996 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



In a specimen at room temperature the drift velocity of electrons is given 

 by the equation 



Vd = 3600 E cm/sec (2.1) 



when E is expressed in volts per cm.^ At 100 volts per cm, for example, 

 (which is below the non-linear range) the velocity of electrons should be 

 3.6 X 10^. This estabhshes the drift velocity scale for room temperature. 

 From other measurements of the germanium specimen of Fig. 2, it is con- 

 cluded that the number of electrons available for conduction is substan- 

 tially independent of temperature down to liquid air temperatures. Conse- 

 quently, for this temperature range the drift velocity should be directly 

 proportional to the current in the specimen. The other two sets of data 

 are accordingly simply scaled in proportion to their currents. 



On the figure we also show extrapolated lines at 45 degrees corresponding 

 to Ohm's law. From these we see that decreases in mobility of tenfold or 

 more have been produced in these experiments for high field conditions. 



The data for each temperature fall approximately on three lines: The low 

 field or Ohm's law region, an intermediate region over which Vd is propor- 

 tional to E^'^ and n is proportional to E~^'^j and a saturation region. The 

 break at low fields comes at drift velocity of about 3 X 10® cm/sec for all 

 three cases. This break, according to theory, should come when the drift 

 velocity is several times the speed of sound in germanium, the speed of 

 sound being about 5.4 X 10^ cm/sec. The limiting drift velocity at higher 

 fields is associated with the energy required to excite a particular type of 

 atomic vibration, called an "optical mode." It comes at approximately 

 the value of drift velocity predicted by theory.® The theoretical curves, 

 computed in the appendices, do not break into the sharp line section sug- 

 gested on Fig. 2. However, they show the distinct influences of separate 

 causes and fit the data reasonably well, as we shall show below in connection 

 with Fig. 5. 



3. Theory of Deviations from Ohm's Law 



3a. Electrons in n-Type Germanium^ 



The specimens we shall consider are of «-type germanium and have 

 resistivities of several ohm cm. The conductivity arises from the presence 



» J. R. Hayr.es and W. Shockley, Phys. Rev. 81, 835 (1951). 



•The observation and explanation of these general features was presented in our 

 first publications: E. J. Ryder and W. Shockley P/iys. Rev. 81, 139 (1951) and 82, 330 

 (1951). 



' The material under this heading is treated in more detail in the author's book, 

 "Electrons and Holes in Semiconductors," D. van Nostrand (1950), Chapter I. This 

 book will be referred to subsequently as E and 11 in S. 



