ELECTRICAL NOISE IN SEMICONDUCTORS 909 



A second situation arises when noise is measiu'ed at frequencies high 

 enough so that the transit time of holes between segments is not neg- 

 ligible. In this case we should expect the correlation between the noise 

 voltages to be improved by incorporating in one channel of the meas- 

 uring circuit a delay equal to the transit time between segments. 



In order to calculate the correlation resulting from the first situalion, 

 we set up a theoretical model based on a few simplifying assumptions: 

 (a) The noise process may be represented by an array of nois}' hole cur- 

 rent generators which are statistically independent; (b) These generators 

 are uniformly distributed along the filament over the segments where 

 the noise is to be observed, and for a suHicient distance on either side 

 to produce uniform conditions over the segments; (c) The hole currents 

 from the generators decay exponentially with a decay constant deter- 

 minal)le from the lifetime; (d) Measurements are made at low enough 

 frequencies so that time of transit of holes may be neglected. We will 

 consitler later an alternative to the second assumption. The correlation 

 coefficient between two voltages of instantaneous values Vi and Vo may 

 be defined as 



Pi2 = ViV2/{vl X vD 



1/2 



where the bars represent time averages. To evaluate this expression, the 

 contribution of a single generator to the noise voltage in each segment 

 is determined by integrating over the appropriate portion of the decay 

 curve. The total contribution from all generators to the mean voltage 

 product and the mean squared voltages is then determined by inte- 

 grating the product or square over all the generators. The details are 

 carried out in the appendix, and lead to the solid curve of Figs. 14-16, 

 in which the ordinates are the correlation between noise voltages in two 

 segments of a filament and the abscissae are the ratio of life path of a 

 hole to the segment length. 



In an experiment the lifetime r of holes remains fixed, determined 

 chiefly by the recombination properties of the surface. Consequently 

 the life path / is proportional to the hole velocity, which is determined 

 by the electric field, according to the relation 



/ = tijlE 



where E is the applied field in volts per centimeter and n is the drift 

 mobility of holes. Hence, by \-ai\ving the biasing voltage a large range 

 of life path values can be obtained. 



The correlation is measui'ed by carrying the noise voltages through 

 separate amplifying channels having identical pass bands extending 



