes, and on the shape of the particle. For compact shapes, Leff is accurately approximated by 0.65 Lav along each principal axis, where Lav is the ratio of particle volume to its projected area along the relevant axis. Comparison with previous classical and semiclassical calculations is considered, and for spherical particles, we find good agreement with the classical surface scattering model, differing by about 16%. More significant differences are found for other shapes, most notably because the classical theory ignores the dependence of resonance width on the orientation of the field relative to the particle.

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M3 - Article

VL - 79

SP - 6130

EP - 6139

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 12

ER -