Electron-vibration interaction in single-molecule junctions: from contact to tunneling regime

0.21 MB·English

by  O. Tal

Electron-vibration interaction in single-molecule junctions: from contact to tunneling
regime
O. Tal,1 M. Krieger,1,2 B. Leerink,1 and J.M. van Ruitenbeek1
1Kamerlingh Onnes Laboratory, Leiden University,
P.O. Box 9504, 2300 RA Leiden, The Netherlands
2Institute of Applied Physics, University of Erlangen-Nu¨rnberg,
Staudtstrasse 7/A3, D-91058 Erlangen, Germany
(Dated: February 2, 2008)
8
0 Point contact spectroscopy on a H2O molecule bridging Pt electrodes reveals a clear crossover
0 between enhancement and reduction of the conductance due to electron-vibration interaction. As
2
single channel models predict such a crossover at transmission probability of τ=0.5, we used shot

n noise measurements to analyze the transmission and observed at least two channels across the
a junction where the dominant channel has τ=0.51±0.01 transmission probability at the crossover
J conductance,which is consistent with the predictions for single-channel models.

1
2 PACSnumbers: 73.63.Rt,72.10.Di,73.40.-c,73.63.-b,81.07.Lk

]
l A molecule bridging between two metallic electrodes suppressionin the secondcase has been explainedin the
l
a provides the opportunity to explore the interactions limit of perfect electron transmission probability (τ=1)
h
between mechanical motion (molecular vibrations) and bybackscatteringofelectronsthatloseenergytoavibra-
-
s electron transport at the atomic-scale. The influence tion mode and are then restricted by Fermi statistics to
e
of a vibration mode on the conductance of such junc- taking on the opposite momentum since at τ=1 the for-
m
tions is measured by inelastic electron tunnelling spec- wardmomentumstatesarefullyoccupiedatthereduced
.
t troscopy (IETS) [1, 2] or by point contact spectroscopy energy [12].
a
m (PCS) [3, 4]. Both spectroscopies were originally devel- For weak electron-vibration interaction, the effect of
oped for macroscopic junctions. IETS was first inves- vibration excitation on the conductance is determined
-
d tigated for molecules buried inside a metal-oxide-metal merely by the transmission probability across the junc-
n tunneling junction [5] and was later applied to single- tion,whenusingmodelsbasedonthelowestorderexpan-
o
molecule junctions using scanningtunnelling microscopy sion[13]oftheelectron-vibrationcoupling[14–16]andfor
c
[ (STM) [1]. PCS was first investigated for the study of symmetriccouplingofthemoleculetobothleads[17,18].
electron-phonon interactions in metal wires with a sub- In this framework, which is different from the simplified
1
micron size constriction [6], and it was latter applied view presented above, a combined picture for the two
v
1 to single atom [3] and molecule junctions [4] formed by limits (tunnelling and contact) was suggested by sev-
3 mechanically controlled break junctions (MCBJ). These eral single-level models [14, 16–18]. The models predict
0 techniques provide information on the presence of the conductance enhancement below transmission probabil-
3 molecule [7, 8], its structure [4], the molecule orienta- ity of τ=0.5 and suppression of conductance above this,
.
1 tion[9],andthemolecule-leadscoupling[10]. Essentially due to two opposite contributions to the conductance by
0 IETS and PCS are associated with a similar measure- theelectron-vibrationinteraction: aninelasticscattering
8 ment of current (or its first and second derivatives) as a processthatincreasestheconductanceandanelasticpro-
0
function of voltage between the two leads but operate in cess, where a virtual phonon is emitted and reabsorbed
:
v the opposite limits of low conductance (G≪1G0 where by the electron. The latter effect reduces the conduc-
Xi G0 = 2e2/h is the conductance quantum) for IETS [1], tance [15]. In spite of the theoretical efforts invested in
r and conductance close to 1G0 for PCS [4], respectively. exploring the different regimes of the electron-vibration
a In off-resonance [11] IETS and PCS measurements, interactionsinatomicandmolecularjunctions,thisissue
above a certain voltage bias the incoming electrons have has not been addressed experimentally.
sufficient energy to scatter inelastically by exciting a vi- In this letter we present PCS and shot noise measure-
bration mode at the junction. Interestingly, electron- ments across a single-molecule break junction formed
vibration interactionleads to an increase in the junction by Pt electrodes and H O molecules. By altering the
2
conductance for junctions in the tunnelling regime (e.g., electrode distance, we have measured the effect of the
IETS done by STM [1]), however it decreases the con- electron-vibrationinteraction on the differential conduc-
ductance for junctions in the contact regime (e.g., PCS tance (dI/dV) in the transition between tunneling and
across a Pt/H junction [4]). The conductance enhance- contact regimes [19]. The main transmission channels
2
mentinthefirstcaseiscommonlyexplainedbytheopen- across the junctions and their probabilities where deter-
ing ofanadditionaltunnelling channelfor electronsthat mined allowing comparison with single-channel models
lost energy to a vibration mode [5]. The conductance thatascribechangesintheelectron-vibrationinteraction
2

1.0 (a) (b)
unts (normalized)000...468 Pt/H2O Pt 0dI/dV [G]011...900802 Step down 0[dI/dV G]000...222468 Step up
o 0.22
C -80-60-40-20 0 20 40 60 80 -80-60-40-20 0 20 40 60 80
0.2 Bias Voltage [mV] Bias Voltage [mV]
0.0
0.0 0.4 0.8 1.2 1.6 2.0 FIG. 2: Differential conductance (dI/dV) as a function of
Conductance [G0] the bias voltage for two different Pt-H2O-Pt junctions with
zero-bias conductance of 1.02±0.01G0 (a) and 0.23±0.01G0
(b). Abovea certain bias voltage the energy of theincoming
FIG.1: Conductancehistograms (normalized totheareaun-
electrons exceeds the energy of a molecular vibration mode
der thecurves and set to 1 at the Pt peak) for a Pt junction
and some of the electrons (a few percents) lose energy by
(blackcurve),andforPtafterintroducingH2O(filledcurve).
exciting the vibration mode. Consequently the conductance
Each conductance histogram is constructed from 1000 con-
drops (”step down”, a) or is enhanced (”step up”, b) by the
ductancetracesrecordedwithabiasof0.2Vduringrepeated
electron-vibration scattering.
breaking of the contact.
tion at two different zero-voltage conductance values:
to the value of the transmission probability. Our find- 1.02±0.01G (a) and 0.23±0.01G (b). Junctions with
0 0
ings provide experimental support for these models and
different zero-bias conductance are formed by altering
expandtheirimplicationstojunctions involvingmultiple
the distance between the Pt contacts or by re-adjusting
channels.
a new contact. The steps in the conductance that ap-
ThePt/H2Omolecularjunctionswereformedusingan pear at 46mV in Fig. 2 (a), and 42mV in Fig. 2
MCBJ setup [3] at about 5K. Clean Pt electrode apexes (b) indicate the onset of a vibration excitation at these
areformedundercryogenicvacuumconditionsbybreak- voltages (the origin of the steps as due to the electron-
ing a notched Pt wire (poly-crystalline, 0.1mm diame- vibrationinteractionwasverifiedbyisotopesubstitution,
ter, 99.99%purity). The wire was brokenby mechanical e.g. [1, 9]). Vibration modes around 42meV are typical
bending of a flexible substrate to which the wire was at- forPt/H Ojunctionsandmaybeassociatedwitharota-
2
tached. The inter-electrode distance can be accurately tionmode [21]. While in (a)the differentialconductance
adjusted (with sub-atomic precision) by fine bending of is decreased (”step-down”), the curve (b) taken at lower
the substrate using a piezo-element. The formation of a zero-voltage conductance shows an increase in the dif-
clean Pt contact is verified by conductance histograms ferential conductance (”step-up”). These two examples
made from 1000 conductance traces taken during re- demonstrate that both conductance suppression and en-
peated contact stretching as presented in Fig. 1 (black hancement can be observed at a relatively high conduc-
curve). The single peak around 1.4G0 provides a finger- tance (much higher then the typical tunneling conduc-
print of a clean Pt contact [4]. tance).
Deionized H2O [20] was placed in a quartz tube and Collecting many dI/dV spectra at different zero-
was degassed by four cycles of freezing, pumping and voltageconductancevaluesallowustofocusonthetran-
thawing. While the Pt junction was broken and formed sition between the two cases. Figure 3 presents the dis-
repeatedly, H2O molecules were introduced to the junc- tribution of differential conductance curves with step-
tion througha heatedcapillary (baked-outprior to cool- up (grey) and step-down (dark) according to their zero-
ing). The junction exposure to H2O is controlled by a voltage conductance. Curves with step-up appear below
leak-valveatthetopofthecapillaryandbythecapillary 0.57±0.03G and curves with step-down where detected
0
temperature. FollowingwaterintroductionthetypicalPt only above 0.72±0.03G . Thus the crossover between
0
peakintheconductancehistogramissuppressedandcon- conductance enhancement to conductance reduction by
tributions from a wide conductance range are detected the electron-vibration interaction occurs between these
(seeFig. 1filledcurve)withminorpeaksaround0.2,0.6, two values.
and 1.0 G0 (peaks around 0.95, and 1.10 G0 are some- Accordingtothesingle-channelmodelsthecrossoveris
times observed as well). The continuum in the conduc- expected at a transmission probability of τ=0.5 (τ<0.5)
tance counts implies a variety of stable junction configu- forjunctionswithsimilar(different)couplingtotheelec-
rationsthatweexploitforspectroscopymeasurementon trodes and in any case not higher then τ=0.5 [17, 18].
junctions with different conductance as discussed next. The measured conductance at the crossover is above
Figure 2 presents differential conductance measure- 0.5G . However, more then one channel can con-
0
ments as a function of voltage across the Pt/H O junc- tributetothemeasuredconductanceasdemonstratedby
2
3
2.5
35 Step down ]z
H
ber of counts12235050 Step up -262[ oise 10A/112...050 GGG===001...560240+++///---000...000111GGG000,,, 111===000...459815,,, 222===000...010435+++///---000...000111
m n
Nu10 hot
S0.5
5
0 0.0
0.2 0.4 0.6 0.8 1.0 1.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
G(V=0V) [G0] Bias Current [ A]
FIG. 3: Histogram of step-up (grey) and step-down (dark) FIG. 4: Shot noise as a function of the bias current.
features in dI/dV spectra for Pt/H2O junction as a function The symbols present shot noise measured on contacts with
of zero-bias conductance. A crossover is observed between G=0.52±0.01G0 (bullets), G=0.64±0.01G0 (open triangles),
0.57 and 0.72±0.03G0. and G=1.00±0.01G0 (open squares). Fitting the data with
Eq.(1)(solidcurves)givesthedecompositionofthetotalcon-
ductancein terms of theconduction channels (τ1 and τ2).
′
Landauers formula [22, 23]: G = G0 iτi, where τi is
the transmission probability of the i−Pth channel across
the junction. In order to examine our findings in view acteristic of the measurement setup, the data was cor-
of the theoretical predictions we determined the number rected for the transfer characteristics obtained from the
oftransmissionchannelsandtheirprobabilityusingshot thermalnoise whichwasmeasuredatzerobias [25]. The
noise measurements. 1/f noise contribution was identified by its dependence
Shotnoise resultsfromtime-dependent fluctuations in on V2 (unlike the shot noise dependence on V) and was
the electrical current caused by the discreteness of the removedfromthe curvestakenatnon-zerobias. Finally,
electroncharge. When electrons flow acrossa point con- the thermalnoise is removedby subtractionof the curve
tact (e.g. a single atom or molecule junction), the noise taken at zero bias from the rest of the curves taken at
level is determined by the number of available transmis- different finite biases.
sion channels across the junction and their transmission Following this analysis several sets of shot noise as a
probabilities,τi. Thetotalnoiselevelofaquantumpoint function ofcurrentbias were obtainedfor junctions with
contact for temperature T and applied bias voltage V is different zero bias conductance. Figure 4 presents three
given by [24]: examplesforsuchdatatakenonjunctions withzerobias
conductance of 0.52 (bullets), 0.64 (open triangles), and
eV 2e2 2e2
SI =2eVcoth τi(1−τi)+4kT τi2 1.00±0.01G0 (open squares)zero-bias conductance. The
(cid:18)2kT(cid:19) h h
Xi Xi transmissionprobabilityofthe main channelscanbe de-
(1) terminedbyfittingEq. (1)tothemeasurednoiseandus-
where k is Boltzmann’s constant. Thus in combination ing Landauer’sequationto obtainthe totaltransmission
with Landauer’s equation the main transmission proba- probabilities from the measured conductance. Since the
bilities canberesolvedfromnoiseandconductancemea- fitting is extremely sensitive to the number of channels
surements. and their probabilities [25, 28], the freedom in choosing
We have measured noise using the method described the main transmissionprobability is limited, in this case
in Ref. [25]. Once a stable contact was established at a to ±0.01, while choosing more then two channels is re-
certain conductance, the noise power was measured as stricted to small additional channels that do not affect
a function of frequency at different current bias values, the main probability (in the range of ±0.01).
where at each bias 10,000 noise spectra where averaged. Themaintransmissionprobabilitiesobtainedforjunc-
dI/dV spectra were measured before and after every set
of noise measurements to verify that the same contact
was maintained during the measurements, and to avoid G[Go],τ 0.52 0.62 0.64 0.96 1.00 ±0.01
junctionswithconsiderabledI/dV fluctuationwithinthe τ1 0.48 0.51 0.51 0.93 0.95 ±0.01
measurement bias range (conductance fluctuations are τ2 0.04 0.11 0.13 0.03 0.05 ±0.01
τ1/τ [%] 92±2 82±2 80±2 97±1 95±1
ascribedtoelectroninterferenceduetoscatteringcenters
inthevicinityofthejunction[26]). Thenoiseatnon-zero
biasiscomposedfromthermalandshotnoise(seeEq.(1); TABLE I: Zero bias conductance, total transmission proba-
both are white noise in the measured frequency range of bility (τ), main transmission probabilities (τ1 and τ2), and
0-100KHz) and 1/f-noise [27]. Since the noise signal is the ratio between the main transmission probability and the
suppressed at high frequencies due to the low-pass char- total transmission for different Pt/H2O junctions.
4
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OT is also grateful for the AVS-Welch scholarship. MK
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greatlyacknowlegdesthesupportbytheEuropeanCom-
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mission (RTN DIENOW). We thank A. Nitzan, J. C. D. Djukic, J. C. Cuevas, and J. M. van Ruitenbeek, to
Cuevas and A. Levy Yeyati for fruitful discussions. be published.
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