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Quantum Numbers02:43

Quantum Numbers

52.4K
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
52.4K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

59.8K
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.
59.8K
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal Field Theory - Tetrahedral and Square Planar Complexes

48.7K
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
48.7K
The Dot Product01:26

The Dot Product

266
Measuring how one directional quantity affects another along a specific path involves comparing their orientation and strength. When two such quantities are represented using direction and amount, a numerical result is computed to show how much one acts along the path of the other. This result comes from a rule combining both inputs' horizontal and vertical parts and adding the results.This calculation gives a single value that grows larger when both inputs point in similar directions and...
266
Dot Product01:29

Dot Product

1.0K
The dot product is an essential concept in mathematics and physics.
In engineering, the dot product of any two vectors is the product of the magnitudes of the vectors and the cosine of the angle between them. It is denoted by a dot symbol between the two vectors.
Consider a vehicle pulling an object along the ground using a rope. If the rope makes an angle with the horizontal axis, the work done can be calculated using the dot product of the force applied and the object's displacement.
The dot...
1.0K
Dot Product: Problem Solving01:21

Dot Product: Problem Solving

724
The dot product is a powerful tool in problem-solving involving vectors, given that the dot product of two vectors is the product of their magnitudes and the cosine of the angle between them measured anti-clockwise. Solving problems involving the dot product requires understanding its properties and developing a step-by-step process to solve them. Here are the main steps to follow when solving any general problem involving the dot product:
Identify the problem: Start by reading the problem and...
724

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Related Experiment Video

Updated: Feb 15, 2026

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
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Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Published on: June 3, 2015

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A fabrication guide for planar silicon quantum dot heterostructures.

Paul C Spruijtenburg1, Sergey V Amitonov1, Wilfred G van der Wiel1

  • 1NanoElectronics Group, MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands.

Nanotechnology
|February 1, 2018
PubMed
Summary

Fabricating silicon quantum dots requires careful control of material properties and fabrication processes to avoid defects. This work details key considerations for creating high-quality, electrostatically defined quantum dots for quantum computing applications.

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Area of Science:

  • Quantum Information Science
  • Materials Science and Engineering
  • Solid State Physics

Background:

  • Quantum dots are essential building blocks for quantum technologies.
  • Fabricating high-quality quantum dots in silicon presents significant challenges.
  • Existing literature often lacks detailed discussion on critical fabrication considerations.

Purpose of the Study:

  • To outline crucial factors for the top-down fabrication of planar quantum dots in silicon.
  • To highlight the interplay between material properties, interfaces, and fabrication processes.
  • To provide insights applicable to various quantum dot systems.

Main Methods:

  • Discusses critical process parameters for silicon quantum dot fabrication.
  • Details considerations for oxidation, physical vapor deposition, and atomic-layer deposition.
  • Emphasizes tailoring processes to mitigate defects and disorder.

Main Results:

  • Identifies key challenges in achieving electrostatically defined quantum dots.
  • Demonstrates the importance of process control to prevent unwanted side effects like defects and dewetting.
  • Presents techniques used in parallel studies for depletion-mode and palladium-gated quantum dots.

Conclusions:

  • Successful fabrication of planar silicon quantum dots relies on meticulous control of intrinsic properties and interfaces.
  • The described principles are general and applicable to 0D and 1D quantum systems.
  • This work provides a foundational guide for researchers in quantum dot fabrication.