ISSN 1063-7397, Russian Microelectronics, 2009, Vol. 38, No. 6, pp. 429–433. © Pleiades Publishing, Ltd., 2009.
Original Russian Text © A.N. Tavkhelidze, A.P. Bibilashvili, L.B. Jangidze, B. B. Olsen, H. Walitzki, A. Feinerman, 2009, published in Mikroelektronika, 2009, Vol. 38, No. 6,
The latest progress in nanotechnology rendered pos-
sible the fabrication of devices such as superlattices,
quantum wells, and others based on the wave properties
of electrons [1, 2]. Under certain conditions an electron
in a solid can be considered as a wave. The main
requirement is that at least one size of the solid should
be less than the mean free path of the electron. In this
case the electron can move without scattering and may
be treated as a de Broglie wave. Charge and heat trans-
fer is carried out by the electrons that have energies
close to the Fermi energies and the mean free path is
deﬁned for these electrons. Other inner free electrons
with energies much below the Fermi level do not partic-
ipate in the heat or charge transfer since the rules of
quantum mechanics forbid energy exchange with the
medium and, therefore, the mean free path turns out to
be formally inﬁnite. Such electrons will remain ballistic
within relatively large structures. In this work we
employ the wave properties of such electrons in order
to modify the electronic structure of a solid. We analyze
what will happens if periodic indents causing interfer-
ence of de Broglie waves are created on the surface of
a thin ﬁlm.
Free electrons inside a rectangular potential box
with an indented wall were studied. We have shown that
the modiﬁcation of the quantum box wall leads to quan-
tum state depression (QSD), i.e., a decrease in the den-
sity of quantum states of an electron [3, 4]. The Fermi
vector and Fermi energy of a thin metallic ﬁlm
increases and, therefore, its work function decreases.
The results obtained for a quantum box were extrapo-
lated to the case of a thin metallic ﬁlm. We studied the
effects of various irregularities of thin ﬁlms such as
grains within the ﬁlm and the roughness of the ﬁlm sur-
face. Thin metallic Au and Cr ﬁlms were deposited
using the wire explosion method with further conden-
sation on the substrate at low and room temperatures.
For Nb ﬁlms, the electron-beam evaporation method
was used. The decrease in the work function was mea-
sured in the cases of thin ﬁlms of Au, Nb, Cr, and SiO
The experimental results were interpreted as limitations
of the QSD effect by the roughness of the ﬁlm surface.
In this work we use wave properties of ballistic elec-
trons for the modiﬁcation of the electronic structure so
that the work function of the solid could be changed
and decreased. Such materials will be widely used in
devices based on electron emission and electron tunnel-
ing as well in the semiconductor industry.
CALCULATION OF THE FERMI ENERGY USING
THE VOLUME PERTURBATION METHOD
Imagine a rectangular potential box with one modi-
ﬁed wall as shown in Fig. 1. The indents on the wall
have a shape of stripes with depth
refer to the box shown in Fig. 1 as an indented potential
box (RPB) in order to distinguish it form a regular or
usual potential box (UPB). The stationary Schrodinger
Quantum State Depressions in Thin Metal Films
with an Indented Surface
A. N. Tavkhelidze
, A. P. Bibilashvili
, L. B. Jangidze
, B. B. Olsen
, H. Walitzki
, A. Feinerman
Tbilisi State University, Tbilisi, Georgia
NIL Technology Oersteds Plads DTU, Denmark
Avto Metals plc, London, United Kingdom
Department of Electrical and Computer Engineering, University of Chicago, Illinois, USA
Received August 31, 2008
—Modiﬁcation of properties of metal ﬁlms caused by indents on their surface are studied. It is shown
that indents on a ﬁlm surface lead to quantum state depression (QSD), i.e., a decrease in the density of quantum
states of a free electron. The density of the wave vector in the
-space decreases throughout the Fermi sphere.
At the same time, the total number of electrons is conserved, since the metal remains electrically neutral.
According to the Pauli Exclusion Principle, some electrons will occupy states with higher wave numbers. The
Fermi vector and the Fermi energy of the thin metal ﬁlms increase and, therefore, the work function decreases.
Experiments have demonstrated a decrease in the work function of the thin indented ﬁlms of Au, Nb, Cr, and
. Experimental results are qualitatively consistent with the theoretical predictions.