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Related Concept Videos

Hydrostatic Pressure Force on a Curved Surface01:04

Hydrostatic Pressure Force on a Curved Surface

Hydrostatic pressure on curved surfaces is a fundamental concept in fluid mechanics with broad applications in the civil engineering field. When fluid is in contact with a curved surface, as in a reservoir, dam, or storage tank, it exerts pressure that varies in magnitude and direction along the curved surface. To assess the total hydrostatic force exerted by the fluid on a curved structure, engineers typically isolate the fluid volume adjacent to the surface and analyze the forces acting on...
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Surface tension is defined as the force per unit length (γ) acting along the surface of a liquid. It arises due to strong intermolecular forces of attraction. A molecule located inside the bulk of the liquid is surrounded by other molecules and experiences equal forces in all directions. However, a molecule at the surface experiences unbalanced forces because there are more neighboring molecules below than above. This creates a net inward force that pulls surface molecules toward the interior,...
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A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...
Tangent Planes to Level Surfaces01:31

Tangent Planes to Level Surfaces

A level surface consists of all points in space where a function of three variables takes the same fixed value. If a point lies on this surface, understanding the surface’s geometry there requires more than just knowing the point’s coordinates; it requires describing how the surface is oriented, or how it tilts, near that point.To probe this local geometry, imagine tracing a path that stays entirely on the level surface and passes through the point of interest. This path can be described as a...
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Related Experiment Video

Updated: Jun 15, 2026

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
06:34

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

Published on: January 6, 2023

Generation of periodic surface corrugations.

L F Johnson, G W Kammlott, K A Ingersoll

    Applied Optics
    |March 4, 2010
    PubMed
    Summary

    This study analyzes surface corrugation generation using ion-beam milling and chemical etching for fine-period gratings on GaAs. It details methods to optimize groove depth and aspect ratio for efficient fabrication.

    Area of Science:

    • Materials Science
    • Nanofabrication
    • Optics

    Background:

    • Periodic surface corrugations are crucial for optical and electronic devices.
    • Fabricating deep grooves with fine periods (Lambda < 3000 Å) on substrates like GaAs presents significant challenges.
    • Understanding the interplay between lithography, etching, and substrate properties is essential for optimizing grating generation.

    Purpose of the Study:

    • To analyze the generation of periodic surface corrugations via ion-beam milling and chemical etching.
    • To develop a general treatment for grating fabrication on substrates with arbitrary reflectivity.
    • To identify optimal conditions for creating deep grooves and fine periods on GaAs.

    Main Methods:

    • Analysis of photoresist intensity distribution considering p- and s-polarized beams and substrate reflectivity.

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    Last Updated: Jun 15, 2026

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    Published on: January 6, 2023

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  • Modeling of standing wave effects and intensity maxima at the photoresist-substrate interface.
  • Examination of ion-beam milling erosion profiles and their influence on groove geometry.
  • Investigation of combined ion-beam milling and chemical etching techniques.

    • Main Results:

    • P-polarized beams reduce standing waves, but substrate reflectivity and incidence angle limit groove depth.
    • Optimal conditions for intensity maximum at the interface were determined for chemical etching.
    • A quarterwave intermediate oxide layer on GaAs imposes a lower limit on grating period.
    • Groove aspect ratio in GaAs is limited to approximately 1.2, even at the photoresist's maximum removal rate.
    • A combination of milling and etching achieved gratings with aspect ratios >0.6 on GaAs.

    Conclusions:

    • The study provides a comprehensive analysis for fabricating fine-period gratings on GaAs.
    • Optimized process parameters are identified to overcome limitations in groove depth and aspect ratio.
    • Effective methods combining ion-beam milling and chemical etching enable high-quality grating fabrication.