Studies of the Dielectric Constant of Thin Film Bismuth Nanowire Samples Using Optical Reectometry
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Studies of the Dielectric Constant of Thin Film Bismuth Nanowire Samples Using Optical Re ectometry M. R. Black ) , Y.-M. Lin ) , S. B. Cronin ) , O. Rabin ), M. P adi) , M. S. Dresselhaus Department of EECS, Massachusetts Institute of Tec hnology, Cambridge, MA Department of Physics, Massach usetts Institute of Technology, Cambridge, MA Department of Chemistry, Massach usetts Institute of Technology, Cambridge, MA Currently on leav e from MIT Electronic mail: [email protected] a;e
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ABSTRACT Arrays of 10 to 120 nm diameter single crystalline bismuth nanowires hav e been formed inside amorphous alumina templates. Since bismuth has a small e ective mass compared to other materials, signi cant quantum mechanical con nement is expected to occur in wires with diameter less than 50nm. The subbands formed b y quantum con nement cause in teresting modi cations to the dielectric function of bismuth. This study measures the dielectric function of bismuth nanowires in an energy range where the e ects of quantum con nement are predicted (0.05 to 0.5 eV). Using F ourier transforminfrared re ectometry, the dielectric constant as a function of energy is obtained for the alumina/bismuth composite system. E ective medium theory is used to subtract the e ect of the alumina template from the measurement of the composite material, thus yielding the dielectric function of bismuth nanowires. A strong absorption peak is observed at 1000 cm 1 in the frequency dependent dielectric function in the photon energy range measured. The dependence of the frequency and intensity of this oscillator on incident light polarization and wire diameter are reviewed. In addition, the dependence of the optical absorption on antimony and tellurium doping of the nanowires are reported.
Introduction Scientists and engineers use the e ects of low dimensions as another means of tailoring a material to a desired application [1, 2, 3, 4]. In order for the design of a material to be optimized, the key parameters of the low dimensionality need to be measured and compared to theoretical calculations. This paper expands on previous work of looking at quantum con nement in bismuth nanowires b y optical re ection. Bismuth is an ideal material for quantum con nement studies. First of all, when a material's size approaches the de Broglie wa v elengthof its free carriers, the carriers become quantum con ned. The electron and hole energy bands then split into subbands characteristic of a low dimensional material. F ora given sample size, the energy separation of these subbands increase as the carriers' e ective mass decreases. Since bismuth has small electron and hole e ective mass tensors at the L-point (the mass components m v ary from 0.001m0 to 0.26 m0 depending on the crystalline direction), the separation between subbands is signi cant ev enat sample dimensions as large as 40 nm. Bismuth also has a large mean free path, 250 nm at 300 K[5], which in addition to the small e ective mass is required for quantum con nement. As a result
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