We study the covariant entropy bound in the context of gravitational collapse. First, we discuss critically the heuristic arguments advanced by Bousso. Then we solve the problem through an exact model: a Tolman-Bondi dust shell collapsing into a Schwarzschild black hole. After the collapse, a new black hole with a larger mass is formed. The horizon, L, of the old black hole then terminates at the singularity. We show that the entropy crossing L does not exceed a quarter of the area of the old horizon. Therefore, the covariant entropy bound is satisfied in this process.
This study presents a novel method based on the surface acoustic wave (SAW) sensor, for monitoring the thickness of a silicon membrane in real time during wet etching. Similar to accelerometers and pressure sensors, some micro-electro-mechanical systems (MEMS) devices require the thickness of silicon membranes to be known precisely. Precisely controlling the thickness of a silicon membrane during wet etching is important, because the thickness strongly affects post-processing and device performance. Moreover, the proposed surface acoustic wave sensor allows the thickness of a silicon membrane to be monitored from a few µ m to hundreds of µ m in situ, which depends on the periodicity of interdigital transducers (IDT). A novel method, which differs from any in previous work on etch-stop techniques, is developed in-situ for monitoring the thickness of a silicon membrane during wet etching. In summary, the proposed method for measuring the thickness of a silicon membrane in real time, is highly accurate; is simple to implement, and can be mass-produced. This work also describes the principles of the method used, detailed process flows, the method of taking measurements and the simulated and experimental results. The theoretical and measured values differ by an error of less than 2.50µm, so the results closely agree with each other.
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