180 BELL SYSTEM TECHNICAL JOURNAL 



insulators there exists a region of energy values, just above the allowed band, 

 which are not allowed. The height of this unallowed band is expressed in 

 equivalent electron volts, A£. Above this unallowed band there exists an 

 allowed band; but at low temperatures there are no electrons in this band. 

 When a iield is applied across such a semiconductor, no electron can be 

 accelerated, because if it were accelerated its energy would be increased to 

 an energy state w^hich is either tilled or unallowed. As the temperature is 

 raised some electrons acquire sufficient energy to be raised across the un- 

 allowed band into the upper allowed band. These electrons can be ac- 

 celerated into a slightly higher energy state by the applied field and thus 

 can carry current. For every electron that is put into an "activated" 

 state there is left behind a "hole" in the normally filled band. Other 

 electrons having slightly lower energies can be accelerated into these holes 

 by the applied field. The physicist has shown that these holes act toward 

 the applied field as if they were particles having a charge equal to that of an 

 electron but of opposite sign and a mass equal to or somewhat larger than 

 the electronic mass. In an intrinsic semiconductor about half the con- 

 ductivity is due to electrons and half due to holes. 

 The quantity A£ is related to B in equation (1) by: 



2B = (A£) e/k (8) 



in which B is in centigrade degrees, A£ is in volts, e is the electronic charge 

 in coulombs, k is Boltzmann's constant in joules per centigrade degree. 

 The value of e/k is 11,600 so that 



A£ = Z^/5800. (8a) 



The difference between metals, semiconductors, and insulators results 

 from the value of A£. For metals A£ is zero or very small. For semicon- 

 ductors A£ is greater than about 0.1 volt but less than about 1.5 volts. 

 For insulators A£ is greater than about 1.5 volts. 



Some impurities with positive valencies which may be present in the semi- 

 conductor may have energy states such that A£i volts equivalent energy 

 can raise the valence electron of the impurity atom into the allowed con- 

 duction band. See Figure 6. The electron now can take part in conduc- 

 tion; the donator impurity is a positive ion which is usually bound to a par- 

 ticular location and can take no part in the conductivity. These are excess 

 or A^ type conductors. The conductivity de[)ends on the density of dono- 

 tors, A£i , and T. 



Similarly some other impurity with negative valencies may have an 

 energy state A/S2 volts above the top of the lilled band. At room temi)era- 

 ture or higher, an electron in the filled band may be raised in energy and 



