Abstract

The current theoretical formulations of optical absorption by small metal particles are critically reviewed. Several inconsistencies of the usual dielectric-function calculations are noted, and an improved expression is proposed. The results indicate that optical spectra should have a bearing on the difficult question of the level distribution in small particles. Finite ionization potential effects are shown to be important for small particles and are included in the dielectric formulation. The new results agree with hydrodynamic theories that state that the position of the anomalous absorption peak essentially depends on the degree of diffuseness of the metal-particle surface.

© 1981 Optical Society of America

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  1. J. D. Ganiere, R. Rechsteiner, and M. A. Smithard, "On the size dependence of the optical absorption due to small metal particles," Solid State Commun. 16, 113–115 (1976).
  2. A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765–72 (1966).
  3. L. Sander, "Quantum theory of perpendicular electrical conductivity in a thin metallic film," J. Phys. Chem. Solids 29, 291–94 (1968).
  4. M. Cini and P. Ascarelli, "Quantum size effects in metal particles and thin films by an extended R.P.A.," J. Phys. F. 4, 1998–2008 (1974).
  5. A. A. Lushnikov and A. J. Simonov, "Surface plasmons in small metal particles," Z. Phys. 270, 17–24 (1974).
  6. L. Genzel, T. P. Martin, and U. Kreibig, "Dielectric function and plasma resonances of small metal particles," Z. Phys. B21, 339–46 (1975); L. Genzel and U. Kreibig, "Dielectric function and infrared absorption of small metal particles," Z. Phys. B37, 93–101 (1980).
  7. R. Ruppin and H. Yatom, "Size and shape effects on the broadening of the plasma resonance absorption in metals," Phys. Status Solidi B 74, 647–54 (1976).
  8. C. J. Duthler, S. E. Johnson, and H. P. Broida, "Plasma-resonance scattering from small sodium particles formed in a flowing gas stream," Phys. Rev. Lett. 26, 1236–39 (1971).
  9. S. Norrman et al., "Optical properties of discontinuous gold films," Phys. Rev. B 18, 674–95 (1978).
  10. P. Ascarelli and M. Cini, "Red shift of the surface plasmon resonance absorption by fine metal particles," Solid State Commun. 18, 385–88 (1976).
  11. R. Ruppin, "Optical properties of a metal sphere with a diffuse surface," J. Opt. Soc. Am. 66, 449–53 (1976).
  12. R. Ruppin, "Plasmon frequencies of small metal spheres," J. Phys. Chem. Solids 39, 233–37 (1978).
  13. A. D. Boardman and B. V. Paranjape, "The optical surface modes of metal spheres," J. Phys. F. 7, 1935–45 (1977).
  14. R. Denton, B. Muhlsclegel, and D. Scalapino, "Electronic heat capacity and susceptibility of small metal particles," Phys. Rev. Lett. 26, 707–11 (1971).
  15. M. Cini, "Ionization potentials and electron affinities of metal clusters," J. Catal. 37, 187–90 (1975).
  16. M. Ya. Amusia and N. A. Cherepkov, Case Studies in Atomic Physics 5 (North-Holland, Amsterdam, 1975), p. 140.
  17. A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, London, 1977), p. 22.

1978 (2)

S. Norrman et al., "Optical properties of discontinuous gold films," Phys. Rev. B 18, 674–95 (1978).

R. Ruppin, "Plasmon frequencies of small metal spheres," J. Phys. Chem. Solids 39, 233–37 (1978).

1977 (1)

A. D. Boardman and B. V. Paranjape, "The optical surface modes of metal spheres," J. Phys. F. 7, 1935–45 (1977).

1976 (4)

P. Ascarelli and M. Cini, "Red shift of the surface plasmon resonance absorption by fine metal particles," Solid State Commun. 18, 385–88 (1976).

R. Ruppin, "Optical properties of a metal sphere with a diffuse surface," J. Opt. Soc. Am. 66, 449–53 (1976).

J. D. Ganiere, R. Rechsteiner, and M. A. Smithard, "On the size dependence of the optical absorption due to small metal particles," Solid State Commun. 16, 113–115 (1976).

R. Ruppin and H. Yatom, "Size and shape effects on the broadening of the plasma resonance absorption in metals," Phys. Status Solidi B 74, 647–54 (1976).

1975 (2)

L. Genzel, T. P. Martin, and U. Kreibig, "Dielectric function and plasma resonances of small metal particles," Z. Phys. B21, 339–46 (1975); L. Genzel and U. Kreibig, "Dielectric function and infrared absorption of small metal particles," Z. Phys. B37, 93–101 (1980).

M. Cini, "Ionization potentials and electron affinities of metal clusters," J. Catal. 37, 187–90 (1975).

1974 (2)

M. Cini and P. Ascarelli, "Quantum size effects in metal particles and thin films by an extended R.P.A.," J. Phys. F. 4, 1998–2008 (1974).

A. A. Lushnikov and A. J. Simonov, "Surface plasmons in small metal particles," Z. Phys. 270, 17–24 (1974).

1971 (2)

C. J. Duthler, S. E. Johnson, and H. P. Broida, "Plasma-resonance scattering from small sodium particles formed in a flowing gas stream," Phys. Rev. Lett. 26, 1236–39 (1971).

R. Denton, B. Muhlsclegel, and D. Scalapino, "Electronic heat capacity and susceptibility of small metal particles," Phys. Rev. Lett. 26, 707–11 (1971).

1968 (1)

L. Sander, "Quantum theory of perpendicular electrical conductivity in a thin metallic film," J. Phys. Chem. Solids 29, 291–94 (1968).

1966 (1)

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765–72 (1966).

Amusia, M. Ya.

M. Ya. Amusia and N. A. Cherepkov, Case Studies in Atomic Physics 5 (North-Holland, Amsterdam, 1975), p. 140.

Ascarelli, P.

P. Ascarelli and M. Cini, "Red shift of the surface plasmon resonance absorption by fine metal particles," Solid State Commun. 18, 385–88 (1976).

M. Cini and P. Ascarelli, "Quantum size effects in metal particles and thin films by an extended R.P.A.," J. Phys. F. 4, 1998–2008 (1974).

Boardman, A. D.

A. D. Boardman and B. V. Paranjape, "The optical surface modes of metal spheres," J. Phys. F. 7, 1935–45 (1977).

Broida, H. P.

C. J. Duthler, S. E. Johnson, and H. P. Broida, "Plasma-resonance scattering from small sodium particles formed in a flowing gas stream," Phys. Rev. Lett. 26, 1236–39 (1971).

Cherepkov, N. A.

M. Ya. Amusia and N. A. Cherepkov, Case Studies in Atomic Physics 5 (North-Holland, Amsterdam, 1975), p. 140.

Cini, M.

P. Ascarelli and M. Cini, "Red shift of the surface plasmon resonance absorption by fine metal particles," Solid State Commun. 18, 385–88 (1976).

M. Cini, "Ionization potentials and electron affinities of metal clusters," J. Catal. 37, 187–90 (1975).

M. Cini and P. Ascarelli, "Quantum size effects in metal particles and thin films by an extended R.P.A.," J. Phys. F. 4, 1998–2008 (1974).

Denton, R.

R. Denton, B. Muhlsclegel, and D. Scalapino, "Electronic heat capacity and susceptibility of small metal particles," Phys. Rev. Lett. 26, 707–11 (1971).

Duthler, C. J.

C. J. Duthler, S. E. Johnson, and H. P. Broida, "Plasma-resonance scattering from small sodium particles formed in a flowing gas stream," Phys. Rev. Lett. 26, 1236–39 (1971).

Ganiere, J. D.

J. D. Ganiere, R. Rechsteiner, and M. A. Smithard, "On the size dependence of the optical absorption due to small metal particles," Solid State Commun. 16, 113–115 (1976).

Genzel, L.

L. Genzel, T. P. Martin, and U. Kreibig, "Dielectric function and plasma resonances of small metal particles," Z. Phys. B21, 339–46 (1975); L. Genzel and U. Kreibig, "Dielectric function and infrared absorption of small metal particles," Z. Phys. B37, 93–101 (1980).

Johnson, S. E.

C. J. Duthler, S. E. Johnson, and H. P. Broida, "Plasma-resonance scattering from small sodium particles formed in a flowing gas stream," Phys. Rev. Lett. 26, 1236–39 (1971).

Kawabata, A.

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765–72 (1966).

Kreibig, U.

L. Genzel, T. P. Martin, and U. Kreibig, "Dielectric function and plasma resonances of small metal particles," Z. Phys. B21, 339–46 (1975); L. Genzel and U. Kreibig, "Dielectric function and infrared absorption of small metal particles," Z. Phys. B37, 93–101 (1980).

Kubo, R.

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765–72 (1966).

Lushnikov, A. A.

A. A. Lushnikov and A. J. Simonov, "Surface plasmons in small metal particles," Z. Phys. 270, 17–24 (1974).

Martin, T. P.

L. Genzel, T. P. Martin, and U. Kreibig, "Dielectric function and plasma resonances of small metal particles," Z. Phys. B21, 339–46 (1975); L. Genzel and U. Kreibig, "Dielectric function and infrared absorption of small metal particles," Z. Phys. B37, 93–101 (1980).

Migdal, A. B.

A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, London, 1977), p. 22.

Muhlsclegel, B.

R. Denton, B. Muhlsclegel, and D. Scalapino, "Electronic heat capacity and susceptibility of small metal particles," Phys. Rev. Lett. 26, 707–11 (1971).

Norrman, S.

S. Norrman et al., "Optical properties of discontinuous gold films," Phys. Rev. B 18, 674–95 (1978).

Paranjape, B. V.

A. D. Boardman and B. V. Paranjape, "The optical surface modes of metal spheres," J. Phys. F. 7, 1935–45 (1977).

Rechsteiner, R.

J. D. Ganiere, R. Rechsteiner, and M. A. Smithard, "On the size dependence of the optical absorption due to small metal particles," Solid State Commun. 16, 113–115 (1976).

Ruppin, R.

R. Ruppin, "Plasmon frequencies of small metal spheres," J. Phys. Chem. Solids 39, 233–37 (1978).

R. Ruppin and H. Yatom, "Size and shape effects on the broadening of the plasma resonance absorption in metals," Phys. Status Solidi B 74, 647–54 (1976).

R. Ruppin, "Optical properties of a metal sphere with a diffuse surface," J. Opt. Soc. Am. 66, 449–53 (1976).

Sander, L.

L. Sander, "Quantum theory of perpendicular electrical conductivity in a thin metallic film," J. Phys. Chem. Solids 29, 291–94 (1968).

Scalapino, D.

R. Denton, B. Muhlsclegel, and D. Scalapino, "Electronic heat capacity and susceptibility of small metal particles," Phys. Rev. Lett. 26, 707–11 (1971).

Simonov, A. J.

A. A. Lushnikov and A. J. Simonov, "Surface plasmons in small metal particles," Z. Phys. 270, 17–24 (1974).

Smithard, M. A.

J. D. Ganiere, R. Rechsteiner, and M. A. Smithard, "On the size dependence of the optical absorption due to small metal particles," Solid State Commun. 16, 113–115 (1976).

Yatom, H.

R. Ruppin and H. Yatom, "Size and shape effects on the broadening of the plasma resonance absorption in metals," Phys. Status Solidi B 74, 647–54 (1976).

J. Catal. (1)

M. Cini, "Ionization potentials and electron affinities of metal clusters," J. Catal. 37, 187–90 (1975).

J. Opt. Soc. Am. (1)

J. Phys. Chem. Solids (2)

R. Ruppin, "Plasmon frequencies of small metal spheres," J. Phys. Chem. Solids 39, 233–37 (1978).

L. Sander, "Quantum theory of perpendicular electrical conductivity in a thin metallic film," J. Phys. Chem. Solids 29, 291–94 (1968).

J. Phys. F. (2)

M. Cini and P. Ascarelli, "Quantum size effects in metal particles and thin films by an extended R.P.A.," J. Phys. F. 4, 1998–2008 (1974).

A. D. Boardman and B. V. Paranjape, "The optical surface modes of metal spheres," J. Phys. F. 7, 1935–45 (1977).

J. Phys. Soc. Jpn. (1)

A. Kawabata and R. Kubo, "Electronic properties of fine metallic particles II. Plasma resonance absorption," J. Phys. Soc. Jpn. 21, 1765–72 (1966).

Phys. Rev. B (1)

S. Norrman et al., "Optical properties of discontinuous gold films," Phys. Rev. B 18, 674–95 (1978).

Phys. Rev. Lett. (2)

R. Denton, B. Muhlsclegel, and D. Scalapino, "Electronic heat capacity and susceptibility of small metal particles," Phys. Rev. Lett. 26, 707–11 (1971).

C. J. Duthler, S. E. Johnson, and H. P. Broida, "Plasma-resonance scattering from small sodium particles formed in a flowing gas stream," Phys. Rev. Lett. 26, 1236–39 (1971).

Phys. Status Solidi B (1)

R. Ruppin and H. Yatom, "Size and shape effects on the broadening of the plasma resonance absorption in metals," Phys. Status Solidi B 74, 647–54 (1976).

Solid State Commun. (2)

J. D. Ganiere, R. Rechsteiner, and M. A. Smithard, "On the size dependence of the optical absorption due to small metal particles," Solid State Commun. 16, 113–115 (1976).

P. Ascarelli and M. Cini, "Red shift of the surface plasmon resonance absorption by fine metal particles," Solid State Commun. 18, 385–88 (1976).

Z. Phys. (1)

A. A. Lushnikov and A. J. Simonov, "Surface plasmons in small metal particles," Z. Phys. 270, 17–24 (1974).

Z. Phys. B (1)

L. Genzel, T. P. Martin, and U. Kreibig, "Dielectric function and plasma resonances of small metal particles," Z. Phys. B21, 339–46 (1975); L. Genzel and U. Kreibig, "Dielectric function and infrared absorption of small metal particles," Z. Phys. B37, 93–101 (1980).

Other (2)

M. Ya. Amusia and N. A. Cherepkov, Case Studies in Atomic Physics 5 (North-Holland, Amsterdam, 1975), p. 140.

A. B. Migdal, Qualitative Methods in Quantum Theory (Benjamin, London, 1977), p. 22.

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