HOT ELECTRONS IN GERMANIUM AND OHM S LAW 



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using the wave length X as a variable, we use the wave number or (1/X). 

 For long waves the frequency is simply 



y = c/\ = c(l/X). 



(3.2) 



This corresponds to the straight line portion for low frequencies in Fig, 3* 

 This portion extends to a wave length equal to twice the lattice constant a 

 of the crystal. 



Figure 3 shows another curve which has a high frequency even for 

 (1/X) = or infinite wave length. The presence of this branch of the "vi- 

 brational spectrum" is due to the fact that the diamond structure has two 



WAVE NUMBER 



1/2 3 



Fig. 3 — Frequency of longitudinal vibrations in [100] direction in the diamond struc- 

 ture. (In this particular direction of propagation the acoustical and optical branches 

 join smoothly at the same frequency; for other directions, there is a discontinuity in fre- 

 quency. The dependence of u upon 1/X is approximated by a sine wave.) 



atoms per unit cell. (The diamond structure is made of two face centered 

 cubic arrays of atoms, juxtaposed so that each atom of one array is cen- 

 trally situated in respect to a tetrahedron of four atoms of the other array, 

 with which it forms four electron-pair bonds. The unit cell contains one 

 atom of each array.) As a consequence of this it is possible to have a vibra- 

 tion in which one atom vibrates in the plus x direction while the other atom 

 vibrates oppositely and to have this same motion occur in phase in every 

 unit cell. Such a vibration is considered to have infinite wave length, since 

 every unit cell does the same thing at the same time. It has the highest 

 possible frequency since the pattern of motion involves directly opposed 

 motions of nearest neighbors. If the motion is modified so as to have dif- 



