Abstract
In chapter I, we have linearized the problem of screening by writing exp(e φ/k B T) ≈ 1 + e φ/k B T for the case of classical statistics and \( \int_{E_F }^{E_F + e\varphi } \eta (E) dE \approx \eta (E_F )e\varphi \) for the case of the degenerate Fermi gas. These approximations are justified only for |φ| small, namely in the limiting cases \( \left| \varphi \right| \ll k_B T/e \), respectively. In practice, many situations are encountered where this linear approximation is not usable. In the present chapter, we will first outline a general framework for addressing such problems, then illustrate it through various examples taken from semiconductor physics, and show how a similar approach may apply to electrochemical and biophysical problems. Finally, we will consider the case of degenerate Fermion systems and discuss the limitations and the possible improvements of this approach.
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Chazalviel, JN. (1999). Screening of a Static Charge Distribution Beyond the Linear Regime. In: Coulomb Screening by Mobile Charges. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1762-6_3
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DOI: https://doi.org/10.1007/978-1-4612-1762-6_3
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