538 THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1956 



ceptors. This question has been discussed in two papers,^- ® and only its 

 principle aspects will be considered. 



To gain perspective it is convenient to consider a system representing 

 the prototype of most systems to be discussed here. Consider a single 

 crystal of silicon containing substitutional boron atoms. Boron, a group 

 III element, is an acceptor, and being substitutional cannot readily dif- 

 fuse^ at temperatures much below the melting point of silicon. If this 

 crystal is immersed in a solution containing lithium, e.g., a solution of 

 lithium in molten tin, lithium will diffuse into it and behave as a donor. 

 Evidence suggests that lithium dissolves interstitially in silicon, thereby 

 accounting for the fact that it possesses a high diffusivity^ at a tempera- 

 ture where boron is immobile, for example, below 300°C. When the 

 lithium is uniformly distributed throughout the silicon its solubility in 

 relation to the external phase can be determined. Throughout this process 

 boron remains fixed in the lattice. 



If both lithium and boron were inert impurities the solubility of the 

 former would not be expected to depend on the presence or absence of 

 the latter, for the level of solubility is low enough to render (under 

 ordinary circumstances) the solid solution ideal.* On the other hand the 

 impurities exhibit donor and acceptor behaviors respectively, and some 

 unusual effects might exist. We shall first speculate on the simplest possi- 

 bility in this direction, with the assistance of the set of equilibrium reac- 

 tions diagrammed below.* , 



Li{Sn) «=± Li{Si) t± Li+ + e~ 



+ 

 B{Si) :f±B- + e+ (2.1) 



Ti 

 eV 



At the left lithium in tin is shown as Li(Sn). It is in reversible equilib- 

 rium with Li(Si), un-ionized lithium dissolved in silicon. The latter, in 

 turn, ionizes to yield a positive Li'^ ion and a conduction electron, e~. 

 Boron, confined to the silicon lattice as B(Si) ionizes as an acceptor to 

 give B" and a positive hole, e"*". The conduction electron, e~, may fall 

 into a valence band hole, e"*", to form a recombined hole-electron pair, 

 e"^e~. This process and its reverse are indicated by the vertical equilibrium 

 at the right. 



All of the reactions in (2.1), occuring within the silicon crystal are 

 describable in terms of tansitions between states in the energy band dia- 



A glossary of symbols is given at the end of this article. 



