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.     

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     

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     

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).<>     

Modified 1/f trapping noise theory and experiments in MOS transistors biased from weak to strong inversion—Influence of interface states

Low-frequency 1/f noise in Si n-channel MOSFET's is measured from weak to strong inversion, through the relative spectral density of the drain current fluctuationsS_{I}_{D}/I^{2}_{D}. Under specific conditions, a plateau is observed in the variations ofS_{I}_{D}/I^{2}_{D}versus the gate voltage in weak inversion followed by a steep decrease in strong inversion. A modified trapping noise theory based on the McWhorter's assumptions and valid in all the working regimes is developed to account for this behavior. Excellent agreement is obtained with the variations of several parameters: gate and drain biases, geometry, oxide and depletion capacitance, temperature, and technologies. The influence of fast interface states is particularly studied and is related to the noise variations and the oxide trap densities.     

A new theory of g-r and 1/f noise

A new unified formulation for generation-recombination (g-r) and 1/fnoise theory is attempted by introducing the total carrier number fluctuation mechanism via the trapping-detrapping processes between every discrete energy level in the conduction band and single degenerate traplevel without assuming the 1/τ distribution.     

Diffusion and recombination 1/f noise in long n+-p Hg1—xCdxTe diodes

1/f noise in long n⁺-p Hg1-xCdxTe diodes with x = 0.30 is studied at 193 K. The 1/f noise is considered to be generated by diffusion and recombination fluctuations. A distinction is made between cases a (all minority carriers contribute to the 1/f noise) and b (only the excess minority carriers contribute to the 1/f noise). Measurements on long nonplanar diodes show that case a is valid, indicating that all minority carriers contribute equally to the 1/f noise; this should be valid for any long-junction device in which the current flow is by diffusion and recombination of minority carriers. The lifetime τnof the electrons in the p-region is measured by the input impedance method, and the Hooge parameter αHof the device is evaluated. τnis of the order of 10^-6to 10^-7s and depends somewhat on bias. Near zero bias αHis of the order of 5 × 10^-3in close agreement with Handel's coherent state 1/f noise theory, which yields αH= 4.6 × 10^-3. Due to the nonplanar geometry of the studied diodes, the measurement of τnis not always equally reliable. Larger values of τnare accompanied by larger values of αH, because the noise measurements give αH/τn, and its value practically independent of bias. We also evaluated τnby putting αH= 4.6 × 10^-3; the τnvalues are then much closer and agree rather well with Honeywell lifetime tables. Preliminary measurements at 113 K also indicate coherent state 1/f noise, whereas data at 273 K give αH= 5 × 10⁵, in agreement with the Umklapp 1/f noise theory.     

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.     

On the theory of 1/f noise of semi-insulating materials

The 1/f noise phenomena associated with devices involving semi-insulating materials, for instance GaAs MESFET's on semi-insulating GaAs, has long been a perplexing problem. In this particular case the 1/f noise corner frequency can be up to 100 MHz before the mean square noise current at the drain is dominated by the Nyquist noise associated with the channel conductance. No reasonable explanation has ever been given, although there are many different theories. 1/f noise is a common phenomena in nature and other devices involving semi-insulating materials. We propose here that this 1/f noise is a bulk phenomena associated with localized high frequency variations and long range low frequency fluctuations, the lowest frequency being limited only by the volume of the material. Specifically the proposal here is that injection of a current I into a semi-insulating material will result in a mean square noise voltage at the point of injection given by v/sub n//sup 2/~=2(kT/q)q/spl Delta/fR(/spl omega//sub c///spl omega/) Volts/sup 2/ where /spl omega//sub c/=1/t/sub t/, for the radian frequencies, /spl omega/, larger than /spl omega//sub c/ which is the reciprocal of the transit time of the carriers. For a long sample and long transit times then this 1/f noise voltage due to current injection will be larger than the Nyquist mean square noise of the sample alone as long as the DC voltage developed across the semi-insulating sample exceeds ((2kT/q)l/sup 2/(/spl omega///spl mu/))/sup 1/2/. This theory then gives the 1/f or 1//spl omega/ frequency dependence. The dc current I might be injected for instance by the substrate current in a GaAs MESFET being injected into the semi-insulating substrate, or gate current in an IGET being injected into the gate insulator.<>     

Low-frequency noise sources in polysilicon emitter BJT's: influenceof hot-electron-induced degradation and post-stress recovery

The noise properties of polysilicon emitter bipolar transistors are studied. The influences of the various chemical treatments and annealing temperatures, prior and after polysilicon deposition, on the noise magnitude are shown. The impact of hot-electron-induced degradation and post-stress recovery on the base and collector current fluctuations are also investigated in order to determine the main noise sources of these devices and to gain insight into the physical mechanisms involved in these processes     

Low-frequency noise in Cr—SiO2—N-Si tunnel diodes

Low-frequency noise of Cr-SiO2-n-Si tunnel diodes with about 30-Å-thick oxides is investigated as function of bias, frequency, and temperature. Measurements of1/fnoise are explained by a theory employing the two step tunneling model of Sah. Electrons from the Si conduction band are trapped by states at the Si-SiO2interface and then tunnel into bound states of the oxide located close to the interface. The oxide states of density N00can be represented by a frequency dependent parallel admittance exhibiting frequency-dependent thermal noise that modulates the dc currentItunneling through the oxide barrier. This generates flicker noise at the device terminals proportional toI^{2}N_{00}and inversely proportional to frequencyfand tunneling areaA. The valueA = 5. 10-3A0, determined by fitting theoretical and experimental curves at low frequency, is only a small fraction of the gate area A0, since tunneling preferentially occurs through the thinnest parts of the oxide. The currentIalso exhibits full shot noise at high frequency and low current. Qualitative agreement between theoretical and measured noise is found over 9 decades. Measurements at low temperature show additional noise of generation-recombination centers at larger frequencies and currents.     

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     

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.     

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.<>     

Semiconductor-diode v.h.f. and u.h.f. noise sources

The v.h.f. and u.h.f. noise properties of silicon and gallium-arsenide diodes are discussed. A formula for calculating the noise output is given.     

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.     

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.     

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.     

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.