Recombination of Correlated Electron–Hole Pairs With Account of Hot Capture With Emission of Optical Phonons

Kirkin, R.; Mikhaĭlin, V. V.; Vasil’ev, A. N.

doi:10.1109/tns.2012.2194306

Cited by 71 publications

(57 citation statements)

References 15 publications

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“…Then the operatorsΘ x,y induce the space shift and yield the particular solution (8) for the initial function f (x, y) = δ(x, y), which evolves in the Gaussian as follows:…”

Section: Propagation Of a Heat Surge With Fourier Heat Diffusion Typementioning

confidence: 99%

“…A good description of the major numerical methods is given, for example, in [1][2][3][4][5][6]. Here they allow numerical modelling of complicated physical processes [7][8][9][10][11][12][13][14][15][16][17][18][19], including multidimensional heat transfer in rectangles and cylinders [20][21][22][23]. However, proper understanding of the solutions and of the obtained results can be best done when they are obtained in analytical form.…”

Section: Introductionmentioning

confidence: 99%

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Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Zhukovsky

2016

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Abstract:We studied physical problems related to heat transport and the corresponding differential equations, which describe a wider range of physical processes. The operational method was employed to construct particular solutions for them. Inverse differential operators and operational exponent as well as operational definitions and operational rules for generalized orthogonal polynomials were used together with integral transforms and special functions. Examples of an electric charge in a constant electric field passing under a potential barrier and of heat diffusion were compared and explored in two dimensions. Non-Fourier heat propagation models were studied and compared with each other and with Fourier heat transfer. Exact analytical solutions for the hyperbolic heat equation and for its extensions were explored. The exact analytical solution for the Guyer-Krumhansl type heat equation was derived. Using the latter, the heat surge propagation and relaxation was studied for the Guyer-Krumhansl heat transport model, for the Cattaneo and for the Fourier models. The comparison between them was drawn. Space-time propagation of a power-exponential function and of a periodic signal, obeying the Fourier law, the hyperbolic heat equation and its extended Guyer-Krumhansl form were studied by the operational technique. The role of various terms in the equations was explored and their influence on the solutions demonstrated. The accordance of the solutions with maximum principle is discussed. The application of our theoretical study for heat propagation in thin films is considered. The examples of the relaxation of the initial laser flash, the wide heat spot, and the harmonic function are considered and solved analytically.

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“…Then the operatorsΘ x,y induce the space shift and yield the particular solution (8) for the initial function f (x, y) = δ(x, y), which evolves in the Gaussian as follows:…”

Section: Propagation Of a Heat Surge With Fourier Heat Diffusion Typementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Zhukovsky

2016

Axioms

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“…The use of pulsed lasers to measure transient behavior in the picosecond regime 8 and to induce specific ionization densities allowing measurement of nonlinear processes at carrier densities found in the gamma ray induced electron tracks 9 is another. There has been commensurate progress in the theoretical understanding of energy deposition and subsequent transport and recombination along the ionized tracks [10][11][12][13][14][15][16][17][18] .…”

Section: -4mentioning

confidence: 99%

Coupled rate and transport equations modeling proportionality of light yield in high-energy electron tracks: CsI at 295 K and 100 K; CsI:Tl at 295 K

Bizarri

et al. 2015

Phys. Rev. B

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A high-energy electron in condensed matter deposits energy by creation of electron-hole pairs whose density generally increases as the electron slows, reaching the order of 10 20 eh/cm 3 near the end of its track. The subsequent interactions of the electrons and holes include nonlinear rate terms and transport as first hot and then thermalized carriers in the nanometer-scale radial dimension of the track. Charge separation and strong radial electric fields occur in a material such as CsI with contrasting diffusion rates of self-trapped holes and hot electrons. Eventual radiative recombination has a nonlinear relation to the primary electron energy because of these interactions. This socalled intrinsic nonproportionality of electron response limits achievable energy resolution of a given scintillation radiation detector material. We use a system of coupled transport and rate equations to describe a pure host (3 equations) and one dopant (4 more equations per dopant). Applying it first to the experimentally well-characterized system of CsI and CsI:Tl in this work, we use results of picosecond absorption spectroscopy, interband z-scan measurements of nonlinear rate constants, and other experiments and calculations to determine most of the more than 20 rate and transport coefficients required for modeling. The model is solved in a track environment approximated as cylindrical and is compared to the proportionality curve and total light yield of undoped CsI at temperatures of 295 K and 100 K, as well as thallium dopant in CsI:Tl at 295 K. With this degree of validation, the space-and time-distributions of carriers and excitons, both untrapped and trapped, are examined within the model to gain an understanding of the main competitions controlling the nonproportionality of response.

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“…Modeling of the thermalization stage in alkali halides has been extensively developed recently. 15 First-principle calculations using the Monte Carlo method can give the energy distribution of secondary excitations 4,5 . It was shown that peculiarities of the electron-hole recombination strongly depend on their respective spatial distribution at the end of the thermalization stage 16 .…”

Section: Introductionmentioning

confidence: 99%

Kinetic Model of Energy Relaxation in CsI:A (A = Tl and In) Scintillators

et al. 2015

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A model of energy relaxation in alkali halide scintillators doped with Tl-like activators is presented. Interaction between thermalized charge carriers, their diffusion, and capture by traps are considered. The model of energy relaxation suggested in the work includes essential electron excited states in alkali halides doped with Tl-like activators. Self-trapping of holes occurs in alkali halides at LNT, giving rise to creation of self-trapped excitons (STEs). Thallium-like activator impurity can act both as an electron or a hole trap. Once both of the charge carriers are trapped by the dopant, activator recombination channel comes to action. The model is verified using CsI classical scintillation crystals doped with thallium and indium ions in a range of concentrations from 10–4 to 10–1 mol %. Temperature dependences of the STE and the activator-induced emission yield are measured as a function of the activator concentration under continuous X-ray excitation. A system of rate equations is used to simulate the applicability of the model under different excitation conditions. Evaluation of the parameters of the system is done for a numerical solution. The model of energy relaxation suggested allows to explain energy losses in CsI:A scintillators in a 10–300 K temperature range.

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Recombination of Correlated Electron–Hole Pairs With Account of Hot Capture With Emission of Optical Phonons

Cited by 71 publications

References 15 publications

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Coupled rate and transport equations modeling proportionality of light yield in high-energy electron tracks: CsI at 295 K and 100 K; CsI:Tl at 295 K

Kinetic Model of Energy Relaxation in CsI:A (A = Tl and In) Scintillators

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