We study thermalization in open quantum systems using the Lindblad formalism. A method that both thermalizes and couples to Lindblad operators only at edges of the system is introduced. Our method leads to a Gibbs state of the system, satisfies fluctuation-dissipation relations, and applies both to integrable and non-integrable systems. Possible applications of the method include the study of systems coupled locally to multiple reservoirs. Our analysis highlights the limits of applicability of the Lindblad approach to study strongly driven systems. arXiv:1711.02699v2 [cond-mat.stat-mech]

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High aspect ratio (HAR) structures found in three-dimensional NAND memory structures have unique process control challenges. The etch used to fabricate channel holes several microns deep with aspect ratios beyond 50:1 is a particularly challenging process that requires exquisitely accurate and precise control. It is critical to carefully analyze multiple aspects of the etch process, such as hole profile, tilt, uniformity, and quality during development and production. X-ray critical dimension (XCD) metrology, which is also known as critical dimension small-angle x-ray scattering, is a powerful technique that can provide valuable insights on the arrangement, shape, and size of periodic arrays of HAR features. XCD is capable of fast, nondestructive measurements in the cell-area of production wafers, making XCD ideal for in-line metrology. Through several case studies, we will show that XCD can be used to accurately and precisely determine key properties of holes etched into hard mask, multilayer oxide/nitride film stacks and slit trenches. We show that the measurement of hole and slit tilt can be achieved without the aid of a structural model using a Fast Tilt methodology that provides sub-nanometer precision. Measurements were performed across several production wafers to determine the etch uniformity and quality. Particular attention was given at the edge of the wafers to account for large variations observed. In addition, we used a detailed physical model to characterize the HAR structures beyond linear tilt. This approach provides a more complete picture of the etch quality.