ISSN 1063-7397, Russian Microelectronics, 2008, Vol. 37, No. 6, pp. 373–381. © Pleiades Publishing, Ltd., 2008.
Original Russian Text © E.V. Zavitaev, A.A. Yushkanov, 2008, published in Mikroelektronika, 2008, Vol. 37, No.6, pp. 429–438.
The electrical behavior of conducting objects whose
characteristic linear dimension is comparable with the
electron mean free path differs greatly from that of bulk
objects made of the same material .
Dingle  calculated the electrical conductivity of a
circular wire of radius much less than the length that is
exposed to a stationary electric ﬁeld (without experi-
Other workers [3–7] addressed the case of a mag-
netic ﬁeld. The calculations involved solving the Boltz-
mann equation for conduction electrons in a metal.
Manykin et al.  investigated quantum-mechanical
effects associated with the interaction between elec-
trons and an alternating electromagnetic ﬁeld.
These topics are of relevance to microelectronics as
it uses such wires extensively.
This paper calculates a distribution function for the
linear response of electrons in a circular homogeneous
wire to an alternating electric ﬁeld aligned with the axis
of symmetry of the wire. The calculation is made
within transport theory. The distribution function is
used to derive a relation of the admittance to wire
radius, ﬁeld frequency, and electron reﬂectance.
2. FORMULATION OF THE PROBLEM
We consider a circular nonmagnetic-metal wire of
much smaller than length
that experiences an
alternating electric ﬁeld aligned with its axis of symme-
try. The radius is assumed to be smaller than the skin
depth, which allows us to neglect the skin effect.
The electric ﬁeld is assumed to be uniform in space
and sinusoidal in time:
The resultant high-frequency current density in the wire
is denoted by
We are interested in the case where
is at most
comparable with the electron mean free path
metal. This leads to a relationship between
is essentially nonlocal. To describe it, we will write an
approximate transport equation for the degenerate
Fermi gas of electrons.
be the equilibrium Fermi distribution
function, and f
be a small departure from f
the electric ﬁeld. When the ﬁeld is sufﬁciently weak, we
are the electronic charge, velocity, and
relaxation time, respectively [9–11].
, where f
electronic energy and effective mass, respectively. Let
us take the approximation
High-Frequency Admittance of a Thin Circular Metal Wire
E. V. Zavitaev and A. A. Yushkanov
Moscow State Forest University, Mytishchi-5, Moscow oblast, Russia
Received October 31, 2007
—The high-frequency admittance is calculated of a linear metal wire with circular cross section in the
case where the radius is much less than the length. Different values of electron specularity are considered. Par-
ticular attention is given to limiting cases. Calculated data are compared with published experimental results.
The respective specularities of copper and silver are evaluated on this basis.
PACS numbers: 78.67.-n
MICRO- AND NANOSTRUCTURE