HOT ELECTRONS IN GERMANIUM AND OHM's LAW 991 



If a solid contains voids, then under a certain pressure it will crumble and 

 fill the voids. This is a secondary effect. If the sample is homogeneous, 

 however, high pressures will produce fundamental deviations from Hooke's 

 law, these deviations arising from the nonlinearity of the forces between 

 atoms. Studies of these nonlinear effects by Bridgman have, among other 

 things, put on a firmer basis the understanding of the forces between ions 

 in ionic crystals and the pressures of electron gases in metals. 



Deviations from Ohm's law for electronic conduction in semiconductors 

 are almost the rule rather than the exception, but the most familiar cases 

 are secondary rather than primary. The primary linear relation for the 

 conduction process is that between the drift velocity of an electron, or hole, 

 and the electric field that drives it. This relationship is 



va = MO (r) E, (1.1) 



where the mobility /xo(?^) is a function of the temperature T of the specimen. 

 By di. fundamental deviation from Ohm's law we shall mean a deviation in this 

 linear relationship arising from the largeness of E rather than other causes. 



Thermistor action is typical of a secondary deviation from Ohm's law. 

 A thermistor is usually a two-terminal circuit element in which the current 

 flows through an electronic semiconductor. The semiconductor has the 

 property that its resistance decreases rapidly as the temperature increases; 

 and the physical basis for this decrease is an increase in the number of con- 

 ducting electrons (or holes or both) with increasing temperature. The 

 passage of current heats the thermistor and its resistance changes; conse- 

 quently the Hnear relation between current and voltage fails and in fact 

 there may result a decrease of voltage with increasing current so that a 

 differential negative resistance is observed. The electric fields are so low, 

 however, that equation (1.1) is vahd provided the dependence of /zo on the 

 temperature is taken into account. An experimental proof that no funda- 

 mental deviation of Ohm's law occurs is furnished by applying a small 

 a-c. test signal on top of a d-c. bias that produces heating. If the frequency 

 is much higher than the thermal relaxation rate, the a-c. resistance is found 

 to be simply that expected for the observed temperature. 



The principal nonhnearities of crystal rectifiers, or varistors, and of tran- 

 sistors are also secondary and are associated with changing numbers of 

 current carriers. 



In this article we shall discuss some experimental evidence of funda- 

 mental deviations in Ohm's law for electrons in «-type germanium obtained 

 by E. J. Ryder of Bell Telephone Laboratories.^ We shall describe his ex- 



1 E. J. Ryder and W. Shockley, Phys. Rev. 81, 139 (1951). 



