Ab-Initio Modeling of the Resistance Switching Mechanism in RRAM Devices: Case Study of Hafnium Oxide (HfO 2 )
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Ab-Initio Modeling of the Resistance Switching Mechanism in RRAM Devices: Case Study of Hafnium Oxide (HfO2) Dan Duncan1, Blanka Magyari-Kope1, and Yoshio Nishi1 1 Stanford University Department of Electrical Engineering, 350 Serra Mall Stanford, CA, U.S.A. ABSTRACT The structures and energies of stoichiometric and oxygen-deficient monoclinic HfO2 were calculated using density functional theory. The electronic interactions in HfO2 were calculated using the LDA+U and GGA+U formalisms, where on-site Coulomb corrections were applied to the 5d electrons of hafnium (Ud) and the 2p electrons of oxygen (Up). Properties calculated using these techniques are compared to results obtained from LDA, GGA, hybrid functionals, and experiment. Ultimately, we show that LDA+Ud+Up and GGA+Ud+Up calculations of HfO2's electronic and structural properties achieve a level of accuracy on par with much more computationally demanding hybrid functional techniques, such as PBE0 and HSE06. INTRODUCTION Hafnium oxide is a material that is most well known for its application as a high-k dielectric in advanced gate stacks.1-3 However, due to its resistance switching (memristive) properties, it has recently become a material of interest for nonvolatile solid state memory applications as well. Many other oxides are also being explored for this purpose, although hafnium oxide has the advantage of also being currently used in integrated circuit fabrication processes. Hafnium oxide's resistive switching behavior is mediated by the motion of oxygen vacancies as a result of an applied voltage or current pulse at its electrodes.4 This vacancy migration can form or sever a conductive filament between the electrodes, thus switching between a low-resistance state (LRS) and a high-resistance state (HRS). While this general understanding exists, a detailed picture of the mechanisms of forming, switching, and conduction is still lacking. As a result, many control and reliability issues exist in hafnium oxide resistancechange memory (HfO2 RRAM) devices. In particular, it is currently difficult to tightly control such macroscopic properties as SET and RESET voltages and currents, as well as ON and OFF resistance values (LRS and HRS).5-8 There are many parameters that can be tuned to tighten the statistical distribution of device properties, such as deposition methods,10,11 anneal temperature,9 oxide material,4 electrode materials,9,12,13 doping and impurities,9 and use of multi-layer oxide stacks.5,14 However, it is difficult to effectively optimize these parameters without a firmer understanding of the underlying physics. This presents an opportunity to use density functional theory simulation techniques to demonstrate the relationship of nanoscale quantities, such as vacancies and defect states, with macroscopic quantities that can be experimentally measured. For example, in previous theoretical work,6,7,28 it has been shown that thermodynamically-stable filament structures can be formed by ordered chains of single oxygen vacancies or O vacancy pairs. In order
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