Electron transmission through molecular layers

Article abstract of DOI:10.1021/jp980427g

This article discusses general issues associated with electron transmission through thin molecular films. On the experimental side, we emphasize recent investigations of photoemission through organized organic films adsorbed on metal surfaces. Theoretical and numerical approaches to transmission and tunneling through such films are discussed. We focus on the relation between the structure of the film and its transmission properties. In the experimental work, these are controlled by varying the organic layer, by changing its thickness and by inducing disorder via thermal heating and by depositing mixtures of two molecular types. In numerical simulations of simple model systems, we consider the dimensionality of the process, effect of molecular ordering, and relation between electronic band structure in the film and its transmission properties. It is shown that electron transmission through thin molecular layers constitutes a sensitive tool for investigating molecular film properties in addition to providing a convenient prototype system for the study of electron transport in molecular electronic devices.

Full text of DOI:10.1021/jp980427g

3658
J. Phys. Chem. B 1998, 102, 3658-3668
FEATURE ARTICLE
Electron Transmission through Molecular Layers
R. Naaman* and A. Haran
Department of Chemical Physics, the Weizmann Institute of Science, RehoVot 76100, Israel
†
A. Nitzan, D. Evans, and M. Galperin
School of Chemistry, Tel AViV UniVersity, Tel AViV 69978, Israel
ReceiVed: December 4, 1997; In Final Form: March 10, 1998
This article discusses general issues associated with electron transmission through thin molecular films. On
the experimental side, we emphasize recent investigations of photoemission through organized organic films
adsorbed on metal surfaces. Theoretical and numerical approaches to transmission and tunneling through
such films are discussed. We focus on the relation between the structure of the film and its transmission
properties. In the experimental work, these are controlled by varying the organic layer, by changing its
thickness and by inducing disorder via thermal heating and by depositing mixtures of two molecular types.
In numerical simulations of simple model systems, we consider the dimensionality of the process, effect of
molecular ordering, and relation between electronic band structure in the film and its transmission properties.
It is shown that electron transmission through thin molecular layers constitutes a sensitive tool for investigating
molecular film properties in addition to providing a convenient prototype system for the study of electron
transport in molecular electronic devices.
1
. Introduction
through thin molecular films adsorbed on suitable substrates.
Such processes can be realized in several ways. A typical
experiment of this type is electron photoemission through
adsorbed molecular layers. Here the signal is the (angle- and
velocity-resolved) transmitted electron flux as a function of
incident photon energy, molecular film thickness, adsorbate, and
substrate types and temperature. A closely related experiment
Electron transfer, a fundamental chemical process underlying
all redox reactions, has been under experimental and theoretical
study for many years.1 The process involves a donor and
acceptor pair, a solvent affecting fluctuations in the donor and
acceptor electronic energies, intramolecular nuclear modes of
the donor and the acceptor, and the electronic coupling
responsible for the transfer. The different roles played by these
aspects-of the process and the way they affect qualitative and
quantitative aspects of the electron transfer process have been
repeatedly discussed in the past half-century. These kinds of
processes, which dominate electron transitions in molecular
systems, are to be contrasted with electron transport in the solid
statesmetals and semiconductors. These two domains of
physical/chemical phenomena overlap in the field of electro-
chemistry, where the fundamental process is interfacial electron
transfer between a molecule or an ion in solution and an
electronically conducting solid. In recent years we have seen
the emergence of a new field of study, involving molecular
4
is low-energy electron transmission (LEET) where a mono-
chromatic electron beam hits an adsorbed molecular layer from
the vacuum side; the transmission is monitored via the current
generated in the conducting substrate. The same experimental
setup can be used to study reflection. Both transmission and
reflection are studied as functions of the incident electron energy,
substrate type, and characteristics of the molecular layer.
Relevant information for lower energy regimes may also be
obtained by monitoring current vs voltage in contacts made of
5
two metal electrodes separated by a molecular spacer or in
6
scanning tunneling microscopy, STM, where a surface scan
of the current vs bias voltage can be measured as a function of
2
,3
“
wires” connecting metal or semiconductor contacts.
Here
film thickness (i.e., tip-substrate separation). An older tech-
7
the traditional molecular view of electron transfer between donor
and acceptor species gives rise to a novel view of the molecule
as a current-carrying conductor, and observables such as
electron-transfer rates and yields are replaced by the conductivi-
ties of such molecular junctions or, more generally, by a
current-voltage relationship.
nique, inelastic tunneling spectroscopy, is used to obtain
information on nuclear motions in the barrier by observing their
effect on the electron-tunneling process.
The purpose of the experimental work described below is to
study electron transmission through adsorbed molecular layers
and the physical factors controlling it: the initial energy input
This feature article deals with a related but somewhat different
type of electron-transfer process: the transmission of electrons
(photon energy in case of photoemission, electron beam energy
in LEET experiments), the substrate work function as affected
by the adsorbed molecular layer, the chemical nature of the
adsorbed layer, its thickness, structure, and the temperature. We
†
Present address: Department of Chemistry, University of New Mexico,
Albuquerque, NM 87131.
S1089-5647(98)00427-1 CCC: $15.00 © 1998 American Chemical Society
Published on Web 04/22/1998

Feature Article
J. Phys. Chem. B, Vol. 102, No. 19, 1998 3659
note that photoemission, which is the main tool used by our
group, and LEET supplement each other in an interesting way:
in LEET we control the energy and direction of the incident
electron beam, while in photoemission we can resolve the energy
and direction of the transmitted signal. Both types of experi-
ments look at electron transmission through thin films at positive
(relative to vacuum) electron energies. From the theoretical
point of view both processes, as well as the other electron
transmission processes mentioned above, are controlled by
similar physical factors: those which affect the magnitude of
the electronic coupling and determine the transmission prob-
ability.
From the theoretical viewpoint, our aim is to understand the
interrelationship between the layer structure and chemical
composition and between its transmission properties. In
particular we will argue that besides specific effects related to
the detailed properties of particular layers and molecules, there
are some generic issues: order vs disorder, effects of band
structure and band gaps in the layer, resonance effects, and the
relation between different observables. Understanding of these
generic effects on electron transmission is the purpose of the
theoretical work described below.
Figure 1. (a) A double well and (b) its barrier part, used in the text to
demonstrate the relation between the decay of a prepared state and a
scattering process. (c) and (d) are the left- and right-side structures
whose eigenstates are used as zero-order states in the treatment of the
transmission problem.
In the next sections experimental and theoretical backgrounds
are given followed by descriptions of the experimental and
computational methods. In sections 6 and 7 the experimental
and numerical results are presented, respectively, followed by
the discussion.
electrodes with OOTF spacers was measured. By the nature
of such experiments, the dependence of the process on the
electron energy cannot be monitored. Moreover, such processes
involve in principle both minority and majority carriers and are
therefore not easy to control and to interpret. Finally, the effect
on the film resistivity of possible pinholes in the organic film
makes quantitative analysis uncertain. The photoemission work
described below overcomes some of these difficulties by
focusing on electrons as majority carriers and by providing the
possibility for energy resolution in the outgoing beam.
2. Experimental Background
The effect of adsorbates on photoelectrons emitted from
surfaces has been studied for almost a century.8,9 These
experiments were partially motivated by their practical ramifica-
tions whereby the surface work function was modified by the
1
0,11
adsorbate.
Recently, with the development of tunable UV
3
. Theoretical Background
light sources, the field of energy-resolved photoelectron spec-
troscopy has been developed.12 The photoelectron energy
distribution was measured for electrons produced from a Pt-
While the experimental part of the present article focuses on
photoemission through adsorbed molecular layers, all electron-
transfer and -transmission phenomena mentioned in section 1
are controlled by similar physical factors. This section briefly
outlines the corresponding theoretical approaches and the
relations between them. Broadly speaking we may distinguish
between processes for which lifetimes, rates, (more generally
the time evolution), or yields are the main observables and those
which monitor fluxes or currents. The latter group may be
further divided into processes that measure current-voltage
relationships, mostly near equilibrium, and those that monitor
the nonequilibrium flux. The latter may be observed as a
transient following optical pulse excitation or (ideally) as a
steady-state signal caused by a constant incident photon or
electron beam.
The relation between these different observables is easily
illustrated using the simple well/barrier model shown in Figure
1. Figure 1a depicts a simple model of an asymmetric double
well, characterized by two rectangular wells bounded from the
outside by infinite potential walls and separated from each other
by a rectangular barrier of height V and width D. Viewed as a
model for an initial value problem, the system is assumed to
be at time t ) 0 in an eigenstate of the well depicted in Figure
1c, which is identical to the left well of Figure 1a except that
the barrier is continued to infinity on the right. This initial state
interacts with states associated with the well on the right, which
may be approximated by eigenstates of the well of Figure 1d.
We expect an exponential decay, exp(-Γt), of the initial state
in the limit where the width, L2, of the right well becomes
1
3
(
111) surface covered with several layers of water. It was
found that the transmission probability decreases exponentially
with increasing number of water layers but is independent of
the energy of the electrons. Similarly, LEET experiments were
performed on solid water.14 Less attention has been given to
the effect of organic adsorbate on the efficiency of photoelectron
emission, and only a few works on the subject have been
1
5,16
published.
Electron transmission through organic thin films condensed
on metal substrates has been investigated in the past mainly by
17
low-energy electron-transmission (LEET) spectroscopy. It was
suggested that for films of saturated hydrocarbon chains of
various lengths, the low-energy electron transmission is gov-
erned mainly by the film electronic band structure.1
8,19
In other
LEET studies, it has been established that the conduction band
in many alkane layers is at about 0.2-0.8 eV above the vacuum
2
0
level. Also in the case of ordered rare gas and other simple
21
22
molecular layers, the transmission, as well as the reflection
were found to correlate strongly with the band structure of the
corresponding crystals.
Organized organic thin films (OOTFs), which are the subject
of our present experimental studies, have the advantage of being
well-defined in terms of orientation and packing. Owing to their
nature, their thickness can be modified in a controlled manner
with a single-layer resolution. Electron-transport properties of
2
3,24
such films have been studied extensively in the past.
In
those studies, the current versus voltage applied between

3660 J. Phys. Chem. B, Vol. 102, No. 19, 1998
Naaman et al.
infinitely large so that the eigenstates of the corresponding well
in Figure 1d constitute a continuum. Figure 1b shows the
equivalent problem of a barrier identical to that in Figure 1a,
separating two infinite half-spacessa typical model of a
scattering process. An incident particle of energy E, represented
the sizes of the corresponding wells. As they continue into the
barrier region these states decay exponentially with the distance
from the corresponding barrier edge. Obviously these two
groups of states are not orthogonal to each other even though
orthogonality exist within each group. It may be shown that
the effective coupling matrix element Vif to be used in (4) is
given by
-1
1/2
by an incoming wave function exp(ikx) (k ) p (2mE) , where
m is the electron mass) is scattered such that its outgoing
components are At(E) exp(ikx) to the right and Ar(E) exp(-ikx)
to the left of the barrier. The simplest observable is the
V ) 〈i|H|f〉 - E 〈i|f〉
(6)
if
i
2
transmission coefficient T(E) ) |At(E)| . When Figure 1b
Now, evaluating Γi for the model depicted in Figure 1a (with
L2 f ∞), then taking the limit of the resulting rate as L1 f ∞,
we may write the resulting expression in terms of the transmis-
represents a model of a junction connecting two ideal one-
dimensional conductors which lead into electrons reservoirs
characterized by electron chemical potentials µ1 on the left and
µ2 on the right (µ2 - µ1 ) -e∆Φ where e is the electron charge
and ∆Φ ) Φ2 - Φ1 is the electrostatic potential difference
between the reservoirs), the transmission coefficient determines
the conductivity of the junction in the linear response regime
2
8
sion probability. The result is
2
p ki
2
Γ ) |C |
T(Ei)
(7)
i
i
m
25,26
according to the Landauer formula
i.e. µ ) EF)
(for temperature T ) 0,
Note that this result could be obtained simply by postulating
that the decay rate Γ and the transmission probability T are
related by Γ/p ) flux‚T, together with the observation that the
2
I
e
2
flux impinging on the barrier is |Ci| ‚(pki)/m. In the three-
G )
)
T(EF)
(1)
e∆Φ πp
dimensional case one has to sum over all final “decay channels”,
i.e. all possible directions of the transmitted electron. In this
case an equation similar to (7) is obtained, in which the
transmission probability T(E) is replaced by the sum of
transmission probabilities into all final states, i.e., all final
transmitted directions:
where I is the current induced by the potential difference ∆Φ.
The three-dimensional analog of this result is given by the
multichannel Landauer formula27
2
e
G )
N(EF)
(2)
2
πp
p ki
2
2
Γ ) |C |
|S (E )|
(8)
i
i
∑
if
i
where N(E) is the so-called cumulative reaction probability at
energy E. In terms of the transmission amplitudes, Sif(E),
between an incident state i and a transmitted state f, both of
energy E, the cumulative reaction probability is
m
f
Finally consider a photoemission or a LEET experiment. The
simplest models for this experimental situation is a nonequi-
librium steady-state distribution of electrons incident on the
barrier from, say, the left. In a LEET experiment the initial
electron state may be sharply defined in terms of energy and
direction and the monitored signal corresponds to all possible
final states. The monitored signal is therefore proportional to
2
N(E) )
|S (E)|
(3)
∑i ∑f if
Note that Sif is in fact just the scattering matrix between the
incoming and transmitted outgoing free electron states i and f.
Returning to the time evolution of an initially prepared state
i on the left, we consider the limit L2 f ∞, so that the time
evolution is characterized by an exponential decay. The decay
rate Γi is given by the golden rule formula
2
∑ |S (E )| . In the photoemission experiment the initial electron
f
if
i
states span a broad energy range between zero and up to pω -
E , where ω is the exciting photon frequency and E is the
F
F
substrate’s work function. However, energy selection can be
affected by resolving the energy of the transmitted electron.
Assuming that the optical excitation generates an electron
distribution that is uniform in angular space, the monitored signal
2
2
Γi ) 2π |V | δ(E - E ) = 2π(|V | F )
(4)
∑f if
f
i
iF
F E )E
f i
2
is proportional to ∑i|Sif(Ef)| . Thus, the two types of experiments
convey equivalent information and are related to the transmis-
sion probability of the “one-to-all” type. Note, however, that
in reality the angular distribution of the photoelectrons is not
necessarily isotropic, though this probably holds for the low-
energy secondary electrons. For primary electrons this distribu-
tion is determined by the photoexcitation conditions,29 providing
another experimentally controlled variable.
where F denotes the continuum of states {f}, eigenstates of the
right well, characterized by the density of states FF, and where
we have assumed that Vif ) ViF is independent of the level f in
the group of states that conserve energy. (The latter assumption
is rigorously valid in the one-dimensional model of Figure 1a,
while greater care is needed in the analogous three-dimensional
problem). The states {i} and {f} are eigenstates of the zero-
order Hamiltonians associated with the potentials of parts c and
d of Figure 1, respectively, and the use of the weak coupling
expression 4 implies that we consider only energies small
enough relative to the barrier height V. In their respective wells
these states have the general form
We thus see that photoemission through adsorbed molecular
layers, as well as the other electron-transfer and -transmission
processes discussed above, are controlled by electron-transmis-
sion probabilities through the corresponding barriers, e.g., the
simple square barrier of Figure 1b. Evaluating such probabilities
for realistic barriers is obviously much more difficult, and some
numerical approaches are discussed below.
ψ (x) ) 2C sin[k (x - x1(2))]
(5)
i(f)
i(f)
i(f)
4
. Experimental Methods
where x1 and x2 are, respectively, the left edge of the left well
and the right edge of the right well and where the parameters
ki and kf and the normalization parameters Ci and Cf depend on
We have discussed above the interrelation between different
observables associated with electron transmission. Here we

Feature Article
J. Phys. Chem. B, Vol. 102, No. 19, 1998 3661
focus on the experiments carried out in our group: photoemis-
sion through organized organic thin films (OOTFs).
Film Preparation and Characterization. Several types of
OOTFs were prepared. We used, for the work described here,
30
Langmuir Blodgett films. The LB films were deposited using
a Nima 611, GB trough and transferred either to a quartz
microscope slide coated with 150 nm thick silver or gold films
or to a silicon wafer (100). Three organic molecules were used,
-
2+
cadmium stearate (CdSt), (CH3(CH2)16COO )2Cd , and cad-
mium salts of arachidic and brassidic acids, (Cdar) )
Figure 2. Schematic representation of electron transmission through
a molecular film. An electronic plane wave (I) is incident on the barrier
(II) from the left, and the transmission (III) is monitored from the right.
-
2+
(
(
(
CH3(CH2)18COO )2Cd and (CdBr) ) (CH3(CH2)7CHdCH-
-
+2
CH2)11COO )2Cd . All acids were dissolved in chloroform
1 mg/mL) and then spread on aqueous solution of 0.001 M
were attached to a temperature-controlled holder and inserted
into an ultrahigh-vacuum (UHV) chamber pumped to below
CdCl2. The pH of the solution was balanced at 8.5 by small
amount of ammonia. At this pH the films are transferred. The
depositions were performed at temperature of 20 °C and surface
pressure of 28 mN/m, at a low lift speed of 1 cm/min.
-
8
1
0
mbar by adsorption and ion pumps. The 223 nm (5.56
eV) light with a 10 ns pulse of energy 0.1 µJ was obtained by
mixing the output of a frequency-doubled Nd:Yag pumped dye
laser with a 1064 nm light from the Nd:Yag laser. The laser
beam is introduced into the chamber, and after reflecting from
the sample it exits through quartz windows. The photoelectron
kinetic energy distribution was measured via the retarding field
The quality of the LB layers was determined by the transfer
ratio from the trough, by ellipsometric studies that probe the
thickness of the layers, and by IR spectroscopy. For successfully
deposited films, the contact angle with water was 111-113°.
The ellipsometric data for CdSt and CdBr show that the
thickness of each single layer is about 2.40 ( 0.05 nm,
independent of the film composition. This number indicates
that the CdBr layers, despite being slightly longer than CdSt,
are tilted relative to the surface normal, and therefore the
thickness of the layers of the two types of film are almost
identical. Atomic force microscopy studies confirmed the
results obtained from ellipsometry. Layers in which there was
a 1:1 mixture of the two molecules were also produced and
3
7
38
method or by time-of-flight electron energy analyzer. In
the first method, a grid made of nickel was placed 3 mm in
front of and parallel to the silver/OOTF-coated slide. The grid
could be biased with a negative or positive voltage relative to
the silver surface, which was kept at ground potential. The close
proximity of the grid and the silver surface ensures high
collection efficiency and unperturbed collection of low-energy
electrons. This kind of plane-parallel detector collects electrons
according to the part of their kinetic energy corresponding to
the velocity component perpendicular to the surface, E⊥ . If a
negative potential -V is applied on the grid, electrons with E⊥
probed by the same methods, and their quality was found to be
the same as that of the other layers.31 From other studies32 it
is known that the 1:1 mixed layer is homogenous, and no
domains are formed.
<
eV cannot pass the mesh and therefore do not reach the
detector. A newly developed microsphere plate (MSP made
by El-Mul, Israel) was placed 5 mm behind the grid and biased
by 200 V relative to it. The MSP serves as an electron
multiplier, in the same way as does a regular microchannel plate.
An anode placed behind the MSP collected the amplified
electron signal, which was processed by a gated integrator
For each film, the grazing angle Fourier transform infrared
(
FTIR) spectrum was measured and the intensities of the C-H
stretching bands (CH3 asymmetric, CH2 asymmetric, and CH2
-
1
symmetric at 2958, 2917, and 2849 cm , respectively) were
monitored. In addition atomic force microscopy (AFM) mea-
surements were performed on the films. Usually the films have
(Stanford Research Systems). The laser pulse intensity was kept
3
3
roughness similar to that of the original clean substrate.
low so that nonlinear effects were eliminated. The signal
measured by the retarding field method is an integral of the
emitted current over the emitted electron energy up to the energy
corresponding to the voltage applied on the grid. Hence, by
differentiating the signal with respect to grid voltage, the emitted
electron energy distribution is obtained. Although the method
is inherently of low resolution, it has the advantage of being
sensitive to the low-energy electrons. The electron energy
distributions obtained by both methods were consistent.
Photoelectron Energy Distribution Measurements. Two
experimental setups were used for obtaining the transmission
function of photoelectrons through the OOTFs. In the first,
described in ref 34, a commercial UPS system was utilized
(Kratos Analytical, AXIS-HS). The UV source was a helium
lamp emitting mainly at the He(I) line (21.21 eV), owing to
-
7
the He pressure conditionss0.6-1.0 × 10 mbar. In order to
minimize damage to the organic film, the current through the
lamp was reduced to the minimum required to obtain stable
UV radiation (30 mA). We examined the effect of OOTF on
the secondary electron emission (SEE) peak of the silver
substrate. Each set of measurements was comprised of mea-
surement of two samples; a Cdar-coated silver film and a bare
silver film as a reference. To account reliably for the peak shape
of the very slow (secondary) electrons, special experimental
conditions were chosen as described in ref 34. The signal from
silver coated with OOTF was found to be stable only for
relatively short times. This problem originates from the e-beam-
induced damage to the OOTF. The results presented below were
obtained from fresh samples whose exposure to the electron
beam did not exceed 3 min.
5
. Computational Methods
Following the discussion of section 3, we need to compute
transmission probabilities of either the “one-to-all” or the
cumulative” type. This is in principle a three-dimensional
“
under-barrier tunneling or over-barrier transmission problem.
Figure 2 depicts a typical one-to-all example: an electronic plane
wave is incident on the barrier from the left, and the transmission
(into all exit directions) is monitored on the right. The
corresponding cumulative transition probability involves a sum
over all incident directions l. For a nonuniform initial angular
distribution, this sum should include a corresponding weight
function. The computational problem can be quite challenging,
in particular in situations where the barrier is very high so that
In the second scheme, the experimental system as described
in refs 35 and 36 was used. The slides coated with the OOTF

3662 J. Phys. Chem. B, Vol. 102, No. 19, 1998
Naaman et al.
the transmission probability is very low. A prerequisite to any
numerical treatment is a knowledge of the electron-barrier
interaction. This is never known exactly in any realistic case,
and two approximations have been used:
widths and level shifts to basis functions associated with some
of the molecular centers. The cumulative and the “one-to-all”
transmission probabilities are given by
4
7-52
2
(1) A pseudopotential is constructed for the interaction of
N(E) ) 2π(F F |T | )
(12)
(13)
(14)
L
R
lr E )E )E
r j
the electron with different atomic cores of the molecular layers.
Such potentials have been constructed and successfully used in
studies of energetics and dynamics of excess electrons in
and
water,3
9,40
ammonia , methanol , rare gases, and simple
41
42
43
2
P (E ) ) 2π(F |T | )
l
l
R
lr Er)El
alkanes.44 Obviously such an approach can be valid only if
the process under study involves only the excess electron, while
the core electrons are taken care of only indirectly via the
pseudo-potential. This can be true only in hosts with closed
electronic shells and high electronic excitation and ionization
energies. Once a suitable pseudopotential is available, the
potential barrier for the electron transmission can be constructed
if we assume that the total potential experienced by the electron
as it moves from region I to III in Figure 2 is the sum of the
potential experienced by the electron in the absence of the
molecular layer (“the vacuum potential”) and the potential
associated with the electron-molecule interaction. The Schr o¨ -
dinger equation associated with the resulting one-electron
Hamiltonian is then expressed on a grid spanning regions I, II,
and III, and the transmission can be computed either as an initial
value problem starting from a suitable wave packet on the left
or as a scattering problem. We have found the latter formalism
particularly useful, using the imaginary boundary conditions in
respectively, where
T ) V +
V Gmm′Vm′r
lr ∑∑ lm
lr
m m′
-1
G ) (E(I + S) - H - ∑(E)) ; ∑(E) ) ∆(E) - (1/2)iΓ(E)
(15)
Here l and r denote states in the unspecified continuous
manifolds (with density of states FL and FR respectively) on the
left and on the right of the barrier respectively, and {m} are the
intermediate states that are considered explicitly. Σ is the self-
energy matrix (with ∆ and (1/2)Γ its real and imaginary parts)
of the molecular basis {m} associated with its coupling to these
manifolds. The coupling elements Vlr Vlm Vmr connect the
molecular manifold to the continua of incoming and outgoing
states and can be calculated or approximated within specified
models of these continua. Again, when the number of orbitals
associated with the intermediate state manifold is large, iterative
inversion is the method of choice for evaluating the Green’s
function.
4
5
Green’s function method of Seidman and Miller.
In this
method the potential is supplemented with an imaginary function
of position along the transmission direction, V f V + iꢀ(z),
where ꢀ(z) is taken to vary smoothly from zero in most of the
bulk of the system to some suitably chosen large value near
the edges. The cumulative transmission probability is then given
The two approaches described above differ from each other
mostly in the basis functions used to describe the transmission
process and also in the philosophy behind the corresponding
descriptions. The molecular basis approach is useful when the
transmission is supported by well-defined intermediate states
45
by
2
N(E) ≡
|S (E)| ) 4tr[(1 - h)ꢀGhꢀG*]
(9)
∑l ∑r lr
(“through bond transfer”) even though direct coupling can be
where h(z) is a step function, h(z < 0) ) 0, h(z g 0) ) 1, and
G is the Green’s operator
accommodated, e.g., the first term on the right of (14) (“through
space transfer”). The spatial grid approach is more useful when
the transmission is not dominated by specific intermediate
molecular states or when through space coupling dominates.
Thus, in the simulations of transmission through water and argon
layers described below, a pseudo-potential/spatial grid technique
was found to be very useful.
1
Gˆ (E; ꢀ) )
(10)
E - Hˆ + i ꢀˆ (r)
Similarly, the “one-to-all” transmission probability is then
calculated from
6
. Experimental Results
2
+
+
Pl(E) ≡ |S (E)| ) 〈ψ | Fˆ |ψ 〉
∑r lr
(11)
l
l
Figure 3 (Figure 3 in ref 35) presents the electron energy
distribution of photoelectrons from silver coated with one (A),
three (B), and five (C) monolayers of CdSt, [(CH3(CH2)16
COO )2Cd ]. The importance of film order to electron
transmission is demonstrated in Figure 4 (Figure 3 in ref 34),
which presents the current density as function of electron energy,
for photoelectrons transmitted through 13 layers of Cdar,
[(CH3(CH2)18COO )2Cd ], before (circles) and after (squares)
they were heated to 378 K. The results indicate that before
heating, electrons with energies above ca. 1eV are transmitted
through the band almost ballistically. Following the heating,
the electron energy distribution indicates an extensive scattering
process.
When the SEE peak was monitored for surfaces covered with
OOTF, it was found to be narrower than the peak for the bare
substrate. The results are presented in Figure 5 (Figure 1 in
ref 34) as the transmission function through one (solid line)
and three (dashed line) layers of Cdar. The transmission curve
where ψ +l ) (E - H + iꢀ) iꢀφl, with φl being the incident
-1
-
1
-
2+
state, and where Fˆ ) ip [H, h(z)] is the flux operator.
Obviously, the applicability of the above expressions depends
on our ability to evaluate the grid Green’s function in an efficient
and accurate way (see methods reviewed in ref 46). In general,
the size of a typical problem requires the use of iterative methods
for the matrix inversion, and the calculation is facilitated by
the fact that the Hamiltonian matrix defined on the grid is sparse.
-
2+
(
2) A finite basis set {m} is constructed for the electron in
the barrier region, and, for metal junctions, sometimes also for
finite parts of the adjacent regions I and III. The basis functions
and the associated Hamiltonian (Hmm′ ) 〈m|H|m′〉) and overlap
(
Smm′ ) 〈m|m′〉) matrix elements are usually obtained in terms
of the appropriate atomic orbitals within the extended H u¨ ckel
formalism. The infinite nature of the system in the direction
of the transmission is represented by assigning appropriate decay

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J. Phys. Chem. B, Vol. 102, No. 19, 1998 3663
Figure 5. Transmission probability of photoelectrons through one (solid
line) and three (dashed line) layers of Cdar.
Figure 3. Electron energy distribution of photoelectrons from silver
coated with one (A), three (B), and five (C) monolayers of cadmium
stearate.
Figure 4. Electron energy distribution as measured by the retarding
field method for photoelectrons transmitted through 13 organized
(circles) and unorganized (squares) layers of Cdar.
was calculated by dividing the electron signal at each electron
energy, obtained from silver film coated with the OOTF, by
the electron signal of the bare silver film.
Figure 6. Transmission probability of electrons as a function of the
photoelectron energy for layers of Cdar (dashed) and CdBr (dotted),
and of mixed layers (solid) for three (A) and nine (B) layers.
The low-energy part (<1 eV) of the curve obtained in this
way is consistent with the results obtained by the retarding field
method monitoring low-energy electrons, whereas at higher
energies new information is obtained. One observes a decrease
in the transmission probability for electrons with energy of above
ca. 1.0 eV. This decrease is more abrupt, in terms of energies,
when the film is composed of more layers.
Another aspect of the interplay between film structure and
its transmission properties is shown in Figure 6, which presents
the transmission probability of electrons as a function of the
photoelectron energy for layers of Cdar (dashed), CdBr (dotted),
and of mixed layers (solid) for three (Figure 6a) and nine (Figure
6b) layers. As is clearly evident, the electron transmission
through the mixed layers is significantly less efficient than that
through the Cdar or CdBr layers themselves. Not only is the
transmission intensity reduced, but the energy distribution is
also different. While the energy distribution for electrons
transmitted through three layers of Cdar or CdBr peaks at 0.8
and 0.7 eV, respectively, the electron energy distribution of

3664 J. Phys. Chem. B, Vol. 102, No. 19, 1998
Naaman et al.
electrons transmitted through the mixed layers is almost flat.
In the case of the nine layered samples, the energy distribution
of electrons transmitted through layers of Cdar or CdBr layers
peaks at 0.7 and 0.9 eV, respectively. Generally, in the case of
nine layers, less electrons are transmitted through the film.
Figure 6 shows that in the case of the neat films, namely,
films of either Cdar or CdBr alone, electrons with energies above
some threshold value (V0) are transmitted almost unperturbed,
while the transmission is lower for low-energy electrons. This
type of energy-dependent transmission indicates the existence
of band structure in the film, as was discussed above, with the
bottom of the conduction band at V0. However, the distribution
of electrons transmitted through the mixed layer indicates an
extensive scattering process incompatible with the band model.
This means that despite the fact that the order and packing of
the layers is very similar for all three type of layers used (Cdar,
CdBr, and mixed layers), the fact that in the mixed layers case
not all the chains are identical, this fact by itself, causes the
reduction in electron transmission.
Some word of caution is in place at this point. The notion
of electronic bands is of course related to the electronic structure
of ordered bulk solids, and applying it to thin films is in principle
questionable. Indeed, it is sufficient to associate high transmis-
sion probabilities with states of the excess electron in the film
that are extended on the scale of the film thickness. In fact,
the numerical results presented below suggest that the cor-
respondence with the band structure of the bulk material is
substantial even for very thin films.
Figure 7. Tunneling probability vs electron energy through a film of
water molecules. The film thickness is ∼10 Å, and the water density
3
is ∼1 g/cm , which amounts to three monolayers of water in the film.
The water-electron potential is superimposed on a “vacuum barrier”
of height 5 eV. The nonpolarizable electron-water pseudo-potential
of Barnett et al.39 is used here (see ref 46 for more details). Full line:
Tunneling probability vs electron energy calculated for a particular
three-dimensional water configuration in the barrier. Dashed line:
Average over 256 tunneling probabilities calculated for linear one-
dimensional sections through the same barrier. Dotted line: Tunneling
probability through the bare rectangular barrier of height 5 eV.
7. Some Numerical Results
While the numerical methodologies described in section 3b
are general and can in principle be applied to the experimental
systems described above, the numerical results described below
are used to illustrate the principle factors affecting the transmis-
sion using simpler model systems. We consider (a) the
dimensionality of the process, (b) the effect of layer structure
and order, (c) the effect of resonances in the barrier, and (d)
the signature of band motion. Details of the pseudopotentials,
grids, basis sets, and matrix elements are provided in the
corresponding references. It should be emphasized that even
though the systems so far studied numerically are very different
than the organized organic layers that are the subjects of our
experimental work, these factors and the way they affect the
transmission characteristics appear to be general.
Many theoretical studies of tunneling use one-dimensional
models, the rationale being that a process dominated by
nonresonance tunneling, and therefore exponentially diminishing
with tunneling path length, must take the shortest possible route.
Figure 7 (Figure 6 of ref 46) shows that the situation is more
complex. This figure shows the “one-to-all” tunneling prob-
ability for an electron incident in the normal direction on a 1.0
nm layer of water. In this calculation water configurations are
obtained from classical trajectories at 300 K, and the electron
water pseudo-potential is the one developed by Barnett et al.,
which uses a two-body term to account for the water electronic
polarizability. This pseudo-potential is superimposed on a
vacuum potential modeled by a rectangular barrier of height 5
eV and width 1.0 nm. Figure 7 compares the result of a full
Figure 8. Tunneling probability vs electron energy calculated for a
particular three-dimensional water configuration in the barrier (same
barrier as in Figure 7). Dotted line: tunneling through the vacuum
barrier. Thin dashed line: tunneling through the water film, using the
nonpolarizable electron-water pseudo-potential. (These two lines
appear also in Figure 7.) Full line: tunneling through the same water
film, using the fully polarizable electron-water interaction (see ref 53
for details). The thick dashed line represents the tunneling probability
calculated for a rectangular barrier of width 10 Å and height 3.8 eV.
tion tunneling through these paths is suppressed by a very high
kinetic energy barrier, hence the actual 3-D tunneling probability
is much smaller.
It should be noted that while Figure 7 shows quite dramati-
cally the importance of taking the correct dimensionality of the
system into account, the absolute results for electron tunneling
through water do not account for experimental observations.
Experiments indicate that the effective barrier to tunneling in
water is considerably lower (by ∼1 eV) than in vacuum, while
the results of Figure 7 show a different trend. We have found
that the problem originates from disregarding the electronic
polarizability of water in the water-electron pseudo-potential.
This is shown in Figure 8 (Figure 3 of ref 53) where the
predictions of the polarizable and nonpolarizable models of the
electron-water pseudo-potential are compared. The polarizable
model accounts quite well for the observed reduction in the
3-D calculation to that obtained as an average over 256 one-
dimensional paths through the same water configurations. The
resulting relatively large one-dimensional transmission was
found to be dominated by just a few paths with very low barriers.
These paths are embedded as very narrow potential windows
in the three-dimensional water configuration. In a 3-D calcula-

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J. Phys. Chem. B, Vol. 102, No. 19, 1998 3665
Figure 9. Computed tunneling probability through 10 Å water layers.
Dotted line: normal equilibrium configuration obtained from MD
simulations at 300 K. Dashed line: configurations in which the water
molecules are oriented so that their dipoles are pointing opposite to
the tunneling direction. Dashed-dotted line: same where the water
dipoles point in the tunneling direction. The full line is the vacuum
Figure 10. Two-dimensional model calculation of the transmission
of an electron incident in a perpendicular direction on a rectangular
barrier in which two chains of wells lie parallel to each other in the
direction of transmission. The rectangular barrier height is 0.1 au, and
its width in the tunneling direction is 36 au. Each “chain” is made of
wells of size 4 × 4 au and depth below the barrier of 0.05 au, lying at
a distance of 8 au between their centers. Plotted as a function of the
(no water) tunneling probability. (See ref 54 for more details.)
interchain distance and for different electron energies is the ratio T
2T ), where T is the computed transmission probability and T is the
transmission probability for a single chain.
2
/
effective barrier to tunneling in water as compared with vacuum.
Another demonstration of the importance of the 3-D structure
of the water layer on the characteristic of the tunneling process
is shown in Figure 9 (Figure 3 of ref 54). Here, using the
polarizable model for the electron-water interaction we show
the “one-to-all” transmission probability for an electron incident
in the normal direction on a 1.0 nm water layer in which the
water molecules are oriented in the tunneling direction by a
strong electric field. This figure compares the vacuum tunneling
to tunneling through a normal water layer and through a similar
water layer oriented in the opposite to the tunneling direction.
We emphasize that the strong asymmetry predicted cannot be
obtained in a one-dimensional calculation because of constraints
imposed by microscopic reversibility.
(
1
2
1
In a molecular layer made of adsorbed chain molecules, the
dimensionality issue can be expressed with a slightly different
emphasis: does the transmission occur predominantly along
single chains or do cross-interactions between chains affect it
in an essential way? This is obviously an issue of interaction
strengths and distances and should be studied using detailed
models. As a demonstration of the effects of cross-chain
interactions, we show in Figure 10 the result of a two-
dimensional calculation of the transmission of an electron
incident in a perpendicular direction on a barrier in which two
chains of wells lie parallel to each other in the direction of
transmission. The rectangular barrier height is 0.1 au, and its
width in the tunneling direction is 36 au. Each “chain” is made
of wells of size 4 × 4 au, lying at a distance of 8 au between
their centers. Figure 10 shows the ratio T2/(2T1) between the
computed transmission probability T2 and twice the transmission
probability associated with an isolated chain as a function of
the interchain distance. This ratio should be approximately 1
if cross-chain interactions are absent and if through-wells
transmission dominates. We see that for the parameters chosen,
interchain interactions become important at distances smaller
than 15 au. We may conclude that such effects may be
important at molecular distances for normal hydrocarbon layers.
Finally, consider ordered vs disordered layer structure. Figure
Figure 11. (a) Transmission probability through 1-D rectangular barrier
characterized by height of 3 eV and width of 12 Å, as a function of
incident electron energy measured relative to the barrier top. (b) Full
line: electron transmission through a slab made of four Ar layers, cut
out of an fcc Ar crystal in the (100) direction. Dashed line: same results
obtained for a disordered Ar slab prepared as described in the text.
distribution of the incident electrons) through a one-dimensional
rectangular barrier of height 3 eV and width 1.2 nm as a function
of the incident electron energy measured relative to the barrier
top, to the transmission through a 3-D slab of four Ar layers
cut out of an Ar crystal in the (100) direction. The latter results
are obtained with a spatial grid technique using the electron-
11 (Figure 2 of ref 34) compares the transmission probability
(“one-to-all” with the incident electron perpendicular to the
barrier; note that a complete solution of the transmission problem
corresponds to averaging the transmitted flux over the angular
4
3
Ar pseudo-potential of Space et al. The oscillations shown

3666 J. Phys. Chem. B, Vol. 102, No. 19, 1998
Naaman et al.
the three-dimensional character of the transmission process and
(b) the dependence on the electronic band structure of the
underlying bulk molecular solid.
Dimensionality Issues. Because of the exponential damping
of tunneling probability with barrier width, it is tempting to
regard the electron transfer as a one-dimensional process, and
in fact theoretical discussions of electron transfer often use such
models. For overbarrier transmission (or for electron transport
through extended electronic states in the barrier, e.g., through
conduction band states) this argument does not apply, and the
transmission probability may be affected by the full three-
dimensional structure of the molecular film. Even in this case
the relative importance of conduction along the backbone of a
single chain molecule and of interchain coupling is an interesting
issue. The computational results displayed in Figures 7 and 9
clearly indicate that even for deep tunneling processes 1-D
models are generally inadequate and may miss important
physical aspects of the process. No detailed calculations for
transmission through organized layers made of chain molecules
are available yet; however, the model calculation of Figure 10
demonstrates how interchain effects may come in as the distance
between molecular chains decreases. In accordance with these
observations, the experimental results in Figure 6 show that not
only the structure of the dielectric in the direction of propagation
Figure 12. Computed transmission probabilities, vs electron energy,
for an electron incident on slabs cut out of an fcc Ar crystal in the
(100) direction. (a) Slabs made of two (dashed line) and four (full line)
monolayers. (b) Slabs with four (full line) and six (dashed line)
monolayers. (The full lines in (a) and (b) are identical.)
in Figure 11a are interference patterns associated with the finite
width of the layers. The full line in Figure 11b also shows
such oscillations, but in addition, a prominent dip above 4 eV
corresponds to a band gap, already well-developed in this thin
ordered layer. The dashed line in Figure 11b shows similar
transmission results for disordered layers, obtained from the
crystalline layer by a numerical thermal annealing at 400 K next
to an adsorbing wall using molecular dynamics propagation.
The results shown are averaged over four such disordered Ar
configurations. The transmission through the disordered layer
is considerably less structured (very likely, smoother shapes will
be obtained with more configurational averaging); in particular,
the dip associated with the band gap has largely disappeared.
Another issue of interest is the development of the band
structure as the film thickness increases. Figure 12 compares
the transmission (one-to-all) versus electron energy, for an
electron incident in the normal direction on ordered Ar films
made of two, four, and six atomic monolayers (“prepared” by
cutting them off an Ar crystal as described above). Already at
six-layer thickness the observed transmission dip is very close
to its bulk value, indicating that the band structure is already
well-developed.
(Z-direction) of the electron but also its structure in the
perpendicular XY plane are important in determining the
transmission probability. This observation is significant because
each chain considered independently is a periodic structure
which could support one-dimensional band conduction. Still,
the DeBroglie wavelength (≈1.2 nm for electron energy of 1
eV) is longer than the spacing between chains and an electron
moving in the Z-direction samples the potential from neighbor-
ing chains so its motion can be sensitive to disorder in the XY-
plane. Indeed, Figure 6 shows that lateral disorder in the
potential, in the case of the mixed layers, is enough of a
perturbation to decrease the efficiency of electron transmission.
Band Structure Effects. The transmission of an electron
through a molecular film depends on the electronic structure of
the film, in the same way that bridge assisted electron transfer
is dominated by the electronic structure, particularly LUMOs
(lowest unoccupied molecular orbitals) of the bridge. It should
be kept in mind that the relevant electronic states in the present
context are excess electron states in the film. For ordered
molecular layers such states may be extended, at least on the
scale of the film thickness, and constitute the precursor of what
would become the conduction band in the macroscopic bulk
solid. Band structure effects have been indeed seen in the LEET
The examples described above have used the imaginary
boundary conditions Green’s function/spatial grid technique to
evaluate the transmission probability. In the case of transmis-
sion through organic layers, the proximity of molecular orbitals
to the energy of the transmitted electron suggests that the
approach based on a molecular basis set may be better and more
efficient. Recent model calculations of the conductivity of
1
8
experiments of Sanche and co-workers. The consequences
of such band motion are seen also in the experimental and
numerical results presented above. It is interesting to note
(Figures 11 and 12) that signature of the bulk band structure is
seen even for very thin Ar layers; in fact, even a film consisting
of two atomic monolayers shows a structure that can be
identified as the precursor of the bulk band gap (Figure 12).
For the Cdar system, even a monolayer is considerably thicker
than the simulated system, so we expect that the energy
dependence of the transmission through such layers will be
dominated by the electronic band structure and/or impurity and
defect states in these layers. X-ray studies indicate that, at room
temperature, three layers of Cdar or more show clear crystalline
carbon chains and of STM images of organic mole-
cules47,48,50-52,55-62
on metal substrates show the viability of
this approach. Applications of this method to adsorbed chain
molecules are currently underway.
8
. Discussion
Electron transmission through organized organic thin films
depends sensitively on details of the composition and structure
of the film and on the nature of the substrate. Still the result
presented above show several modes of behavior, which, in
comparison with the model calculations, are expected to be
general. While the model computations described above are
not dealing yet with the actual experimental systems, they do
show generic characteristics of these processes. These are (a)
6
3
diffraction, while a single layer is less ordered. Hence it is
expected that the band structure in the three-layer system will
be better defined, as indeed indicated by the sharper transmission
peak for electrons transmitted through three Cdar layers,

Feature Article
J. Phys. Chem. B, Vol. 102, No. 19, 1998 3667
compared to those transmitted through a single layer (Figure
(6) (a) A. Ikai, Surf. Sci. Rep. 1996, 26. (b) DeRose, J. A.; Leblanc,
R. M. Surf. Sci. Rep. 1995, 22 and references cited therein.
5). Furthermore, the orthorhombic crystalline structure of the
(7) Wolf, E. L. Principles of electron tunneling spectroscopy; Oxford
Cdar film is destroyed upon heating the films to 378 K, and
University Press: Oxford, 1985.
63
the amphiphilic chains are not ordered above this temperature.
(8) Gurney, R. W. Phys. ReV. 1935, 47, 479.
(
9) Ueba, H. Surf. Sci. 1991, 242, 266.
From Figure 4 it is evident that after heating there is an efficient
scattering process that suppresses the transmission peak similarly
to what is observed in the calculated dashed line of Figure 11b.
These results indicate that “band conduction”, or transmission
through electronic states which are extended at least along the
film normal, is the cause of the efficient electron transmission
through amphiphiles. This picture also explains the high
(
(
(
10) Albano, E. V. Appl. Surf. Sci. 1982, 14, 183.
11) Lang, N.; Kohn, W. Phys. ReV. B 1970, 1, 4555.
12) Duwez A.-S.; Paolo S. D.; Ghijsen J.; Riga J.; Deleuze M.; Delhalle
J. J. Phys. Chem. B 1997, 101, 884.
(13) Jo, S. K.; White, J. M. J. Chem. Phys. 1991, 94, 5761.
(14) Michaud, M.; Sanche, L. Phys. ReV. 1987, A36, 4672.
(15) Kim, C.-W.; Villagran, J. C.; Even, U.; Thompson, J. C. J. Chem.
Phys. 1991, 94, 3974.
16) Petrank, A. Ph.D. Thesis, Weizmann Institute of Science, 1987.
(
conductance through organic layers as measured with scanning
tunneling microscopy.64 It also rationalizes the observation that
(17) For a review, see: Sanche, L. In Excess Electrons in Dielectric
Media; Ferradini, C.; Jay-Gerin, J.-P., Eds.; CRC Press: Boca Raton, FL,
electrons are better conducted through all-trans amphiphilic
1
1
1
991; Chapter 1, p 1.
(18) Perluzzo, G.; Bader, G.; Caron L. G.; Sanche, L. Phys. ReV. Lett.
985, 55, 545.
6
5
chains than through chains containing some gauche bonds:
When the chains are in “all-trans” configuration, the layer is
ordered and the electronic wave functions in the band are
delocalized. The formation of the gauche bonds amounts to
introducing disorder which increases scattering and reflection
and, when pronounced enough, localizes the electronic wave
function.
It is also important to note that the observed role of bandlike
motion in the electron-transmission process indicates that
classical multiple scattering approaches to such processes are
inadequate and emphasizes the importance of treating the
electron-transmission quantum mechanically.
(
19) Caron, L. G.; Perluzzo, G.; Bader, G.; Sanche, L. Phys. ReV. B
986, 33, 3027.
(20) Maeda, T.; Miyano, K.; Sugita, K.; Ueno, N. Thin Solid Films 1989,
79, 327. Ueno, N.; Nakahara, H.; Sugita, K.; Fukuda, K. Thin Solid Films
989, 179, 161. Ueno, N.; Sugita, K. Phys. ReV. B 1990, 42, 1659.
1
1
(
21) Bader, G.; Perluzzo, G.; Caron, L. G.; Sanche, L. Phys. ReV. 1984,
B30, 78.
(22) (a) Michaud, M.; Sanche, L.; Gaubert, C.; Baudoing, R. Surf. Sci.
988, 205, 447. (b) Goulet, T.; Jung, J.-M.; Michaud, M.; Jay-Gerin, J.-P.;
Sanche, L. Phys. ReV. 1994, B50, 5101.
23) Vincett, P. S.; Roberts, G. G. Thin Solid Films 1980, 68, 135 and
references cited therein.
1
(
(
(
(
(
24) Polymeropoulos, E. E.; Sagiv, J. J. Chem. Phys. 1978, 69, 1836.
25) Landauer, R. IBM J. Res. DeV. 1957, 1, 223.
26) Landauer, R. Philos. Mag. 1970, 21, 863.
As discussed in section 3, the electron-transmission processes
that were the focus of the present work are closely related to
27) Imry, Y. Physics of mesoscopic systems. In Directions in Condensed
the general class of electron-transfer phenomena. Following
Matter Physics; Grinstein, G., Mazenko, G., Eds.; World Scientific:
Singapore, 1986; p 101.
Marcus,66 most treatments of electron transfer focus on the
(
(
28) M. Galperin, D. Segal, and A. Nitzan, to be published.
29) A. Haran, S. P. Ananthavel, and R. Naaman, in preparation.
electronic states of the donor and acceptor species, treating the
surrounding solvent as a dielectric continuum. By its very
nature, the study of photoemission through molecular overlayers
focuses on the molecular structure of these layers, the equiva-
lents of the bridge and solvent in other electron-transfer
processes. We have already commented on the analogy between
transmission through such layers and between bridge-assisted
electron-transfer processes, and experiments of the kind de-
scribed here focus directly on the effect of the electronic
structure of such (three-dimensional) bridges. It is possible from
the photoelectron transmission studies and from LEET to obtain
the effective barrier height and the energy-dependent transmis-
sion probability through such bridges, information which is not
directly available in other types of electron-transfer processes.
Current studies in our laboratories aim at establishing if and
how the character (angular distribution, momenta, polarization
etc.) of the electrons affect the transmission probabilities.
(30) Blodgett, K. B. J. Am. Chem. Soc. 1935, 57, 1007. Blodgett, K.
B.; Langmuir, I. Phys. ReV. 1937, 51, 964.
(
31) Kadyshevitch A.; Ananthavel S. P.; Naaman R. J. Chem. Phys.
1
977, 107, 1288.
32) Popovitz-Biro, R.; Wang, J. L.; Majewski, J.; Shavit, E.; Leisero-
vitch, L.; Lahav, M. J. Am. Chem. Soc. 1994, 116, 1179.
33) Trakhtenberg S.; Naaman R.; Cohen S. R.; Benjamin I. J. Phys.
Chem. 1997, 101, 5172.
34) Haran A.; Kadyshevitch, A.; Cohen, H.; Naaman, R.; Evans, D.;
Seidman, T.; Nitzan, A. Chem. Phys. Lett. 1997, 268, 475.
(
(
(
(
(
(
(
35) Kadyshevitch A.; Naaman R. Phys. ReV. Lett. 74,3443.1995, .
36) Kadyshevitch A.; Naaman R. Thin Solid Films 1996, 288, 139.
37) DuBridge, L. A. Phys. ReV. 1933, 43, 727.
38) We thank Prof. O. Cheshnovsky for advising us on the construction
of the time-of-flight spectrometer.
39) Barnett, R. N.; Landmann, U.; Cleveland, C. L. J. Chem. Phys.
988, 88, 4420.
40) Rossky, P. J.; Schnitker, J. J. Phys. Chem. 1988, 92, 4277.
(
1
(
(41) Sprik, M.; Klein, M. L. J. Chem. Phys. 1988, 89, 1592.
(42) Turi, L.; Mosyak, A.; Rossky, P. J. J. Chem. Phys. 1997, 107, 1687.
(
43) Space, B.; Coker, D. F.; Liu, Z. H.; Berne, B. J.; Martyna, G. J.
Chem. Phys. 1992, 97, 2002.
44) Liu, Z.; Berne, B. J. J. Chem. Phys. 1993, 99, 9054.
Acknowledgment. This work was partially supported by the
Ministry for Science and Technology and by the United States-
Israel Binational Science Foundation. R.N. thanks the partial
support from the Israel Science Foundation and from the
MINERVA Foundation.
(
(45) Seidman, T.; Miller, W. H. J. Chem. Phys. 1992, 97, 2499.
(46) Mosyak, A.; Nitzan, A.; Kosloff, R. J. Chem. Phys. 1996, 104,
1
549.
47) Mujica, V.; Kemp, M.; Ratner, M. A. J. Chem. Phys. 1994, 101,
849, 6856.
48) Kemp, M.; Roitberg, A.; Mujica, V.; Wanta, T.; Ratner, M. A. J.
Phys. Chem. 1996, 100, 8349.
49) Samanta, M. P.; Tian, W.; Datta, S.; Henderson, J. I.; Kubiak, C.
(
6
(
References and Notes
(
(
1) Kuznetsov, A. M. Charge Transfer in Physics, Chemistry and
Biology; Gordon and Breach: New York, 1995.
2) (a) Carter, F. L. Molecular Electronic DeVices; Marcel Dekker
Inc.: New York, 1987; Vol. 2. (b) Lehn, J. M. Angew. Chem. 1988, 100,
9. (c) Molecular and Biomolecular Electronics; Birge, R. R., Ed.; American
P. Phys. ReV. B 1996, 53, R7626.
(50) Sautet, P.; Joachim, C. Phys. ReV. B. 1988, 38, 12238.
(51) Sautet, P.; Joachim, C. Chem. Phys. Lett. 1991, 185, 23.
(52) Joachim, C.; Gimzewski, J. K.; Schlittler, R. R.; Chavy, C. Phys.
ReV. Lett. 1995, 74, 2102.
(
8
Chemical Society: Washington DC, 1994. (d)Aviram, A.; Ratner, M. A.
Chem. Phys. Lett. 1974, 29, 277.
(53) Mosyak, A.; Graf, P.; Benjamin, I.; Nitzan, A. J. Phys. Chem. A
1997, 101, 429.
(
3) Molecular Electronics; Jortner, J., Ratner, M., Eds.; Blackwell
(54) Benjamin, I.; Evans, D.; Nitzan, A. J. Chem. Phys. 1997, 106, 1291.
(55) Chavy, C.; Joachim, C.; Altibeli, A. Chem. Phys. Lett. 1993, 214,
569.
Science Ltd: Oxford, 1997.
(4) Sanche, L. Scanning Microsc. 1995, 9, 619.
(
5) Barraud A.; Millie P.; Yakimenko I. J. Chem. Phys. 1996, 105,
(56) Cheong, A.; Roitberg, A. E.; Mujica, V.; Ratner, M. A. J.
Photochem. Photobiol. A 1994, 82, 81.
6
972 and references cited therein.

3668 J. Phys. Chem. B, Vol. 102, No. 19, 1998
Naaman et al.
(
(
57) Joachim, C.; Gimzewski, J. K. Europhys. Lett. 1995, 30, 409.
58) Kemp, M.; Mujica, V.; Ratner, M. A. J. Chem. Phys. 1994, 101,
(62) Sautet, P.; Joachim, C. Chem. Phys. 1989, 135, 99.
(63) Tippmann-Krayer, P.; Kenn, R. M.; Mohwald, H. Thin Solid Films
1992, 210/211, 577.
5
6
172.
(
59) Mujica, V.; Kemp, M.; Ratner, M. A. J. Chem. Phys. 1994, 101,
(64) DeRose, J. A.; Leblance, R. M. Surf. Sci. Rep. 1995, 22, 75.
(65) Haran, A.; Waldeck, D. H.; Naaman, R.; Moons E.; Cahen, D.
Science 1994, 263, 948.
(66) Marcus, R. A. Oxidases and Related Redox Systmes; King T. E.,
Mason H. S., Morrison, M., Eds.; Pergamon Press: New York, 1982; p 3.
856.
(
60) Sautet, P.; Dunphy, J. C.; Ogletree, D. F.; Joachim, C.; Salmeron,
M. Surf. Sci. 1994, 315, 127.
61) Sautet, P.; Joachim, C. Chem. Phys. Lett. 1988, 153, 511.
(