Prof. Giancarlo Cavalleri Profile

Prof. Giancarlo Cavalleri

at Univ Cattolica del Sacro Cuore

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Proceedings Article | 8 June 2007 Paper

Very long decay time for electron velocity distribution in semiconductors and consequent 1/f noise

G. Cavalleri, E. Tonni, L. Bosi

Proceedings Volume 6600, 66000M (2007) https://doi.org/10.1117/12.729352

KEYWORDS: Semiconductors, Diffusion, Correlation function, Particles, Oscillators, Metals, Stochastic processes, Electrodynamics, Scattering, Chemical species

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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⟩ = ⟨(a_D.C. + a_ZPF)²⟩ ≃ a²_ZPF, 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.

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