Terahertz Conductivity of Silver Nanoparticles Abstract: The electrical conductivity for bulk metal is described by the well-known Drude model. As the size of the metal is reduced to the nanometer scale however, the energy levels become discrete, rather than continuous. The average spacing between adjacent energy levels in a metal nanoparticle is called the Kubo gap, and is related to the Fermi energy of the metal and the size of the nanoparticle. For instance, in a silver nanoparticle of 3-nm diameter containing ~10 3 atoms, the Kubo gap is around 5-10 meV. Therefore, at room temperature when the thermal energy is greater than this gap, the electrical conductivity will be the same as in bulk metal. As the temperature is lowered however, the Kubo gap becomes significant and the nanoparticle becomes an insulator. Although the DC properties of this metal-to-insulator transition are well understood, the experimental observations and theoretical description for AC conductivity are much less comprehensive. The AC conductivity of silver nanoparticles will be measured in an interesting frequency range that corresponds with the Kubo gap of the nanoparticles. Conductivity will be measured using terahertz time-domain spectroscopy based on a mode-locked laser. Aaron Shojinaga with Jie Shan Department of Physics, Case Western Reserve University Introduction: Metal nanoparticles are small clusters of metal, less than 100 nm in size. Although metal nanoparticles have been used in various scientific and other fields for some time, their physical and electronic properties are still not fully understood. The potential applications for metal nanoparticles include use in nanoelectronics, electronics with components of nanometer scale. Detailed understanding of the electrical properties of these nanoparticles is crucial in developing nanoelectronics. If the size of a metal cluster is less than the de Broglie wavelength of an electron, conduction electrons will be confined to certain allowed energy levels. The average spacing between allowed energy levels is called the Kubo gap. The effect of the Kubo gap will not be apparent at room temperature, because the thermal energy is greater than this energy gap. In this case, the nanoparticles have metallic conductivity. If the thermal energy is less than the Kubo gap, however, the nanoparticle conductivity should be like an insulator. The Kubo gap for a 3 nm diameter silver nanoparticle is around 5-10 meV, which corresponds to electromagnetic radiation with frequencies around 1-2 THz. Terahertz time- domain spectroscopy can be used to study the conductivity in the frequency range of the Kubo gap. By measuring the frequency-dependent conductivity as the temperature is varied, the transition from metallic to insulator conductivity and the effect of the Kubo gap can be observed. Methods: Terahertz time-domain spectroscopy is used to measure the electric field of terahertz radiation as a function of time. Time-domain spectroscopy allows for recovery of amplitude and phase information of the terahertz signal. By measuring the signal after it has passed through the nanoparticle sample and comparing to a reference signal, the frequency-dependent optical properties of the sample can be calculated. Ultrashort laser pulses generated from a mode-locked Ti:sapphire laser are used to generate and detect terahertz radiation. Terahertz radiation is emitted when these laser pulses strike a GaAs semiconductor. The THz radiation is detected using a commercially available photoconductive antenna. The nanoparticle composite sample is placed between one set of parabolic mirrors, where the terahertz radiation is focused to a small point. Figure 1: Experimental set up. Silver nanoparticle composites are created by mixing a silver nitrate solution with polyvinyl alcohol and evaporating the mixture until a thin film remains. The resulting film contains silver nanoparticles suspended in a polymer matrix. Results: The terahertz signals were measured as a function of time and the FFT was computed to retrieve the frequency dependence of the signals. Figure 2: Terahertz signal in time domain. Figure 3: FFT of terahertz signal. The absorption coefficient (k) and refractive index (n) of the films were calculated from the frequency-dependent signals. Figures 3 and 4: Absorption coefficient and refractive index of nanoparticle films. Conclusions and Future Work: The optical properties of silver nanoparticle films were measured in a range corresponding to the Kubo gap of the nanoparticles. Further measurements must be made in order to extract the conductivity of the nanoparticles themselves from that of the films. The next step is repeat the measurements at different temperatures in order to observe a transition to insulator conductivity. Further optimizations to the terahertz set-up might be necessary to achieve a signal-to-noise ratio large enough to observe the effects of the Kubo gap. In particular, there are several noticeable spikes in the terahertz spectrum that are due to absorption by water vapor in the air. The resolution in the vicinity of these absorption peaks can be increased by removing water vapor from the air. Acknowledgements: I would like to thank my advisor, Jie Shan for guidance in the concept and execution of my project. I also thank the graduate students in my lab, Brian Kubera, Chris Ryan, and Xia Chen, for providing assistance and technical support. References: 1. Kubo. J. Phys. Soc. Jpn. 17 (1962). 2. C.N.R. Rao, G.U. Kulkarni, P.J. 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