700 



BELL SYSTEM TECHNICAL JOURNAL 



bility that any particular energy state be occupied is given by the 

 Fermi-Dirac factor/ 



1 



/ 



E — Ei 

 g JcT _ I 



(9) 



This factor is shown in Fig. 22c and the corresponding filling of energy 

 levels is shown schematically in 22b. A physical picture which is 

 helpful in understanding this result may be obtained by considering the 

 distribution of energy levels, Fig. 22a, to be the cross-section of a 

 trough or tank. If we pour water into this tank it will fill to a certain 

 level, El. If we let each molecule of water in the tank represent an 

 electron in the crystal, then the distribution in energy of the electrons 

 is correctly represented by the distribution in height of the molecules. 

 Thermal agitation is represented by shaking the tank; this will produce 

 surface ripples as in Fig. 22d which represent crudely the Fermi-Dirac 

 distribution. 



0.05 



Q 0.04 



uj O 

 a. t- 



^< 

 iU5 

 a < 0.03 



^ *" 0.02 



^ 0.01 



2 4 6 8 10 12 14 16 18 20 



ABSOLUTE TEMPERATURE IN DEGREES KELVIN 



Fig. 23 — Specific heat of iron at low temperature. 



Under certain conditions, however, the electronic specific heat is not 

 negligible. We have seen that the number of electrons participating in 

 specific heat is proportional to ^T and that these have a more or less 

 normal specific heat. Hence the electronic specific heat is proportional 

 to T. On the other hand, at low temperatures the Debye specific heat 

 is proportional to T^. Hence for sufficiently low temperatures the 

 electronic specific heat is the larger. In Fig. 23 we give the specific 



