Linköping University Post Print New quantum limits in plasmonic devices

Surface plasmon polaritons (SPPs) have recently been recognized as an important future technique for microelectronics. Such SPPs have been studied using classical theory. However, current state-of-the-art experiments are rapidly approaching nanoscales, and quantum effects can then become important. Here we study the properties of quantum SPPs at the interface between an electron quantum plasma and a dielectric material. It is shown that the effect of quantum broadening of the transition layer is most important. In particular, the damping of SPPs does not vanish even in the absence of collisional dissipation, thus posing a fundamental size limit for plasmonic devices. Consequences and applications of our results are pointed out. Copyright c © EPLA, 2008 The excitation and propagation of surface modes at plasma interfaces have long been important in space physics, magnetic confinement fusion, and laboratory plasma physics [1–4]. Moreover, studies of electron oscillation excitations (surface plasmons, surface plasmon polaritons (SPPs) and magnetoplasmons) [5–7] in nanostructured systems [8–11] have recently attracted much interest. It has been found that at condensed matter interfaces, such plasmon excitations could be of crucial importance in future electronic components [12–15], the latter referred to as plasmonic devices [16,17]. Furthermore, the field of quantum plasmas has recently developed rapidly [18]. This field started already in the 1960’s, when Pines studied the excitation spectrum of quantum plasmas [19], with a high density and a low temperature as compared to normal plasmas. In such systems, the finite width of the electron wave function makes quantum tunnelling effects crucial, leading to an altered dispersion relation. Since then, a number of theoretical studies of quantum statistical properties of plasmas have been published (see, e.g., ref. [20] and references therein). For example, Bezzerides and DuBois presented a kinetic theory for the quantum electrodynamical properties of nonthermal plasmas [21], while Hakim and Heyvaerts used a covariant Wigner function approach (a)E-mail: [email protected] (b)Also at Department of Physics, Linköping University SE-58183 Linköping, Sweden, EU. for relativistic quantum plasmas [22]. It has also been shown that, under certain conditions, plasmas can display remarkable properties due to the quantum properties of the constituents. Thus, there are quantum multistream instabilities [23,24], quantum modified Zakharov dynamics [25,26] together with soliton formation and nonlinear quantum interactions [27,28], spin effects on the plasma dispersion [29,30], quantum plasma turbulence [31], ferromagnetic plasma behaviour and Jeans-like instabilities due to quantum effects [32]. Many of the current studies involving quantum plasmas are motivated by the rapid experimental progress and development of new materials, e.g., nanostructured materials [33] and quantum wells [34], and the laboratory realization of ultracold plasmas [35] and experimental demonstration of quantum plasma oscillations in Rydberg systems [36]. Quantum dispersive effects can also be important for diagnostics of inertial fusion plasmas [37]. In parallel, the field of plasmonics and its use of surface waves, such as surface plasmon polaritons (SPPs), has emerged as a new route to electronic devices [38]. In this letter, methods from quantum plasma physics are used for analyzing SPPs in nanoscale systems. In particular, we determine the dispersion relation for quantum SPPs on a conductor-dielectric interface. It is shown that wave function dispersion introduces an intrinsic damping, even in the absence of collisions. Such damping is due to the irreversible propagation of resonant plasmons towards lower density regions. This is of importance for the