Langhammer Christoph, Kasemo Bengt, Zorić Igor
Department of Applied Physics, Chalmers University of Technology, 412 96 Göteborg, Sweden.
J Chem Phys. 2007 May 21;126(19):194702. doi: 10.1063/1.2734550.
Localized surface plasmons (LSPs) of metallic nanoparticles decay either radiatively or via an electron-hole pair cascade. In this work, the authors have experimentally and theoretically explored the branching ratio of the radiative and nonradiative LSP decay channels for nanodisks of Ag, Au, Pt, and Pd, with diameters D ranging from 38 to 530 nm and height h=20 nm, supported on a fused silica substrate. The branching ratio for the two plasmon decay channels was obtained by measuring the absorption and scattering cross sections as a function of photon energy. The former was obtained from measured extinction and scattering coefficients, using an integrating sphere detector combined with particle density measurements obtained from scanning electron microscopy images of the nanoparticles. Partly angle-resolved measurements of the scattered light allowed the authors to clearly identify contributions from dipolar and higher plasmonic modes to the extinction, scattering, and absorption cross sections. Based on these experiments they find that absorption dominates the total scattering cross section in all the examined cases for small metallic nanodisks (D<100 nm). For D>100 nm absorption still dominates for Pt and Pd nanodisks, while scattering dominates for Au and Ag. A theoretical approach, where the metal disks are approximated as oblate spheroids, is used to account for the trends in the measured cross sections. The field problem is solved in the electrostatic limit. The spheroid is treated as an induced dipole for which the dipolar polarizability is calculated based on spheroid geometry and the (bulk) dielectric response function of the metal the spheroid consists of and the dielectric medium surrounding it. One might expect this model to be inappropriate for disks with D>100 nm since effects due to the retardation of the incoming field across the metallic nanodisk and contributions from higher plasmonic modes are neglected. However, this model describes quite well the energy dependence of the dipolar resonance, the full width at half maximum, and the total extinction cross section for all four metallic systems, even when 100<D<500 nm, indicating that the combined contribution of the effects not included in the model is small for the systems studied. For this reason the authors have extended the use of the same model to study scattering/absorption branching ratios. The main conclusions include the following. (i) Both the magnitude and peak position in extinction cross section are well accounted for by the model. (ii) The branching ratio for radiative and nonradiative decay is reasonably well accounted for. (iii) The model fails to account for the correct magnitudes of the measured absorption and scattering cross sections for larger particles in the case of Ag and Au. Possible reasons for this discrepancy are discussed.
金属纳米颗粒的局域表面等离子体激元(LSPs)通过辐射或电子 - 空穴对级联的方式衰变。在这项工作中,作者通过实验和理论研究了直径D在38至530纳米之间且高度h = 20纳米、支撑在熔融石英衬底上的Ag、Au、Pt和Pd纳米盘辐射和非辐射LSP衰变通道的分支比。通过测量吸收和散射截面作为光子能量的函数来获得两个等离子体衰变通道的分支比。前者是通过测量消光系数和散射系数得到的,使用积分球探测器并结合从纳米颗粒的扫描电子显微镜图像获得的颗粒密度测量值。对散射光的部分角度分辨测量使作者能够清楚地识别偶极和更高等离子体模式对消光、散射和吸收截面的贡献。基于这些实验,他们发现对于小金属纳米盘(D <100纳米),在所有研究的情况下吸收占总散射截面主导。对于D> 100纳米,Pt和Pd纳米盘吸收仍占主导,而Au和Ag则是散射占主导。一种理论方法,即将金属盘近似为扁球体,用于解释测量截面的趋势问题。场问题在静电极限下求解。将扁球体视为一个感应偶极子,并根据扁球体的几何形状以及构成扁球体的金属和周围介质的(体)介电响应函数来计算偶极极化率。对于D> 100纳米的盘,人们可能会认为这个模型不合适,因为忽略了穿过金属纳米盘的入射场的延迟效应以及更高等离子体模式的贡献。然而,即使对于100 <D <500纳米,该模型也能很好地描述所有四种金属系统的偶极共振能量依赖性、半高宽和总消光截面,这表明在所研究的系统中,模型未包含的效应的综合贡献很小。因此,作者扩展了使用相同模型来研究散射/吸收分支比。主要结论如下:(i)模型很好地解释了消光截面的大小和峰值位置。(ii)辐射和非辐射衰变的分支比得到了合理的解释。(iii)在Ag和Au的情况下,对于较大颗粒,该模型未能正确解释测量的吸收和散射截面的大小。讨论了这种差异的可能原因。