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Gionni Marchetti1

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|November 1, 2018
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Calculating electron-impurity scattering with a Yukawa potential yields wave vector transfer inconsistent with the Thomas-Fermi approximation for semiconductors. This discrepancy is significant for degenerate electron dynamics but not for nondegenerate cases.

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Area of Science:

  • Condensed Matter Physics
  • Semiconductor Physics

Background:

  • Electron-impurity scattering is crucial for understanding semiconductor properties.
  • The Thomas-Fermi approximation is commonly used for electron screening in metals and semiconductors.

Purpose of the Study:

  • To investigate the consistency between electron-impurity scattering calculations and the Thomas-Fermi approximation.
  • To analyze the impact of potential form and electron degeneracy on scattering dynamics.

Main Methods:

  • Calculating the electron-impurity scattering rate using Fermi's golden rule.
  • Employing a Yukawa-form localized impurity potential.
  • Examining differential cross-sections in the first Born approximation.

Main Results:

  • The computed wave vector transfer distribution is inconsistent with the linearized Thomas-Fermi approximation for n-type semiconductors under degenerate conditions.
  • This inconsistency is not observed in nondegenerate carrier dynamics due to negligible average wave vector transfer.
  • Scattering probabilities calculated using the first Born approximation show minimal deviation (≤1%) from random phase approximation estimates for most collisions.

Conclusions:

  • The choice of impurity potential and electron degeneracy significantly affects the validity of approximations in electron-impurity scattering.
  • The linearized Thomas-Fermi approximation may not accurately describe electron screening in degenerate n-type semiconductors under certain scattering conditions.