Nanoscale Mapping of Molecular Vibrational Modes via Vibrational

Subscriber access provided by UNIVERSITY OF ADELAIDE LIBRARIES

Communication

Nanoscale Mapping of Molecular Vibrational Modes via Vibrational Noise Spectroscopy Duckhyung Cho, Shashank Shekhar, Hyungwoo Lee, and Seunghun Hong Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b04457 • Publication Date (Web): 02 Jan 2018 Downloaded from http://pubs.acs.org on January 5, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Nano Letters is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Nanoscale Mapping of Molecular Vibrational Modes via Vibrational Noise Spectroscopy

Duckhyung Cho,† Shashank Shekhar,† Hyungwoo Lee,‡ and Seunghun Hong*,†

†

Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul 08826, Korea.

‡

Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.

*Email: [email protected]

1

ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract

We have developed a “vibrational noise spectroscopy (VNS)” method to identify and map vibrational modes of molecular wires on a solid substrate. In the method, electrical-noises generated in molecules on a conducting substrate were measured using a conducting atomic force microscopy (AFM) with a nano-resolution. We found that the bias voltage applied to the conducting AFM probe can stimulate specific vibrational modes of measured molecules, resulting in enhanced electrical noises. Thus, by analyzing noise-voltage spectra, we could identify various vibrational modes of the molecular wires on the substrates. Further, we could image the distribution of vibrational modes on molecule patterns on the substrates. In addition, we found that VNS imaging data could be further analyzed to quantitatively estimate the density of a specific vibrational mode in the layers of different molecular species. The VNS method allows one to measure molecular vibrational modes under ambient conditions with a nanoresolution, and thus it can be a powerful tool for nano-scale electronics and materials researches in general.

KEYWORDS: scanning probe microscopy, vibrational mode spectroscopy, scanning noise microscopy, molecular wires, vibrational mode imaging

2


Page 2 of 31

Page 3 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Experimental measurements about molecular vibrational modes of molecular species adsorbed on solid substrates provide versatile information about their molecular structures and often allow one to identify unknown molecular species.1 Well-known workhorse techniques for such measurements include Raman spectroscopy,1 infrared spectroscopy,2 and inelastic electron tunneling spectroscopy (IETS).3-4 For some applications such as molecular electronics and nanomaterials analyses, it is important to map the distribution of adsorbed molecular species on solid substrates with a nanoscale resolution by measuring their vibrational modes.5 In such cases, one could take advantage of the strategy combining the molecular vibrational spectroscopy techniques with scanning probe microscopy (SPM) methods such as a scanning tunneling microscopy (STM)6 and an atomic force microscopy (AFM).5 For an example, STM probes have been used to perform nanoscale inelastic electron tunneling spectroscopy (IETS) measurements, enabling nanoscale mapping of molecular vibrational modes of organic molecules on solid substrates.7 However, it usually requires cryogenic temperatures, restricting its application for samples at room temperature.8 Also, Raman spectroscopy and infrared spectroscopy have been combined with various SPMs to optically image molecular vibrational modes with nanoscale resolutions at room temperature conditions.2,5,6 However, exquisite experimental setups with highly-optimized SPM probes are often required for the methods, making the measurements quite costly.2,9,10 On the other hand, electrical noises, the temporal fluctuations of currents, in molecular junctions have been drawing attentions because the noises can provide versatile information that is often very difficult to obtain by other measurement methods.11-13 Previous studies showed that molecular vibrational mode could be evaluated by statistically analyzing the fluctuations of multiple current (I)-bias voltage (Vb) spectra measured on a molecular junction.14,15 However, it is often time-consuming to measure such multiple I-Vb data enough to

3


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

obtain statistically meaningful results. In addition, such repetitive electrical measurements on a fixed location possibly cause damages on measured samples. Thus, the method has been very difficult to be used for the nanoscale imaging of molecular vibration modes. Herein, we report a method to identify and map vibrational modes of molecular wires on a conducting solid substrate. In this method, a conducting probe installed on an AFM made a direct contact with molecular-wire layers on a conducting substrate and swept on the layer while measuring noise power spectral density (PSD). Then, the noise PSD data measured with different bias voltages were utilized to identify the molecular vibrational modes stimulating the electrical noises. We found that an external bias voltage stimulated a specific molecular vibration mode, resulting in an enhanced electrical noise at the voltage. In this sense, the method is named here as “vibrational noise spectroscopy (VNS)”. Using the method, we could identify versatile molecular vibrational modes of molecular wires on Au substrates. Furthermore, we could map the distribution of vibrational modes on the patterns comprised of different molecular wires. Interestingly, we found that the strength of enhanced noise PSD under different bias voltages could be utilized to quantitatively estimate the densities of specific vibration modes in the layers of different molecular wires. Since our method allows one to map molecular vibrational modes under ambient conditions with a nanoscale resolution, it can be a simple but powerful tool for basic researches and applications on molecular electronics and nanoscale material analyses in general.

Scanning Vibrational Noise Spectroscopy Setup. The schematic diagram in Figure 1a shows our setup for the noise and current measurements for the patterned layers of molecular wires on a gold substrate. The sample preparation procedures are described in the Methods section. For a

4


Page 4 of 31

Page 5 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

noise spectroscopy experiment, a Pt-based conducting probe (25Pt300B from Park Systems, spring constant ~18 N/m) installed on an AFM system (XE-70, Park System) was placed on a molecular-wire sample to form a metal/molecule/metal junction. The contact force of the probe was maintained as 1 µN via a contact force feedback loop in the AFM system. For the mapping of electrical currents and noises, a dc bias voltage was applied between the gold substrate and the Pt probe by using a function generator (DS345, Stanford Research Systems). The electrical currents through the gold/molecule/Pt probe were measured and converted to amplified voltage signals by using a low-noise preamplifier (SR570, Stanford Research Systems). Simultaneously, electrical noises, the fluctuating components of the current signals, were collected using a bandpass filter (6 dB) in the SR570 preamplifier, and the RMS power of the collected noises was obtained by a homemade RMS-to-DC converter built using an AD737 chip (purchased from Analog Devices).16 By dividing the square of the measured RMS noise power with the bandwidth of the band-pass filter, we obtained the absolute current-noise PSD value (SI) at the central frequency of the band-pass filter. The current and noise PSD values measured at a specific location on the molecular layers were recorded. By scanning the AFM probe on the molecular patterns during the measurement, the two-dimensional maps of currents and noise PSDs could be obtained. The measured current and noise PSD maps were analyzed to obtain the map showing the distribution of molecular vibrational modes on the molecular layer. Note that our noise PSD measurements are based on the frequency-domain measurement of currents using a band-pass filter and a RMS to DC converter. This enabled the real-time measurements of the noise PSD value at a frequency (f), enabling the fast high-resolution imaging of electrical noises on molecular wire layers.

5


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1b shows the structures of molecules used in our experiments. We used a set of alkanethiol molecules with different alkyl chain lengths, namely, dodecanethiol (DT) and octanethiol (OT). In addition, the benzenedithiol (BDT) and 2,5-dimercapto-1,3,4-thiadiazole (DMcT) molecules were studied. All the molecules bind on a gold substrate by forming S-Au bonds.

Spectral Characteristics of Noises Measured on a Molecule-Patterned Gold Substrate. Figure 2a shows an AFM topography image measured on the self-assembled monolayers (SAMs) of OT molecules patterned on a gold substrate. The widths of the OT and the gold regions were ~4 µm and ~6 µm, respectively. The measured height of the OT monolayer was about ~1.1 nm, which is consistent with the previously-reported length of OT.17 The topography image shows the uniform layers of OT without any serious defects on the layers. In addition, it should be mentioned that when the conducting AFM probe was damaged during the measurement, the topography images were easily distorted. Thus, the clean topography image without sudden fluctuations indicates that the conducting probe did not change and it made a stable electrical contact with the molecular wire layer during the measurement. We could measure the map of current-normalized noise PSD (SI/I2) (at 173 Hz) while simultaneously obtaining the topography (Figure 2b). The bias voltage of a 5 mV was applied between the gold substrate and the conducting probe. Note that the noise level on the OT molecules (~10-5 Hz-1) was much higher than that on the bare gold region (~10-8 Hz-1). The low noise level in the gold region indicates rather small background noises in our system. On the other hand, the high noise level in the OT molecular region implies that the OT molecules between the gold and the conducting probe were the major source of electrical noises. In this

6


Page 6 of 31

Page 7 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

case, we could assume that the most of the noises originated in the fluctuation in the molecule parts and analyze the noise data to obtain the information about the molecular wires. We could place the conducting AFM probe at a specific location on the molecule layer and measure frequency-dependent noise PSD spectra from that location. Figure 2c shows current-normalized noise PSD spectra which were measured at a bare gold region (red line) and an OT molecule region (blue line). In both cases, noise PSDs were quite high at a low-frequency condition and rapidly decreased with an increasing frequency, showing the existence of strong frequency-dependent noises. We fitted the noise PSD spectra to the function of A/f β to estimate the scaling factor β, where A is a constant fitting parameter. Note that the PSD measured at the gold region showed a typical 1/f noise behavior (β ~ 1). However, when we measured noise spectra in the OT molecule region, a 1/f2 noise behavior (β ~ 2) was observed. Such 1/f2 noises have been widely observed in a nanoscale molecular junction where noises are mainly generated by a small number of noise sources with nearly uniform characteristics.11,18-20 On the other hand, in a large-scale molecular device,12 a large number of noise sources with different characteristics can coexist, and 1/f noises can be observed as the sum of noises from such inhomogeneous noise sources.11,12,18 In our works, this characteristic feature of noise PSDs from molecular wires was utilized as a means to qualitatively distinguish the noises of molecules from that of bare Au surfaces.18 We could measure the scaling factor β on each point on the OT pattern and obtain a scaling factor map (Figure 2d). Here, the noise PSD values were measured in the frequency range of 5.47 ~ 173 Hz at each point of the surface and utilized to estimate the scaling factors. Note that the scaling factor map shows a strong contrast between the OT region (β ~ 2.0) and the gold region (β ~ 1.0). We could consistently obtain the scaling parameter ~ 2 from all molecular 7


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 31

wires in this study, supporting that measured noise signals in molecules were from the molecule parts rather than other conducting parts in our measurement setup. The clear identification of noise sources can be a significant advantage of our method, because the source of current fluctuations has often been very difficult to identify especially in nanoscale junctions such as molecular-wire junctions.

Identification of Molecular Vibrational Modes Using Bias Dependence of Current Noises. Figure 3a shows the current-noise PSD (at 95 Hz) versus bias voltage Vb graph measured on OT molecules using our noise imaging setup. As indicated with a fitting curve Sfit (black dashed line), the noise PSD was found to be approximately proportional to the square of the bias voltage, with small deviations from the fitting curve. The current noises in molecular wire junctions were reported to originate mainly from two different mechanisms: a tunnelingresistance fluctuation19,20 and an electric-field fluctuation by a local-heating effect14,21 (Figure 3b). Thus, the total current-noise PSD SI (at a frequency f) in a molecular wire junction under a bias voltage Vb can be written like

= , + ,

(1)

where SI,resistance and SI,local heating are the noise PSD components from the tunneling-resistance fluctuation and local heating effect, respectively. The fluctuation of the tunneling resistance (R) in a molecular wire junction can be resulted from various origins such as the instability of the molecules-electrode bonding.19,20,22 When the bias voltage Vb on a molecular wire junction is

8


Page 9 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

rather small (Figure 3b-(i)), the current-noise PSD SI,resistance by the tunneling-resistance fluctuation is reported to be proportional to the Vb2 like

, ~ ×

(2)

with the fitting parameter Ar.22 On the other hand, as the applied bias voltage increases and reaches the energy of a molecular vibrational mode in the molecular wire junction, electrons tunneling through the junction can donate energies to the molecular wires to excite their vibrational modes (Figure 3b-(ii)). The vibrationally-excited molecular wires relax to their ground states giving back the energies to the electron sea in the gold and Pt probes,21,23-25 increasing the kinetic energies of the electrons near the junction (Figure 3b-(iii)). This effect is typically called as the local heating effect of a molecular junction.21,23-25 The random electron motions enhanced by the local heating can induce the fluctuation of electric fields in the junction, generating current noises.14,21 The noise PSD SI,local heating from the local heating is usually small compared with the SI,resistance from the resistance fluctuation, and the SI,local heating can reach a maximum value when the electron energy by the applied voltage corresponds to the energy of a molecular vibrational mode in the junction.26 Thus, in the Figure 3a, the large component proportional to Vb2 can be explained as the SI,resistance generated by the tunneling-resistance fluctuation, while the small deviations from the fitting curve can be considered to show the SI,local heating

from the molecular vibrational modes.14 Thus, from eq 1, the SI,local heating can be written as,

, = − , ≅ − ×

9


(3)

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 31

This equation shows that the SI,local heating can be estimated by fitting the measured SI curve to the Ar x Vb2 as a baseline and subtracting the fitting curve from the SI curve. Further, in this work, we define the normalized noise PSD Sn like,

≡

, !"# $%#&'() *+ *,

=

*+ -,.%/'/&#("% *+ *,

~

*+ -0. ×*+1 *,

(4)

where SI(V0) is the measured SI at a fixed bias voltage V0. Here, the SI,local heating is normalized to the SI(V0), in order to remove the influence of the AFM probe size. In our system, a probe and an Au surface are connected by different numbers of molecular wires, depending on the probe size. Assuming that individual molecular wires incoherently transport currents and generate electrical noises, the total noise PSD SI through the probe should be approximately proportional to the size of the probe.18,22 In this case, by normalizing the measured SI(Vb) by SI(V0), we should be able to minimize the probe-size effect and obtain the information about the properties of molecular wires. Thus, the Sn should be very useful in identifying the intrinsic property of a molecular wire itself in the junction. More specifically, the Sn can be regarded to represent the efficiency of a molecular wire for the generation of SI,local heating, when an electron passes through the molecular wire under a bias voltage Vb. The molecular vibrational modes were identified by evaluating the peaks in the graph of the normalized PSD Sn. Figure 3c shows the graph of the Sn which was calculated from the SI data in Figure 3a using eq 4 and V0 = 200 mV. The results show peaks at Vb = 30, 76, 128 and 162 mV. Note that if we convert the peak voltage to the charge carrier energies by multiplying the peak voltage by a carrier charge e, the distribution of the peak energies matches well with the energies of well-known molecular vibrational modes on the OT molecules.14,27 The 10


Page 11 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

corresponding molecular vibrational mode for each peak is marked in the graph, and the peak positions and assigned modes were summarized in the Table 1. The identified molecular vibrational modes from the peaks are the Au-S stretching mode (ν(Au-S)), C-S stretching mode (ν(C-S)), C-C stretching mode (ν(C-C)), and CH2 out-of-plane wagging mode (γω(CH2)). The modes are known to have net dipole moments perpendicular to the gold-OT interface and thus easily interact with the tunneling electrons generating strong signals in the electrical vibrationalmode spectroscopy.27 Interestingly, the intensity of the peak assigned to ν(C-C) mode is distinctively high compared with the other peaks. Previously, it was reported that the ν(C-C) mode can generate a dominant signal in the vibrational mode spectroscopy of alkanethiol molecules due to its peculiar vibrational feature favorable to the vibration mode-electron interactions,28 which is consistent with our observation. The results show that the analyses of electrical noises in a molecular wire junction can provide information about the vibrational modes of molecular wires in the junction. Our method provides a new way of the vibrational mode spectroscopy applicable to nanoscale materials and can be used for versatile basic researches and applications on nanoscale systems. Figure 3d shows the averaged Sn graph obtained by averaging Sn graphs measured at 10 different positions on the OT layer using our noise microscopy. Here, the red line shows the averaged Sn values and the gray region shows the error band of one standard deviation. In the graph, the peaks of ν(Au-S), ν(C-S), ν(C-C), and γω(CH2) can be clearly identified, showing the high statistical reliability of our analysis method using the noise microscopy. The error band was quite thick near the peaks, presumably because the peak positions and intensities can be slightly different at different gold-OT junctions depending on the atomic configurations of Au-S contacts in the junctions.29 However, vibrational modes such as the in-plane rocking δr and scissoring δs 11


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

modes of CH2 were not detected just like the IETS measurements.27 These results indicate that the VNS has similar selection preferences to those of the IETS. Presumably, it is because both of d2I/dV2 signals in the IETS and Sn signals in our VNS originate in the excitation of the molecular vibrational modes by the tunneling electrons in biased molecular junctions. On the other hand, the Raman spectroscopy and infrared spectroscopy based on the interaction between the photon and vibrational modes are known have selection rules different from the IETS or VNS.30 Figure 3e shows the histogram of the peak positions in the Sn graphs measured on the OT layer. The Vb value at any local maximum of a Sn graph was identified as a peak position. The histogram well reproduced the results in the Sn graphs, confirming that the Sn spectrum can be used to measure the molecular vibrational modes on a molecular junction. The slight variations may come partly from some mechanical instability of contacts between molecular wires and the conducting probe. Previous works showed that, when the contact force between the probe and the sample is rather weak, the probe-sample contact can be unstable and the mechanical instability can generate the significant amount of mechanical noises.31 As a matter of fact, we also found unstable noise signals presumably due to unstable junctions when the contact force is below 0.1 µN, while we could obtain reliable vibrational noise spectra with a rather large contact force from 1 µN as shown in Figure 3e. Thus, we applied a 1 µN or larger contact forces during the measurements of noise maps presented in this study. It should be mentioned that a large contact force from a rather sharp AFM tip can exert a high pressure on the underlying molecular layers, which may damage the layers.32,33 For example, it was reported that a rather sharp AFM tip with its contact area smaller than ~30 nm2 on an alkanethiol layer can exert a contact force only up to 70 nN without damaging the layer.32 It indicates the pressure larger than ~3.3 nN/nm2 may damage the molecular layers during the AFM measurements. In our measurements, we

12


Page 12 of 31

Page 13 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

utilized a rather blunt AFM tip in order to form a stable electrical contact between the tip and molecular layers. The contact area between our tip and molecular layers can be estimated as ~2000 nm2 from the reported resistance values of OT molecules and the measured current levels on the molecular layer.34,35 This result is also consistent with the contact area value calculated in a previous work using the same AFM tip as used in our VNS measurements.35 In this case, when the contact force of 1 µN was applied on the tip, the pressure on the molecular layer can be estimated as ~0.5 nN/nm2. Thus, the contact pressure in our experiment was actually quite smaller than the previously reported value of the pressure which has been exerted on the molecular layer without damaging it.32 Nevertheless, occasionally, a tip or molecular layer could be damaged during the measurements, which usually resulted in an abrupt change or distortion in current images. In such cases, the data were discarded, and only reliable data without such changes were used for our VNS analysis. We would like to point out that we used a maximum tip-contact force as possible without causing damage to the SAMs, because a weak contact force can result in an unstable tip-SAM contact which can seriously degrade the reliability of the measured noise data.31 To demonstrate the general applicability of our noise analysis method for the investigation of molecular vibrational modes, we conducted the analysis on various molecular wires with different structures. Figure 3f and 3g show the averaged Sn graphs measured on a BDT molecular layer and a DMcT molecular layer, respectively. Both molecules also showed 1/f2 noise behaviors (Figure S1 in the Supporting Information) and their Sn spectra could be obtained from their SI spectra. For both cases, the peak positions are in a good agreement with the reported vibrational modes of the molecules, as summarized in the Table 1.24,29 It should be noted that BDT and DMcT molecules may form Pt-S bonds with our Pt-based AFM probe,

13


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

which may appear in our signals. However, the energy for the ν(Pt-S) mode is reported to be nearly identical with that of the ν(Au-S) mode.36 Thus, it is difficult to separate the ν(Pt-S) signals from the ν(Au-S) signals in our measurement. Comparing our results with previous reports on vibrational modes of the molecules,24,29 one can see that our analysis method allows us to observe all molecular vibration modes observable by the conventional IETS methods. One of the advantage in our method is that the local heating induced by inelastic tunneling in a molecular junction always increases the current noises and, thus, the signals from the vibrational modes should be observed as positive peaks which are usually much easier to identify than other signals such as negative dips or inflection points in some conventional methods.1,3,14,27 Figure 3h and 3i show the histograms of peak positions in the Sn graphs measured at the BDT and DMcT layers, respectively. The results show that Sn peaks were frequently observed near the molecular vibrational mode energies, showing the reliability of our analysis.

Mapping of Molecular Vibrational Modes. Our VNS method can be used for mapping molecular vibrational modes on molecular layer patterns (Figure 4). Figure 4a shows a schematic illustration showing the method for the vibrational mode mapping. Here, we measured the normalized PSD Sn at a bias corresponding to a specific vibration mode energy on each location (x, y) in a desired region and utilized the data to form a map representing the molecular vibration mode. In brief, we first measured multiple (usually four or more) maps of SI with different voltages (Vb s) in the same region of the molecular patterns. Then, the measured SI (Vb, x, y) values at a location (x, y) (marked by a square) were fitted by the function of Ar x Vb2 to obtain the fitting parameter Ar(x, y) at the location. Then, SI (Vb, x, y) measured with a bias voltage corresponding to a specific vibration mode energy is subtracted by Ar x Vb2, and it was divided by

14


Page 14 of 31

Page 15 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

the current noise PSD values SI at the 200 mV (S0) to obtain the normalized noise PSD Sn (Vb, x, y) at each location (x, y), forming the map of molecular vibration modes in the region. Figure 4b shows the maps of normalized PSD Sn measured on a sample patterned with DT and BDT molecules at 130 mV (left) and 198 mV (right). The 130 and 198 mV corresponds to the molecular vibrational modes of C-C stretching and C=C stretching, respectively, as marked in the images. The details of the sample preparation procedure are described in the method section. The region of the DT molecules could be identified in a topography map measured along with the noise maps and is marked by a black square in the figures. In the left figure showing the C-C stretching mode, stronger signals were observed in the DT region, presumably due to the alkane chains in DT molecules. On the other hand, in the right figure representing a C=C mode, the BDT region appeared brighter, implying the existence of the C=C stretching mode in the BDT molecules. The results show that our analysis method can be used to obtain the distribution maps of molecular vibrational modes on the patterned molecular wires. Figure 4c and 4d show the maps of Sn measured on a DT/DMcT and BDT/DMcT patterned molecular samples, respectively. We could observe the C-C stretching mode in the DT region and C=N stretching mode at DMcT region, in the Figure 4c. The observation implies the abundance of C-C structure and C=N structure in the DT and DMcT molecule, respectively. Similarly, in Figure 4d, we could observe the C-C-C and C=N molecular structure in the BDT and DMcT molecules, respectively. These results show the VNS could be applied to versatile molecular species with different structures.

Quantitative Evaluation of Molecular Vibrational Modes. Figure 5a and b show the maps of Sn for the Au-S and the C-C stretching mode measured on a pattern comprised of C10

15


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(decanethiol) and C16 (hexadecanethiol) molecular wires, respectively. Note that the molecules are alkanethiol molecules with different chain lengths. Since both molecules had the Au-S bonding with a similar physical property, the intensities of the Au-S mode in the C10 and C16 regions were found to be similar as expected (Figure 5a). It also should be noted that the Sn intensity from C16 regions appeared less homogeneous than C10 regions. Presumably, because C16 patterns were first deposited via a quick stamping method, the C16 layers may have rather inhomogeneous properties than C10 layers deposited later by a solution process, as reported previously.37 On the other hand, the intensity of the C-C stretching mode was higher in the C16 region compared with that in the C10 region (Figure 5b). Presumably, electrons tunnel through a longer alkanethiol molecule can get more frequent chances to interact with the C-C stretching mode compared with those through a shorter one because the longer molecule has a larger number of C-C bonds in its chain than the shorter one.38 These results imply that the normalized PSD Sn data in our method can be used to quantitatively evaluate the physical properties of molecular chains. Figure 5c shows the normalized PSD Sn values for the Au-S stretching mode of various alkanethiols on gold substrates. Here, octanethiol (C8), decanethiol (C10), dodecanethiol (C12), tetradecanethiol (C14), and hexadecanethiol (C16) molecules were patterned on gold substrates and the peak values of Sn at 28 mV was measured for the analysis. The Sn for the Au-S stretching mode was quite uniform around 0.1 for all molecular species with some variation comparable to the error bars.11,17,18 This implies that the Au-S mode-tunnel current interaction was rarely influenced by the species of alkanethiols. On the other hand, Figure 5d shows the Sn at the C-C stretching mode in the different alkanethiol molecules. In this case, the Sn values were found to increase as the chain length increases. The Sn values were approximately linearly proportional to

16


Page 16 of 31

Page 17 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

the number of C-C bonds as indicated with a dashed line in the figure (Figure 5d). These tendencies were consistent for all alkanethiol molecules studied in this work. Previous works suggested that the electron-vibrational mode interactions at individual C-C bonds in an alkanethiol can be regarded as mutually independent processes.38 In this case, the Sn from C-C bonds in a molecule should be the linear sum of the Sn from each C-C bond in it. Thus, we can expect the measured peak values corresponding to the C-C vibration mode energy should be proportional to the number of C-C bonds in the molecules, as our observation. The results show that our analysis method can provide valuable information about physical properties of molecular chains even in a quantitative manner.

Summary. We have developed a strategy, named as “vibrational noise spectroscopy”, to identify and map vibrational modes of molecular wires on a solid substrate. In the strategy, a Pt-based conducting probe made a direct contact with a molecular-wire layer on a conducting substrate to measure current-noise PSDs. Interestingly, we found that the bias voltage applied to the Pt probe can stimulate specific molecular vibrational modes of the molecular wires, and the noise PSDs increased suddenly when the voltage reaches a vibrational mode energy of measured molecular wires. Thus, analyzing noise-voltage spectra, we could identify the vibrational modes of molecular wires on a gold substrate. Further, the VNS strategy could be utilized to map vibrational mode distributions on the patterns of different molecular wires. In addition, we found that the mapping data can be further analyzed to quantitatively estimate the density of a specific vibration mode in different molecular-wire layers. Since the VNS method enables the nanoscale mapping of molecular vibrational modes under ambient conditions, it can be a simple but

17


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

powerful tool for basic researches and applications in various areas of nanoscale electronics and material analyses.

Methods. Preparation of Molecular Samples. As a substrate, gold films were prepared on SiO2 substrates using a thermal evaporation method. Typically, a 10 nm of Ti (rate ~ 0.1 nm/s) was first deposited as an adhesion layer and, then, a 30 nm of gold (rate ~ 0.2 nm/s) was deposited with a background pressure of 3 x 10-6 Torr. All molecular substances including OT and DT were purchased from Sigma-Aldrich Korea. The self-assembled monolayer patterns of molecules were prepared via the micro-contact printing method as reported previously.39 In this process, a polydimethylsiloxane (PDMS) stamp was first dipped in a solution of specific molecules (2 mM in ethanol) for 1 min and gently blown with N2 for 10s. Then, the stamp was pressed down on a gold substrate for 3 sec so that molecules were transferred from the stamp to the substrate and formed the self-assembled monolayer patterns of the molecules. Then, the substrate was rinsed with ethanol, thus removing unattached molecular wires and providing a clean surface. For a multi-molecule pattern shown in Figure 4, a substrate stamped with the first molecular species was dipped in a 0.2 mM solution of the other molecular species so that molecules in the solution filled up the remaining bare gold region.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

18


Page 18 of 31

Page 19 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by BioNano Health-Guard Research Center funded by the Ministry of Science, ICT & Future Planning (MSIP) of Korea as Global Frontier Project (No. HGUARD_2013M3A6B2078961). S.H. also acknowledges the support from NRF grants (Nos. 2017R1A2B2006808, 2014M3A7B4051591).

Supporting Information Available. Supplementary data showing current-normalized noise power spectral density spectra measured on benzenedithiol and 2,5-dimercapto-1,3,4-thiadiazole molecules.

REFERENCES 1 2 3 4

Aouani, H.; Šípová, H.; Rahmani, M.; Navarro-Cia, M.; Hegnerová, K.; Homola, J.; Hong, M.; Maier, S. A. ACS Nano 2013, 7, 669–675. Kjoller, K.; Felts, J. R.; Cook, D.; Prater, C. B.; King, W. P. Nanotechnology 2010, 21, 185705. Adkins, C. J.; Phillips, W. A. J. Phys. C: Solid State Phys. 1985, 18, 1313-1346. Hansma, P. K. Tunnelling spectroscopy: capabilities, applications, and new techniques; Plenum: New York, 1982.

19


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

Stockle, R. M.; Suh, Y. D.; Deckert, V.; Zenobi, R. Chem. Phys. Lett. 2000, 318, 131–136. Pettinger, B.; Ren, B.; Picardi, G.; Schuster, R.; Ertl, G. Phys. Rev. Lett. 2000, 92, 096101. Hapala, P.; Temirov, R.; Tautz, F. S.; Jelínek, P. Phys. Rev. Lett. 2014, 113, 226101. Sonntag, M. D.; Pozzi, E. A.; Jiang, N.; Hersam, M. C.; Van Duyne R. P. J. Phys. Chem. Lett. 2014, 5, 3125–3130. Poliani, E.; Nippert, F.; Maultzsch, J. Phys. Status Solidi B 2012, 249, 2511–2514. Huang, T.-X.; Huang, S.-C.; Li, M. H.; Zeng, Z.-C.; Wang, X.; Ren, B. Anal. Bioanal. Chem. 2015, 407, 8177–8195. Ochs, R.; Secker, D.; Elbing, M.; Mayor, M.; Weber, H. B. Faraday Discuss. 2006, 131, 281–289. Clément, N.; Pleutin, S.; Seitz, O.; Lenfant, S.; Vuillaume, D. Phys. Rev. B 2007, 76, 205407. Kim, Y.; Song, H.; Kim, D.; Lee, T.; Jeong, H. Acs Nano 2010, 4, 4426–4430. Tsutsui, M.; Taniguchi, M.; Kawai, T. Nat. Commun. 2010, 1, 138. Tsutsui, M.; Taniguchi, M.; Kawai, T. Nano Lett. 2008, 8, 3293-3297. Engelson, M. Modern spectrum analyzer theory and applications; Artech House: Norwood, 1984. Scaini, D.; Castronovo, M.; Casalis, L.; Scoles, G. Acs Nano 2008, 2, 507–515. Cho, D.; Lee, H.; Shekhar, S.; Yang, M.; Park, J. Y.; Hong, S. Sci. Rep. 2017, 7, 43411. Xiang, D.; Lee, T.; Kim, Y.; Mei, T.; Wang, Q. Nanoscale 2014, 6, 13396–13401. Sydoruk, V. A.; Xiang, D.; Vitusevich, S. A.; Petrychuk, M. V.; Vladyka, A.; Zhang, Y.; Offenhausser, A.; Kochelap, V. A.; Belyaev, A. E.; Mayer, D. J. Appl. Phys. 2012, 112, 014908. D’Agosta, R.; Sai, N.; Ventra, M. D. Nano Lett. 2006, 6, 2935-2938. Kogan, S. Electronic noise and fluctuations in solids; Cambridge University Press: Cambridge, 1996. Huang, Z.; Chen, F.; D'agosta, R.; Bennett, P. A.; Di Ventra, M.; Tao, N. Nat. Nanotechnol. 2007, 2, 698–703. Tsutsui, M.; Taniguchi, M. J. Appl. Phys. 2013, 113, 084301. Ward, D. R.; Corley, D. A.; Tour, J. M.; Natelson, D. Nat. Nanotechnol. 2011, 6, 33–38. Safonov, S. S.; Savchenko, A. K.; Bagrets, D. A.; Jouravlev, O. N.; Nazarov, Y. V.; Linfield, E. H.; Ritchie, D. A. Phys. Rev. Lett. 2003, 91, 136801. Wang, W.; Lee, T.; Kretzschmar, I.; Reed, M. A. Nano. Lett. 2004, 4, 643-646. Okabayashi, N.; Konda, Y.; Komeda, T. Phys. Rev. Lett. 2008, 100, 217801. Lin, L.-L.; Wang, C.-K.; Luo, Y. ACS Nano 2011, 5, 2257–2263. Hipps, K. W.; Mazur, U. J. Phys. Chem. 1993, 97, 7803-7814. Lee, M. H.; Hwang, C. S. Nanoscale 2011, 3, 490–502. Wold, D. J.; Frisbie, C. D. J. Am. Chem. Soc. 2001, 123, 5549-5556. Smaali, K.; Desbief, S.; Foti, G.; Frederiksen, T.; Sanchez-Portal, D.; Arnau, A.; Nys, J. P.; Leclère, P.; Vuillaume, D.; Clément, N. Nanoscale 2015, 7, 1809–1819. Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Science 2001, 294, 571-574. Shekhar, S.; Cho, D.; Lee, H.; Cho, D.-G.; Hong, S. Nanoscale 2016, 8, 835–842. Kim, Y.; Song, H.; Strigl, F.; Pernau, H.-F.; Lee, T.; Scheer, E. Phys. Rev. Lett. 2011, 106, 196804. Losic, D.; Shapter, J. G.; Gooding, J. J. Langmuir 2001, 17, 3307-3316. 20


Page 20 of 31

Page 21 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

38 Yan, L. J. Phys. Chem. A 2006, 110, 13249-13252. 39 Wilbur, J. L.; Kumar, A.; Kim, E.; Whitesides, G. M. Adv. Mater. 1994, 6, 600-604.

21


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure and Table Captions Figure 1. Schematic diagram depicting our scanning vibrational noise spectroscopy setup and the structures of molecular wires used in this work. (a) Schematic diagram showing our scanning vibrational noise spectroscopy setup. We combined a conducting AFM system with an electronic noise measurement system including a homemade spectrum analyzer, to measure current and noise maps on the patterns of molecular wires. The measured current and noise PSD values were analyzed to map the distribution of molecular vibrational modes. All measurements can be performed in the atmosphere at room temperature, which can be an important merit for practical applications such as nanoscale materials analyses. (b) Structures of molecules used in our work.

Figure 2. Identification of electrical noises from the junctions of molecular wires via frequency spectra. (a) AFM topography image showing line-shaped patterns of OT molecules on a gold substrate. (b) Current-normalized noise PSD map on the OT pattern. (c) Graph showing currentnormalized noise PSD versus frequency spectra measured on the regions of a bare gold surface (red) and OT molecular layers (blue). The spectra could be fitted by a 1/fβ curve to obtain the values of the scaling factor β. The noise PSD spectra from a molecular region could be fitted by a 1/f2 curve corresponding to the scaling factor of ~2.0, while those from the gold region exhibited a typical 1/f behavior with a scaling factor of ~1.0. (d) Map of the scaling factor

β estimated from the noise PSD measurements at different frequencies. The regions of OT molecules and gold exhibited the scaling factor β of ~2.0 and ~1.0, respectively.

22


Page 22 of 31

Page 23 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 3. Identification of molecular vibrational modes using voltage-dependent noise PSD spectra. (a) SI (at 95 Hz) versus Vb graph measured on OT molecules. By subtracting noise component proportional to the Vb2 (black dashed line) from the SI, we could obtain the SI,local heating

from molecular vibrational modes. (b) Schematic diagram showing the electron tunneling (i,

ii) and noise generation processes via local heating (iii) in a molecular junction. When the inelastic tunneling occurs at the junction, electrons near the junction are locally heated and the enhanced kinetic motions of the electrons induce additional electrical noises. (c) Sn versus Vb plot calculated from the Figure 3a with V0 = 200 mV. The distribution of peaks in the graph agreed well with reported molecular vibrational modes of the OT. (d) Graph showing the average of the Sn graphs measured at different positions on the OT layer. The averaged Sn also has peaks at the vibrational mode energies of the OT. (e) Histogram showing the distribution of peaks in Sn graphs from the OT. The peaks were frequently observed near the vibrational mode energies. (f,g) Averaged Sn graph on a BDT and DMcT layers, respectively. Vibrational modes assigned to the observed peaks were indicated. (h,i) Histograms showing the distribution of peaks in Sn graphs measured on BDT and DMcT layers, respectively.

Figure 4. Mapping of molecular vibrational modes with a nanoscale resolution. (a) Schematic diagram showing the vibrational mode mapping method. (b) Sn maps measured on a sample patterned with DT and BDT molecules at 130 mV (left) and 198 mV (right) of bias voltages which correspond to the molecular vibrational modes of C-C stretching mode and C=C stretching mode , respectively. (c) Sn maps measured on a DT/DMcT sample with 130 mV (left) and 182 mV (right) correspond to the C-C stretching mode and C=N stretching mode,

23


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

respectively. (d) Sn maps measured on a BDT/DMcT sample with 94 mV (left) and 182 mV (right) of bias voltages, which correspond to the C-C-C bending mode and C=N stretching mode, respectively.

Figure 5. Quantitative evaluation about the density of specific vibrational mode using Sn maps. (a) Sn map measured on a molecular layer patter of C10 and C16 molecules with a bias voltage corresponding to the Au-S stretching mode. Sn values for the Au-S mode were found to be similar in the C10 and C16 regions, indicating both molecules had Au-S bonds with similar physical properties. (b) Sn map measured on the molecular layer of C10 and C16 with a bias voltage corresponding to the C-C stretching mode. Here, Sn values for the C-C mode were measured clearly higher in the C16 region compared with those measured in the C10 region, presumably due to the higher density of C-C bonds in the C16 than in the C10. (c) Sn values for the Au-S stretching mode of different alkanethiols on gold. The values were quite uniform for all molecular species. (d) Sn values for the C-C stretching mode in different alkanethiol molecules. A longer molecule exhibited a larger Sn value compared with a shorter one.

Table 1. List of vibrational modes of OT, BDT and DMcT molecules reported previously.24,29

24


Page 24 of 31

Page 25 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

TOC Graphic 52x26mm (300 x 300 DPI)


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1 202x158mm (150 x 150 DPI)


Page 26 of 31

Page 27 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 2 123x99mm (300 x 300 DPI)


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3 207x196mm (300 x 300 DPI)


Page 28 of 31

Page 29 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Figure 4 241x181mm (300 x 300 DPI)


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5 82x69mm (300 x 300 DPI)


Page 30 of 31

Page 31 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Table 1 197x147mm (120 x 120 DPI)


Nanoscale Mapping of Molecular Vibrational Modes via Vibrational

Recommend Documents