Radial breathing mode in silicon nanowires: Anab initiostudy

Abstract

We study by means of first-principles calculations the phonon spectrum of silicon nanowires oriented along the ͗110͘ direction with a diameter ranging from 1.0 to 2.4 nm. We analyze in particular the evolution of the radial breathing mode frequency as a mean to calibrate experimentally the diameter through Raman analysis. Remarkably, the results of elastic theory analysis are very reliable even in the limit of ultrathin wires with significant deviations from the cylindrical shape.The compatibility of silicon nanowires ͑SiNWs͒ with silicon based technology is certainly an important factor explaining the large amount of work devoted to the synthesis and characterization 1 of these semiconducting 1D systems with promising applications in electronic, 2 optoelectronic or photovoltaic 3 devices, molecular recognition, and sensing 4 or thermoelectricity. 5 An important tool for the characterization of wires is provided by the analysis of phonon modes. The wealthiness of information drawn from such measurements has been largely exemplified in the case of carbon nanotubes with a particular emphasis on the study of the diameter dependent Ramanactive radial breathing mode. 6 While much ab initio simulations have addressed topics related to structural, electronic, or transport properties, studies of vibrational modes with first-principle approaches remain limited to a recent study of the phonon band structure of SiNWs, 7 complementing previous analysis based on empirical potential calculations of the optical modes 8 and Raman active modes. 9 In the present Brief Report, we study by means of ab initio calculations the radial breathing mode of small freestanding hydrogen-passivated SiNWs grown along the ͗110͘ direction. The diameter of the studied SiNWs ranges from 1.0 to 2.4 nm. We provide in particular a scaling law as a function of the NWs radius for the radial breathing mode ͑RBM͒ frequency and compare the associated radial displacements with elastic theory analysis.Our calculations are performed within the densityfunctional theory using pseudopotentials and the PBE exchange-correlation functional. 10 For wires up to 62 atoms per cell, we performed plane-wave-based calculations with the PWSCF package 11 with a kinetic energy cutoff of 25 Ry using ultrasoft pseudopotentials. These calculations were repeated using the SIESTA code 12 with a double-zeta polarized basis for Si and double-zeta basis for H. The reduced size of the localized basis allowed further to study a larger wire comprising 144 atoms per cell with a diameter of 2.4 nm. The sampling of the one-dimensional ͑1D͒ Brillouin zone ͑BZ͒ was performed with 16 k points. Cell sizes along the wire axis and atomic positions were relaxed with a 0.1 eV/ Å threshold criteria. A minimal distance of 10 Å was kept between periodic image wires in the transverse direction.We plot in Figs. 1͑a͒-1͑d͒ the symbolic representation of the wires studied in the present work. Since the wires are not perfectly cylindrical, the diameter is defined following Niquet and co-workers in Ref. 13...

Lattice Vibrational Modes and their Frequency Shifts in Semiconductor Nanowires

“…Several unique phonon properties of nanostructures have been identified; − however, it is difficult to assess the accuracy of these model calculations. More recent first-principles calculations revealed interesting properties of the phonon modes of SiNWs in the low-frequency regime, such as the radial breathing mode (RBM) and a significant reduction of group velocity . Those confined modes are expected to provide essential structural information, but the RBM and its Raman activity will inevitably decay for thicker NWs because of weaker quantum confinement there.…”

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Synthesis and optical properties of II–VI 1D nanostructures

“…Eqn (1) indicates that the radial breathing mode frequency follows a 1/R behavior, which is similar to the results of RBMs in CNTs. Recent ab initio calculation shows the frequency evolution of RBM can be fitted by the following empirical power law for silicon nanowires: 116,117 u RBM ðdÞ ¼…”