CHEMICAL INTEKACTIONS AMONG DEFECTS IN Ge AND Si 541 



contrast silicon and germanium offer possibilities of an entirely new order. 

 The advent of the transistor has not only provided large supplies of pure 

 single crystal material, but it has also made available a store of funda- 

 mental information concerning the physical properties of these sub- 

 stances. For example, data exists on their energy band diagrams includ- 

 ing impuritj^ states — also on resistivity — impurity density curves, 

 diffusivities of impurities, etc. Furthermore, the amount of ionizable 

 impurities can be controlled within narrow limits, and can be changed 

 at will and measured accurately. Consequently it is reasonable to assume 

 that experiments on germanium and silicon will be more successful than 

 similar investigations using other materials. 



A t this point it is in order to examine whether or not the treatment of 

 electrons and holes as normal chemical entities satisfying the law of 

 mass action is altogether simple and straightforward. This problem has 

 been investigated by Reiss who found the treatment permissible only 

 as long as the statistics satisfied by holes and electrons remain classical. 

 The validity of this contention can be seen in a very simple manner. 

 Consider a system like that in (2.1). Let the total concentration of donor 

 (ionized and un-ionized) be No , the concentration of ionized donor be 

 D"*", the concentration of conduction electrons be n, and that of valence 

 band holes be p. Let A''^ and A~ denote the concentrations of total ac- 

 ceptor and acceptor ions respectively. Finally, let a be the thermody- 

 namic activity'^ of the donor (lithium in (2.1)) in the external phase. 



Then, corresponding to the heterogeneous equilibrium in which lith- 

 ium distributes itself between the two phases we can write 



^» - ^" = K, (2.4) 



a 



in which Ko depends on temperature, but not on composition. This as- 

 sumes the semiconductor to be dilute enough in donor so that the ac- 

 tivity of un-ionized donor can be replaced by its concentration. No — D^. 

 For the ionization of the donor we can write the mass action relation, 



Z)+ 



n 



and for the acceptor. 



Nd - D+ 

 A~p 



= Kd (2.5) 



= Ka (2.6) 



iVx - A- 

 while for the electron-hole recombination equilibrium 



np = Ki (2.7) 



