1010 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



FilqE since dP^/dt = qE. The average momentum is evidently P2/2 and 

 the average velocity is 



va = Pillm = {hvojlmyi'' (4.4) 



and is independent of E. The optical modes correspond to a temperature of 

 about 520°K and this leads to 



Vd = 6.3 X 10« cm/sec. (4.5) 



in general agreement with the observed value. 



The theory in the appendices indicates that both optical and acoustical 

 modes are active simultaneously and their interplay leads to the theoretical 

 curves shown. (In the Appendices a further discussion is presented and some 

 additional data are compared with theory.) 



The tendency of the theoretical curves to fall below the data for 193°K 

 and 298°K for field values below the optical point is thought to arise largely 

 from the approximations employed in the theory. The approximations 

 neglect the ability of the optical modes to enable the electrons to lose energy 

 for fields below the indicated value. Actually some electrons will be scattered 

 by the optical modes and this will contribute in an important way to hold- 

 ing the temperature down and the mobility up. A correct treatment would, 

 therefore, raise the theoretical curve appreciably in the region where it 

 deviates most from the data. 



4c. Electron ''Temperatures'' 



From the theory it follows that the average electron energies correspond 

 to about 520°K at the points marked Op on Fig. 5. The highest point on the 

 298°K curve corresponds to '^700°K and the highest point on the 77°K 

 curve corresponds to 550°K. For this last case the electron temperature is 

 more than seven times as high as that of the atomic vibrations. In the ap- 

 pendix we quote some other earlier data of Ryder's that indicates electron 

 temperatures of about 4000°K while the crystal itself remains at room 

 temperature. 



5. An Explanation of the Low Field Discrepancy 



The failure to deviate from Ohm's law at the low fields predicted indicates 

 that the electrons can dissipate their excess energy more effectively than 

 would be expected on the basis of their mobihty. This conclusion is forced 

 on us by the observation that they apparently retain their thermal dis- 

 tribution and normal mobility to higher fields than predicted. It is not pos- 

 sible to explain the discrepancy by assuming a large or a small value for the 

 effective mass, since the value of the effective mass does not enter into the 

 final comparison with experiment. 



