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Inconsistency between linearized Thomas-Fermi approximation and electron-ionized impurity scattering rate in the
1National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn, Estonia.
Summary
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.
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.
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