Far Infrared Magneto-Optical Absorption in Small Bismuth Particles
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FAR INFRARED MAGNETO-OPTICAL ABSORPTION IN SMALL BISMUTH PARTICLES ROBERT P. DEVATY AND RALPH E. SHERRIFF University of Pittsburgh, 100 Allen Hall, Pittsburgh, PA 15260 ABSTRACT A semiclassical model based on the measured properties of the free carriers in bulk bismuth successfully accounts for far infrared (Z < 60 cm-') magnetic field dependent resonances observed in free-standing powders of -0.5 um diameter Bi particles prepared by inert gas evaporation. In earlier work, we found that particles with each of the three principal axes aligned parallel to the applied field were required to explain the data. The conclusion that these particles are bulk-like in nature remains valid when an ensemble of randomly oriented particles is treated using a Monte Carlo method.
INTRODUCTION The semimetal bismuth is an important model system for metals physics [1-3] because its characteristic energies are small. This feature is especially important for magneto-optical studies [4-20], since interesting phenomena are readily observable with laboratory magnetic fields. Although Bi is metallic, far infrared (FIR) transmission studies are possible because the electrons are easily driven into the extreme quantum limit in the presence of a magnetic field [7]. Much is known about the anisotropic free-carrier properties of bulk Bi. A small particle of Bi in a magnetic field is an example of the problem of the gyrotropic sphere [21]. Other examples include powdered semiconductors [22,23], electron-hole droplets [24], and 3Dconfined semiconductor microstructures [25]. The theory of the interaction of electromagnetic radiation with a gyrotropic sphere has attracted recent interest [21,23,26]. Even in the long wavelength limit, there are subtleties in this problem that do not exist in the Mie theory [27]. If the Bi particles are sufficiently small, interesting size induced phenomena may be observed. Bi should be a favorable system for the observation of quantum size effects (QSE's) by direct absorption between discrete levels. An estimate of the energy level spacing at the Fermi energy of a metallic particle is given by the Kubo [28] gap 6=4EF/3nV, where EF is the Fermi energy, n the 7 3 28 carrier density, and V the volume of the particle. For Bi, EF=0.0 eV and n=-1.0X101 cm- for 3 Figure particle diameter in Angstroms. . x is the each electron pocket, so b[cm-']=5.75x1O9/(x[A]) 1 shows the size dependence of the Kubo delta for Bi and several other metals. This simple estimate suggests that the effects of discrete levels may be observable in the far infrared for Bi particles several hundreds of Angstroms in diameter, for a sufficiently monodisperse size distribution. From this perspective, a small Bi particle may resemble a zero dimensional semiconductor quantum dot [29-31]. A second argument, not specifically based on QSE's, can be made to support the possibililty of interesting size dependent behavior in Bi particles of -200 A diameter. If one takes the carrier densities fos bulk Bi and inverts them to estimate the volume per carrier, the
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