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Related Concept Videos

Resistivity01:22

Resistivity

4.1K
When a voltage is applied to a conductor, an electrical field is generated, and charges in the conductor feel the force due to the electrical field. The current density that results depends on the electrical field and the properties of the material. In some materials, including metals at a given temperature, the current density is approximately proportional to the electrical field. In these cases, the current density can be modeled as:
4.1K
Electrical Conductivity01:13

Electrical Conductivity

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In perfect conductors, the electric field inside is always zero due to the abundance of free electrons, which nullify any field by flowing. As a result, any residual charge resides on the surface.
In a practical conductor, an applied electric field may be sustained, causing a flow of electrons, which produce a current. The differential form of the current, the current density, is related to the electric field.
More generally, it is related to the force per unit charge, which involves the...
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Non-ohmic Devices00:51

Non-ohmic Devices

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In most substances, the current flow is proportional to the voltage applied to it. A simple relationship between the values of current, voltage, and resistance is known as Ohm's law. Nonohmic devices do not exhibit a linear relationship between voltage and current. One such device is the semiconducting circuit element known as a diode. A diode is a circuit device that allows current flow in only one direction.
Consider a simple circuit consisting of a battery, a diode, and a resistor. A...
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Resistance and Conductance01:25

Resistance and Conductance

253
A conductor's DC resistance at a given temperature is influenced by its resistivity, length, and cross-sectional area. Resistivity is an inherent property of the conductor material, with annealed copper serving as the international standard for measurement. For instance, the resistivity of hard-drawn aluminum at 20 degrees Celsius is 61% of the standard conductivity of annealed copper.
Various factors impact the resistance of a conductor. Spiraling in stranded conductors increases their...
253
Electric Field of Parallel Conducting Plates01:16

Electric Field of Parallel Conducting Plates

1.4K
Gauss' law relates the electric flux through a closed surface to the net charge enclosed by that surface. Gauss's law can be applied to find the electric field and the charge enclosed in a region depending on its charge distribution.
Consider a cross-section of a thin, infinite conducting plate having a positive charge. For such a large thin plate, as the thickness of the plate tends to zero, the positive charges lie on the plate's two large faces. Without an external electric field, the...
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Resistance01:19

Resistance

5.4K
When a current moves through any conductor, the conductor causes some level of difficulty for the current to flow. The measure of that difficulty is known as the resistance of the material and is represented by R. Every material has its own resistance. In the case of conductors, heat is emitted whenever a current passes through them. Resistance depends on the resistivity of the material. Resistivity is a characteristic of the material used to fabricate electrical components, whereas the...
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Effective electrical resistivity in a square array of oriented square inclusions.

Benny Guralnik1,2, Ole Hansen3, Henrik H Henrichsen1

  • 1CAPRES-a KLA company, Diplomvej 373B, DK-2800 Kgs. Lyngby, Denmark.

Nanotechnology
|January 14, 2021
PubMed
Summary
This summary is machine-generated.

This study presents a generalized formula for the effective electrical resistivity of nanostructured grids, crucial for quality control in miniaturized devices. The new approximation accurately models various inclusion sizes, aiding nanofabrication metrology.

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Area of Science:

  • Nanotechnology
  • Materials Science
  • Electrical Engineering

Background:

  • Miniaturization of optoelectronic devices and rise of metamaterials challenge nanofabrication.
  • Need for array-based metrologies for quality control of nanoscale features.
  • Square grids with quadratic sub-features are common in nanotechnology.

Purpose of the Study:

  • To generalize the effective electrical resistivity (ρ_eff) for thin sheets with doubly-periodic arrays of square inclusions.
  • To provide a closed-form approximation for ρ_eff applicable to arbitrary inclusion sizes (0 < c < 1).
  • To develop data reduction schemes for micro four-point probe (M4PP) metrology of periodic nanostructures.

Main Methods:

  • Combined first-principle approximations, numerical modeling, and mathematical analysis.
  • Developed an approximation formula for ρ_eff valid for inclusion sizes 0.01 ≤ c ≤ 0.99.
  • Validated the approximation against finite element simulations, achieving <0.3% error.

Main Results:

  • A generalized approximation for ρ_eff is derived: [Formula: see text] [Formula: see text].
  • Asymptotic values for α were found at limiting cases: α → 2.039 (c → 0) and α → 1/c - 1 (c → 1).
  • The approximation's applicability to complex structures (nested inclusions, nonplanar topologies) was demonstrated.

Conclusions:

  • The developed formula provides accurate effective electrical resistivity for periodic nanostructures.
  • This work addresses a critical gap in metrology for nanoscale periodic materials.
  • The findings support advanced quality control in nanofabrication for optoelectronics and metamaterials.