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Related Concept Videos

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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.
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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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Related Experiment Video

Updated: Jan 28, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
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Band alignment in quantum wells from automatically tuned DFT+U.

Grigory Kolesov1, Chungwei Lin, Andrew Knyazev

  • 1Mitsubishi Electric Research Laboratories, 201 Broadway, Cambridge, MA 02139, USA. gkolesov@seas.harvard.edu.

Physical Chemistry Chemical Physics : PCCP
|March 7, 2019
PubMed
Summary
This summary is machine-generated.

We present a practical DFT+U method to accurately calculate band alignment in quantum wells. This approach efficiently determines band offsets, even for complex alloys, with computational costs similar to LDA.

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Area of Science:

  • Materials Science
  • Computational Physics
  • Solid-State Chemistry

Background:

  • Band alignment is crucial for semiconductor devices, but traditional methods like Density Functional Theory (DFT) have limitations.
  • Standard DFT approximations (LDA, GGA) underestimate bandgaps, while accurate hybrid methods are computationally expensive for large systems like quantum wells.

Purpose of the Study:

  • To develop a computationally efficient and accurate method for calculating band alignment in quantum wells.
  • To apply the DFT+U method with tunable parameters to predict band offsets in complex alloy systems.

Main Methods:

  • Utilized the DFT+U method, treating the 'U' parameter as tunable for each atomic shell.
  • Automated fitting of bulk bandgap and lattice constant to determine optimal 'U' parameters.
  • Applied the derived 'U' parameters to large supercell calculations for band alignment determination in quantum wells.

Main Results:

  • Successfully applied the method to InP/In0.5Ga0.5As, In0.5Ga0.5As/In0.5Al0.5As, and InP/In0.5Al0.5As quantum wells.
  • Achieved good agreement between calculated band offsets and experimental results.
  • The method accounts for lattice relaxation, providing accurate valence and conduction band offsets.

Conclusions:

  • The proposed DFT+U approach offers a practical and computationally feasible alternative for accurate band alignment calculations.
  • This method provides reliable band offsets for complex semiconductor alloys, bridging the gap between computational cost and accuracy.
  • The technique is valuable for predicting band alignments in advanced material systems relevant to nanotechnology and optoelectronics.