12.3 Surface Plasmon Enhanced GaN-Based LED
273
Wherein, E m, E e represent the dielectric constant of the surrounding dielectric and
metal environment. Im(α) and |α| are the imaginary part and the real part of the
susceptibility. It can be seen from the formula that the scattering cross section is
proportional to the square of the polarizing rate, and the absorption is linear with the
polarizing rate, and the polarizing rate is proportional to the volume of the particles.
Therefore, as the particle size increases, the scattering rate of the LSP increases.
The absorption and scattering of different materials’ LSP can be analyzed through
metal’s band structures. For metal nanoparticles, the absorption of LSP mainly
derives from the excitation of electrons and holes in the metal’s band. For Drude-like
metal, such as Au and Ag, electrons show low inter-band transition activity when
lower than the interband transition threshold, scattering is the main part of dissipation; for Pd and Pt which have large interband transition activity, absorption is the
main part of dissipation.
The thresholds of strong s-d interband activity for Au and Ag are 2.4 and 3.8 eV.
When the energy of LSP is less than the threshold, the interband transition activity
of electrons is low so that the dissipation mainly derives from scattering. When
the energy of LSP is greater than the threshold, dissipation mainly comes from the
absorption caused by the interband transition. For Pt and Pd, the s-band near the
Fermi level overlaps with the d-band so that the activity of the interband transition
is very high through the entire wave band from ultraviolet to near-infrared, which is
why strong non-radiative electron-hole transitions are observed in these metals. Al
is a very interesting metal that combines the characteristics of the above two types
of metals. Al has a strong narrow band transition near the 1.5 eV. When it is lower
or higher than this value, Al shows low interband transition activity, hence relatively
high scattering efficiency.
12.3.1.3 Factors Affecting LSP Resonance Energy
The resonance energy of LSP is affected by factors such as metal material, particle
size, particle shape, dielectric environment and particle spacing. Variation rules may
be generally summarized as follows: (1) generally, as the particle size increases,
the LSP dipole resonance peaks show red shift, and high-order dipole’s resonance
peak appears; (2) the LSP’s resonance peak is very sensitive to the particles’ shape
change. The general rule is that the stronger the circular symmetry of the particle,
the larger the LSP energy is; (3) the larger the refractive index of the dielectric
environment, the smaller the resonance energy of the LSP is; (4) as the particle
spacing decreases, the LSP resonance peak has a red-shift tendency; (5) under the
same dielectric environment, LSP’s resonance energy of three commonly used metals
Ag, Au and Al which have the same particle morphology has following relationship:
Al > Ag > Au.
273
Wherein, E m, E e represent the dielectric constant of the surrounding dielectric and
metal environment. Im(α) and |α| are the imaginary part and the real part of the
susceptibility. It can be seen from the formula that the scattering cross section is
proportional to the square of the polarizing rate, and the absorption is linear with the
polarizing rate, and the polarizing rate is proportional to the volume of the particles.
Therefore, as the particle size increases, the scattering rate of the LSP increases.
The absorption and scattering of different materials’ LSP can be analyzed through
metal’s band structures. For metal nanoparticles, the absorption of LSP mainly
derives from the excitation of electrons and holes in the metal’s band. For Drude-like
metal, such as Au and Ag, electrons show low inter-band transition activity when
lower than the interband transition threshold, scattering is the main part of dissipation; for Pd and Pt which have large interband transition activity, absorption is the
main part of dissipation.
The thresholds of strong s-d interband activity for Au and Ag are 2.4 and 3.8 eV.
When the energy of LSP is less than the threshold, the interband transition activity
of electrons is low so that the dissipation mainly derives from scattering. When
the energy of LSP is greater than the threshold, dissipation mainly comes from the
absorption caused by the interband transition. For Pt and Pd, the s-band near the
Fermi level overlaps with the d-band so that the activity of the interband transition
is very high through the entire wave band from ultraviolet to near-infrared, which is
why strong non-radiative electron-hole transitions are observed in these metals. Al
is a very interesting metal that combines the characteristics of the above two types
of metals. Al has a strong narrow band transition near the 1.5 eV. When it is lower
or higher than this value, Al shows low interband transition activity, hence relatively
high scattering efficiency.
12.3.1.3 Factors Affecting LSP Resonance Energy
The resonance energy of LSP is affected by factors such as metal material, particle
size, particle shape, dielectric environment and particle spacing. Variation rules may
be generally summarized as follows: (1) generally, as the particle size increases,
the LSP dipole resonance peaks show red shift, and high-order dipole’s resonance
peak appears; (2) the LSP’s resonance peak is very sensitive to the particles’ shape
change. The general rule is that the stronger the circular symmetry of the particle,
the larger the LSP energy is; (3) the larger the refractive index of the dielectric
environment, the smaller the resonance energy of the LSP is; (4) as the particle
spacing decreases, the LSP resonance peak has a red-shift tendency; (5) under the
same dielectric environment, LSP’s resonance energy of three commonly used metals
Ag, Au and Al which have the same particle morphology has following relationship:
Al > Ag > Au.