The equilibrium ON and OFF states of resistive random access memory (RRAM) are due to formation and destruction of a conducting filament. The laws of thermodynamics dictate that these states correspond to the minimum of free energy. Here, we develop a numerical model that, through the minimization of free energy at a given voltage, determines the filament parameters and thus the electric current. Overall, it simulates the current-voltage (I-V) characteristics of RRAM. The model describes mutual transformations of RRAM states through SET (ON→OFF) and RESET (OFF→ON) processes. From the modeling perspectives, these states and processes constitute four programming modules constructed here in COMSOL Multiphysics software tackling the electrodynamic and heat transfer equations and yielding RRAM energy and I-V. Our modeling uniquely reproduces the observed I-V varying with voltage ramp-rates. That is achieved by accounting for the ramp-rate dependent activation energy of conduction. The underlying mechanism is due to the deformation interaction caused by the double well atomic potentials universally present in amorphous materials and having exponentially broad distribution of relaxation times. As another unique feature, our modeling reproduces the observed cycle-to-cycle variations of RRAM parameters attributed to the lack of self-averaging in small ensembles of double well potentials and electronic states in geometrically small (nano-size) RRAM structures. * Electronic address: dipesh.niraula@rockets.utodeo.edu † Electronic address: victor.karpov@utoledo.edu FIG. 1: Top left: Schematic of the circuitry where input voltage source VS, load resistor RL and a simple RRAM device RD are connected in series. Bottom left: plot of input voltage pulse where λ is the voltage ramp-rate and Vamp is the amplitude. Top right: Representation of a typical I-V characteristics of RRAM [4-7]. VD is the voltage drop across RRAM device. The SET current ISET is the maximum current limited by the Vamp. Bottom right: Customary representation of the I-V with absolute valued current axis. The dashed domain represents very fast nucleation processes.the source voltage ramping; they represent the SET and RESET processes. Their characteristic features are voltage snapback A-B followed by the vertical domain B-C for SET, and voltage snapforward D-E followed by the horizontal domain E-F for RESET. arXiv:1806.01397v2 [cond-mat.mes-hall]
We study the heat transport in filamentary RRAM nano-sized devices by comparing the accurate results of COM-SOL modeling with simplified analytical models for two complementary mechanisms: one neglecting the radial heat transfer from the filament to the insulating host, while the other describing the radial transport through the dielectric in the absence of the filament heat transfer. For the former, we find that the earlier assumed simplification of the electrodes being ideal heat conductors is insufficient; a more adequate approximation is derived where the heat transport is determined by the adjacent proximities of the filament tips in the electrodes. We find that both complementary mechanisms overestimate the maximum temperature yet offering acceptable results. However, the two in parallel provide a better analytical approximation. In addition, we show that the Wiedemann-Franz-Lorenz law helps the analysis when the Lorenz parameter is chosen from the actual data. We present an approximate expression for the SET voltage possessing a high degree of universality and predicting that filament materials with low Lorenz numbers can be good candidates for the future low set voltage devices.Index Terms-Heat transfer, resistive random access memory (RRAM), switching.
Subtle differences in a patient’s genetics and physiology may alter radiotherapy (RT) treatment responses, motivating the need for a more personalized treatment plan. Accordingly, we have developed a novel quantum deep reinforcement learning (qDRL) framework for clinical decision support that can estimate an individual patient’s dose response mid-treatment and recommend an optimal dose adjustment. Our framework considers patients’ specific information including biological, physical, genetic, clinical, and dosimetric factors. Recognizing that physicians must make decisions amidst uncertainty in RT treatment outcomes, we employed indeterministic quantum states to represent human decision making in a real-life scenario. We paired quantum decision states with a model-based deep q-learning algorithm to optimize the clinical decision-making process in RT. We trained our proposed qDRL framework on an institutional dataset of 67 stage III non-small cell lung cancer (NSCLC) patients treated on prospective adaptive protocols and independently validated our framework in an external multi-institutional dataset of 174 NSCLC patients. For a comprehensive evaluation, we compared three frameworks: DRL, qDRL trained in a Qiskit quantum computing simulator, and qDRL trained in an IBM quantum computer. Two metrics were considered to evaluate our framework: (1) similarity score, defined as the root mean square error between retrospective clinical decisions and the AI recommendations, and (2) self-evaluation scheme that compares retrospective clinical decisions and AI recommendations based on the improvement in the observed clinical outcomes. Our analysis shows that our framework, which takes into consideration individual patient dose response in its decision-making, can potentially improve clinical RT decision-making by at least about 10% compared to unaided clinical practice. Further validation of our novel quantitative approach in a prospective study will provide a necessary framework for improving the standard of care in personalized RT.
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