352 lil'-l.l. SYSTEM TPXIIXICAr. JOrRXAL 



s'.owu on the Figure, are derived as follows: 



Normal conductivity o-n = (/M""ii , {'2.2) 



conductivity with holes present a = i]n„n + (/tx,,p 



= (lH„(n, + p) ^ qn.p = cr„[l + (1 + b-'){p //o)l. (2.3) 



The conductance, 



G = (A + /.)/Al', 

 between Pi and Pi is proportional to the local conductivity, and hence to 



! + (!+/> '){p II,), 



so that a measurement of the conductance gives a measurement of p/nn . 

 Letting G and Go be the conductances between the points with and without 

 hole injection, we have 



^- = - = 1 + (1 + b-')(p/no) (2.4) 



tro (To 



or 



p _ <T — ffo _ (G/Go) — 1 /^ -\ 



m ~ <ro(l + b-^) ~ 1 + 5-1 * 



The ratio of hole current to electron current is qupp/cjUnU and the fraction 

 of the current carried by holes is thus 



In + Ip qt^nfi + qixpp bno + (1 + b)p 



p/fio _ l-(Go/G) 



b[l + (1 + b-')(p/no)] I -\- b 



Hence from the measured values of G, it is possible to obtain the fraction 

 of the current carried by holes. Multiplying this fraction by /. + h then 

 gives the actual hole current flowing past the probe points.* If there were 

 no decay, the current past the probe points would be 7/, and since /, is 

 known, 7 could be easily determined. Actually, however, there may be quite 

 an appreciable decay. However, if the current h is increased, the holes will 

 be swept more rapidly from the emitter to the probes and less decay will 

 result. Thus by increasing /;, , the effect of recombination can be minimized 

 and the value of hole current can be extrapolated to the value it would have 

 in the absence of decay. This value is, of course, 7/, . 



* In these calculations the formulae n = p + wo, corresponding to completely ionized 

 donors and acceptors, has been used. In germanium this is a good approximation. For 

 silicon, however, modifications will be necessary. 



