1/f noise

1/f noise is a nonstationary random process suitable for modeling evolutionary or developmental systems. It combines the strong influence of past events on the future and, hence somewhat predictable behavior, with the influence of random events. Nonstationary autocorrelation functions for 1/f noise are developed to demonstrate that its present behavior is equally correlated with both the recent and distant past. The minimum amount of memory for a system that exhibits 1/f noise is shown to be one state variable per decade of frequency. The system condenses its past history into the present values of its state variables, one of which represents an average over the most recent 1 unit of time, one for the last 10 time units, 100 units, 1000, 10000, and so on. Each such state variable has an equal influence on present behavior.     

1/f noise sources

This survey deals with 1/f noise in homogeneous semiconductor samples. A distinction is made between mobility noise and number noise. It is shown that there always is mobility noise with an α value with a magnitude in the order of 10^-4. Damaging the crystal has a strong influence on α, α may increase by orders of magnitude. Some theoretical models are briefly discussed none of them can explain all experimental results. The α values of several semiconductors are given. These values can be used in calculations of 1/f noise in devices     

Theory of 1/f noise in bipolar silicon planar transistors

A theory of 1/f low-frequency noise in silicon planar transistors is developed. It relates this noise to fluctuations in base current produced by fluctuations of occupied traps in the silicon dioxide. It is shown that the theoretical relationship of noise is consistent with experiment.     

Estimation of 1/f noise

Several models have emerged for describing 1/f^γ noise processes. Based on these, various techniques for estimating the properties of such processes have been developed. This paper provides theoretical analysis of a new wavelet-based approach which has the advantages of having low computational complexity and being able to handle the case where the 1/f^γ noise might be embedded in a further white-noise process. However, the analysis conducted here shows that these advantages are balanced by the fact that the wavelet-based scheme is only consistent for spectral exponents γ in the range γ∈(0, 1). This is in contradiction to the results suggested in previous empirical studies. When γ∈(0, 1) this paper also establishes that wavelet-based maximum-likelihood methods are asymptotically Gaussian and efficient. Finally, the asymptotic rate of mean-square convergence of the parameter estimates is established and is shown to slow as γ approaches one. Combined with a survey of non-wavelet-based methods, these new results give a perspective on the various tradeoffs to be considered when modeling and estimating 1/f^γ noise processes     

Simplified 1/f noise calculations

A new tool, called the equivalent number of decades ND/sub e/, is introduced to simplify the analysis of noise in circuits containing 1/f noise sources. ND/sub e/ is similar to the familiar concept of equivalent noise bandwidth for white sources. A simple expression for ND/sub e/ is derived for a single-pole lowpass filter and is shown to be approximately correct for Butterworth and Chebyshev filters as well.<>     

Unified presentation of 1/f noise in electron devices: fundamental 1/f noise sources

1/f noise in semiconductors, semiconductor devices, and collision-free devices (like vacuum tubes) is presented from a unified point of view, using an extended version of the F.N. Hooge equation (Physica, vol. 83b, p.9, 1976), which is generalized to all collision-dominated systems involving mobility, diffusion, and cross-section fluctuations. It also applies to collision-free processes involving vacuum tubes, Schottky barrier diodes operating in the thermionic mode, and in devices such as p-i-n diodes in which collision processes are not the determining factor. A generalized schematic is given for expressing the noise spectrum S/sub 1/(f) in the external circuit in terms of distributed noise sources of the nonuniform devices in terms of alpha /sub H/, so the latter can be determined from the former. It is then found that the Hooge parameter. alpha /sub H/ introduced by this equation can be used as a general measure of the noisiness of a system or device. Several cases in which the noise does not obey the quantum 1/f noise theory are discussed. Measurements on many different devices are examined, and an attempt is made to correlate measured values of the Hooge parameter with the values calculated from P.H. Handel's quantum theory of 1/f noise (1975, 1980).<>     

Leakage currents, surface current and 1/f noise in planar bipolar transistors

Using arguments based on the d.c. equivalent circuit of a planar bipolar transistor, it is shown that the ratio ICEO/ICBO is a measure of the significance of surface recombination current. Measurements of 1/f noise and ICEO/ICBO for a variety of transistors provide new evidence that the 1/f noise is due to the surface recombination current.     

Measurement of white and 1/f noise within burst noise

A measurement method is described which enables the separate measurement of the power spectra of the normal noise (white and l/f) superimposed on burst noise. With this method the power spectra of normal noise can be determined for each burst noise level. It is found that the clean burst noise and the superimposed normal noise are generated by statistically independent processes. The fact that burst noise devices have a higher 1/f noise power content than devices without burst noise indicates that there exists a common condition for the generation of burst noise and 1/f noise.     

1/f noise in multicarrier systems

The 1/f noise power produced by several r.f. carrier currents in a carbon resistor is shown to be proportional to the total r.f. power dissipated in the resistor. This confirms that the noise is not a consequence of resistance fluctuations.     

Variance fluctuations of 1/f noise

The difference in behaviour between the variances of 1/f noise and of thermal noise is related to the differences in the ratios of fourth moment to the second moment of the distributions. This ratio is found experimentally to be significantly different in the two cases.     

1/f noise in HgCdTe photodiodes

1/f noise in HgCdTe photodiodes has been attributed to a variety of sources, most of which are associated with some form of excess current. At DRS, we have measured the 1/f noise in vertically integrated (VIP) and high-density vertically integrated photodiodes (HDVIP), over a wide range of compositions and temperature, for strictly well-behaved diffusion current limited operation. It is found that (1) the 1/f noise current is directly dependent on dark current density; (2) material composition and temperature are irrelevant, except in as much as they determine the magnitude of the current density; (3) in high-quality diodes, the 1/f noise is independent of background flux; and (4) surface passivation is relevant. These observations have been compared to the 1/f noise theory of Schiebel, which uses McWhorter’s fluctuation of the surface charge tunneling model to modulate diode diffusion current. Agreement is obtained with Schiebel’s theory for realistic surface trap densities in the 10¹²/cm² range, which will obviously be characteristic of the passivation used. The relevance of this work relative to high operating temperature phtodiodes is discussed.     

Variance of simulated 1/f noise

A recently introduced mathematical model supporting the observed high variance of variance of excess noise is extended to a process having a 1/f spectrum. The variance of variance found by simulation was even higher than that of a Gauss-Poisson square wave.     

Theory and experiments of 1/f noise in Schottky-barrierdiodes operating in the thermionic-emission mode

A 1/f noise model for diodes operating in the thermionic-emission mode under forward-bias conditions has been developed. The model is based on mobility and diffusivity fluctuations occurring in the space-charge region and accounts for the current-limiting role of the metal-semiconductor interface The bias dependence of the 1/f noise spectral density calculated from this model is in excellent agreement with the results of the authors' experiments but is at variance with the predictions of a model developed by T.G.M. Kleinpenning (1979). From the experimental data, a value of 4.2×10^-9 for the Hooge parameter is derived. This value is in good agreement with theoretical calculation for electrons in silicon     

1/f noise and resistance between circular electrodes

Results are presented of calculations and experiments for the relative 1/f noise C and the resistance R between circular contact electrodes on a 2-dimensional conductor. The results can also be used for 3-dimensional conductors such as ionic solutions with a pair of parallel cylindrical electrodes of the same length. The experimental results on carbon sheet conductors are in good agreement with the calculated values.     

Discrete-time simulation model for 1/f noise

This paper proposes a simulation model based on the fact that 1/f processes belong to the class of statistically self-similar random processes. Unlike most of the earlier modeling approaches, which were confined to the spectral domain, the model generates 1/f noise in the time domain with a simple white noise input and is parameterized by a quantity whose value can be adjusted to reflect the desired slope of the 1/f spectrum. To verify the fit between the model and actual 1/f noise measurements, experiments were conducted with a p-i-n photodiode at various bias conditions and sampling frequencies.     

Avalanche-induced 1/f noise in bipolar transistors

It has been proposed that degradation of low current hFE, as a result of avalanching the emitter-base junction of a bipolar transistor, can be attributed to an increase in surface recombination velocity within the emitter-base space-charge region. This work shows that 1/fnoise is also increased during avalanche and that this increase is consistent with a previously reported correlation between surface recombination velocity and 1/fnoise.     

Bipolar transistors with low 1/f noise

Bipolar transistors employing low concentration emitter diffusion were obtained which show no current gain fall-off at low current levels, as well as significantly reduced 1/f noise. These devices may favourably be applied in low noise amplifiers.     

1/f noise of GaAs resistors on semi-insulating substrates

A new theory is used to analyze the 1/f noise of GaAs resistors on semi-insulating substrates. It is demonstrated that this model can explain previously published results at moderately high frequencies for, in this example, resistive filaments on semi-insulating GaAs substrates. The model is based on a distributed equivalent circuit representation of the substrate, and shows that 1/f noise is a bulk phenomenon associated with the high resistivity substrates. The 1/f noise is not associated with number or mobility fluctuations in the channel, nor surface effects. One consequence of the theory is that in this particular instance Hooge's parameter is in reality no parameter, but is given by a simple formula which has a simple physical interpretation as the ratio of two charges: the thermal charge developed across the substrate capacitance and the charge associated with ionized donors in the resistor channel