Monte Carlo simulation of time-dependent dielectric breakdown of oxide caused by migration of oxygen vacancies

In this article, the Monte Carlo method is used to study the formation and migration of oxygen vacancies in metal oxide dielectric. The time-dependent breakdown of the dielectric is simulated. In the direction of the electric field across the metal oxide, the migration barrier and migration work function of oxygen vacancies are found to be reduced by the applied electric field. This finding provides a good foundation for further studying the breakdown mechanism and evaluating the reliability of high κ gate dielectric. The Monte Carlo process is described as follows. Firstly, a three-dimensional metal oxide dielectric layer is built with two-dimensional symmetrical grid, where the thickness of the oxide layer is set to be 9 lattice points and the oxygen vacancies can migrate to the adjacent 8 arbitrary lattice positions in this simulation. Secondly, the possibilities of formation and migration of oxygen vacancies are calculated according to the distribution of oxygen vacancies. Finally, the Monte Carlo method is used to simulate the new distribution of oxygen vacancies. Therefore, we simulate the breakdown process of the metal oxide dielectric layer with different oxygen vacancy migration functions (E_a=1:15, 1.35 eV) at the interface. And we obtain the results as follows. 1) When the migration function is small, many oxygen vacancies accumulate largely at the forming interface. And the vacancies would migrate from the interface to the dielectric, forming a conductive channel. The breakdown time is determined by the migration barrier of oxygen vacancies in the dielectric. 2) When the migration function of the oxygen vacancies at the interface becomes larger, the formed oxygen vacancies will rapidly migrate to the other interface, and the reverse propagation of the conductive channel causes the dielectric breakdown. Therefore, larger migration function of the oxygen vacancies at the interface can effectively improve its reliability. 3) The original defects within the dielectric will seriously influence the migration of oxygen vacancies, and the breakdown is easier to occur with more primary defects. 4) The simulation shows that the oxygen vacancy migration function can be improved by optimizing the interface formation process. And the breakdown time could also be prolonged. Therefore, this simulation tool can be applied to the research of metal-oxide-semiconductor transistor gate dielectric breakdown and the assessment of its reliability accurately.