648 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1953 



theory. On it are based the computed curves in Montgomery's paper 

 showing the change in noise power with magnetic field. 



To see how such a change comes about, we imagine the magnetic 

 field applied normal to one pair of the long faces of a rectangular fila- 

 ment. This field, and the longitudinal drift current used to measure the 

 noise, 3deld a sidewise thrust on the carriers, directed at right angles 

 to the other pair of long sides. As a result the density distribution over 

 the cross section is distorted, the minority carriers tend to accumulate 

 near one of those sides, while the neighborhood of the opposite side is 

 depleted. But for the usual conditions the recombination of carriers 

 occurs mainly near the surface, and is proportional to their density 

 there. Hence the magnetic field will change their lifetime.^* ^ Clearly the 

 amount of noise is dependent on the length of time carriers are able to 

 contribute to the change in conductivity, that is, dependent on their 

 lifetime. Therefore, the magnetic field should change the noise power. 

 In simple extreme cases one can even make a semiquantitative argument 

 for the maximum variation to be expected on the basis of such 

 considerations. 



FORMULATION OF THE PROBLEM 



In order to make an exact calculation, we require a few preliminaries: 

 The conductivity g is supposed to undergo a small time-dependent 

 fluctuation Ag{t) about its mean value. 



The fluctuation arises from certain sources each of which, for macro- 

 scopic purposes, may be considered to emit a noise-current J(t) of minor- 

 ity carriers. Thus in a small time-interval dt^ near i' the excess charge 

 injected is J{t') dt' . This charge decays by recombination. Let r{t — t') de- 

 note the fraction of carriers left over at time t{>t'). Then at time t 

 there remains a charge r{t — t') J{t') dt' of the original injection. Now 

 provided the excess density is small compared with the mean density, 

 Ag{t) is proportional to the excess charge at time t, due to all the previous 

 emissions added together. Therefore 



Ag(0 oc f r{t- tViO dt'. (1) 



In practice we do not literally plot Ag{t) as a function of <, but rather 

 its frequency component Agr(/) in a narrow range df of frequencies near/. 

 In other words, we single out for observation* the contribution to Agr 

 from that part J{J) of the injected current J{t') which varies as e~^'*-^' 

 Suppose now that 1// is large compared with the time over which r{t) 



