HOT ELECTRONS IN GERMANIUM AND OHM*S LAW 1007 



For comparison with experiment we note that for a value of 



£ = 4£, = 6.04<;/mo (3.37) 



such that if Ohm's law held 



Vd = 6.04c, (3.38) 



the value of Vd should be less than half the value predicted by Ohm's law. 

 We shall shortly discuss the discrepancy between this prediction and ex- 

 periment. 



The "temperature" of the electrons may be conveniently expressed in 

 terms of the ratio E/Ec . Since the electrons for the high field case are not 

 in a Maxwellian distribution of velocities, one cannot define their ''tem- 

 perature" unambiguously. As a measure of their temperature we shall take 

 their average kinetic energy divided by k. This leads to a ratio of electron 

 temperature T{E) to crystal temperature T of 2vi/3vt . Since to a first 

 approximation the ratio of mobihties at low and high fields is Avi/Sir^'hr , 

 the ratio of temperatures is 



r(£)_3xr MO ?_3x£ 



This ratio may also be thought of in terms of the square of the ratio of 

 drift velocity on the extrapolated Ohm's law line to the drift velocity on the 

 £1/2 line: 



nE)/T = {3T/S)yoEME)]\ (3.41) 



Either of these equations may be used to estimate electron temperature 

 from the data in the range in which the E^''^ formula is a good approximation. 



4. Comparison Between Theory and Experiment 



4a. Discrepancy in Critical Field 



In Fig. 5 we repeat Ryder's data of Fig. 2 together with data on an addi- 

 tional sample at 77°K. This new sample is considered more reliable than 

 the first since its low field resistivity varies in just the proper ratio [see 

 (3.25) and subsequent text] of (298/77)^/^ compared to its valua at room 

 temperature. Also we show the theoretical curves that will be discussed 

 below. 



The deviations of the data from Ohm's law do not occur at fields as low 

 as those predicted in Section 3e. For c = 5.4 X 10^ cm/sec, the critical 

 drift velocity should be 



Vdc = 1.5k = 8.2 X 105 cm/sec. (4.1) 



