596 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



bulk of the wafer where Nd almost equals Na , but is as low as Do/(l + 

 ^Na) near the surface where Nd « A''^ . If Q,Na is very much larger 

 than unity as it will be under conditions where appreciable pairing oc- 

 curs, the diffusivity will, therefore, be much smaller near the surface 

 than at the high end of the diffusion cui-ve, deeper within the specimen. 

 The surface will then offer resistance to diffusion, and it may be expected 

 that the measured value of the diffusivity Avill correspond more closely 

 to the slow process near the surface rather than to the faster process 

 occurring deeper in the semiconductor. Of course this cannot be entirely 

 true because the resistance at the surface coupled with the lack of re- 

 sistance inside the wafer will tend to steepen the concentration gradient 

 near the surface. This wdll give the impression of a diffusivity somewhat 

 higher than the one corresponding to the surface. 



If the current flowing in the wafer under the conditions of measure- 

 ment is I, and the potential measured between the points is V, then the 

 conductance between the points is 



S = I/V. (11.10) 



In Appendix E it is shown (under the assumption that D is constant) 

 that 



S/S. = 1 + ?:?«|v^ (1^) V^ (lUl) 



where So is the conductance after the specimen is saturated with 

 lithium, but before any lithium has diffused out, and S^ is the con- 

 ductance before lithium has been added. Na is the uniform concentration 

 of acceptor, and Nd° is the initial uniform concentration of lithium, while 

 d is the thickness of the wafer. ?? is a correction factor which arises be- 

 cause the mobility of holes varies from point to point in the wafer, as 

 the density of lithium varies. There are two extreme types of variation. 

 The first takes place in a specimen in which, at room temperature 

 (where the conductance measurement is made) ion pairing is complete. 

 Then the local density of impurity scatterers will be A''^ — Nd ■ At 

 the other extreme no ion pairing occurs, and the density of scatterers is 



Na + Nd. 



The nature of t> depends on how much pairing is involved. In Fig. 22 d^ 

 has been evaluated in its dependence on Nd° for the extreme cases men- 

 tioned. Furthermore it has been assumed then that Nd is given by a 

 Fick's law solution of the diffusion problem, and that diffusion begins in 

 a nearly compensated specimen. 



The first thing to notice is that ?? is not very different from unity in 



