1/f-Noise in Hall Voltage

Abstract

The relative 1/f noise spectral density of a homogeneous semiconductor can generally be represented by the empirical relation $S_V /V^2 = S_G /G^2 = \alpha /Nf$ , where V is the voltage applied to the conductor, G the conductance, a is an experimental constant of about 2x10^-3, N is the total number of free charge carriers, and f is the frequency [1]. It is assumed that the 1/f fluctuations are spatially independent. Furthermore, from 1/f noise in thermo-emf, it is concluded that 1/f fluctuations in the conductance are energetically uncorrelated [2]. Hence the cross-correlation spectral density of 1/f fluctuations in the conductivity can be written as

$$ S_\sigma \left( {\vec r_1 ,\vec r_2 ,\varepsilon _1 ,\varepsilon _2 ,f} \right) = \frac{{a'}} {{n\left( {\varepsilon _1 } \right)f}}\sigma _0^2 \left( {\varepsilon _1 } \right)\delta \left( {\vec r_1 - \vec r_2 } \right)\delta \left( {\varepsilon _1 - \varepsilon _2 } \right) $$

(1)

where σ(ε) and n(ε) are the conductivity and carrier density with energy ε. For lattice scattering $a' = \left( {8/3\pi } \right)\alpha \left[ 3 \right]$. For fluctuations in the number of free charge carriers, the conductivity fluctuations are energetically correlated. Consequently 1/f noise cannot be caused by number fluctuations but is caused by mobility fluctuations [2].