F.N. Hooge

1/f noise

Abstract A survey is given of the recent literature on 1/ f noise. Proposals for mathematical models, for empirical relations and for physical models are discussed. The present situation is evaluated and some unsolved problems are indicated.

The relation between 1/ƒ noise and number of electrons

Abstract The validity of the empirical relation for 1/ƒ noise, S R /R 2 = α/Nƒ , is studied. An alternative version with a factor 1/A instead of the factor 1/N is considered. N is the number of electrons and A the number of atoms. Experimental and theoretical arguments for the relation in its original form are put forward.

On the correlation function of 1/f noise

Abstract The correlation function is derived of noise with a 1/f spectrum between a low-frequency fl and a high-frequency h. The essential term in the correlation function is a − ln t term. The usual interpretation of 1/f noise as a summation of Lorentzian spectra is discussed. The model of 1/f noise from a random series of t − 1 2 pulses is correct. The − ln t correlation function is also derived from such a series.

Experimental studies of 1f noise in n-GaAs

Abstract The literature on 1 f noise in n-type GaAs is reviewed. Reported values of αmeas are converted into αlatt values. At 300 K . These values do not agree with theoretical predictions.

On the additivity of generation-recombination spectra. Part 2: 1/f noise

Abstract The McWhorter model explains 1/f noise as an addition of generation-recombination spectra. Here we investigate whether addition of spectra is allowed. A condition for additivity is derived. If that condition is not met, then the GR spectra do not add together but they mix; resulting in one Lorentzian with τL given by 1/τL=∑1/τi. A 1/f-like spectrum appears at very low frequencies. A numerical estimate for the 1/f noise parameter α follows from our analysis. The disagreement with experimental values found with MOSTs makes it very unlikely for the McWhorter model to be correct.

A simple test of the Gaussian character of noise

Abstract The test consists in the measurement of the noise intensity at the output of a bandpass filter, and the estimation of the accuracy of the measurement. The confidence interval for the estimate is calculated under the assumption that the noise is stationary and Gaussian. This assumption is called “zero-hypothesis”. If a considerable part of the experimental data is outside the confidence interval, then the zero-hypothesis does not hold. The effect of noise being non-Gaussian is investigated analytically. Experimental data of 1/ f noise in GaAs epitaxial films are presented and discussed.

Temperature dependence of 1/ƒ noise in epitaxial n-type GaAs

Abstract The 1/ƒ noise of n-type epitaxial GaAs was measured between 77 and 300 K. The 1/ƒ noise turns out to be a fluctuation in the lattice scattering. At low temperatures αlatt ≅ 7 × 10−5. At high temperatures the noise generation is thermally activated with an activation energy of about 0.13 eV.

On the additivity of generation-recombination spectra. Part 1: Conduction band with two centres

Abstract If a semiconductor contains two generation–recombination centres, A and B, the noise spectrum either is the simple addition of the two characteristic A and B spectra, or a Lorentzian spectrum with a relaxation time τ given by τ −1 = τ A −1 + τ B −1 . The latter situation is called mixing. We can derive the mathematical criterion that decides whether addition or mixing occurs: Addition if n ⪢ a * , n ⪢ b * . Mixing if n ⪡ a * , n ⪡ b * . The number n is the number of free electrons in the conduction band. The number a * either is a, the number of occupied A states, or the number of empty states, ( A – a ), depending on which is smaller. A qualitative physical interpretation is given of the precise mathematical condition.

On generation-recombination noise

Abstract We deal with the generation-recombination noise of a three-level system, consisting of a conduction band and two traps. This problem has long been solved, but the results were expressed in a complicated formalism. We present here simple explicit relations which make it easy to interpret experimentally observed GR spectra. We derive the conditions under which the spectrum is the sum of two Lorentzians, each of them characterizing one trap. We also give results for the cases where these conditions are not fulfilled.

On expressions for 1f noise in mobility

Abstract Mobility fluctuations can be defined in two ways, giving expressions with or without a factor 1 N , N being the total number of charge carriers. No revision of literature is necessary.