“…It should be noted, that only E 1 symmetry phonons are IR active in s -polarization [ 9 ]. Initial frequencies of E 1 (LO) and E 1 (TO) phonons for GaN and sapphire substrate were taken from the IR reflectance [ 29 ] and Raman scattering [ 6 , 14 ] experiments. Typical values of GaN phonon frequency are ω TO = 560 cm −1 and ω LO = 740 cm −1 .…”
Section: Resultsmentioning
confidence: 99%
“…Considering the lack of native GaN substrates, it was shown that using sapphire substrates for epitaxial growth of GaN film is optimal for exploiting in devices which operate at high temperatures. IR reflection spectroscopy studies of hexagonal sapphire [ 14 ] showed a complex spectrum, the shape of which strongly depends on the polarization and the angle of incidence. This greatly complicates measurements and determination of the spectral characteristics of phonon modes and properties of free carriers in thin GaN film grown on sapphire substrates.…”
Infrared (IR) reflectance spectroscopy is applied to study Si-doped multilayer n+/n0/n+-GaN structure grown on GaN buffer with GaN-template/sapphire substrate. Analysis of the investigated structure by photo-etching, SEM, and SIMS methods showed the existence of the additional layer with the drastic difference in Si and O doping levels and located between the epitaxial GaN buffer and template. Simulation of the experimental reflectivity spectra was performed in a wide frequency range. It is shown that the modeling of IR reflectance spectrum using 2 × 2 transfer matrix method and including into analysis the additional layer make it possible to obtain the best fitting of the experimental spectrum, which follows in the evaluation of GaN layer thicknesses which are in good agreement with the SEM and SIMS data. Spectral dependence of plasmon-LO-phonon coupled modes for each GaN layer is obtained from the spectral dependence of dielectric of Si doping impurity, which is attributed to compensation effects by the acceptor states.
“…It should be noted, that only E 1 symmetry phonons are IR active in s -polarization [ 9 ]. Initial frequencies of E 1 (LO) and E 1 (TO) phonons for GaN and sapphire substrate were taken from the IR reflectance [ 29 ] and Raman scattering [ 6 , 14 ] experiments. Typical values of GaN phonon frequency are ω TO = 560 cm −1 and ω LO = 740 cm −1 .…”
Section: Resultsmentioning
confidence: 99%
“…Considering the lack of native GaN substrates, it was shown that using sapphire substrates for epitaxial growth of GaN film is optimal for exploiting in devices which operate at high temperatures. IR reflection spectroscopy studies of hexagonal sapphire [ 14 ] showed a complex spectrum, the shape of which strongly depends on the polarization and the angle of incidence. This greatly complicates measurements and determination of the spectral characteristics of phonon modes and properties of free carriers in thin GaN film grown on sapphire substrates.…”
Infrared (IR) reflectance spectroscopy is applied to study Si-doped multilayer n+/n0/n+-GaN structure grown on GaN buffer with GaN-template/sapphire substrate. Analysis of the investigated structure by photo-etching, SEM, and SIMS methods showed the existence of the additional layer with the drastic difference in Si and O doping levels and located between the epitaxial GaN buffer and template. Simulation of the experimental reflectivity spectra was performed in a wide frequency range. It is shown that the modeling of IR reflectance spectrum using 2 × 2 transfer matrix method and including into analysis the additional layer make it possible to obtain the best fitting of the experimental spectrum, which follows in the evaluation of GaN layer thicknesses which are in good agreement with the SEM and SIMS data. Spectral dependence of plasmon-LO-phonon coupled modes for each GaN layer is obtained from the spectral dependence of dielectric of Si doping impurity, which is attributed to compensation effects by the acceptor states.
“…In the particular simple case of the non-radiative transition between two separate states, the non-radiative transition rate τ nr −1 is given by 15,16 where 〈 n ( T )〉 is the thermal average occupation number of ω co energy phonons, ω co being the cutoff vibrational energy in the crystal, (measured 25 as 908 cm −1 ), C nr is Burshtein’s multi-phonon non-radiative coefficient factor, which has been theoretically calculated 15 aswhere is the reduced Planck constant, c is the vacuum speed of light constant, e is the elementary charge value, N c is the number of atoms occupying the primitive unit cell (correspondingly forming the ligand for each embedded ion), n is the ion host matrix refractive index, is the average atomic mass in the unit cell, ω co is the cut-off angular frequency of the matrix vibrations (phonons), E g is the energy gap between two initial and final separated states, D is the characteristic dissociation energy of a Morse-type configuration potential 26 (related to the primitive unit cell vibrating in free-space at ω co angular frequency), υ , defined as υ ≡ E g / ω co represents the number of ω co phonons involved in the non-radiative transition. The 〈 n ( T )〉 quantity in Eq.…”
Section: Resultsmentioning
confidence: 99%
“…6. The following basic material parameters of Ti:sapphire were used: = 20.3922 amu, N c = 10, ω co = 908 cm −1 25 , n = 1.761, and (0) assumed as 0.276 (a fit at T → 0 K; correspondingly D (0) = 3,285 cm −1 ). Other process parameters are listed in Table 2.Figure 6Semi-logarithmic plot of the non-radiative fluorescence decay rate τ nr −1 (T) of Ti 3+ ions in the sapphire matrix as a function of 1000/T.…”
We have measured the fluorescence quantum efficiency in Ti3+:sapphire single crystals between 150 K and 550 K. Using literature-given effective fluorescence lifetime temperature dependence, we show that the zero temperature radiative lifetime is (4.44 ± 0.04) μs, compared to the 3.85 μs of the fluorescence lifetime. Fluorescence lifetime thermal shortening resolves into two parallel effects: radiative lifetime shortening, and non-radiative transition rate enhancement. The first is due to thermally enhanced occupation of a ΔE = 1,700 cm−1 higher (top) electronic state of the upper multiplet, exhibiting a transition oscillator strength of f = 0.62, compared to only 0.013 of the bottom electronic state of the same multiplet. The non-radiative rate relates to multi-phonon decay transitions stimulated by the thermal phonon occupation. Thermal enhancement of the configuration potential anharmonicity is also observed. An empiric expression for the figure-of-anharmonicity temperature dependence is given as (T) = (0)(1 + β exp(−ℏωco /kBT )), where (0) = 0.276, β = 5.2, ℏωco = 908 cm−1, and kB is the Boltzmann constant.
“…According to specific symmetry, crystals with different optical properties can be classified into three catagories: cubic crystal, uniaxial crystal and biaxial crystal. For uniaxial crystal, the two refracted lights propagate in it are known as ordinary ray ( o ray) and extraordinary ray ( e ray), which are the subjects widely studied [ 3 , 4 , 5 , 6 ].…”
Mid-infrared reflection spectra of
c
- and
m
-plane bulk AlN show a reststrahlen band related to the formation of phonon polaritons. However, it is worth noting that there are additional hump- and spike-shaped peaks in the spectra, which cannot be explained by the phonon-polaritons model applicable to optically isotropic crystals. Here, considering the existence of quasiphonons in wurtzite crystals, we suppose that the extra peaks result from the generation of quasiphonon polaritons (QPPs) induced by the coupling between photon and quasi-transverse optical phonon. On the basis of this point, a QPPs model applicable to optically anisotropic wurtzite crystals is developed, which successfully explains the reststrahlen band of bulk AlN. Besides, on the ground of our model, a series of reststrahlen band of bulk AlN under various configurations is also predicted and presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
