350 BELL SYSTEM TECILXICAL JOURNAL 



current are s\vej)t along the filament from left to right. In the small filaments 

 used for these experiments, the resulting concentration of holes is so high 

 that large changes in conductivity are produced to the right of the emitter 

 point and, as we shall describe below, these changes can be measured and 

 the results used to determine the hole current at the emitter jioint. In order 

 to treat this situation quantitatively, we introduce a ciuantity 7 defined as 

 follows: 



7 — the fraction of the emitter ctirreut carried by holes. 



Accordingly, a current yh of holes flows to the right from e and produces a 

 hole density, denoted by p, which is neutralized by an equal added electron 

 density. A fraction (1 — 7)/^ of electrons flows to the left; these electrons 

 do not, however, produce any increased electron density to the left of the 

 emitter since they are of the sign normally {^resent in the //-type material. 

 The presence of the holes to the right in the filament increases the con- 

 ductivity a (as shown in Fig. 3c) both because of their own presence and 

 the presence of the added electrons drawn in to neutralize the space charge 

 of the holes. The mobility of electrons is greater than the mobility of holes, 

 the ratio being'^ 



h = /x„ Vj) =1.5 for germanium 

 and the electrons are always more numerous than the holes* 



// = ;/o + p, (2.1) 



where ;?o is the concentration of electrons which would be present to neu- 

 tralize the donors if p were equal to zero; consequently, the current carried 

 by electrons is greater than the current carried by holes. The concentration 

 of holes diminishes to the right due to the fact that holes may recombine 

 with electrons as they flow along the filament. 



From this experiment the value of 7 and the lifetime of a hole in the 

 filament can be determined. The measurements are made with the aid of 

 the two probe points I\ and P-i . The conductance of the filament between 

 these points is obtained by measuring the voltage difference AV and dividing 

 it into the current //, -|-- T( , no current being drawn by the probes them- 

 selves. The necessary formulae for calculating hole density and hole current, 



* The notation used in the eriuations is as follows: n, p, »o = respectively density of 

 electrons, of holes, of electrons when no holes are injected. Nd and Na are the densities of 

 donors and acceptors, assumed ionized so that uo = Nd — .Va. Ii, h, Ic are as shown on 

 Figs. 3 and 9. {E used for the probe collector in Figures 1 and 8 does not enter the 

 equations.) q = \q\ is the charge on the electron, used to be consistent with Ref. 4, where 

 e is used for 2.718 • • •. 



