New peculiarity in the temperature and size dependence of electron-lattice energy exchange in metal nanoparticles

Abstract

The work is dedicated to the development of the electron-lattice energy exchange theory in metal particles and it dependence of on particle size and electron temperature. We obtained the expressions for the constants of the electron-lattice energy exchange using the quantum-kinetic approach for infinite metal, and compared it with the result of classical kinetic approach. Both methods give the same result. But for the metal particles smaller than the mean free path of electrons, as we show, a quantum-kinetic approach (in its standard form) can not be applied, while the classical approach can be easily generalized to the particle of such sizes.We found a new peculiarity of the electron-lattice energy exchange -its temperature dependence around certain size -"magic size" of metal nanoparticles. Our calculation shown, that this changes of the electron-lattice energy exchange are associated with alteration of acoustic subzones which takes part in energy transfer. The change of the electron temperature can also lead to changes (around the "magic size") in the acoustic subzones, which are involved in energy transfer. As a result, constant of the electron-phonon interaction in nanoparticles can be either much higher or much lower than the corresponding constant for infinite metal. 2 3 4 5 6 7 8

Електрон-Ґратковий Енергообмін І Гарячі Електрони В Острівкових Металевих Плівках

“…The results of computational experiments confirmed the fundamental concepts of the theory of hot electrons in metal island films developed by P.M. Tomchuk with co-authors [2,3,[7][8][9][10][11][12][13][14][15][16]. The appearance of hot electrons in metal island films at relatively low input powers is possible owing to the peculiarities of the energy exchange in those objects.…”

“…Taking the oscillatory character of the electron motion along the axis [see Eq. 5] into account, let us expand (R, ) in the Fourier series in || and the Fourier integral over R ⊥ (the details can be found in works [8,9]):…”

“…In accordance with Eq. (4), the energy spent by the electron on the sound generation (the details of calculation can be found in works [8,9]). For the real part of / , we obtain [8,9] Re…”

“…In works [8,9], it was shown that the Cherenkov mechanism of sound generation by electrons, which is the main channel for the hot-electron relaxation in massive metals, is no more active in metal nanoparticles whose sizes are smaller than a certain critical value. Furthermore, the decrease in the intensity of electron-lattice energy exchange with the reduction of the particle size and its approach to the critical value was found to be not smooth, but quasiperiodic.…”

Integral Equations in the General Theory of Light Absorption and Scattering

“…The electron heating is fa-vored by the features of the electron-lattice energy exchange in small clusters. Those features are reduced to a decrease (in a quasioscillatory way) of the intensity of electron-lattice energy exchange, when the nanocluster sizes diminish [4]. Such a weakening of the energy exchange arises, when the nanoparticle dimensions become smaller than the mean free path of electrons.…”