Accounting for the Local Field When Determining the Dielectric Loss Spectra of Metals in the Region of the Frequencies of Volume, Surface and Localized Plasmon Oscillations
oleh: Tatiana Perova, Igor Shaganov, Kevin Berwick
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2020-01-01 |
Deskripsi
The optical constant of bulk metal is used to determine the dispersion of the local field under one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) confinement. 3D confinement, expressed as <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>ε</mi> <mn>2</mn> <mrow> <mi>m</mi> <mi>i</mi> <mi>c</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow> <mn>3</mn> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, corresponds to the dielectric loss spectra of spherical particles with a diameter, <i>d</i>, much less than the wavelength of the beam used to measure the spectrum (<i>d</i> << λ). Excellent agreement with the results of Mie theory and experimental data for solid colloids within alkali halide crystals was observed. The function expressed as <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>ε</mi> <mn>2</mn> <mrow> <mi>m</mi> <mi>i</mi> <mi>c</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow> <mn>1</mn> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> allows the measurement of spectral micro-characteristics in the frequency range of the longitudinal collective motion of the free electrons. This corresponds to the spectrum of dielectric losses of bulk plasma oscillations. The function <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>ε</mi> <mn>2</mn> <mrow> <mi>m</mi> <mi>i</mi> <mi>c</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow> <mn>2</mn> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> describes the spectra of the dielectric losses of surface plasma oscillations in thin metal films. It is shown that the peak positions of <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>ε</mi> <mn>2</mn> <mrow> <mi>m</mi> <mi>i</mi> <mi>c</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow> <mn>3</mn> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>ε</mi> <mn>2</mn> <mrow> <mi>m</mi> <mi>i</mi> <mi>c</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow> <mn>2</mn> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <msubsup> <mi>ε</mi> <mn>2</mn> <mrow> <mi>m</mi> <mi>i</mi> <mi>c</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>ω</mi> <mrow> <mn>1</mn> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula> spectra for simple metals, viz. alkali metals as well as Al, Be, Mg, Ga, In, Sn and Si, are in agreement with experimental results from electron-energy-loss spectroscopy and various optical techniques.