I used the classification task of tunneling versus molecular traces to compare the performance of different algorithms, using a manually labeled dataset. I demonstrated, that a recurrent neural network employing LSTM units, capable of taking into account the temporal evolution of the conductance traces, or a simpler double-layer feed-forward network, using the one-dimensional single trace histograms as input, both perform well in this classification task. This also demonstrates, that due to the monotonic nature of the measured conductance traces, one-dimensional conductance histograms contain all the relevant information for this classification task. In comparison to the recurrent network, the simpler feed-forward layout provides a more robust solution, as the classification performance does not depend heavily on the network parameters. Furthermore, the simple layout enables us to investigate the decision making aspects of the network and determine the key features that identify the trace classes. I showed that the summed weight product (SWP) of the trained network can be used to highlight the relevant conductance ranges that contain important information about the trace classes.
The training of these neural networks requires a set of labeled conductance traces.
Manual classification is not only against objective data handling, but in many cases, we also lack the a priori knowledge for judgment, and therefore we seek computer algorithms to automatically find the relevant trace classes, which would help us to understand the various possible junction configurations. To this end, we have developed a combined method, which automatically generates training data according to the extreme values of the principal component projections, then the network captures the features of these characteristic traces and generalizes its inference to the entire dataset. Using this com-bined method, we achieved classification results, comparable to the networks trained on manually labeled traces.
Then I used the combined classification method to recognize different junction tra-jectories in gold–4,4’ bipyridine–gold break junction data, measured at low temperature.
This analysis revealed, that at cryogenic temperature, the atomic chain formation dictates the binding configuration of bipyridine molecule. Then I applied the combined classifica-tion method for the closing traces to select the conductance traces that exhibit molecular signatures during both the opening and the subsequent closing of the junction. The sim-ilarities and the correlations of the opening and closing junction trajectories imply, that after the rupture of the molecular junction, it is likely that the molecule stays protruding from one electrode, thus the same molecular junction is reestablished when the electrodes are closed again. Finally, I demonstrated that auxiliary measured quantities, like rupture force, can also be used for generating labels for the training of the neural network.
Chapter 7
Summary and thesis points
I summarize the results of my work in the following thesis points:
1. Measurement system developments
I developed measurement control programs to perform break junction and point con-tact spectroscopy measurements. Through the utilization of hardware triggers, these pro-grams enable the controlled investigation of metallic and molecular junctions by opening and closing the junction until a preset conductance value is reached. During point contact spectroscopy measurements, this can be used to automatically prepare a junction with a predefined conductance to perform current-voltage measurements. In break junction measurements, closing the junction until the same conductance is especially important when investigating temporal correlations and structural memory effects in metallic and single-molecule junctions [1].
I developed an FPGA based measurement control program, which can be used to perform automated measurements with a wide variety of measurement schemes, defined by a sequence of commands [2]. These commands include custom conditions for stopping the elongation/compression of the junction. Then a customized voltage signal can be applied on the junction, or the electrode separation can be further adjusted using the piezo positioner. I demonstrated the application of this measurement control system by performing automated I(V) measurements on gold–4,4’ bipyridine–gold junctions, at low temperature.
2. Investigation of dimer molecular junctions
I investigated the formation of stacked dimers in break junction measurements with 4,4”-diamino-p-terphenyl, and 2,7-diaminofluorene molecules, and compared the elec-tronic and mechanical characteristics of dimer and monomer junctions. I showed that the probability to form dimer junctions increases with increasing molecular concentra-tion. A comparison of the conductance histograms for a series of molecules implies that the amine linkers play an important role in mechanically stabilizing the dimer junctions.
I showed that the relation between the noise power and junction conductance can be used to distinguish between through-bond coupled monomer junctions and dimers with through-space intermolecular coupling. Then I performed noise measurements, confirming the hypothesis of dimer formation. I performed force measurements to demonstrate that
a significantly smaller force is required to rupture dimer junctions, compared to monomer junctions. This result is consistent with a weak N–π interaction when compared with an Au-N donor-acceptor bond. Finally, I demonstrated, that for these dimer junctions, conductance and force decrease as the junction is elongated, which implies that the ex-tent of the overlap between the two molecules dictates both the electronic and mechanical characteristics of dimers [3].
3. Temporal correlations in metallic junctions
I demonstrated that temporal histograms and shifted correlation plots can be utilized for visualizing and characterizing spontaneous or triggered temporal variations in break junction data, like the waving of conductance plateaus or the appearance of repeating traces as the contact is trained. I have shown, that any feature in the shifted correlation plot indicates statistically dependent conductance traces. The decay of these features, as the function of the shift number (s), characterizes the length of the temporal correlations.
Using these techniques, I demonstrated that when atomic-sized gold contacts are ruptured at room temperature, the surface diffusion induced flattening of the electrodes helps to produce statistically independent conductance traces, whereas at low temperatures the rigid contacts are likely to show repeating traces and waving plateaus as long as the closing setpoint is not high enough. I showed that the closing setpoint, required to produce statistically independent conductance traces, can be determined using the opening/closing correlation analysis technique [1].
4. Structural memory effects in Au–4,4’ bipyridine–Au junctions
I analyzed gold–4,4’ bipyridine–gold junctions measured at room temperature and at 4.2 K, using an MCBJ setup and an in-situ evaporation technique for the dosing of the molecules. I demonstrated, that at room temperature, almost all opening and closing con-ductance traces exhibit molecular plateaus after the successful dosing of molecules. Using the opening/closing cross-correlation, I showed that the junction trajectories, observed during the opening and subsequent closing of the junction, are mostly independent. This result implies that after the rupture of the junction, the electrode structure flattens and the attached molecule relaxes on the surface, preventing contact memory effects. In contrast, at low temperature, a significant amount of tunneling traces are observed. Through using the combined classification method to recognize distinct junction trajectories, I demon-strated that the atomic chain formation, observed at cryogenic temperature, dictates the binding configuration of bipyridine molecule [5]. I further analyzed the conductance traces that exhibit molecular signatures during both the opening and the subsequent closing of the junction. The similarities and the correlations of the opening and closing junction trajectories imply, that after the rupture of the molecular junction, it is likely that the molecule stays protruding from one electrode, thus the same molecular junction can be reestablished upon closing the junction.
5. Unsupervised feature recognition in single-molecule break junction data
I used the classification task of tunneling versus molecular traces to compare the per-formance of different algorithms, using a manually labeled dataset. These include feature filtering algorithms based on the measured step length or linear regression, as well as neu-ral networks with different architectures. I demonstrated, that a recurrent neuneu-ral network employing LSTM units, capable of taking into account the temporal evolution of the con-ductance traces, or a simpler double-layer feed-forward network, using the one-dimensional single trace histograms as input, both perform well in this classification task [4, 5]. This also demonstrates, that due to the monotonic nature of the measured conductance traces, one-dimensional conductance histograms contain all the relevant information for this clas-sification task. In comparison to the recurrent network, the simpler feed-forward layout provides a more robust solution, as the classification performance does not depend heavily on the network parameters. Furthermore, the simple layout enables us to investigate the decision making aspects of the network and determine the key features that identify the trace classes.
The training of these neural networks requires a set of labeled conductance traces.
Manual classification is not only against objective data handling, but in many cases, we also lack the a priori knowledge for judgment, and therefore we seek computer algo-rithms to automatically find the relevant trace classes, which would help us to understand the various possible junction configurations. To this end, I have developed a combined method, which automatically generates training data according to the extreme values of the principal component projections, then the network captures the features of these characteristic traces and generalizes its inference to the entire dataset. The classification results obtained using this combined method are comparable to the results when using networks trained on manually labeled traces. Finally, I demonstrated that auxiliary mea-sured quantities, like rupture force, can also be used for generating labels for the training of the neural network [5].
Acknowledgments
I would like to express my gratitude to everyone, who helped me during my Ph.D.
work. First and foremost, I’m thankful to my supervisor, Prof. Andr´as Halbritter for allowing me to work on a wide range of interesting projects and for providing me with inspiring ideas and discussions.
I’m grateful to Prof. Latha Venkataraman for inviting me to her research group and for the many discussions and help, she gave me during my visits and also later, while working on joint research projects. I’m also thankful to the members of her research group for their support and contribution. I would like to thank the Fulbright Foundation for the financial support I received during my first visit to Columbia University.
I thank my colleagues: Dr. Zolt´an Balogh, N´ora Balogh, Gr´eta Mezei, and Anna Ny´ary for their contributions to our work. I’m also thankful to Dr. L´aszl´o P´osa, Botond S´anta, Dr. Mikl´os Csontos, Dr. ´Agnes Gubicza, and all other present and former members and staff of the Nanoelectronics Laboratory at Budapest University of Technology and Economics.
I’m thankful to Dr. Kasper Primdal Lauritzen and Prof. Gemma Solomon for involving me in applying machine learning to the analysis of break junction measurements.
I would like to thank Dr. G´abor M´esz´aros for building the logarithmic current to voltage converter and for the help he provided.
Finally, I express my gratitude to my family for their continued support and under-standing during the years of my Ph.D. I especially thank Mikl´os Keresztes for inspiring me to learn physics.
Publications related to the thesis points
[1] A. Magyarkuti, K. P. Lauritzen, Z. Balogh, A. Ny´ary, G. M´esz´aros, P. Makk, G. C.
Solomon, and A. Halbritter. Temporal correlations and structural memory effects in break junction measurements. Journal of Chemical Physics,146, 092319 (2017).
[2] G. Mezei, Z. Balogh, A. Magyarkuti, and A. Halbritter. Voltage-controlled bi-nary conductance switching in gold-4,4’-bipyridine-gold single-molecule nanowires.
arXiv:2006.04460, (2020).
[3] A. Magyarkuti, O. Adak, A. Halbritter, and L. Venkataraman. Electronic and Mechanical Characteristics of Stacked Dimer Molecular Junctions. Nanoscale, 10, 3362–3368 (2018).
[4] K. P. Lauritzen, A. Magyarkuti, Z. Balogh, A. Halbritter, and G. C. Solomon. Clas-sification of conductance traces with recurrent neural networks. Journal of Chemical Physics, 148, 084111 (2018).
[5] A. Magyarkuti, N. Balogh, Z. Balogh, L. Venkataraman, and A. Halbritter. Unsu-pervised feature recognition in single-molecule break junction data. Nanoscale, 12, 8355–8363 (2020).
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