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Inelastic Electron Tunneling via Molecular Vibrations in Single-Molecule Transistors

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Inelastic Electron Tunneling via Molecular Vibrations in Single-Molecule Transistors

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In single-molecule transistors, we observe inelastic cotunneling features that correspond energetically to vibrational excitations of the molecule, as determined by Raman and infrared spectroscopy. This is a form of inelastic electron tunneling spectroscopy of single molecules, with the transistor geometry allowing in situ tuning of the electronic states via a gate electrode. The vibrational features shift and change shape as the electronic levels are tuned near resonance, indicating significant modification of the vibrational states. When the molecule contains an unpaired electron, we also observe vibrational satellite features around the Kondo resonance.
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arXiv:cond-mat/0408052v1 [cond-mat.mes-hall] 3 Aug 2004
Inelastic electron tunneling via molecular vibrations in single-molecule transistors
L.H. Yu
1
, Z.K. Keane
1
, J.W. Ciszek
2
, L. Cheng
2
, M.P. Stewart
2
, J.M. Tour
2
, D. Natelson
1,3
1
Department of Physics and Astronomy,
2
Department of Chemistry and Center for Nanoscale Science and Technology,
3
Department of Electrical and Computer Engineering,
Rice University, 6100 Main St., Houston, TX 77005
(Dated: February 2, 2008)
In single-molecule transistors, we observe inelastic cotunneling features that correspond energeti-
cally to vibrational ex citations of the molecule, as determined by Raman and infrared spectroscopy.
This is a form of inelastic electron tunneling spectroscopy of single molecules, with the transistor
geometry allowing in-situ tuning of the electronic states via a gate electrode. The vibrational fea-
tures shift and change shape as the electronic levels are tuned near resonance, ind icating significant
modification of the v ibrational states. When the molecule contains an unpaired electron, we also
observe vibrational satellite features around the Kondo resonance.
PACS numbers: 73.22.-f,73.23.-b,73.23.Hk
Electron tunneling is widespread throughout chem-
istry and condensed matter physics. Electron transfer
through molecules by nonresonant tunneling has long
been known[1, 2], and tunneling electrons can interact
inelastically with molecules, exciting vibrational modes.
This is the basis of inelastic electron tunneling spec-
troscopy (IETS)[3, 4], recently refined to probe gr oups
of molecules via crossed wires[5, 6, 7] and nanopores[8],
and single molecules via scanning tunneling microscopy
(STM)[9]. Similar inelastic, nonresonant tunneling oc-
curs in single-electron transistors (SETs)[10, 11], three-
terminal devic e s in which a gate electrode allows in-situ
adjustment o f the energ y levels. To date, this tuning has
not been possible in the chemical systems examined by
IETS.
In this Letter we report inelastic cotunneling processes
in single-molecule transistors (SMTs)[12, 13, 14, 15],
and identify them with vibrational excitations of the
molecules, as determined by Raman and infrared spec-
troscopy. Tuning electronic levels near resonance reveals
shifts in inelastic lineshapes and peak positions, suggest-
ing significantly modified electron-vibrational coupling in
this region. The vibrational features persist in the Kondo
regime, indicating a complicated conduction process in-
volving vibratio nal excitations of a many-body e lec tronic
system.
A confined electro nic system (“island”) coupled by
tunneling to source and drain electrodes is shown
schematically in Fig. 1a. The energy to promote an
electron from the highest occupied (HO) to the lowest
unoccupied (LU) orbital is the single-particle level spac-
ing, ∆. Ignoring spin, adding an electron to the island
also requires additional Coulomb ”charging energy”, E
c
,
often approximated in SETs by the charging energy of
a clas sical capacitor. In molecules, a manifold of vi-
brational excitations is associated with each electronic
state. In a thr ee-terminal device, the island levels may
be shifted via a gate potential. Fig. 1b maps the dif-
ferential conductance, I
D
/∂V
SD
, of a generic SET as a
function of source-drain bias , V
SD
, and gate voltage, V
G
,
while Fig. 1c shows possible electronic transpor t mecha-
D
S
E
F
E
c
HO
LU
n
n+1
1
4
3
2
5
c
b
a
1
3
4
2
5
V
SD
V
G
0
1’
FIG. 1: (a) Energetics of single-electron transistor, with
single-particle level spacing, E
c
charging energy. Dashed
levels indicate manifold of vibrational excitations in molecular
devices. (b) Map of I
D
/∂V
SD
(brightness) of such an SET,
vs. source-drain bias V
SD
and gate voltage V
G
, showing one
Coulomb transition from n to n+1 electrons on the island. (c)
Conduction processes corresponding to the numbered points
in (b): 1 = elastic cotunneling; 2 = inelastic cotunneling; 3
= resonant conduction; 4 = resonant inelastic conduction; 5
= Kondo resonant condu ction.
nisms. For low biases (Fig. 1c , 1,1’) the average number
of electrons on the is land is fixed; transport is suppressed
(Coulomb blockade) and can only occur by higher or der
tunneling through v irtual sta tes . An example of this in
chemical electron transfer is “superexchange”[2], and in
SETs such processes are called “elastic cotunneling”[10].
At higher biases in the blockaded regime, “inelastic co-
tunneling” via an excited virtual state (Fig. 1c, 2) is po s-
sible. For an excitation of energ y E
, the opening of the
inelastic channel results in a feature in
2
I
D
/∂V
2
SD
at
eV
SD
= E
. Inelastic cotunneling via electronically ex-
2
cited states has been seen in semiconductor[11] and car -
bon nanotube SETs[16]. Inelastic cotunneling via vibra-
tionally excited molecules is responsible for conventional
IETS[17], but has not been studied in three-terminal de-
vices. IETS lineshapes are predicted to vary significantly
depending on the energetics of the virtual states[18],
and can be peaks, dips, or intermediate structures in
2
I
D
/∂V
2
SD
. At still higher source-drain biases (Fig. 1c,
3) C oulomb blockade is lifted leading to s ignificant reso-
nant conduction, while at still higher biases (Fig. 1c, 4)
additional resonant conduction occurs when eV
SD
is suf-
ficient to leave the island in an electronically[19, 20, 21]
or vibrationally[12, 13, 15, 22] excited state.
When the effects of unpaired spins are included, the
Kondo resonance becomes a possible conduction mecha-
nism, and is detected as a sharp conductance peak near
zero bias[23, 24] at temperatures low compared to a char-
acteristic energ y scale, k
B
T
K
. The maximum peak con-
ductance possible is 2e
2
/h, for a system with perfectly
symmetric coupling between the island and the source
and drain electrodes. Kondo physics has been obser ved
recently in single-molec ule transistors[13, 14, 15].
Single-molecule transistors open the possibility of
examining inelastic cotunneling in individual, tunable
chemical systems, in both the blockaded and Kondo
regimes. We fabricate SMTs (Fig. 2a) using an electromi-
gration method that has been described extensively[12,
13, 14, 15]. The source and drain electrodes are 15 nm
Au films with 1 nm Ti adhesion layers, prepared by elec-
tron beam lithography, e -b e am evaporation, liftoff, and
oxygen plasma cleaning. The gate oxide is 200 nm SiO
2
,
with a degenerately doped p+ Si (100) wafer as the un-
derlying gate elec trode. While this thickness of oxide
guarantees relatively weak gate couplings due to simple
geometric considerations, we routinely obtain excellent
device reliability up to g ate fields of 5 × 10
8
V/m with
negligible leakage.
The starting molecule, 1, (Fig. 2b) comprises a single
transition metal ion (Co
2+
) coordinated by conjugated
ligands; the valence state of the ion may be controlled
electrochemically (Fig. 2c). The structure of 1 has been
verified by x-ray crystallogra phy. Compound 1 under-
goes loss of the (CN) moieties upo n assembly on gold in
tetrahydrofuran (THF), yielding the corresponding di-
or tri-thiolate, which is bound covalently to surface Au
atoms[25]. Both 1 and its self-assembly have been char-
acterized extensively by x-ray photoemission, ellipsome-
try, and electrochemical methods[26].
A 2mM solution of 1 in THF is allowed to self-assemble
on the electrode sets for 48 hours. The chip is then rinsed
in THF, dried in a nitrogen stream, and placed in a vari-
able temperature vac uum probe station (Desert Cryogen-
ics). This cryostat does not have magnetic field capabili-
ties, but does permit characterization of many junctions
at once. The junctions are partially broken to the kΩ
level by electromigration at room temperature, cooled to
liquid helium temperatures, and broken by further elec-
tromigration into separate source and drain electrodes.
FIG. 2: (a) Diagram of typical single-molecule transistor fab-
ricated by electromigration. (b) Stru cture of 1, the com-
pound of interest. (c) Cyclic voltammograms showing re-
versible change in Co ion charge state[26]. (d) Differential
conductance of a transistor containing 1, at 5 K. White cor-
respond s to I
D
/∂V
SD
= 3 × 10
6
S. The zero-bias peak in
the righthand charge state is characteristic of Kondo resonant
conduction.
At a variety of temperatures, we have measured I
D
as a function of V
SD
at V
G
from -100 V to +10 0 V
using a semiconductor parameter analyzer (HP4145B),
with the source grounded and the drain electrode swept.
We compute the differential conductance I
D
/∂V
SD
and
2
I
D
/∂V
2
SD
as a function of V
SD
and V
G
by numerical
differentiation. Spot compariso ns between this approach
and lock-in techniques show ex c e llent agreement[26]. To
avoid artifacts we identify features in
2
I
D
/∂V
2
SD
by
comparing multiple data sets taken at the same or nearby
gate voltages.
We have examined 407 elec trode pair s on 10 sepa-
rate substrates, w ith statistics similar to those in pre-
vious investigations[15]. Of the electrode pairs exam-
ined we found 57 devices with no detectable current
(electrodes too far apart for measurable conduction);
166 with linear, nongatea ble current-voltage character-
istics (like ly no molecule present at the junction); 108
with nonlinear but ungateable current-voltage charac-
teristics (either molecules or metal nanoparticles with
negligible gate coupling); and 76 nonlinear but signifi-
cantly gateable current-voltage characteristics. From this
last group, fo ur were identified as single-electron devices
based on unintentionally produced metal nanoparticles.
This identification was based on the observation of many
regularly spaced Coulomb blockade regions with typical
electron addition energies less than 50 meV. In working
devices, bias sweeps were restricted to |V
SD
| < 20 0 mV
to minimize the chances of current-induced irr e versible
changes. Device stability is poo r at high current den-
sities and temperatures significantly above 4.2 K, likely
3
due to the atomic diffusion of the Au elec trode material.
There are 27 devices that cleanly display a single
Coulomb degeneracy point, the vast majority of which
show a resonance at zero V
SD
in one charge state identi-
fied as a Kondo resonance, as in Fig. 2d. Control devices
with electrodes exposed to THF without 1 never display
such conductance properties. As can be seen from the
edges of the Coulomb blockade region, the electron ad-
dition energy for the device in Fig. 2d exceeds 100 meV;
this is typical. The Kondo properties are very similar to
those reported in e arlier SMTs based on Co
2+
-containing
complexes[13]. Typical Kondo temperatures as inferred
from the temperature dependence of the Kondo reso-
nance height and the low temperature width of the reso-
nance are 40 K. The low temperature limit of the res-
onance peak height is often reduced from the theoretical
maximum value of 2e
2
/h, indicating asymmetric coupling
of the molecule to the source and drain electrodes. A full
discussion of Kondo physics in 1 and related molecules
will be repor ted elsewhere.
In 12 devices, the co nductance in the classically block-
aded region and/or outside the Kondo resonance is large
enough to allow clean measurements of
2
I
D
/∂V
2
SD
. In
Figs. 3, we show maps of this quantity as a function
of V
SD
and V
G
in two different devices at 5 K. We
have indicated two prominent features within the block-
aded (Kondo) re gime with black arrows. Features in
2
I
D
/∂V
2
SD
of opposite sign are symmetrically located
around zero source-drain bias, consistent with features
exp ected from inelastic tunneling. Some asymmetry in
shape is unsurpr ising, given that the low peak conduc-
tance in the Kondo regime for these devices indicates
significantly asymmetric coupling of the mo lecule to the
leads.
FIG. 3: Maps of
2
I
D
/∂V
2
SD
as a function of V
SD
and V
G
at 5 K for two d evices. Smoothing window in V
SD
is 5 mV.
Brightness scales are 8 × 10
5
A/V (black) to 3 × 10
5
A/V
(white), and 2 × 10
5
A/V (black) to 2 × 10
5
A/V, re-
spectively. The zero-bias features correspond to Kondo p eak s
in I
D
/∂V
SD
. Prominent inelastic features are indicated by
black arrows. In both devices, when the inelastic features ap-
proach the boundaries of the Coulomb blockade region, these
levels shift and alter lineshape (white arrows). Black dashed
line in left map traces an inelastic feature across across the
boundary and into the Kondo regime.
The
2
I
D
/∂V
2
SD
features in the blockaded region occur
at ess e ntially constant values of V
SD
until V
G
is varied
such that the feature approaches the edge of the block-
aded region. This constancy in V
G
has bee n identified
as a feature of inelastic cotunneling in semiconductor[11]
and nanotube[16] single-electron devices. The changes in
these features as the boundaries o f the Coulomb stabil-
ity region are crossed indicate that the inelastic processes
are native to the SMT itself, and not due to some pa rallel
conduction channel. The inelastic modes oc c ur at ener-
gies low c ompared to (100s of meV), implying that
the modes being excited are unlikely to be electronic. By
examining the
2
I
D
/∂V
2
SD
data for features at fixed V
SD
as a function of V
G
, we identified a total of 43 candi-
date inelastic features at V
SD
< 120 meV, ranging in
apparent width from 5 mV to 20 mV at 5 K. The nar-
rowest inelastic features clearly show a broadening as the
temper ature is elevated above 20 K. Further studies w ill
seek to compare this broadening with standa rd theoreti-
cal treatments of linewidths in IETS.
Fig. 4 shows a histogram (bin = 1 mV) of the V
SD
positions o f those features, from detailed examination of
2
I
D
/∂V
2
SD
vs. V
SD
data. The lower panel shows Raman
(Stokes) peak p ositions (data taken on a powder of 1) and
IR absorption pe ak positions of 1 (in pellet form, blended
with KBr)[26]. The co rrelations between the spectra and
inelastic features in
2
I
D
/∂V
2
SD
confirm that vibrational
inelastic cotunneling processes are at work in the molecu-
lar transistors. This is consistent with the observation of
IETS in single molecules by STM[9]. The fact that differ-
ent SMTs exhibit different subsets of features is a natural
consequence of the sensitivity of IETS to the nanoscale
structure of the molecular junction[27]. Comparisons
with Raman of 1 and related compounds (e.g. ligands
without -SCN; ligands without Co
2+
) suggest tentative
peak assignments. The peaks near 36 meV and 55 meV
are likely the Co-N stretch[28], while that near 44 meV
is tentatively a -SCN deformation[28] (implying that not
every S is bonded to an Au surface ato m, consistent
with x-ray photo e mission da ta[26]). The 24 meV peak
is tentatively the Au-S bond[29]; this claim is further
supported by the app earance of a 28 meV Raman peak
in films of 1 assembled on Au electrodes, while such a
peak is absent in Raman spectra of both unassembled 1
and bare electrodes.
As indicated by white arrows in Fig. 3, inelastic
features shift and change near the boundary of the
Coulomb blockade region. These changes as a function
of V
G
are qualitatively consistent with recent theoret-
ical expectations[18], though detailed modelling would
be required for q uantitative comparisons. The energy of
the virtual cotunneling states is shifted by V
G
, altering
the (complex) amplitude for that process. Changing the
cotunneling amplitude compared to quasi-elastic (with
the virtual ex citation and readsor ption of a vibrational
quantum) or direct source-dra in tunneling is predicted to
severely alter lineshapes. These effects cannot be exam-
ined in two-terminal tunneling structures, which lack the
ability to shift the relevant virtual states. We note that
occasiona lly inelastic features shift significa ntly in energy
as the blockade boundary is approached (e.g. the 24 meV
features in Fig. 3(left)). This would be consistent with a
4
0 200 400 600 800
0
1
2
3
4
0 25 50 75 100
Raman/IR
peak
Peak position [cm
-1
]
Bias position (mV)
Number
FIG. 4: (top) Histogram of |V
SD
| positions of 43 features in
I
2
D
/∂V
2
SD
that are persistent at constant V
SD
over at least
a 10 V gate voltage range, for the 12 samples discussed. Bin
size is 1 meV. Width of actual features is at least 5 meV, with
position indicating feature center. (bottom) Raman (black)
and IR (gray) peak positions taken of 1 in the solid state at
room temperature. The indicated R aman peak near 28 meV
is only present in films of 1 self-assembled on Au electrodes.
modified (dressed) electron- vibrational coupling near the
electronic resonance .
We observe tha t the IETS features persist into the
Kondo regime in the form of satellite features paralleling
the zero-bias Kondo res onance. Often specific features
may be trace d from the blockaded region into the Kondo
region, an example of which is indicated by the dashed
line in Fig. 3(left). Through the transition the inelastic
feature lineshapes change, as do their intensities. Such
inelastic satellites par alleling the Kondo resonance have
been suggested pr eviously[14, 15], and the consistency in
feature pos itio n in our data lend strong support to this
idea. Recent expe riments in semiconductor devices[30]
have demonstrated the existence of satellite Kondo peaks
when the Kondo system can interact inelastically with
photons of a well defined energy. In the molecular tran-
sistor c ase, the inela stic ex change occurs with the vibra-
tional quanta of the molecule, demonstr ating a quantum
mechanically coherent coupling between the electronic
many-body Kondo state, and the mechanical r e sonances
of the molecule. These Kondo mea surements illustrate
how the tunability of single-molecule transistors permits
the examination of vibrational proc esses as a function of
the energetics of the electronic levels, a study not possible
in standard two-terminal devices.
The authors thank A. Nitzan and M. Di Ventra for
useful discussions. DN a cknowledges financial support
from the Research Corporation, the Robert A. Welch
Foundation, the David and L ucille Packard Foundation,
an Alfred P. Sloan Foundation Fellowship, and NSF
award DMR-0347253. JMT acknowledges support from
DARPA and the ONR.
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... It has been shown that morphology manipulation of semiconductor QDs such as size, shape, strain distribution, or inhomogenities can influence the coupling strength of electron-phonon (e-ph) interactions [49]. The phononic effects appears not only in sequential tunneling, but also in the Kondo regime where vibrational sidebands have been also observed [45,[50][51][52][53][54]. The interplay of electron-phonon coupling and Kondo effect has been also studied theoretically [55][56][57][58][59][60]. ...
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