Current noise spectral density

We present the theoretical overview first for the case of voltage bias [1]. In a junction with a low transparency barrier (which corresponds to our samples) biased by a dc voltage V, the current noise spectral density (related to the... 

In the course of the measurement, the tip is positioned at a place of interest above the sample. Having obtained enou f-points to perform the time averaging, one may move to another space point in order to end up with the maps of 7 (u) and [u x,y) is the lateral coordinate along the surface]. Another important characteristic would be the current noise spectral density 5([Pg.47]

Where 5/ is the current noise spectral density,/ is the frequency, N is the total number of carriers in the sample active region, I is the device DC current and a is an empirical constant, which is now extensively used to characterize the device structure perfectness. 

In lasers, luminescent diodes, power diodes and solar cells it was found that in the low injection region the current noise spectral density is a quadratic function of the forward current. Typically, the excess current is a dominant current component in this region. The current noise spectral density vs. frequency for PN junction is shown in Fig. 19. Curve 1 denotes the current noise spectral density for the low injection range, curve 2 is the current noise spectral density for the... 

Our research was aimed to identify the sources of fluctuations in the dielectric layer prepared by anodic oxidation and to find the method for self-healing kinetics study. Charge carrier transport in thin isolating layer creates excess noise, which is the superposition of 1 /f and G-R noise. It has been observed, that samples with the same DC current have different noise spectral densities. We suppose that DC current is a sum of at least two independent current flow mechanisms, which have not the same noise intensity. 

The noise spectral density is l/f type in the frequency band 10 mHz to 300 Hz in normal and reverse operation mode. Noise spectral density is a quadratic function of the current, when the electric field strength in isolating layer is so low that avalanche process caimot occur. Measurement performed at very low frequency band 10 mHz to 1 Hz reveals that for some samples noise is l/f type, but it was observed some time instability, which is probably related to the self-healing process. 

The noise spectral density Su is superposition of g-r and 1/f noise as is shown in Fig. 18. For constant gate voltage and variable drain voltage it was foimd that 1/f noise spectral density decreases due to that the channel carrier concentration increases with temperature (Simoen et al. 1997). On the other hand, for constant gate voltage and constant drain current 1/f... 

The noise sources in the noise model for an op-amp are composed of a mixture of white and 1 // noise as shown for a voltage noise source in Fig. 7.98. At low frequencies, l/f noise dominates, and at high frequencies, white noise dominates. The boundary is called the corner frequency and is denoted as fey in Fig. 7.98. A similar plot appHes to the noise spectral density of current noise sources in the op-amp model. The corner frequency for a noise current source is denoted as f. ... 

To analyze an op-amp circuit with resistive feedback, we also need noise models for resistors. Two models for a noisy resistor are shown in Fig. 7.100. The thermal noise (Johnson noise) of the resistor is modeled by a voltage noise source with spectral density as shown in Fig. 7.100(b). The power density of this source is e = 4fcTJ V /Hz where fi is in ohms, k is Boltzmann s constant = 1.38 x 10" J/K, and T is temperature in degrees Kelvin. Thus, thermal noise is white. At 25 C, the noise spectral density is approximately Cr Ay/R nV/ Hz where K is expressed in kilohms. Figure 7.100(c) shows an equivalent resistor noise model that includes a current noise source having power density i = AkT/R A /Hz. 

Noise Spectral Density It can be shown that, for white noise, the total noise voltage or current is proportional to the square root of the bandwidth A/. Even if the noise is not pure white, the square root of bandwidth rule is often used ... 

Noise is characterized by the time dependence of noise amplitude A. The measured value of A (the instantaneous value of potential or current) depends to some extent on the time resolution of the measuring device (its frequency bandwidth A/). Since noise always is a signal of alternating sign, its intensity is characterized in terms of the mean square of amplitude, A, over the frequency range A/, and is called (somewhat unfortunately) noise power. The Fourier transform of the experimental time dependence of noise intensity leads to the frequency dependence of noise intensity. In the literature these curves became known as PSD (power spectral density) plots. 

More detailed information can be obtained from noise data analyzed in the frequency domain. Both -> Fourier transformation (FFT) and the Maximum Entropy Method (MEM) have been used to obtain the power spectral density (PSD) of the current and potential noise data [iv]. An advantage of the MEM is that it gives smooth curves, rather than the noisy spectra obtained with the Fourier transform. Taking the square root of the ratio of the PSD of the potential noise to that of the current noise generates the noise impedance spectrum, ZN(f), equivalent to the impedance spectrum obtained by conventional - electrochemical impedance spectroscopy (EIS) for the same frequency bandwidth. The noise impedance can be interpreted using methods common to EIS. A critical comparison of the FFT and MEM methods has been published [iv]. 

The first source of nonequilibrium noise, described as early as 1918 (23) (in fact 10 years earlier than Johnson noise), was shot noise that stems from the discrete nature of charge transfer. The current spectral density, Sj(/), of this noise is white (independent of frequency /) up to frequencies of the order of the inverse time of elementary charge transfer and is given by... 

Nonequilibrium noise generated by carrier-mediated ion transport was studied in lipid bilayers modified by tetranactin (41). As expected, deviations of measured spectral density from the values calculated from the Nyquist formula 1 were found. The instantaneous membrane current was described as the superposition of a steady-state current and a fluctuating current, and for the complex admittance in the Nyquist formula only a small-signal part of the total admittance was taken. The justification of this procedure is occasionally discussed in the literature (see, for example, Tyagai (42) and references cited therein), but is unclear. 

Figure 5. Spectral density of polymer-induced current noise in the open alamethicin channel vs. polymer molecular weight (46). Data represent noise in different channel-conducting levels at 150 mV in the presence of polyethylene glycols of different sizes added to 1-M NaCl aqueous solutions to obtain 15% weight-to-weight concentration. The vertical scale is given in 10 27 A2/Hz...

Studies of single channels formed in lipid bilayers by Staphylococcus aureus alpha toxin showed that fluctuations in the open-channel current are pH-dependent (47). The phenomenon was attributed to conductance noise that arises from reversible ionization of residues in the channel-forming molecule. The pH-dependent spectral density of the noise, shown in Figure 6, is well described by a simple model based on a first-order ionization reaction that permits evaluation of the reaction parameters. This study demonstrates the use of noise analysis to measure the rate constants of rapid and reversible reactions that occur within the lumen of an ion channel. 

Figure 6. Noise of protonation in the current through an open alpha-toxin channel as a function of pH (47). Spectral density is white at low frequencies and is represented by values averaged over the 200-2000-Hz range. The data were obtained in 1-M NaCl solutions at 150 mV of membrane voltage. The solid line is a two-parameter fit to the first-order ionization reaction that describes a reversible protonation of residues in the channel-forming molecule.

In a different approach, the time record of potential or current is converted into a power spectral density (PSD), which is the distrihution of the power in the frequency domain. This transformation is usually made hy means of the fast Fourier transform (FFT) algorithm [115]. Alternatively, the maximum entropy method (MEM) can also be used [116], although with some limitations [117]. In corrosion systems, both the potential noise and current noise are of the 1// type, that is, the maximum occms at low frequencies. 

K. Tachibana, K. Miya, K. Furuya, G. Okamoto, Changes in the power spectral density of noise current on type 304 stainless steels during the long time passivation in sulfuric acid solutions, Corros. Sci. 31 (1990) 527-532. 

Heterostructure and bipolar devices as lasers, diodes, solar cells (Chobola 2001) and transistors (Koncza-kowska 1987) are similar from the point of view of the physical processes, taking place during the device operation. This infers that the basis of the methods of their quahty testing can be similar for all of them. The main source of noise is the excess current which has 1/f spectral density. Occasionally the g-r noise, created by burst processes, is observed. Qualitative characterization of the 1/f excess noise is possible with the use of generalized Hooge s formula (6). The measurable quantity of sample quality and reliability is the indicator Mg given by... 

Because DNA translocation events have main power spectral densities with a bandwidth of 10 kHz and R is also negligible compared to Rj, is approximated to Ri / 1 + ]2%f-Cj Rj ). As a result, at low frequencies, can be simplified to AkT/Rj, which is proportional to the conductance of the nanopore. Nanopore flicker noise is given by (a x F)/ (Nc xf). Here, I, a, and are the direct current, the Hooge parameter, and the number of charge carriers [18], respectively, all of which are associated with the KCl buffer concentration and nanopore material. To increase Rj, a nanopore with a narrow diameter should be adopted. For instance, the a-hemolysin pore with a limiting diameter of 1.5 nm has a resistance of 3 GO, in 0.3 M KCl or 1 GQ in 1 M KCl. 

The membrane component of the background noise consists mainly of shot noise [8-11], that is the expected electrical noise created by the ions that cross the membrane by leakage or ionic pumps. The spectral density of shot noise is directly proportional to the unidirectional membrane current. Thus, the spectral density of the noise will increase by increasing the surface of the membrane patch, and consequently the total current (leakage and pumps). This implies that the noise conditions will be improved when current is recorded from a small piece of membrane (a patch). 

Figure 7.99 shows the op-amp noise model. A noisy op-amp is modeled by three noise generators and a noiseless op-amp. Polarities and reference directions are not shown since noise generators do not have true polarity or reference direction assignments. The spectral densities of the current sources... 

Noise analysis has been particularly fruitfiil in characterizing various aspects of hydrodynamics, as noted above for the specific case of corrosion processes. First of all, multiphase flows were investigated, either gas/water [78], solid/liquid [79, 80], oil/water [81] or oil/brine [82]. In these flows, fluctuations are due primarily either to fluctuations in transport rates to an electrode or to fluctuations in electrolyte resistance. If one phase preferentially wets the electrode, then there may be fluctuations due to variation in the effective electrode area. Each of these phenomena has a characteristic spectral signature. Turbulent flows close to a wall have been investigated by means of electrochemical noise by using electrochemical probes of various shapes, by measuring the power spectral density of the limiting diffusion current fluctuations [83-86],... 

Recently, a more rigorous theoretical and experimental analysis has been made comparing the spectral noise resistance obtained at each frequency with both the polarization resistance obtained from the zero frequency limit of impedance data lZ(frequency dependent impedance of two electrodes [67-71], The spectral noise resistance R ,(c ) was determined by taking the square root of power spectral density of the voltage noise (V /Hz) md dividing it by the square root of power spectral density of the current noise (A /Hz) at each frequency using the same two-electrode arrangement as discussed above [70,71],... 

The other parameters include the pitting index, which is defined as the standard deviation of current noise divided by the mean current (PI = ci//mean) the power spectral density of a noise, which can be calculated using the MEM (maximum entropy method) and the FFT (fast Fourier... 

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