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).<>     

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.     

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     

Location of 1/f noise sources in BJT's—II. Experiment

The exact location and magnitude of 1/f noise sources in silicon transistors was determined by a simple technique described in a previous publication [1]. This method, implementing the natural feedback action of actively biased devices, can generally be utilized to locate low-frequency noise generators in bipolar transistors. This paper presents measurements done on two silicon p⁺-n-p transistors. In the first device, the dominant noise source is due to generation-recombination, whereas the other less noisy device exhibits mainly diffusion noise.     

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.<>     

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.     

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.     

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.     

Location of 1/f noise sources in BJT's and HBJT's—I. theory

The most general case of1/fnoise in transistors can be described by three independent noise current generators: ibebetween base and emitter, ibcbetween base and collector, and iecbetween emitter and collector. By short-circuiting the base and the collector to ground and comparing the base and collector noise spectraS_{IB}(f)andS_{IC}(f)for the case of zero feedback from the emitter with the base and collector noise spectraS'_{IB}(f)andS'_{IC}(f)for the case of strong feedback from the emitter, one can evaluate the relative strength of the three noise sources. By measuring the current dependence ofS_{IB}(f),S_{IC}(f),S'_{IB}(f), andS'_{IC}(f), one can assign physical processes to the current generators ibc, ibe, and iec. It is the aim of this paper to demonstrate theoretically a simple method for locating1/fnoise sources in BJT's and HBJT's by comparing the base and collector1/fnoise for the cases without and with strong emitter feedback. In later papers we shall demonstrate experimentally how this method is applied to practical situations.     

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.     

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 of continuous-wave semiconductor lasers

Using linearised rate equations, the intensity fluctuations in the output of c.w. d.h. GaAlAs-diode lasers have been calculated in the low-frequency range, where the flicker noise dominates. The theoretical results are compared with the optical-intensity fluctuations, which are obtained experimentally. Our measurements indicate that 1/f noise in lasers is mainly caused by 1/f noise from carrier transport in the bulk material and the contacts.     

Extracting 1/f noise coefficients for BJT's

We present a method for extracting the BJT SPICE noise model parameters AF and KF based on a general analysis of the small-signal equivalent circuit and the role of the internal BJT noise sources. The analysis is valid even for transistors with poor current gain and large base-collector conductance, for which the output noise characteristics may not be dominated by base flicker and shot noise. The method consists of interpreting the measured 1/f corner frequency versus DC current data in terms of the BJT's internal noisy small signal equivalent circuit. Measured data is presented for an implanted-emitter and two polysilicon-emitter bipolar technologies     

Low 1/f noise design of Hi-CMOS devices

Low-frequency noise characteristics of High-Performance CMOS(Hi-CMOS) devices were measured. It was found that the equivalent input noise power SVg,eqfor n-channel MOSFET's has a 1/fα spectrum (0.8 < α < 0.95) above 10 µA, even for sealed-down devices with channel lengths LGof 2 µm. The SVg,eqis clearly proportional to 1/Leffdown to 0.8 µm. The noise characteristics of p-channel and n-channel MOSFET's were compared. It was found that in Hi-CMOS devices, noise reduction in normally-off-type p-channel devices was obtained by light boron-ion implantations at doses below 10¹²cm^-2. The 1/f noise level of p-channel devices was reduced to 1/10- 1/20 that of n-channel devices. In n-channel devices, the low-frequency noise power is a slow increasing function of the drain current. In p-channel devices, on the other hand, a threshold current was observed at which the noise begins to increase rapidly. The results are discussed in this paper in relation to the theoretical model of 1/f noise. The device design for reducing 1/f noise in CMOS differential amplifiers is also examined.     

1/f noise in n-channel silicon-gate MOS transistors

It is found that equivalent gate noise power for l/f noise in n-channel silicon-gate MOS transistors at near zero drain voltage at room temperature is empirically described by two noise terms, which vary asK_{1}(q/C_{ox}) (V_{G} -V_{T})/f and K_{2}(q/C_{ox})^{2}/f, where V_{G}is gate voltage, VTis threshold Voltage, and Coxis gate-oxide capacitance per unit area. Unification of carrier-density fluctuation (McWhorter's model)and mobility fluctuation (Hooge's model) can account for the experimental data. The comparison between the theory and experiment shows that the carrier fluctuation term K2is proportional to oxide-trap density at Fermi-level. The mobility fluctuation term K1is correlated to K2, being proportional toradic K_{2}. The origin of this correlation is yet to be clarified.     

Hole-induced 1/f noise increase in MOS transistors

This paper presents experimental evidence for hole-generated 1/f noise traps in gate oxides near the MOS interface. To clarify the microscopic nature of noise traps, 1/f noise is measured in Si MOS transistors in which carriers are intentionally injected into the gate oxides. It was found that 1/f noise increases more rapidly after drain avalanche hot-carrier injection than after channel hot-electron injection. A rapid noise increase is also observed after X-ray irradiation. These results show that the increase in 1/f noise is closely related to holes. We propose a model in which the reaction between holes and oxygen vacancies near the interface creates noise traps, i.e., E' centers and fixed positive charges