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Proceedings Paper

Very long decay time for electron velocity distribution in semiconductors and consequent 1/f noise
Author(s): G. Cavalleri; E. Tonni; L. Bosi
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Paper Abstract

The Boltzmann equation with electron-electron (e-e) interactions has been reduced to a Fokker-Planck equation (e-e FP) in a previous paper. In steady-state conditions, its solution q0(v) (where v is the electron speed) depends on the square of the acceleration a = eE/m. If we introduce the nonrenormalized zero-point field (ZPF) of QED, i.e., the one considered in stochastic electrodynamics, so that ⟨a2⟩ = ⟨(aD.C. + aZPF)2⟩ ≃ a2ZPF, then q0(v) becomes similar to the Fermi-Dirac equation, and the two collision frequencies ν1(v) and ν2(v) appearing in the e-e FP become both proportional to 1/v in a small &dgr;v interval. The condition υ1(v) ∝ υ2(v) ∝ 1/v is at the threshold of the runaways. In the same &dgr;v range, the time-dependent solution q0(v, &tgr;) of the e - e FP decays no longer exponentially but according to a power law ∝ &tgr;-&egr; where 0.004 < &egr; < 0.006, until &tgr; → ∞. That extremely long memory of a fluctuation implies the same dependence τ-&egr; for the conductance correlation function, hence a corresponding power-spectral noise S(f)∝ f&egr;-1 where f is the frequency. That behaviour is maintained even for a small sample because the back diffusion velocity of the electrons in the effective range &dgr;v, where they are in runaway conditions, is much larger than the drift velocity.

Paper Details

Date Published: 8 June 2007
PDF: 11 pages
Proc. SPIE 6600, Noise and Fluctuations in Circuits, Devices, and Materials, 66000M (8 June 2007); doi: 10.1117/12.729352
Show Author Affiliations
G. Cavalleri, CNR-INFM and Univ. Cattolica del Sacro Cuore (Italy)
E. Tonni, CNR-INFM and Univ. Cattolica del Sacro Cuore (Italy)
L. Bosi, CNR-INFM and Politecnico di Milano (Italy)

Published in SPIE Proceedings Vol. 6600:
Noise and Fluctuations in Circuits, Devices, and Materials
Massimo Macucci; Lode K.J. Vandamme; Carmine Ciofi; Michael B. Weissman, Editor(s)

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