A Drude model fit parameters to the dielectric function of free electron metals - silver (Ag), aluminum (Al), gold (Au), copper (Cu), potassium (K), sodium (Na), platinum (Pt)

A Drude model fit parameters to the dielectric function of free electron metals

Metal plasma [eV/cm-1/PHz] damping [meV/cm-1/THz] source
Ag 9.6*/77430/2.32122.8*/183.9/5.513 Blaber
9.013/72700*/2.18 18/145.2*/4.353 Ordal
9.04*/72920/2.18621.25*/171.4/5.139 Zeman
8.6*/69370/2.0845*/363/10.88 Hooper
Al 15.3*/123000/3.7598.4*/48.27/144.7 Blaber
14.75/119000*/3.57 81.8/660*/19.79 Ordal
12.04*/97110/2.911128.7*/1038/31.12 Zeman
Au 8.55*/69000/2.068 18.4*/148.4/4.449 Blaber
9.026/72800*/2.183 26.7/215*/6.46 Ordal
8.89*/71710/2.1570.88*/571.7/17.14 Zeman
9*/72590/2.17670*/564.6/17.71 Berciaud
8.951/72200/2.165 69.1/557.4/17.94 Grady
7.9*/63720/1.91 / / Kreiter
Cu 7.389/59600*/1.914 9.075/73.2*/8.34 Ordal
8.76*/70660/2.118 95.5*/770.3/23.09 Zeman
K 3.72*/30000/0.8896 18.4*/148.4/4.449 Blaber
Na 5.71*/46100/1.381 27.6*/222.6/6.674 Blaber
5.93*/47830/1.434380*/3065/91.89 Zeman
Pt 5.145/41500*/1.244 69.2/558*/16.73 Ordal

The respective source values are indicated by a star. Conversion between different units performed by using
Spectroscopic Unit Converter

In the case of small nanoparticles, the so-called surface scattering corrections to the metal dielectric function have to be taken into account. Read more about the corrections here.

Note in passing that especially in the visible and near infrared you can arrive at contradicting conclusions when using a Drude fit to the metal data instead of true experimental data.

A spectacular example has been provided in Ref. [9]. It has been demonstrated there that on using a Drude fit to silver data, an optimal lattice structure with the largest complete photonic band gap (CPBG) is a square lattice, whereas on using experimental silver data, an optimal lattice structure with the largest CPBG turns out to be a triangular lattice. The reason behind the above behavior is that CPBG is sensitive to the slope of the dielectric constant in the proximity of zero. One can verify that a Drude fit yields typically much smaller slope compared to the real experimental data.

An additional information can be found here.

Do you also wonder why the experimental data are so much scattered? You are not alone! Some differences in the data may be accounted for by differences in samples preparation. Yet the differences in the data appear to be too big to be explained merely by the differences in samples preparation. Let me know if you find a satisfactorily explanation.

REFERENCES

  1. M. G. Blaber, M. D. Arnold, and M. J. Ford, Search for the Ideal Plasmonic Nanoshell: The Effects of Surface Scattering and Alternatives to Gold and Silver, J. Phys. Chem. C 113(8), 3041–3045 (2009) (see compilation from different sources in Table 1 therein).

  2. N. K. Grady, N. J. Halas, and P. Nordlander, Influence of dielectric function properties on the optical response of plasmon resonant metallic nanoparticles, Chem. Phys. Lett. 399(1-3), 167-171 (2004)

  3. M. H. Hider and P. T. Leung, Nonlocal electrodynamic modeling of fluorescence characteristics for molecules in a spherical cavity, Phys. Rev. B 66, 195106 (2002).

  4. I. R. Hooper and J. R. Sambles, Dispersion of surface plasmon polaritons on short-pitch metal gratings, Phys. Rev. B 65, 165432 (2002).

  5. M. Kreiter, S. Mittler, W. Knoll, and J.R. Sambles, Surface plasmon-related resonances on deep and asymmetric gold gratings, Phys. Rev. B 65, 125415 (2002).

  6. M. A. Ordal, R. J. Bell, R. W. Alexander, Jr., L. L. Long, and M. R. Querry, Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W, Appl. Opt. 24, 4493-4499 (1985) (see compilation from different sources in Table 1 therein).

  7. E. J. Zeman and G. C. Schatz, An accurate electromagnetic theory study of surface enhancement factors for silver, gold, copper, lithium, sodium, aluminum, gallium, indium, zinc, and cadmium, J. Phys. Chem. 91(3), 634-643 (1987) (see compilation from different sources in Table 1 therein).

  8. A. D. Rakic, A. B. Djuri\v{i}c, J. M. Elazar, and M. L. Majewski, Optical Properties of Metallic Films for Vertical-Cavity Optoelectronic Devices, Appl. Opt. 37(22), 5271-5283 (1998).
    (They presented models for the optical functions of 11 metals used as mirrors and contacts in optoelectronic and optical devices: noble metals (Ag, Au, Cu), aluminum, beryllium, and transition metals (Cr, Ni, Pd, Pt, Ti, W). The values for the respective plasma frequencies are summarized in Table 1 therein; the remaining Lorentz-Drude model parameters are summarized in Table 2 therein.)

  9. H. van der Lem and A. Moroz, Towards two-dimensional complete photonic-bandgap structures below infrared wavelengths, J. Opt. A: Pure Appl. Opt. 2, 395-399 (2000) [pdf].

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Alexander Moroz

August 16, 2009 (last updated on April 26, 2010)

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