PROPERTIES AND USES OF THERMISTORS 181 



accepted by the impurity which then becomes a negative ion and usually 

 is immobile. However, the resulting hole can take part in the conductivity. 

 In all cases represented in Fig. 6 an electron occupying a higher energy 

 level than a positive ion or a hole has a certain probability that in any 

 short interval of time it will drop into a lower energy state. However, dur- 

 ing this same time interval there will be electrons which will be raised to a 

 higher energy level by thermal agitation. When the number of electrons 

 per second which are being elevated is equal to the number which are de- 

 scending in energy, equilibrium prevails. The conductivity, a, is then 



a = N evi-i- P ev2 (9) 



where N and P are the concentrations of electrons and holes respectively, 

 e is the charge on the electron, z'l and V2 are the mobilities of electrons and 

 holes respectively. 



The above picture explains the following experimental facts which other- 

 wise are difficult to interpret. 1) A^ type oxides, such as ZnO, when heated 

 in a neutral or slightly reducing atmosphere become good conductors, 

 presumably because they contain excess zinc which can donate electrons. 

 If they then are heated in atmospheres which are increasingly more oxidiz- 

 ing their conductivity decreases until eventually they are intrinsic semi- 

 conductors or insulators. 2) P type oxides, such as NiO, when heat treated 

 in strongly oxidizing atmospheres are good conductors. Very likely they 

 contain oxygen in excess of the stoichiometric relation and this oxygen 

 accepts additional electrons. When these are heated in less oxidizing or 

 neutral atmospheres they become poorer conductors, semiconductors, or 

 insulators. 3) When a P type oxide is sintered with another P type oxide, 

 the conductivity increases. Similarly for two N type oxides. But when a 

 P type is added to an N type the conductivity decreases. 4) If a metal 

 forms several oxides the one in which the metal exerts its highest valence is 

 N type, while the one in which it exerts its lowest valence will be P type.^ 



For several reasons it is desirable to survey the whole field of semicon- 

 ductors for resistivity and temperature coefficient. One way in which this 

 might be done is to draw a line in Figure 3 for each specimen. Before long 

 such a figure would consist of such a maze of intersecting lines that it would 

 be difficult to single out and follow any one line. The information can be 

 condensed by plotting log po versus B in equation (1) for each specimen.^ 

 The most important characteristics of a specimen thus are represented by 

 a single point and many more specimens can be surveyed in a single diagram. 

 Figure 7 shows such a plot for a large number of semiconductors investi- 

 gated at these Laboratories or reported in the literature. Values for po 

 and B are given for T = 25 degrees centigrade. The points form a sort of 



