LINEAR THEORY OF FLUCTUATIONS 119 



where 5(w) is called the spectral density of Ri and co is the frequency in 

 radians per second. Now in our notation the CP formula may be expressed 



5(co) = KV-^R^+yoi, (1.2) 



where V is the applied d-c voltage across the contact, ii^ is a constant de- 

 pending upon the temperature and the nature of the contact, and a and b 

 are constants having values of about 1.85 and 1.25 respectively. CP state 

 that the constant K is equal to about 1.2 X 10~'" in the case of a single 

 carbon contact at room temperature. 



In this paper we will regard the nonvanishing of a — 2 as arising from 

 a non-linear effect which should become negligible at a sufficiently low 

 voltage, although this interpretation does not seem completely justified on 

 the basis of the work of CP. Consequently we assume that a -^ 2 as F — > 

 in such a way that F"~- -^ 1. This is in keeping with the idea that the 

 resistance fluctuations are truly spontaneous — at least for small applied 

 voltages. 



Although Eq. (1.2) may represent the observations over a large range of 

 frequency it must break down at very high and very low frequencies in 

 order that the noise power be finite (or, in other words, in order that the 

 integral (1.1) converge). 



One has several clues to be considered in looking for an underlying mecha- 

 nism of the resistance fluctuations. First of all, the mechanical action of 

 the thermal vibrations in the solid electrodes of the contact seems to be 

 unimportant because of the following reasons: (1) there are no resonance 

 peaks in S{w) at the lowest characteristic frequencies of mechanical vibra- 

 tion of the contact assembly; (2) S{w) becomes very large far below the 

 lowest characteristic frequency; and (3), according to CP, Rl is strictly 

 proportional to F^ when the fluctuations are produced by acoustic noise 

 vibrating the contact, whereas Ri is proportional to V°~-, a '^ 1.85, when 

 the fluctuations arise from the dominant mechanism existing in the macro- 

 scopically unperturbed contact. One of the obvious mechanisms left is a 

 diffusional mechanism. Such a mechanism does not violate any of the ob- 

 servations to date and, furthermore, possesses a sufficient density of long 

 relaxation times to give large contributions to S{w) near zero frequency. 



Evidence that diffusion of atoms (or ions) can be important in modulating 

 a current is provided by the "flicker effect" in which the emission of elec- 

 trons from a heated cathode is caused to fluctuate by the fluctuations in 

 concentration of an adsorbed layer. We might suppose that contact noise 

 is a different manifestation of the basic mechanism involved in the flicker 

 effect. 



In view of these considerations it seems worthwhile to investigate in a 



