Application of the symbolic regression program AI-Feynman to psychology.

The discovery of hidden laws in data is the core challenge in many fields, from the natural sciences to the social sciences. However, this task has historically relied on human intuition and experience in many areas, including psychology. Therefore, discovering laws using artificial intelligence (AI) has two significant advantages. First, it makes it possible to detect laws that humans cannot discover. Second, it will help construct more accurate theories. An AI called AI-Feynman was released in a very different field, and it performed impressively. Although AI-Feynman was initially designed to discover laws in physics, it can also work well in psychology. This research aims to examine whether AI-Feynman can be a new data analysis method for inter-temporal choice experiments by testing whether it can discover the hyperbolic discount model as a discount function. An inter-temporal choice experiment was conducted to accomplish these objectives, and the data were input into AI-Feynman. As a result, seven discount function candidates were proposed by AI-Feynman. One candidate was the hyperbolic discount model, which is currently considered the most accurate. The three functions of the root-mean-squared errors were superior to the hyperbolic discount model. Moreover, one of the three candidates was more "hyperbolic" than the standard hyperbolic discount function. These results indicate two things. One is that AI-Feynman can be a new data analysis method for inter-temporal choice experiments. The other is that AI-Feynman can discover discount functions that humans cannot find.

High-low Kelvin probe force spectroscopy for measuring the interface state density.

The recently proposed high-low Kelvin probe force microscopy (KPFM) enables evaluation of the effects of semiconductor interface states with high spatial resolution using high and low AC bias frequencies compared with the cutoff frequency of the carrier transfer between the interface and bulk states. Information on the energy spectrum of the interface state density is important for actual semiconductor device evaluation, and there is a need to develop a method for obtaining such physical quantities. Here, we propose high-low Kelvin probe force spectroscopy (high-low KPFS), an electrostatic force spectroscopy method using high- and low-frequency AC bias voltages to measure the interface state density inside semiconductors. We derive an analytical expression for the electrostatic forces between a tip and a semiconductor sample in the accumulation, depletion, and inversion regions, taking into account the charge transfer between the bulk and interface states in semiconductors. We show that the analysis of electrostatic forces in the depletion region at high- and low-frequency AC bias voltages provides information about the interface state density in the semiconductor bandgap. As a preliminary experiment, high-low KPFS measurements were performed on ion-implanted silicon surfaces to confirm the dependence of the electrostatic force on the frequency of the AC bias voltage and obtain the interface state density.

Hybrid mode atomic force microscopy of phase modulation and frequency modulation.

We propose hybrid phase modulation (PM)/frequency modulation (FM) atomic force microscopy (AFM) to increase the imaging speed of AFM in high-Q environments. We derive the relationship between the phase shift, the frequency shift and the tip-sample interaction force from the equation of motion for the cantilever in high-Q environments. The tip-sample conservative force is approximately given by the sum of the conservative force with respect to the phase shift in the PM mode and that with respect to the frequency shift in the FM mode. We preliminarily demonstrate that the hybrid PM/FM-AFM is a new and very promising AFM operation mode that can increase imaging speed.

Direct measurement of surface photovoltage by AC bias Kelvin probe force microscopy.

Surface photovoltage (SPV) measurements are a crucial way of investigating optoelectronic and photocatalytic semiconductors. The local SPV is generally measured consecutively by Kelvin probe force microscopy (KPFM) in darkness and under illumination, in which thermal drift degrades spatial and energy resolutions. In this study, we propose the method of AC bias Kelvin probe force microscopy (AC-KPFM), which controls the AC bias to nullify the modulated signal. We succeeded in directly measuring the local SPV by AC-KPFM with higher resolution, thanks to the exclusion of the thermal drift. We found that AC-KPFM can achieve a SPV response faster by about one to eight orders of magnitude than classical KPFM. Moreover, AC-KPFM is applicable in both amplitude modulation and frequency modulation mode. Thus, it contributes to advancing SPV measurements in various environments, such as vacuum, air, and liquids. This method can be utilized for direct measurements of changes in surface potential induced by modulated external disturbances.

Charge Behavior of Terminal Hydroxyl on Rutile TiO2(110).

Titanium dioxide (TiO2) is of considerable interest as a photocatalyst and a catalyst support. Surface hydroxyl groups (OH) are the most common adsorbates on the TiO2 surface and are believed to play crucial roles in their applications. Although the characteristics of bridging hydroxyl (OHbr) have been well understood, the adsorption structure and charged states of terminal hydroxyl (OHt) have not yet been experimentally elucidated at an atomic scale. In this study, we have investigated an isolated OHt on the rutile TiO2(110) surface by atomic force microscopy (AFM) and Kelvin probe force microscopy (KPFM). We found that OHt is in a negatively charged state. The unique characteristic of OHt is different from that of OHbr and involves the amphoterism and diversity of catalytic reactions of TiO2.

Elucidating the charge state of an Au nanocluster on the oxidized/reduced rutile TiO2 (110) surface using non-contact atomic force microscopy and Kelvin probe force microscopy.

The charge state of Au nanoclusters on oxidized/reduced rutile TiO2 (110) surfaces were investigated by a combination of non-contact atomic force microscopy and Kelvin probe force microscopy at 78 K under ultra-high vacuum. We found that the Au nanoclusters supported on oxidized/reduced surfaces had a relatively positive/negative charge state, respectively, compared with the substrate. In addition, the distance dependence of LCPD verified the contrast observed in the KPFM images. The physical background of charge transfer observation can be explained by the model of charge attachment/detachment from multiple oxygen vacancies/adatoms surrounding Au nanoclusters. These results suggest that the electronic properties of the Au nanoclusters are dramatically influenced by the condition of the support used.

Imaging the surface potential at the steps on the rutile TiO2(110) surface by Kelvin probe force microscopy.

Although step structures have generally been considered to be active sites, their role on a TiO2 surface in catalytic reactions is poorly understood. In this study, we measured the contact potential difference around the steps on a rutile TiO2(110)-(1 × 1) surface with O2 exposure using Kelvin probe force microscopy. A drop in contact potential difference was observed at the steps, indicating that the work function locally decreased. Moreover, for the first time, we found that the drop in contact potential difference at a <1-11> step was larger than that at a <001> step. We propose a model for interpreting the surface potential at the steps by combining the upward dipole moment, in analogy to the Smoluchowski effect, and the local dipole moment of surface atoms. This local change in surface potential provides insight into the important role of the steps in the catalytic reaction.

Tip-Induced Control of Charge and Molecular Bonding of Oxygen Atoms on the Rutile TiO2 (110) Surface with Atomic Force Microscopy.

We study a low-temperature on-surface reversible chemical reaction of oxygen atoms to molecules in ultrahigh vacuum on the semiconducting rutile TiO2(110)-(1 × 1) surface. The reaction is activated by charge transfer from two sources, natural surface/subsurface polarons and experimental Kelvin probe force spectroscopy as a tool for electronic charge manipulation with single electron precision. We demonstrate a complete control over the oxygen species not attainable previously, allowing us to deliberately discriminate in favor of charge or bond manipulation, using either direct charge injection/removal through the tip-oxygen adatom junction or indirectly via polarons. Comparing our ab initio calculations with experiment, we speculate that we may have also manipulated the spin on the oxygens, allowing us to deal with the singlet/triplet complexities associated with the oxygen molecule formation. We show that the manipulation outcome is fully governed by three experimental parameters, vertical and lateral tip positions and the bias voltage.

Measurement and Manipulation of the Charge State of an Adsorbed Oxygen Adatom on the Rutile TiO2(110)-1×1 Surface by nc-AFM and KPFM.

For the first time, the charge states of adsorbed oxygen adatoms on the rutile TiO2(110)-1×1 surface are successfully measured and deliberately manipulated by a combination of noncontact atomic force microscopy and Kelvin probe force microscopy at 78 K under ultrahigh vacuum and interpreted by extensive density functional theory modeling. Several kinds of single and double oxygen adatom species are clearly distinguished and assigned to three different charge states: Oad-/2Oad-, Oad2-/2Oad2-, and Oad--Oad2-, i.e., formal charges of either one or two electrons per atom. Because of the strong atomic-scale image contrast, these states are clearly resolved. The observations are supported by measurements of the short-range force and local contact potential difference as a function of the tip-sample distance as well as simulations. Comparison with the simulations suggests subatomic resolution by allowing us to resolve the rotated oxygen p orbitals. In addition, we manage to reversibly switch the charge states of the oxygen adatoms between the Oad- and Oad2- states, both individually and next to another oxygen, by modulating the frequency shift at constant positive voltage during both charging and discharging processes, i.e., by the tip-induced electric field of one orientation. This work provides a novel route for the investigation of the charge state of the adsorbates and opens up novel prospects for studying transition-metal-oxide-based catalytic reactions.

Direct observation of atomic step edges on the rutile TiO2(110)-(1 × 1) surface using atomic force microscopy.

Clarifying the atomic configuration of step edges on a rutile TiO2 surface is crucial for understanding its fundamental reactivity, and the direct observation of atomic step edges is still a challenge. AFM is a powerful tool for investigating surface structures with true atomic resolution, and it provides the opportunity to resolve the real structure of step edges with improved techniques. In this work, we successfully imaged the atomic configuration of 001 and 1-11 step edges on the surface of rutile TiO2(110)-(1 × 1), and we present the direct observation of oxygen vacancies along the 1-11 step edges, indicating that one 1-11 step edge site corresponds to one oxygen vacancy using AFM. We also made use of the simultaneous AFM/STM measurements to explore the electronic structure of step edges, which enhanced the evidence of oxygen vacancies existing along the 1-11 step edges and further demonstrated that the 001 step edge was terminated by an O row. The effect of the reduced 1-11 step edges was explored by probing the O2 adsorption and the nucleation behavior of gold clusters. It was found that oxygen vacancies along the 1-11 step edges could contribute to O2 dissociative adsorption and there was no obvious difference compared with the oxygen vacancies on the flat terrace. The reduced step edge and terrace likewise acted as nucleation and growth sites for gold atoms/nanoparticles, in line with previous reports. The present study provides a complete characterization of the atomic configuration of the step edges on the TiO2(110) surface and plays an important role in investigating the surface chemistry of metal oxides.