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The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
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Updated: Mar 7, 2026

Theoretical Calculation and Experimental Verification for Dislocation Reduction in Germanium Epitaxial Layers with Semicylindrical Voids on Silicon
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Temperature-dependent collective effects for silicene and germanene.

Andrii Iurov1, Godfrey Gumbs2,3, Danhong Huang1,4

  • 1Center for High Technology Materials, University of New Mexico, 1313 Goddard SE, Albuquerque, NM, 87106, United States of America.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|February 17, 2017
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Summary

Electron energies and polarization in silicene and germanene were calculated. These materials show similar behaviors with doping and temperature, with unique plasmon splitting relevant for future electronic devices.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Computational Physics

Background:

  • Silicene and germanene are 2D honeycomb materials with unique electronic properties.
  • Understanding their electron exchange-correlation energies and dynamical polarization is key for applications.
  • Buckled honeycomb lattices present complex behaviors influenced by temperature and external fields.

Purpose of the Study:

  • To numerically calculate electron exchange-correlation energies and dynamical polarization functions for silicene, germanene, and similar buckled lattices.
  • To analyze the impact of chemical potential, field-induced gap, and temperature on these properties.
  • To investigate plasmonic behavior and predict unique splitting in these materials.

Main Methods:

  • Numerical calculations of electron exchange and correlation energies.
  • Computation of dynamical polarization functions.
  • Analysis of temperature and chemical potential dependencies.

Main Results:

  • Electron energies increase with doping and decrease significantly at elevated temperatures.
  • Behaviors are qualitatively similar across different buckled honeycomb lattices.
  • Unique plasmon splitting was predicted in buckled lattices, distinct from gapped graphene.

Conclusions:

  • The findings provide crucial insights into the electronic and collective behaviors of silicene and germanene.
  • Results stimulate further research in electronic and transport properties.
  • The study enhances prospects for silicene-based technologies in photovoltaics and transistors.