Thermopower Measurements of Arrays of Small Diameter (18-60 nm) Bi Nanowires
T.E. Huber
1
, A. Adeyeye
1
, T. Odunfa
1
, A. Nikolaeva
2,3
, L. Konopko
2,3
, R. Johnson
4
, and M.J.
Graf
4
1
Howard University, 500 College St. N.W., Washington, DC 20059, Washington, DC, 20059
2
Academy of Sciences Moldova, Kishinev, 3018, Moldova
3
International High Magnetic Fields and Low Temperatures Laboratory, Wroclaw, 0000, Poland
4
Boston College, Chestnut Hill, MA, 02467
ABSTRACT
Theoretical work based on one-dimensional (1D) models indicates that Bi wires with
diameter smaller than 50 nm can exhibit superior thermoelectric properties since the density of
states at the Fermi level of a 1D system can be tuned to very high values. Recently, angle-
resolved photoemission spectroscopy (ARPES) studies of Bi surfaces have shown that Bi
nanowires support Rashba spin-orbit surface states, with high carrier densities of
around
2 12
cm 10 5
−
× , that have not been considered in current models of Bi nanowires. According
to our estimates, the sheath of surface charge on Bi nanowires should contribute substantially to
the thermopower of Bi nanowires. We carried out an experimental study of the transport
properties and thermopower of bismuth nanowire arrays (NWA) with wire diameters ranging
between 60 nm and 13 nm to investigate these phenomena. The Rashba interaction is a spin
orbit interaction that is important for surfaces of materials consisting of heavy ion elements;
thermoelectric materials frequently consist of these elements (i.e. PbTe) because they scatter
phonons strongly and consequently form low-thermal-conductivity materials.
I. INTRODUCTION
Nanowire systems have become the focus of intense experimental and theoretical
investigation. The most exciting prospect involves an ideal quantum wire of a diameter d that is
less than the Fermi wavelength, λ
F
, and with the Fermi level chosen such that the nanowire
transport is mediated by a single conduction channel. The properties of such a one-dimensional
quantum wire have been investigated theoretically for the particular case of Bi nanowires by
Hicks and Dresselhaus [1]. In bulk Bi, there is substantial overlap (E
0
~ 40 meV) between the
electron and hole bands. In a Bi nanowire, the effect of quantum confinement is to raise the zero-
point energy of electrons and to lower that of the holes by roughly
2 *
/
2 2
d m h π , where h is
Plancks constant and m* is the corresponding carrier in-plane effective mass transverse to the
wire axis, thus effectively decreasing E
0
. Theoretically, this effect induces a semimetal-to-
semiconductor (SMSC) transition in Bi nanowires. Detailed calculations [2], which assume that
the effective masses do not change upon confinement, show that the SMSC transition occurs at d
~ 50 nm. This theory also shows that the thermopower and the thermoelectric figure of merit of
materials based on small diameter (d< 50 nm) Bi nanowires, such as Bi nanowire arrays (NWA),
are enhanced by this effect.
We have studied NWAs of various diameters using the method based on Shubnikov de
Haas (SdH) oscillations of the magnetoresistance (MR) that measures the spectra of Landau
levels caused by an applied magnetic field [3,4]. The results that we have obtained are shown in
Mater. Res. Soc. Symp. Proc. Vol. 1044 © 2008 Materials Research Society 1044-U03-05