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Dimensional Analysis03:40

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Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
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Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
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Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
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The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Residue-Free Fabrication of van der Waals Heterostructures of Two-Dimensional Materials
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Atomically precise graphene etch stops for three dimensional integrated systems from two dimensional material

Jangyup Son1, Junyoung Kwon2, SunPhil Kim1

  • 1Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W Green Street, Urbana, IL, 61801, USA.

Nature Communications
|September 30, 2018
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Summary
This summary is machine-generated.

Atomically precise graphene etch stops enable selective etching of 2D materials for advanced nanoelectronics. This breakthrough allows for one-step patterning of complex van der Waals heterostructures and novel devices.

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Area of Science:

  • Materials Science
  • Nanotechnology
  • Condensed Matter Physics

Background:

  • Atomically precise fabrication is crucial for next-generation technologies.
  • Patterning van der Waals heterostructures with atomic precision is a significant challenge in nanoelectronics.
  • Current methods struggle with individually addressing molecular layers in stacked 2D materials.

Purpose of the Study:

  • To develop an atomically thin graphene etch stop for precise patterning of van der Waals heterostructures.
  • To demonstrate a method for selective etching of 2D materials using xenon difluoride gas.
  • To enable one-step patterning of sophisticated nanoelectronic devices.

Main Methods:

  • Utilizing an atomically thin graphene layer as an etch stop.
  • Employing xenon difluoride gas for selective etching of 2D materials.
  • Fabricating graphene transistors with fluorinated graphene contacts.

Main Results:

  • Demonstrated selective etching of 2D materials using graphene etch stops.
  • Achieved high room temperature mobility (40,000 cm² V⁻¹ s⁻¹) in graphene transistors with fluorinated contacts.
  • Obtained low contact resistivity (80 Ω·μm) in fabricated devices.
  • Showcased versatility in 3D integrated nanoelectronics and nanoelectromechanical devices.

Conclusions:

  • Graphene etch stops provide a powerful tool for atomically precise fabrication of van der Waals heterostructures.
  • This method facilitates one-step patterning, accessing buried layers, and forming 1D contacts.
  • The demonstrated technology is versatile for advanced nanoelectronic and nanoelectromechanical systems.