HOT ELECTRONS IN GERMANIUM AND OHm's LAW 993 



minations of va as a function of E. From the theoretical side also the empha- 

 sis has been on fields so high that the linear range is neglected so that the 

 transition from linear to nonhnear is not stressed. 



The current theories of dielectric breakdown are based on the principle 

 of "secondary generation" or "electron multiplication." Thus if an electron 

 acquires enough energy from the electric field, it will be capable of pro- 

 ducing secondaries by collision with bound electrons, and the repetition of 

 this process will lead to an avalanche. Our theory indicates that in ger- 

 manium, even at fields as high as 200,000 volts/ cm, few electrons will have 

 enough energy to produce secondaries. At about those fields, however, 

 another phenomenon occurs. 



In 1934 C. Zener' proposed that dielectric breakdown was due to a pri- 

 mary effect: the field induced generation of hole-electron pairs. His mathe- 

 matical theory is similar to that for field emission from cold metal points 

 and to that for radioactive decay. It involves the "tunneUing" of electrons 

 through regions in which their wave functions are attenuated, rather than 

 running, waves. 



Zener's theory does not seem to apply to breakdown; however, it does 

 apply to the high electric fields produced in rectifying p-n junctions in ger- 

 manium when these are biased in the reverse direction. Under these condi- 

 tions fields of the order of 200,000 volts/cm are produced. The mobiHties 

 of electrons, or holes, in these fields have not been measured. It has been 

 shown,"* however, that secondary production is very small. At these fields 

 a sort of "breakdown" effect occurs and above a critical value of the volt- 

 age a very rapid increase in current is observed. This current appears to 

 be of the nature predicted by Zener. It is stable at a given voltage, has a 

 small temperature coefficient and will probably be useful in semiconductor 

 analogues of "voltage regulator tubes" and protective devices. 



As is shown in the treatment given in quaUtative terms in Section 3 and 

 in more detail in the Appendices, the explanation of the fundamental devia- 

 tions from Ohm's law is based on the theory of electron waves. The investi- 

 gations described in this paper may thus be regarded as furnishing evidence 

 for the wave nature of conduction electrons in germanium and are thus re- 

 lated to the researches of C. J. Davisson, to whom this volume is dedicated, 

 and his collaborator, L. H. Germer. The Davisson-Germer experiments were 

 concerned chiefly with electron waves in free space and with high energy 

 electrons in crystals. Both of these cases are simpler than that dealt with in 

 this paper. Electrons in the conduction band in germanium appear to behave 

 as though they were in a multiply refracting medium in which they may have 



8 C. Zener, Proc. Roy. Soc. 145, 523 (1934). 



* K. C. McAfee, E. J. Ryder, W. Shockley and M. Sparks, Phys. Rev. 83, 650 (1951). 



