ELECTRICAL NOISE IN SEMICONDUCTORS 9i)l 



sity. (b) We restrict the noise measurements to frequencies low enougli 

 so that the period is long compared to the lifetime of a hole. It is tlien 

 evident that the contribution of a hole source to the noise is proportional 

 to the fiuctuatin<>; hole current jicnerated ])y the source and to the aver- 

 age lifetime of the holes. This lifetime depends on the position of the 

 source in the filament, the absorption properties of the surfaces and the 

 electric and magnetic fields.* (c) We assume that the generation prop- 

 erties of the soiu'ces are unaffected by the magnetic field, hence, the 

 calculation of the effect of the field on the noise reduces to a problem of 

 calculating the change in lifetime produced by the field, (d) We neglect 

 body recombination in comparison with surface recombination. In ger- 

 manium filaments of the size usually dealt with, this approximation 

 causes only a small error in the lifetime, (e) Individual soui'(;es (or at 

 any rate groups of sources over regions small compared to the dimen- 

 sions of the filament) will be considered to be statistically independent; 

 therefore, the total effect on the noise can be determined by summing 

 the squares of the contributions from individual sources. Hence we wish 

 to evaluate the following expression: 



Change in noise power at field H = {t (H))/{t (0)) (1) 



where the symbol () indicates an average over all the noise sources. 

 The statments (a) to (e) represent the principal assumptions in de- 

 veloping the theory. 



In order to calculate t as a function of the magnetic field, H, we con- 

 sider a steady state case in which a current of holes Jo is injected into a 

 region in which the average lifetime is t. If the density of holes in the 

 region is p(x, y, z), the total number is 



P = I p{x, y, z) dx dy dz. 



However, P = Jor/q, where q is the charge carried by a hole. Therefore, 



T = "T / vi^, y, 2) d^ dy dz (2) 



Jo J 



This is the method of evaluating r which is used in the qualitative dis- 

 cussion which follows, and also in the calculation of the curves of Figs. 

 10 and 11. 



* It should be pointed out that a consetiuence of the hole injection theory of 

 noise in a filament is that marked frequency dispersion should occur when the 

 frequency- being studied is high enough so that a i)eriod is short compared to the 

 lifetime of holes in the filament. However, we shall neglect this important and 

 interesting aspect of the problem. 



