For the analysis of ZnO luminescence and the influence of surface plasmon resonance (SPR) on it the simplified
approach is proposed. This approach is based on the set of rate equations (SRE), which describes processes taking part in
the luminescence. The SRE includes the set of parameters that describe processes determining luminescence of an
investigated sample. The proposed approach gives an opportunity for modeling the dependence of radiation intensity on
pumping level and to estimate the values of parameters in SRE. As a result it is possible to make conclusions about
peculiarities of samples and investigated processes. A number of experimental facts can be explained using this SRE, in
particular the proposed approach was applied to consideration of insulating spacer role in ZnO/Ag system. It was shown
that it is possible to interpret experimental results using SRE where values of some parameters depend on the spacer
thickness. The proposed approach can be applied not only to ZnO-based structures but also to other emitters.
For the analysis of ZnO luminescence, a set of rate equations (SRE) is proposed. It contains a set of parameters that characterize processes participating in luminescence: zone–zone excitation, excitons formation and recombination, formation and disappearance of photons, surface plasmons (SP), and phonons. It is shown that experimental ZnO microstructure radiation intensity dependence on photoexcitation levels can be approximated by using SRE. This approach was applied for the analysis of ZnO microfilm radiation with different thicknesses of Ag island film covering. It was revealed that the increase of cover thickness leads to an increase of losses and a decrease of the probability of photon-to-SP conversion. In order to take into account visible emission, rate equations for level populations in the bandgap and for corresponding photons and SPs were added to the SRE. By using such an SRE, it is demonstrated that the form of visible luminescence intensity dependence on excitation level (P) like P1/3, as obtained elsewhere, is possible only if donor–acceptor pairs exist. The proposed approach was also applied for consideration of experimental results obtained in several papers taking into account the interpretation of these results based on assumptions about the transfer of electrons from the defect level in the ZnO bandgap to metal and then to the conduction band.
For the analysis of ZnO luminescence the system of rate equations (SRE) was proposed. It contains a set of parameters that characterizes processes participating in luminescence: zone-zone excitation, excitons formation and recombination, formation and disappearance of photons and surface plasmons (SP). It is shown that experimental ZnO microstructure radiation intensity dependence on photoexcitation level can be approximated by using SRE. Thus, the values of these parameters can be estimated and used for luminescence analysis. This approach was applied for the analysis of ZnO microfilms radiation with different thickness of Ag island film covering. It was revealed that the increase of cover thickness leads to the increase of losses and decrease of probability of photons to SP conversion. In order to take into account visible emission, rate equations for levels populations in band-gap and for corresponding photons and SP were added to SRE. By using such SRE it is demonstrated that the form of visible luminescence intensity dependence on excitation level (P) like P1/3, as obtained elsewhere [1], is possible only in case of donor-acceptor pairs existence. The proposed approach was applied for consideration of experimental results obtained in [5-8] taking into account their interpretation of these results based on assumption about transfer of electrons from defect level in ZnO band-gap to metal and then to conduction band in ZnO. Results of performed calculations using modified SRE revealed that effects observed in these papers can exist under only low pumping level. This result will be experimentally checked later.
In luminescence spectra of certain ZnO films there is a second band in the near-ultraviolet region alongside with an
exciton band. With the increasing of pumping this band intensity increases much faster than the intensity of the exciton
band. It is shown that the above second band is not the so called P-line. It is rather connected with shallow level in ZnO
structures. We suggest interpreting the observed effect with a due account of Burstein-Moss effect. For approximate
modeling of the observed process rate equation system has been formulated. It is demonstrated that it is possible to find
such parameters so that the relevant numerical solution gives a dependence of bands emission intensity ratio on pumping
power that simulates quality wise experimental results.
Time-integrated and time-resolved laser spectra for two zinc oxide complex structures mainly consisting of tetrapods and
structures of nanowire type were investigated under nanosecond pumping. Simplified models of observed lasing modes
are suggested on the basis of multiple total internal reflections and analyzed numerically basing on the experimental
results and using spectrum of single tetrapod from Ref.9.
Early observed peculiarities of ZnO random laser spectra are analyzed. By simplified simulation of lasing time
behavior it is shown that plausible origin of lasing spectra variations from shot to shot can be the fluctuations of the
number of spontaneous photons that can serve as a "seed" for laser effect creation in a certain mode. Such
fluctuations are very significant for spatially overlapping modes. Analysis of a statistics of different line appearance
in the lasing spectra showed that the number of lasing modes in monodisperse sample is less than in polydisperse
ones. This finding can explain why lasing spectra variations are more pronounced in polydisperse samples.
We associate observed large line widths with the existence of several lasing acts during every pumping shot and with
the slight changes of some modes frequencies in the course of each lasing act. Preliminary experimental result confirms such supposition.
Investigations of ZnO random lasers spectra due to single shot of nanosecond pumping were performed using CCD camera Videoscan-285. It was obtained that these spectra essentially differ from lasing spectra under picosecond pumping: as a rule the line widths are significantly larger, often spectra have quite smooth shape; often spectra essentially change from shot to shot in random manner on the same pumping spot. From our point of view it can be the result of many lasing acts appearance during single pumping pulse and of lasing lines frequency changing in every lasing act.
For the purpose of creation of a source of stimulated UV radiation investigations of UV radiation of powders and disordered films of zinc oxide manufactured by different methods were conducted. The samples were pumped by the 3rd harmonics of two-stage Nd: YAG-laser with pulse duration -10 ns. Maximum density of energy of pumping pulses was about 480 mJ/cm2. Spectra of spontaneous emission were registered at 300 and 77K. With some of our powdered samples we achieved lasing at 300K. The threshold values of pumping energy density occurred to be higher than that under picosecond pumping for more than two orders of magnitude. Peculiarities of different samples lasing are demonstrated and discussed. Unfortunately we did not yet achieve lasing in the samples of disordered films investigated.
Simplified method of eigenmodes simulation in random media based on numerical solution of the stationary wave equation for two-dimensional (2D) medium with a random distribution of dielectric permittivity is suggested. By means of discretization the wave equation can be reduced to the system of homogeneous linear equations that includes parameter α=(2πb/λ)2, where b is the spacing between the nodes of discretization, λ - the wavelength. The values of a (and corresponding b/λ) for every mode were determined from condition of zero value of the system determinant. The relative field amplitudes in all discretization nodes were calculated with this a. 2D random medium was simulated by matrix whose elements randomly take on two different values. One of them corresponds to dielectric permittivity of the material particles, the other - to permittivity of the spacings between them. Under the assumption made, elements of such matrix represent material particles and spacings between them correspondingly, quantity b - particles size. All calculations were made using MATLAB. Different variants of disordered (and ordered) media were examined. It was shown that localized modes exist only in disordered systems with sufficiently large filling ratio and in a limited range of ratio b/λ .
Simplified method of eigenmodes simulation in random media based on numerical solution of the stationary wave equation for two-dimensional (2D) medium with a random distribution of dielectric permittivity is suggested. By means of discretization the wave equation can be reduced to the system of homogeneous linear equations that includes parameter α=(2πb/λ)2, where b is the spacing between the nodes of discretization, λ - the wavelength. The values of α (and corresponding b/λ) were determined as eigenvalues of this system of linear equations. The relative field amplitudes in all discretization nodes i.e. eigenvectors were calculated with this α. 2D random medium was simulated by matrix whose elements randomly take on two different values. One of them corresponds to dielectric permittivity of the material particles, the other - to permittivity of the spaces between them. Under the assumption made, elements of such matrix represent material particles and spaces between them, quantity b - particles size. All calculations were made using MATLAB. Different variants of disordered (and ordered) media were examined. It was shown that localized modes exist only in disordered systems and in a limited range of ratio b/λ . The dependence of modes character on the value of filling ratio and dielectric permittivity is estimated. Some results for one- and three-dimensional media are represented.
Since the intrinsic lifetime of spontaneous recombination UV radiation in zinc oxide amounts less than ~200 ps it is of interest to obtain stimulated UV radiation of powdered ZnO with pumping pulses of nanosecond duration. This will clarify the possibility of quasi-continuous laser radiation in disordered media. At the same time this effect can open the way for working out a cathodoluminescent screen with narrow spectrum and short persistence time. Investigations of UV radiation spectra of powdered zinc oxide and some disordered films were conducted. The samples were pumped by 3-rd harmonics of the two-stage Nd:YAG-laser (λ=355 nm) with pulse duration ~10 ns. Maximum density of energy of pumping pulses was about 160 mJ/cm2. Spectra of spontaneous emission were registered at 300K and 77K. With some of our powdered samples we achieved lasing at 300K. The threshold values of pumping energy density occurred to be higher than that under picosecond pumping approximately for two orders of magnitude. Peculiarities of different samples lasing are demonstrated and discussed. In spectra of the ZnO films investigated at 300K UV band maximum is situated at ~382 nm, while in powders of ZnO this maximum was located at ~389 nm. Besides, in the films the long-wavelength part of the UV band broadens with increase of pumping power.
By expanding the spatial distribution of a dielectric constant in random media into Fourier series, we analyze the assumption that the resonant feedback is provided by the presence of components with spatial periods satisfying the condition of the Braff diffraction. Numerical simulations of random media allow us to predict specific features of eigenfrequencies of lasing modes, which are similar to those obtained in the literature from the numerical solution of the Maxwell equations. Thus, a plausible explanation of the physical nature of frequency selection in random lasers is revealed. Furthermore, using a simplified description of the Bragg feedback, we show why the threshold gain decreases with the increase in the sizes of the active region.
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