Quantum Mechanical Simulation of Defect Migration and Phase Transition Dynamics Unterlying Resistive Switching in TiO2
Final Report Abstract
The project goal was to gain an in-depth understanding of the migration of oxygen vacancy defects in titanium dioxide, which is the underlying effect of electrically controllable, persistent changes of the electric conductivity of slightly reduced TiO2 . This effect, called the memristor effect, has the potential to enable revolutionary advances in electronic technology. Memristor devices are under investigation as a faster and cheaper replacement technology for FLASH memory, as artificial synapses in neuronal networks and for completely new logic elements in neuromorphic computing. TiO2 was the first material in which the memristor effect could be technologically realized in a controlled manner. It is the prototype for a whole class of materials exhibiting memristive behavior based on changes in the atomic arrangment, triggered by local changes in oxygen content. Here, the memristive effect is governed by two processes: the migration of oxygen deficiency defects leading to changes in the chemical composition, and the resulting crystal structure transitions. The question, which driving force resulting from the switiching current drives both of these basic processes is cruicial to undertsand th ebasic mechanism of the memristive effect. The main candidates are the electric field resulting from the external voltage acting on the charged oxygen and titatium ions, and temperature gradients caused by the heating effect of the switiching current. By static simulations, the applicant was able to demonstrate that the Coulomb force caused by the external voltage is extremely small, much smaller than the forces resulting from the thermal oscillation of the atoms. Therefore it is necessary to examine the action of temperature gradients on oxygen vacancies, i.e. sites in the regular crystal structure that normally contain an oxygen atom but are unoccupied. This undertaking turned out to be highly challenging, since first of all, since forces on these vacancies cannot be directly evaluated. The vacancy ist not a simulated object but an emergent property of the defective crystal structure. To enable the tracking and vacancy defects and even influencing their motion, a new mathematical method to find the vacabcy location depending on the coordinates of the atoms was developed. The simulation of thermal effect requires very careful simulation of the thermal motion of atoms inside the material to avoid producing false results from the thermostat algorithms employed to keep the temperature of different areas of the simulation constant. Using the combination of this vacancy location technique and advanced methods for free energy calculations, it was possible to find the ratelimiting barriers of the oxygen vacancy migration. These vary much more between different crystalline forms of titanium dioxide than expected. In order to improve the understanding of the second part of the memrisitve switching process, i.e. the vacancydriven phase transitions, an empirical model was developed which predicts energy from an the local arrangement of vacancies. This model employs the cluser expansion method and uses pattern recognition of the vacancy topology. Using this method, it could be shown, that the vacancy defects preferentially segregate into planar arrangements, seperated by large areas of undisturbed titania. A highly detailed examination of the electronic structure reveals that these planar arrangements exhibit metallic behavior, i.e. they are highly conductive, while the undisturbed TiO2 is insulating. Thus, a clear sturcture-property relationship between the arrangements of empty oxygen sites and electric resitivty could be proven. This shows that the observed phase transitions are not strictly required for the memristive effect. Instead, a wider class of crystalline phases can exhibit the same lower electric resistance, as long as they contain planar vacancy arrangements. As a side result from the vacancy migration simulation at high temperatures, it was found that oxygen deficiency leads to a pronounced reduction of the melting temperature. At the same time, heating metal oxides leads to a loss of oxygen, unless the experiment is performed in a very high oxygen content atomphere. Since the tabulated experimental melting temperature dependencies were determined by measuing the oxygen content before heating and after cooling, rather than at the melting temperature itself. This result has important implications for trying to understand the partial melting of microscopic oxide particles, where the oxygen content can vary significantly between their core and surface. Such effect are important in the sintering of ceramic materials. Future projects exploring this phenomenon further may have significant economic application potential.
Publications
- J. Chem. Theory Comput. 8.11 (2012). P. 4019
A. J. Page, T. Isomoto, J. M. Knaup, S. Irle, and K. Morokuma
(See online at https://doi.org/10.1021/ct3004639) - “Dynamic Simulation of the Migration of Oxygen Vacancy Defects in Rutile TiO2 .” In: MRS Proceedings. Vol. 1430. 2012, 1430mrss12–1430–e08–10
J. M. Knaup, M. Wehlau, and T. Frauenheim
- Physical Review B 88.22 (2013). 220101(R)
J. Knaup, M. Wehlau, and T. Frauenheim
(See online at https://doi.org/10.1103/PhysRevB.88.220101) - Phys. Status Solidi RRL (2014)
J. M. Knaup, J. Marx, and T. Frauenheim
(See online at https://doi.org/10.1002/pssr.201409042)
