Hooge Formula Research Articles

1/f noise: A nonlinear-generalized-Langevin-equation approach.

The spectrum of the autocorrelation function of the velocity fluctuations is calculated by using the nonlinear generalized Langevin equation which has a random force which is a function of the coordinates of the Brownian particle. We show that while the Nyquist noise and the persistent correlation can be obtained by using the linear generalized Langevin equation, the extra contribution to the noise spectrum due to the nonlinear effect in the nonlinear generalized Langevin equation is inversely proportional to the total number of particles and to a negative power of the frequency. In a hydrodynamic calculation, we derive a formula for the excess noise which has a frequency dependence ${\mathrm{\ensuremath{\omega}}}^{\mathrm{\ensuremath{-}}(4\mathrm{\ensuremath{-}}\mathit{d})/2}$ for the two- and three-dimensional cases (d=2 and 3, respectively). A detailed analysis shows that our two-dimensional excess-noise formula agrees with the empirical Hooge formula, and the theoretical form of the Hooge parameter which we obtain is consistent with the known experimental results. In a many-body calculation, similar results are obtained. Physically, we argue that the 1/f noise arises from at least two basic phenomena: (a) vorticity diffusion in the classical case (or weak localization in the quantum case), and (b) the deviation of the diffusion coefficient from its conventional value due to boundary confinement effects or effects due to low dimensionality.

Interpretation of Hooge's noise formula

Abstract It is emphasized that the appearance of the total number of free carriers in the denominator of the Hooge formula is experimentally established. The earlier interpretation based on independently fluctuating carrier mobilities yields a result which is inconsistent with the correlation-length experiments. Two interpretations are given. The first was based on some fundamental experiments, giving rise, however, to physical questions. The second yields a picture in which the intensity of the 1 ƒ noise sources are related to the Debye length. If the second interpretation is correct, then a re-evaluation of part of the basic experiments is necessary.

A discussion on the “magic number” in Hooge's formula

AbstractAn expression of the “magic number” is given in this paper. On the basis of the expression some important experimental phenomena about 1/f noise are reasonably explained.

Comments on "A theory of the Hooge parameters of solid-state devices"

Handel's quantum theory of 1/f (Q.T.) was developed in the above paper in an ambitious attempt to explain the ubiquity of 1/f noise [1]-[3]. The theory has been used to derive the Hooge equation [4], which in turn has been used for many years now in analyses of experimental data (e.g., [5], [6]). The purpose of this comment is to point out serious flaws in Q.T. and to list recent empirical results which are not explained by the Hooge formula or any of its revisions.

Resistivity dependence of1fnoise in metal films

The $\frac{1}{f}$ noise of a number of different types of metal films has been studied at room temperature. We find that the noise of nominally identical samples can vary by as much as a factor of 10, which is well outside the estimated experimental uncertainties for the quantities thought to be relevant in determining the noise. This suggests that some other variables play an important role in the noise process. Despite these sample-to-sample variations, we find that the minimum level of $\frac{1}{f}$ noise for a given metal is a fairly well-defined quantity. Moreover, the minimum noise level exhibits a systematic resistivity dependence which has not been observed previously, and which cannot be accounted for by the semiempirical formula of Hooge. These results are compared with those of previous workers, and a modification of Hooge's formula is suggested.

A positive temperature coefficient thermistor bolometer

This article describes the performance of a thermistor bolometer using a positive temperature coefficient ceramic element operated at 397K. The temperature coefficient of resistance was 75%°C −1 and for operation at 10 V and 10 Hz with a 3 Hz bandwidth the response to 5 × 10 −5 W of incident 500K black body radiation yielded a D ∗ near 10 8cm W −1 Hz 1 2 after normalisation to 100% absorption. Johnson noise limitation leads to a calculated D ∗ j near 10 10cm W −1 Hz 1 2 and the low observed value is shown to be due to excess 1/ f noise. On the basis of a modified Hooge formula for the excess noise it is predicted that temperature fluctuation noise limited performance should be possible with improved ceramics.