In this talk, I will describe the recent advances in the on-surface synthesis field. Then, I will discuss our recent results to synthetize atomically precise nanoporous graphene, graphene nanoribbons and their chemical functionalization and how to organize them into superlattices. At the end of the day, this talk will demonstrate the full path to synthetize a semiconducting graphene material with a bandgap similar to that of silicon, its atomic-scale characterization, and its implementation in an electronic device. Further potential applications include in photonics and highly selective molecular filtration and sensing systems.
For part I see Adv. The author gratefully acknowledges several helpful discussions with Drs. Birge, P. F Carcia, D. Dixon, D.
Lower-Dimensional Systems and Molecular Electronics : Robert M. Metzger :
Eaton, A. Epstein, C. Fincher, R. Haddon, J. Hopfield, W.
Hsu, B. Parkinson, D. Pensak, R. Salemme, A. Suna, S.
Tozer, M. Ward, and G. Use the link below to share a full-text version of this article with your friends and colleagues. Learn more. Based on the ab initio calculation, a method of one-dimension transmission combined with three-dimension correction approximation OTCTCA is developed to investigate electron-transport properties of molecular junctions.
The method considers that the functional molecule provides a spatial distribution of effective potential field for the electronic transport. The numerical results show that the conductance obviously exponentially decays with the increase of molecular length. When stretching molecular junctions, steps with a certain width are presented in conductance traces. It is noticeable that, due to the rapid progress of single-molecule technologies 1 , 2 , 3 , 4 , various kinds of studies on single-molecules or atomic clusters have been presented recently 5 , 6 , 7 , 8 , and the results of experimental probing of molecular devices are more and more stable and often consist very well with each other although different technologies are employed 8 , 9.
Simultaneously, many theoretical methods have been developed which give deep insights into the electronic transport mechanisms of molecular junctions 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , such as non-equilibrium electron transport 11 , elastic and inelastic electron transports 12 , 21 , photoinduced charge transport 19 , scattering or tunneling effects 17 , 23 , dimension effect of electrodes 15 , and so on.
Based on those theoretical models, the functional properties of single-molecule devices have been studied systematically, including molecular rectifier 24 , molecular switch 8 , molecular transistor 25 , etc. However, there still exist some interesting problems for theoretical studies to deal with which even include the familiar or acknowledged characters of molecular devices.
As relatively simple systems, alkane series with different linker groups are representative examples whose electronic transport properties were investigated experimentally many times and the results were almost close to each other 26 , 27 , It is shown that, in the lower bias voltage regime, their conductance G decreases exponentially with a decay constant per CH 2 group 26 , 29 , The conductance of phenyl chains 31 , 32 and OPE chains 33 also shows exponentially decaying with molecular length. It is appreciated that some theoretical groups have successfully studied the length dependence of molecular conductance and given valuable explanation 23 , 34 , 35 , 36 , 37 , On the base of the studies, we find that the exponential decaying character of length dependence seems still having some difficulties to be simulated theoretically when the same series molecular chains are studied 39 , sometimes even the opposite results to the experiments are given Additionally, in theoretical studies, the interface configurations perform more influence on the electronic transport properties of molecular junctions than in experimental ones 41 , 42 , Hence, when molecular junctions are stretched, steps in conductance traces often as a signature of the molecular junction formed in the experiment are seldom simulated out theoretically 44 , In fact, details of the interface configurations are still difficult to control or even detect in the present experiments 46 , However, existence of steps in the conductance traces, especially the similar conductance value of steps of different samples, seems to indicate that the conductivities of molecular junctions are insensitive or less sensitive to the factors of interface configuration and electrode distance, which is difficult to be understood for theoretical studies.
As one knows, in the lower bias voltage regime, resonant transmissions contributed by delocalized transmission channels are often very weak. Hence, nonresonant transmissions, which attribute to the quantum scattering and quantum transmission effects of effective potential fields 48 that are around functional molecules, will be expected to dominate electron-transport properties of molecular junctions. Thus, considering above problems, we develop a method of one-dimension transmission combined with three-dimension correction approximation OTCTCA to study the electronic transport properties of molecular junction with lower bias voltages.
The results demonstrate that the OTCTCA method not only successfully simulate the length dependence of the molecular conductance, but also reveal the reason that the conductance traces often show steps even double steps when molecular junctions were elongated in experimental investigations 49 , 50 , On the basis of our numerical calculations, we find that the OTCTCA method is very feasible to investigate properties of weak coupling molecular junctions.
In order to simulate the influences of gold electrodes on the molecules, considering the screening effects of inner Au layers and the reliability of results, we construct gold-molecule-gold extended molecular systems by sandwiching the molecules between two gold-atom clusters to simulate molecular junctions Fig. The stretching processes of molecular junctions are simulated by adjusting the distance D between the two electrodes. For each distance, the molecule and some Au atoms which close to the molecule are relaxed by performing geometric optimization, and the other Au atoms are fixed.
The magenta dashed line corresponds to the experiment results 29 , The results with NEGF method are also included dotted and dashdotted lines. The numerical results show that, for each gold electrode, one Au atom can be protruded out by the pulling of the functional molecule with elongation of electrodes. Just before the molecular junctions being broken, the maximum protruded values of the Au atoms are about 0.
After molecular junctions being broken, the protruded Au atoms snap back automatically. Then at equilibrium distances, the effective potential values of grid points of the three-dimension rectangular cubic space that around the molecules are computed. The distance between neighbor grid points is 0. Applying the OTCTCA method with the grid-point potential values, we calculate the electronic transmission for each molecular junction.
Figure 1 b,c show current and conductance of the four molecular systems. The figures show that both current and conductance increase with bias voltage for all of the four molecular junctions, because the transmission probabilities generally increase with enhancement of the incident energies of electrons in quantum well transmission and quantum barrier tunneling. These characters of transmissions are also represented for the four molecular junctions in Fig. In addition, more CH 2 units in the alkane chains result in lower current, conductance and transmission probability values.
The conductance as a function of molecular length expressed by the number of CH 2 units is plotted in Fig. However, when the bias voltage increases up to 1. It is noticeable that the typical nonresonant transmission character that the conductance increases with the increase of bias voltage 3 , 55 is not found in the NEGF results. In fact, the exponentially decaying of conductance versus molecular length exactly indicated that the electronic transports of alkane series are as ones expected mainly contributed by nonresonant transmission which results from quantum scattering and quantum transmission effect of effective potential fields that around the molecules.
As one knows, resonant transmission is mainly influenced by the factors such as a couplings between electronic states of functional molecule and metal electrodes, b delocalization of molecular orbitals and c whether the delocalized molecular orbitals come into bias window 10 , 11 , It is obviously that neither of these factors is related to the molecular length.
However, the transmission probability of nonresonant transmission is influenced by a the number of potential wells and potential barriers, b the shape of potential wells and potential barriers, c the width and the height of potential barriers and d the energy of incident electrons. Thus each repeated unit in the molecule is just as repeated potential wells and potential barriers that will reduce the transmission probability by about equal proportions, which induces the exponentially decaying character of conductance with molecular length for the same series of molecules.
In order to understand the reason that conductance trances often show steps when stretching molecular junctions, we further investigate the conductance and transmission probability after calculating the numerical effective potential values with the electrodes in different distances for C6 molecular systems Fig. The figure shows that, when the molecule is connected with two electrodes by two linker groups, not only the conductance values but also the variation trend of the G - V curves change only a little for the electrodes in different distances.
However, when the molecular junction is ruptured at 1. Figure 2 c shows that, with elongation of the molecular junction, the conductance changes only a little until the molecular junction is ruptured, i. As mentioned above, the potential wells and potential barriers are the dominant factors that influence the electronic transport through molecular junctions. However, the numerical results show that, when the molecule is well linked with two electrodes, a potential-well channel which is well connected with the two electrodes is formed and no potential barrier cuts off the coherent potential-well channel see Fig.
Moreover, when elongating the molecular junction, the change of the potential-well channel has only a little influence on transmission probability. However, when the molecular junction is ruptured by further stretching, a potential barrier appears at the ruptured point, and the relaxation of the molecule and the electrodes makes the potential barrier broadening rapidly just after the molecular junction is broken.
The transmission probabilities of electronic transporting through a potential barrier generally exponentially decay rapidly with the increase of the width and height of the potential barrier. That is to say, the transmission probability is very sensitive to the width and height of potential barrier, but not sensitive to that of potential well. Thus, one can easily understand why steps often present in the conductance traces when stretching molecular junctions in experiment.
The numerical results show that, when the electrode distance is shorter than 1. When the electrode distance is elongated to about 1. One is that the end of the molecule straight shifts to adsorb on the surface Au atom, and further elongation of the electrodes induces the other end of the molecule gliding on the other gold tip until the molecule is approximately perpendicular to the surface of gold tip. Finally, at 1. The second probable process is that, the end of the molecule shifts to close the surface Au atom, simultaneously, the surface Au atom glides on the gold tip from one hollow position to the neighbor hollow position to close the end of the molecule, and further elongation also induces the other end of the molecule gliding on the other gold tip until the molecule is approximately perpendicular to the surface of gold tip.
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However, if the molecule is broken from the electrode without surface Au atom on the tip, the molecular junction is straight ruptured. From the figure one can see that, when the molecule turns to adsorbing on the surface Au atom at about 1. Additionally, Fig. From Fig. If there is no surface Au atom on the gold tips, the conductance decreases straightly when the molecule is broken down from either electrode tip. However, if there is a surface Au atom on one electrode tip and the molecule turns to link with the surface Au atom as processes I and II shown in Fig. These small conductance values are due to the critical state that the molecule is about broken from the flat part of the gold tip and before it links with the surface Au atom.
Actually, this critical state is generally unstable due to the thermal vibration of the molecular systems. Thus, one can expect that this very low conductive state is uneasy to probe in the experiment. Additionally, the width of the lower steps is obviously narrower than that of the higher steps, which attributes to the situation that the easier absorption of molecule on the surface Au atom would induce the easier breaking of molecule from the other flat gold tip. The width of the step for process II is about 0.
The experimental probes also showed that the lower steps are very narrow and with uncertain width 49 , If the molecule is broken from the electrode without surface Au atom on the tip, the conductance is found to decrease straightly at the broken distance Curve III in Fig. The numerical results also show that there is some probability for the molecule broken from the flat part straightly although there is a surface Au atom on the tip. Thus, one can understand why only a small proportion for the molecular junction shows lower conductive state in experiment Furthermore, due to the surface Au atom, the distance to push-back the two electrodes to contact with each other from low conductive state is estimated to be about 1.
When the two electrodes both possess single surface Au atom, the conductance trace still shows two conductance steps Fig. The reason is that the end of the molecule is easier to adsorb on the surface Au atom because of the existence of the surface Au atom at the other electrode. It is noticeable that, if the two surface Au atoms do not straight face to each other, a valley in the middle part of low conductance step appears which also attributes to the critical state before the molecule adsorbs on the other surface Au atom.
However, the thermal vibration of the molecular system may also reduce or eliminate this valley. Nevertheless, the appearance of this wider low conductance step in experimental probing has little probability because the configuration is seldom formed. It is not an occasional event to successfully simulate the dependence of conductance on molecular length and the conductance steps in the stretching processes of the molecular junctions with OTCTCA method.
In fact, these results are inevitable due to the wave character of electrons.
Lower-Dimensional Systems and Molecular Electronics
As one knows, for the electronic transport in the molecular junction, the electronic waves are injected into the functional molecule from electrode and forced to transfer along the negative bias direction in the molecule by external bias voltage. Simultaneously, the atoms in the molecule can be considered as barriers or scattering centers in the path of transmission waves, which result in the diffracting and reflecting of electronic waves.
Additionally, the OTCTCA calculations show that the shape of the effective potential and the number of scattering centers are the key factors to influence nonresonant transmission, which not only matches the essential characteristic of nonresonant transmission, but also matches the original predicted mechanism of exponential length dependence of the conductance 56 , For the strong coupling molecular junctions such as molecular device with dithiol linker groups, the strong coupling may enhance the conductivity of the molecular junction for some extent, which is not included in the present OTCTCA method and will be considered in future.
The conductance of alkane diamines decays exponentially with the increase of CH 2 unit in the alkane diamines molecular chains with decay constant of about 0. Conductance trances are calculated by elongating molecular junctions successively and steps are found in the conductance traces. The exponential decaying of length dependence and the existence of conductance steps both indicate that, in the lower bias regime, nonresonant electronic transmission dominates electronic transport of molecular device. A molecular device consists of a functional molecule sandwiched between two metal electrodes.
In electronic transport process, by driving of bias voltage, the electrons are injected into functional molecule from one electrode defined as source reservoir and scattered by the molecule, at last poured into the other electrode defined as drain reservoir. It is obvious that the spatial distribution of the effective potential that around the molecule dominates electrons transmit through the molecule. The transmission probability in the direction of bias voltage defined as positive x axis and the state density of reservoirs are two key factors when calculate current and conductance of molecular device.
If the incident probability current density is j x , the transmission probability through the molecule is T E , then the current that flows through molecular device is.
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