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Analysis of plasmonic properties of heavily doped semiconductors using full band structure calculations
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10.1063/1.4795339
/content/aip/journal/jap/113/11/10.1063/1.4795339
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/11/10.1063/1.4795339

Figures

Image of FIG. 1.
FIG. 1.

Electron and hole concentrations in Si calculated as a function of the relative Fermi energy eV. The carrier concentrations are calculated for eV. The inset is the Si band structure for which we have calculated the carrier densities.

Image of FIG. 2.
FIG. 2.

Plasma frequency of Si calculated as a function of the relative Fermi energy, . The solid green curve is calculated in the effective mass approximation. The solid black curve is a calculation based on the full band structure at room temperature , and the dashed curve is the same, but at 0 K. The inset shows a zoom near the conduction band edge.

Image of FIG. 3.
FIG. 3.

Calculated plasma frequency as a function of the free carrier concentration. Both n- and p-type dopings are considered. Results are presented for three zincblende semiconductors: Si, Ge, and GaAs.

Image of FIG. 4.
FIG. 4.

Electron and hole concentrations calculated as a function of the relative Fermi energy , for ZnO. The inset display a segment around the Γ-point of the band structure for ZnO used in the calculation of the carrier densities.

Image of FIG. 5.
FIG. 5.

Calculated plasma frequency as a function of the relative Fermi energy . Both polarizations xy and z, perpendicular and parallel to the crystal c-axis, respectively, are presented. The green curve is calculated in the effective mass approximation.

Image of FIG. 6.
FIG. 6.

Calculated (full band structure) plasma frequency as a functionof the free carrier concentrations. Results are presented for both n-and p-type dopings. Two wurtzite semiconductors, ZnO and GaN, are considered.

Image of FIG. 7.
FIG. 7.

Calculated plasma frequency as a function of the free carrier concentrations for ZnO. Results are presented for both n- and p-type dopings. The black curves are full band structure calculations, and the green curves are the result of the effective mass approximation using effective masses of and for electrons and holes, respectively. The magenta curve is the result of the Dirac effective mass model presented in Eq. (14) for eV.

Image of FIG. 8.
FIG. 8.

Band gap narrowing and electron density as a function of the relative fermi energy calculated for ZnO.

Image of FIG. 9.
FIG. 9.

Real and imaginary part of the interband dielectric constant of ZnO for polarization parallel to the crystal c-axis z, where band gap narrowing is taken into account in the calculation. Four different n-type doping concentrations are considered. A phenomenological broadening of eV has been used in the calculation.

Image of FIG. 10.
FIG. 10.

(a) Surface plasmon resonance wavelength calculated as a function of the free carrier density in Si. The solid line is for n-type doping and the dashed line is for p-type doping. (b) Dispersion relation of SPPs on a heavily doped (free carrier density of ) Si film of thickness t = 300 nm. The dashed lines are for p-type doping and the solid lines are for n-type doping. Black curves are the dispersion of long-range modes, green curve are for short-range modes, and magenta lines are the dispersion relation of canonical SPPs, i.e., for . The gray shading is the light cone, which has the dashed black light line as the boundary between propagating and evanescent modes in the surrounding medium. The two horizontal dashed lines are for p- and n-type doping (the lowest is for p-type.) The two insets show the transverse component of the electric field for (1) the long-range mode and (2) the short-range mode.

Image of FIG. 11.
FIG. 11.

(a) The same as in Fig. 10(a) but for ZnO. Results are shown for both polarizations and n- and p-type doping. (b) The same as in Fig. 10(b) but for ZnO, a free carrier concentration of cm , and a film thickness of t = 100 nm. Results are shown for the polarization parallel to the crystal c-axis (z) for both n- and p-type doping.

Tables

Generic image for table
Table I.

Key parameters of the band structures of the zincblende crystals, where is the indirect band gap, is the direct band gap, and is the spin-orbit splitting.

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/content/aip/journal/jap/113/11/10.1063/1.4795339
2013-03-18
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Analysis of plasmonic properties of heavily doped semiconductors using full band structure calculations
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/11/10.1063/1.4795339
10.1063/1.4795339
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