Contains reports on five research projects

Adler, Richard B.

Gross, J.

Hilibrand, J.

Ingersoll, J. G.

Kosowsky, D. I.

Lull, R. E.

McWhorter, A. L.

Wiesner, Jerome B.

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XII. SEMICONDUCTOR NOISEProf. R. B. Adler J. Hilibrand D. I. KosowskyProf. J. B. Wiesner J. G. Ingersoll R. E. LullJ. Gross A. L. McWhorterA. INTRODUCTIONThe problem of noise generated in semiconductors has two major facets, each ofwhich could absorb considerable effort:(a) nature of the physical processes responsible for the noise;(b) effect of the noise upon device performance in circuit applications.A detailed study of (a) necessarily involves considerations on an atomic scale andappears to require the investigation of noise from exceedingly simple structures overa wide range of materials, atmospheres, and temperatures. In addition, the spectralproperties of the "excess (1/f) noise" at extremely low frequencies are bizarre enoughto deserve special attention in any such project. While it is not our intention to empha-size these matters in our noise program, we do plan to continue cooperating with someof those members of Lincoln Laboratory who are engaged principally in these aspectsof the semiconductor noise problem.Our interest resides principally in the effect of noise upon device performance incircuit applications, mentioned in (b) above. Nevertheless, it is not possible to separatecompletely the issues involved in the two aspects of the noise problem. For example,the need for an equivalent-circuit representation of noisy materials or devices is evidentin both parts of the problem. A direct approach to the formulation of a flexible equiva-lent circuit leads us to study noise manifestations in both the linear and nonlinearoperation of semiconductor devices. We must also obtain a fairly complete statisticalpicture of the noise process, in order to take maximum advantage of its special charac-teristics in various applications. Yet to obtain this picture we have to undertake somestudy of the dependence of the noise from devices upon temperature, packaging, surfacetreatment, or atmospheric surroundings, if only to establish controlled conditions underwhich reliable and reproducible noise measurements may be made. Hopefully, of course,such work will collaterally yield information leading to the improvement of the noisecharacteristics of the devices themselves. Thus our program may fairly be called acircuit- and device-oriented study of semiconductor noise.The following paragraphs contain brief descriptions of our current progress andmore extended plans for those phases of the program that are already underway.R. B. Adler, J. B. WiesnerB. NOISE AND CHANNEL EFFECT IN P-N JUNCTIONSIn cooperation with R. H. Kingston, of Lincoln Laboratory, experiments are under-way to establish the definite connection, if any, between the excess noise from a-45-(XII. SEMICONDUCTOR NOISE)reversed-biased p-n junction and the presence of a water-vapor induced "channel"on the p-type material. The techniques used to control and measure the channel prop-erties are essentially those described elsewhere by W. L. Brown (Phys. Rev. 91, 518,1953) and R. H. Kingston (Quarterly Progress Report of Group 35, Transistors andSolid State, Lincoln Laboratory, Oct. 15, 1953, unclassified). To date only broadbandnoise measurements have been made, including all frequencies between 1 kc/secand 5 kc/sec. Tentative results on one n-p-n crystal indicate that the noise currentincreases by a factor of about 10 when the channel is formed. Spectrum measurementswill be made with the new noise analyzer when it is completed (see section E below),and the dependence of the noise and its spectrum upon the operating point and channelparameters will be obtained.A. L. McWhorterC. PROBLEMS IN THE MEASUREMENT OF NOISE AMPLITUDE PROBABILITIESIn merely contemplating the possibility of making measurements of the first (andpossibly second) amplitude probability distributions of excess (1/f) noise from semi-conductors, the problem of the bandwidth of the measurement occurs with seriousimplications. Since much of the excess noise power arises from the exceedingly low-frequency spectral components, the use of dc amplifiers appears unavoidable at firstglance. Yet the long-time stability requirements for such a system would be difficultto meet experimentally. It would therefore be desirable to limit the frequency band atthe low-frequency end. Unfortunately, only a little is known about the effect of band-limiting upon the amplitude probability distribution of nongaussian noise. Thus it is notclear how to estimate the errors that would be committed in attempting to find theamplitude probability distribution of semiconductor excess noise if we assume that itmight not be gaussian and agree to avoid the exceedingly low-frequency end of thespectrum. At the moment, some preliminary study is being undertaken on the theoreti-cal aspects of this general question. Future work may be either experimental or theo-retical, depending upon the progress of the present study.J. HilibrandD. MODULATION NOISE IN SEMICONDUCTOR DEVICESIn the Quarterly Progress Report of July 15, 1953, preliminary experiments werediscussed that suggested the existence of amplitude-modulation noise from point-contact diodes. More refined experiments on this effect are now in progress. Specifi-cally, a 1N34 point-contact diode is biased in the reverse direction by a dc source. Anac source of 10 kc/sec frequency is superimposed, and the voltage across the diode(actually the output of an ac, dc bridge circuit containing the diode) is recorded simul-taneously through two channels. Channel 1 has a passband from 0 cps to approximately-46-(XII. SEMICONDUCTOR NOISE)1 cps. Channel 2 contains a bandpass amplifier centered at 10 kc/sec, followedby an AM detector and an RC filter. The RC filter has a passband similar to that ofchannel 1, and its output is recorded simultaneously with that of channel 1. The simi-larity between the two noise recordings suggests two possible circuit models for thenoisy diode:(a) The V-I characteristic of the diode fluctuates as a whole, giving rise to both thelow-frequency and the AM noise via correlated fluctuations in the static and incrementalresistances at the dc operating point. This model was discussed in greater detail in theQuarterly Progress Report of July 15, 1953.(b) The low-frequency noise acts as a noisy voltage source in series (or a noisycurrent source in parallel) with the nonlinear diode. This source and the applied10 kc/sec signal simply mix in the diode, giving rise to the modulation.Measurements of the relative noise amplitudes and of the conversion efficiency ofthe diode are now being made to determine which of the two processes, described in (a)and (b) above, is predominant.Plans for the future include a study of the noise from transistor oscillators,including both AM and FM noise. Such studies may have to be preceded by investiga-tions of transistor noise in simpler nonlinear situations.J. GrossE. NOISE ANALYZER AND NOISE FROM MICROWAVE DEVICESPlans are being completed for an improved recording noise analyzer to cover thefrequency range from 10 cps to 60 kc/sec. Tentative specifications are as follows:1. Analysis Bandwidth: either 10 cps or 100 cps2. Sweep Rate:(a) 10 cycles swept per second for spectrum between 10 cps and 1 kc/sec;(b) 50 cycles swept per second for spectrum above 1 kc/sec.3. Dynamic Range: 40 db without alteration of gain settings4. Minimum Input Signal (in 10-cps bandwidth):(a) with special low-impedance input circuit (200 ohms): 0. 01 ±v(b) with slight changes of the input circuit for other low-impedancesources: 0. 002 iv(c) with cathode-follower input circuit: 0. 02 iv(Note: Thermal noise at 300*K from a 200-ohm resistor, in a 10-cps bandwidth, is0. 00562 [v.)Other features of the system are that: (a) it is linear and direct-reading on allscales; (b) the recording cycle is entirely automatic; (c) frequency markers are avail-able to provide frequency-scale calibration; and (d) a thermal voltmeter is availablefor all bandwidths.-47-(XII. SEMICONDUCTOR NOISE)Present plans call for the incorporation of this analyzer into a rather broad micro-wave-system noise-study program. This program will consist of two major phases.First, the investigation of AM and FM noise spectra of microwave system components(such as magnetron and klystron oscillators, diode mixers, and i-f amplifiers), andstudy of the effect upon these spectra of the interconnection of components to form asystem.The second phase will be an independent investigation of microwave mixer diodesof the point-contact silicon and germanium types, with special attention given to therole (if any) in these applications of the so-called semiconductor excess noise. Thepossibility of improving mixer conversion loss and/or noise figure by the use of lowambient temperatures will be a special point of consideration. In this connection, sincea great deal more theory is available for junction diodes than for point-contact types,some preliminary work will be done on semiconductor rectifying junctions even thoughthey are not generally suitable for microwave conversion applications.D. I. Kosowsky, J. G. Ingersoll, R. E. LullF. SPECTRUM OF EXCESS NOISE FROM GERMANIUM FILAMENTSIt has been suggested by H. C. Montgomery (Bell System Tech. J. 31, 950, 1952)that in single-crystal germanium filaments the excess noise observed in the presenceof a dc bias current is the result of fluctuations in the concentration of the minoritycarriers. The resulting fluctuation in conductivity produces the excess noise voltage.Montgomery's hypothesis, substantiated quite well by experiment, is that this fluctu-ation is caused by random injection of minority carriers from sources generally dis-tributed over the material (more likely over just the surface), and that the activity ofthese sources is being modified at a slow rate by some unspecified "local influence" insuch a way as to give the observed (1/f) spectrum. It is assumed that there are a largenumber of such sources that may be taken to be statistically independent.It is possible to relate quantitatively the statistical characteristics of the "localinfluence" to those of the measurable noise, by assuming a little more about the detailsof the injection process. We shall give the assumptions, and an outline of the solu-tion, for one model of the injection process that appears to exhibit the correct majorfeatures.We suppose that each source, if undisturbed, would emit minority carriers randomly,according to a Poisson law, but that the effect of the "local influence" is to modulate theshort-term "average" rate of emission by a (slowly varying) random function of time.Specifically, the probability that a minority carrier will be emitted from a givensource during the interval (t, t + dt) is assumed to be g(t) dt, independent of previousemissions. The "local influence" g(t) is taken to be a stationary random process, withthe same statistics for each source. The assumption is also made that the (expected)-48-(XII. SEMICONDUCTOR NOISE)minority-carrier lifetime T of the emitted carriers is a constant, independent ofthe time of emission (especially if the dc field is strong enough to sweep the emittedcarriers away from the source region), and independent of the sources (especially if thelatter are located only on the surface). Under these assumptions, the spectrum of thenoise voltage is proportional to the spectrum of the function which describes the numberof emitted minority carriers, from any one source, that are still unrecombined attime t.Note that the assumptions we have made are not equivalent to assuming that thenoise produced by a given source is simply what it would be if the source were undis-turbed, amplitude-modulated by an independent random function representing the effectof the "local influence." This model would give for the autocorrelation function of thetotal noise the product of those for the undisturbed source and the "local influence;" aresult that would not yield the long-time correlations necessary for a (1/f) spectrum.On the basis of our model, the spectral density of the number of unrecombinedminority carriers can be expressed in terms of that of the random function g(t) whichcharacterizes the "local influence." First, we obtain the autocorrelation function whichresults for any one sample function g(t). This answer is then averaged over the functionspace of the g's, and the power spectrum obtained by Fourier transformation.f P n(t) is the probability of n carriers being unrecombined at time t, then for anyparticular g(t)Pn(t) = e (t) (1)n!whereX(t) = g(t-o-) e-  d, (2)IfOOM(t) = n Pn(t)n= 1is the expected number of carriers present at time t, then the conditional expectationMn(t+u) of the number present at time t + u, given n present at time t, isuMn(t+u) = g(t + u - ) e -(/T) do- + n e - (u/T) (3)tThe derivation essentially follows W. Feller, "An Introduction to ProbabilityTheory," Vol. I, pp. 371-373 (cf. 386-391), John Wiley, New York, 1950.-49-(XII. SEMICONDUCTOR NOISE)Thus the autocorrelation function of the number of minority carriers present, given aparticular g(t), isR(t, t + u g) n Mn(t+u) Pn(t)n 00 -0= g(t +u- ) e - ( 0 /T) d + e - ( u/T) g(t-o-) e - ( - /T) d- (4)We now average Eq. 4 over the function space t of the g's to get the desired auto-correlation function R(u):00 00R(u) E {R(t, t +u g)} = e d - R (u-a-+v) e dv + gre - ( u /T )(5)whereE {g(t+u- o-) g(t-v)} = R (u- o+v) (6)andE {g(t-)} = g (7)Hence the spectral density is2 2G(w) = G () T + 2 (8)1 + (WT) 1 + (W T)The second term of Eq. 8 represents one contribution of the unmodulated sources to thetotal noise, but it is not really distinct from the shot noise (which we have not consideredhere). The first term of Eq. 8 is identified at low frequencies with the so-called excessnoise, usually found to have a (1/f) spectrum. We note that at frequencies low comparedto (1/T) the total noise is proportional to T , and that a frequency dispersion occurs inthe vicinity of w = 1/T. Both of these properties of the excess noise have been pointedout by Montgomery in connection with his magnetic field measurements. The mostimportant fact for our purposes, however, is that the spectrum G (w) of the "localinfluence" g(t) must be the same as that of the excess noise at low frequencies; that is,(1/f) in most cases.A. L. McWhortertSee J. L. Doob, "Stochastic Processes," pp. 62-63, John Wiley, New York, 1953,for the basis of the method and the justification of the required interchanges of limitingprocesses.-50-

Semiconductor Noise

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Semiconductor Noise

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