Noise In Metal Films Research Articles

Quantum theory of flicker noise in metal films

Flicker ( 1 / f γ ) voltage noise spectrum is derived from finite-temperature quantum electromagnetic fluctuations produced by elementary charge carriers in external electric field. It is suggested that deviations of the frequency exponent γ from unity, observed in thin metal films, can be attributed to quantum backreaction of the conducting medium on the fluctuating field of the charge carrier. This backreaction is described phenomenologically in terms of the effective momentum space dimensionality, D . Using the dimensional continuation technique, it is shown that the combined action of the photon heat bath and external field results in a 1 / f γ -contribution to the spectral density of the two-point correlation function of electromagnetic field. The frequency exponent is found to be equal to 1 + δ , where δ = 3 - D is a reduction of the momentum space dimensionality. This result is applied to the case of a biased conducting sample, and a general expression for the voltage power spectrum is obtained which possesses all characteristic properties of observed flicker noise spectra. The range of validity of this expression covers well the whole measured frequency band. Gauge independence of the power spectrum is proved. It is shown that the obtained results naturally resolve the problem of divergence of the total noise power. A detailed comparison with the experimental data on flicker noise measurements in metal films is given.

Onset of long-range diffusion and exponent of 1/fα noise in metal films with electromigration damage

Investigations of low-frequency conductance fluctuations have been done on silver films which have been made to undergo electromigration damage. The system shows a clear increase in noise magnitude after electromigration damage. The noise spectral power shows a distinct presence of 1/f3/2 component arising out of long-range diffusion. The temperature dependence of noise (150 K<T<350 K) shows a marked deviation from the Dutta–Horn type behavior with the 1/f3/2 term showing a strong dominance at higher temperatures. We propose that the increase of noise in metal films after electromigration damage arise predominantly from this spectral component.

Low-frequency 1/ω noise in metal films:mNonequilibrium temperatureand resistance fluctuations

It has been shown theoretically that low-frequency 1/\ensuremath{\omega} temperature fluctuations in metal films may be observed only in the presence of nonlinear Joule heating in them. A qualitative explanation of nonmonotonic Hooge 'constant'---the mean-temperature dependence for metal (Ag, Cu) films---is proposed. It has been proven that a one-to-one connection between 1/\ensuremath{\omega} fluctuations and the instability of mean-temperature profiles in Joule-heated metal films takes place. The simultaneous appearance of a 'spatial' flicker noise 1/\ensuremath{\kappa} for \ensuremath{\kappa}\ensuremath{\rightarrow}0 (\ensuremath{\kappa} is the wave number) and the 1/\ensuremath{\omega} spectrum was established in this case.

Use of a two-frequency ac bridge to measure 1/f noise in copper films.

Polycrystalline copper films have recently received considerable interest as a semiconductor interconnection metallization due to copper's low resistivity and low susceptibility to electromigration. In this paper the 1/f noise in polycrystalline copper films was measured over a temperature range of 300 to 600 K using a two-frequency ac bridge. Two lock-in amplifiers were used to demodulate the voltage across the bridge, resulting in two estimates of R(t) for the film, each measured at a different modulation frequency. The averaged cross-correlation spectrum of the two R(t) signals is a measure of the resistance fluctuation of the sample only, with no contribution from either the samples' Johnson noise and/or preamplifier noise; hence, no subtraction is necessary. With this technique we measured the noise magnitude and slope versus temperature and frequency for copper films. The temperature dependence of the noise magnitude showed a weak peak at 490 K. Using the conventional value of ${\mathrm{\ensuremath{\tau}}}_{0}$ of ${10}^{\mathrm{\ensuremath{-}}13}$ s, characteristic of point-defect diffusion, and the Dutta-Horn model for 1/f noise in metal films, we measured the mean activation enthalpy for grain boundary migration to be \ensuremath{\sim}1.1 eV. This was, subsequently, equated to the expected electromigration activation energy for copper films.

Quantitative "local-interference" model for 1/f noise in metal films.

Electron scattering calculations by Martin are used to predict the magnitude of resistivity fluctuations in metal films arising from the fluctuating interference of electrons in the local environment of a moving defect. A "local-interference" model based on these calculations accounts for the $\frac{1}{f}$-noise magnitude observed in irradiated Cu films and in room-temperature metal films. For relatively ordered metal films at room temperature this model predicts larger noise magnitudes than an alternative model based on universal conductance fluctuations, while the latter model predicts larger noise in metals that are sufficiently disordered and/or at lower temperatures.

The role of temperature in sample-to-sample comparisons of the 1/f noise of metal films

We have performed an extensive study of the 1/f noise of several different kinds of metal films fabricated in different ways. An examination of the temperature dependence of the 1/f noise of tin and indium shows that the previously reported substrate dependence of the noise magnitude generally is only present near room temperature. At other temperatures, especially lower temperatures, the substrate dependence is much smaller or negligible. The noise magnitudes of platinum and bismuth films, on the other hand, depend strikingly on the way that the sample is made, and can vary strongly from sample to sample as a function of temperature. Taken together, these results illustrate that, in contrast to common practice, the room-temperature magnitude of the 1/f noise of metal films is often not a useful parameter on which to base comparisons of the relative noise magnitudes of different films. The implications of these results for the interpretation of some previous studies are discussed, and recommendations are made about the interpretation of future studies of the 1/f noise of metal films.

Volume versus surface origin of 1/f noise in metals.

We have examined the question of whether excess low-frequency (1/f) noise in metal films arises in the bulk or at the sample surface. We measured the noise in continuous Cr films with 80 A\r{}2600 A\r{}, where t is the film thickness. Establishing that the relative noise intensity ${S}_{\ensuremath{\rho}}$(f)/${\ensuremath{\rho}}^{2}$\ensuremath{\propto}1/t supports the hypothesis that the noise is produced throughout the bulk; here, f is the frequency, \ensuremath{\rho} is the resistivity, and ${S}_{\ensuremath{\rho}}$(f) is the power spectral density of fluctuations in \ensuremath{\rho}. By considering a model of noise from the surface shunted by an underlying noise-free conductor volume, we devised a quantitative test which we used to refute the possibility that the noise arises only at the surface of our metal films.

Low-frequency current noise with a 1/fspectrum in solids

The problem of low-frequency current noise with a 1/f spectrum in solids (flicker noise) is reviewed. The fundamental general properties of this noise are described: frequency-dependence of the spectral density, time-dependence of the correlation function, form of the distribution function of the fluctuations, dependence of the spectral density on the potential applied to the specimen, anisotropy of the fluctuations of the resistivity tensor, correlation length of the fluctuations, dependence of the noise on the dimensions of the specimen and on the concentration of current carriers, the empirical Hooge relationship, etc. A model of 1/f noise is presented and discussed that associates its spectrum with the presence in solids of an extensive hierarchy of relaxation times. Concrete models of systems having an exponentially broad spectrum of relaxation times are described (the McWhorter model, two-level tunneling systems, the disordered Ising kinetic model). The theory and experimental data on current noise caused by temperature fluctuations are analyzed. The problem is treated of surface noise in semiconductors and 1/f noise in metal films.

Direct link between 1/f noise and defects in metal films.

We have found that gently annealing a AuPd film has a substantial effect on its 1/f noise. From the temperature dependence of the noise after various amounts of annealing, one can infer changes in the distribution of activation energies of the process responsible for the noise. These changes are consistent with general expectations concerning the effect of annealing on lattice defects. Our results strongly support the idea that at least some of the 1/f noise of metal films is associated with defect motion.

Temperature dependence of the 1/f noise of carbon resistors

We have studied the temperature dependence of the 1/f noise of carbon resistors, and find it to be in good qualitative agreement with the predictions of the model developed by Dutta and Horn to describe the 1/f noise of metal films. This suggests that, as seems to be the case for metals, the noise of carbon resistors is caused by an activated process with a distribution of relaxation times. However, there are small but significant quantitative discrepancies between our experimental results and the predictions of the Dutta–Horn model, and these may yield additional insight into the origin of the noise in this system.

Effect of strain on the1fnoise of metal films

The application of stress has been found to significantly affect the low-frequency excess noise of metal films. We find that in general the resulting noise is similar to the $\frac{1}{f}$ noise thought to be intrinsic to metals. Our results suggest that much of the noise observed in these systems may be caused by a process closely associated with strain relaxation.

A mechanism for 1/ƒ noise in metals

The random motion of frozen-in lattice defects is shown to provide a possible origin for 1/ƒ noise in metal films.

Formula omitted] noise in metal films: the role of the substrate : P. Dutta, J. W. Eberhard and P. M. Horn. Solid St. Commun.27, 1389 (1978)

formula omitted] noise in metal films: the role of the substrate : P. Dutta, J. W. Eberhard and P. M. Horn. Solid St. Commun.27, 1389 (1978)

Excess (1f) noise in metals

We have measured the temperature dependence of the excess ($\frac{1}{f}$) voltage noise in thin films of the group-$\mathrm{I}B$ transition metals and in Ni. In the group-$\mathrm{I}B$ metals, the magnitude of the noise increases rapidly with temperature below room temperature and reaches a peak in Ag and Cu at ${T}_{p}\ensuremath{\simeq}410$ K and ${T}_{p}\ensuremath{\simeq}490$ K, respectively. In Ag, the noise dips through a valley at approximately 520 K, and increases again up to 600 K, while in Au there is flattening but no peak up to 525 K. In Ni, a somewhat slower increase in noise magnitude with temperature is observed, but in contrast to model predictions, which suggest a sharp peak in the noise at the Curie point, only peak structure is observed near ${T}_{c}$. Measurements of the power spectrum ${S}_{v}(f)$ ($\ensuremath{\propto}{f}^{\ensuremath{-}\ensuremath{\alpha}}$) show that $\ensuremath{\alpha}$ decreases slowly with increasing temperature for all four metals. The role of the substrate is examined by measuring the noise in films on substrates whose thermal properties differ greatly (sapphire and fused silica). A comparison of the results leads to the identification of two types of noise in metal films and the explanation of some apparent contradictions in existing data.

Comment on theory of1fnoise in metal films and whiskers

A recent derivation by Liu of 1f noise from equilibrium thermal fluctuations in metal film resistors is shown to be incorrect.Received 28 April 1978DOI:https://doi.org/10.1103/PhysRevB.18.4538©1978 American Physical Society

1/ f noise in metal films: The role of the substrate

We have examined the temperature dependence of voltage (“1/ f”) noise in Cu and Ag films on quartz and sapphire substrates. Our data suggest that two types of voltage noise occur simultaneously in metal films. One type of noise depends on the substrate and is weakly temperature-dependent; the remaining noise is strongly temperature-dependent and independent of the substrate.

1fNoise from Thermal Fluctuations in Metal Films

The observed dependence of the $\frac{1}{f}$ noise in metal films on the temperature coefficient of resistance and on sample volume, and the observation of frequency-dependent spatial correlations of the noise, suggest the noise is due to a thermal-diffusion mechanism. The assumption of a spectrum for the intrinsic temperature fluctuations with an explicit $\frac{1}{f}$ region, and the condition $〈{(\ensuremath{\Delta}T)}^{2}〉=\frac{k{T}^{2}}{{C}_{V}}$, yield quantitative predictions of the noise power in excellent agreement with experiment.

Mechanism of noise formation in electric conduction in thin metal films

On the basis of an experimental study of the effect of ion absorption on the electrical conduction in thin metallic films, a theory is developed to explain current noise in metal films with a granular structure. According to these experiments, trapping of electrons in the substrate surface modulates the transmission coefficient of electrons in the intergrain tunnelling process which is responsible for the electric conduction in these films. The power spectrum of the noise is calculated and compared with the experimental results.