1032 THE BELL SYSTEM TECffiSTICAL JOURNAL, OCTOBER 1951 



SO that the low field relationship 



Vd = fJioE (A7.45) 



is correctly given. 



Range II, Ax- » 1 and x < 1 



In this range the electrons are at high temperature but not high enough 

 to excite tlie optical modes. For it 



22 = ^^.4^ ^ = sV2/^i/4 (A7.46) 



u = z'l'^A"' or Vd = {2cix,Eyi\ {M Al) 



This corresponds to the square root range with a critical field of Ec = 

 2c/fjLo and Vc = 2c. 



Range III, x> 1 



When X is greater than unity, the optical modes enter the picture. For 

 the three cases considered the values of A and AB are: 



77% A = 6.75, AB = 87, 



193% A = 2.69, AB = 34.5, (A7.48) 



296% A = 1.74, AB = 22.3. 



The large value oi AB means that as soon as y is appreciably greater than 

 zero, say 0.5 corresponding to x — 1.15, energy losses to optical modes 

 dominate. As y approaches unity, the value of u is approximately 



u = [AB/{\ + A)]'i^ 



(A7.49) 



= {iiv/^mc'yiy{\ + A-'yi^ 



leading to 



vM. B) = {hu/myf'/(l + A-'yi' 



(A7.50) 

 = z;./[2(l + A-')Y'\ 



For the values of A and B given above, the ranges are not completely sepa- 

 rated. In Fig. A2 we show the theoretical curves used in Fig. 5, together 

 with the limiting lines just discussed. 



For the middle or 193°K curve, we also show the fit that would be ob- 

 tained if c = 5 X 10^ cm/sec, corresponding to i5 = 87 as for (A7.30). It is 

 seen that this deviates much more from the data than does the curve based 



