CHEMICAL INTERACTIONS AMONG DEFECTS IN Gg AND Si 555 



of lithium would have been 2.4 X 10 cm~^. Since this exceeds the 9.3 X 

 10^^ cm" supportable at 25°C, such a sample would have contained some 

 precipitate. It was important to avoid these various pitfalls in preparing 

 the specimens used in the above study. Care was taken to insure that this 

 was the case. 



We now turn to another application of the electron-hole equilibrium. 

 It has been emphasized that just as a fixed acceptor will increase the 

 solubility of lithium in silicon, a fixed donor should decrease it. In fact 

 in a crystal containing a p-n junction" the solubility should be above nor- 

 mal on the p side and below normal on the n side. The built-in field^^ 

 which exists at the junction is a reflection of this difference in solubility, 

 for if it M^ere not present the concentration gradient created by the dis- 

 parity in solubilities would cause the lithium to diffuse from the p to the 

 n side until its concentration was uniform throughout the crystal. Ob- 

 viously this field is in such a direction as to cause lithium ions to move 

 back to the p side.* 



Now in both silicon and germanium the oxide layers on the surface 

 can react readily with dissolved lithium. As a result the surface behaves 

 as a sink, and at temperatures as low as room temperature lithium is lost 

 to the surface from the body of the crystal. At higher temperatures the 

 body of the crystal can be exhausted of lithium in a few minutes. There 

 are many experiments which one would like to perform in which the 

 crystal must be maintained without loss of lithium at an elevated tem- 

 perature for long periods of time. 



The application now to be discussed involves utilization of the built-in 

 field at a p-n junction to prevent lithium from reaching the surface where 



* The distribution of lithium in the space charge region of a p-n junction cannot 

 be computed by the methods advanced thus far. This is because the charge neu- 

 trality condition (2.8) is no longer valid. Instead the concentration of lithium is 

 determined by Boltzmann's law,-' and is given by 



D+ = D^+exp [- qV/kT] 



where q is the charge on a lithium ion, V is the local electrostatic potential, and 

 D^:'*' is the concentration where V is zero. 



V itself must be determined from Poisson's equation^" 



V^V = 



K 



where p is the local charge density and k is the dielectric constant of the medium. 

 In semiconductors p is given in terms of V by'^ 



P = q[H + D+ - 2ni sinh (qV/kT)] 



= q[H + D^+ exp [- qV/kT] - 2ni sinh (qV/kT)] 



where H is the local density of fixed donors less the local density of fixed acceptors. 



