996 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



region be less than the diffusion length of the minority carrier. High sur- 

 face concentration of diffusant is desirable since this facihtates the con- 

 tact problem. This suggests that the diffusion system can be much less 

 involved than that required for diffused transistors.^^ Some of the data 

 presented in this section will show that the open tube diffusion tech- 

 nique^^ can lead to variations in diffusion parameters. 



The diffusion of impurities into silicon is complicated by variations in 

 the boundary conditions at the surface. Frosch^^ has shown that surface 

 concentrations can be varied over six decades. 



5.2.1 Device Diffusion Theory 



Several important impurity distributions have been considered . Two 

 distributions are important in the open tube process: 



1. Error Function Complement, ERFC, Distribution or Infinite Diffus- 

 ant Source. If the diffusant is deposited on the silicon and serves as an 

 infinite source, the added impurities will have an erfc distribution. For 

 one diffusant and a fixed diffusion program this distribution will result 

 in the deepest penetrations and smallest sheet resistances of all possible 

 distributions. The sheet resistance is a measure of the total number of 

 added impurities. The data presented later indicates that the added im- 

 purities frequently have an erfc distribution. 



2. Gaussian and Modified Gaussian Distribution. A number of impurity 

 atoms enters the solid, and a surface barrier builds up with time which 

 prevents additional atoms from entering. ^^ Initially, the diffusant is as- 

 sumed to be present in an infinitely thin layer at the surface with diffu- 

 sion into or out of the material possible. In the range of siHcon doping 

 levels and surface concentrations used, a Gaussian, modified Gaussian 

 or erfc distribution for a given diffusion program lead to approximately 

 equal junction depths. 



The sheet resistance and the diffusion depth have been related to 

 the surface concentration for an erfc distribution. If the distribution is 

 Gaussian instead of erfc, then for the same ^^alue of sheet resistance and 

 diffusion depth the surface concentration should be reduced by one-third. 

 Since the sheet resistance is related to the total number of impurities 

 through a mobility term, quantitative interpretation of the data for any 

 case other than erfc or Gaussian distributions would be difficult. 



5.2.2 Experimental Residts 



The sheet resistance was measured by the four-point probe method, 

 and the diffusion depths, by angle lapping and staining.^ Surface con- 



