MAGNETIC EFFECTS ON NOISE IN A GERMANIUM FILAMENT 653 



negligible for ordinary values of H.) It is convenient to specify a dimen- 

 sionless parameter in the same notation as H. C. Montgomery. 



2ayLF^ ^ 2aBE^ 



By the Einstein Relation Z)//i = kT jq this may be written 



^ 2oBE^ 



~ kT/q 



where q is the absolute value of the electronic charge. $ is the ratio of 

 the voltage corresponding to the transverse field to the thermal voltage 

 kT/q. In terms of $, equation (3) can be rewritten 



dw _ ^ dw _ ^ , . 



dx^ 2a dx 



The integral of this equation has the form 



w = Ae^^'"""^ + B (5) 



where A and B are two constants. Because of the existence of a singu- 

 larity at X = Xo , say, the constants A, B take on different values for 

 X <Xo and x>Xo . To see what these values are, we first write the solu- 

 tion (5) in the form 



w, = Aie*^^-^°^^'" + B, x> xo, 



w, = A 26*^"-^°^^'" + B2 X <Xo. 



At x = Xo the density w must be continuous. Hence 



Ai + Bi = A2-\- B2 (6) 



Further, the discontinuity at Xq must be such that the difference of the 

 currents on the two sides is just unity, the strength of the injected 

 current. Now the total current is 



^ /dw $ \ 



(i.e., the diffusion current plus the drift current), and w is continuous 

 at Xq . Hence the difference between the current on the two sides of Xq is 



l = -DUm((p) -('ip) ) 



h-*o \\ dx /xo+h \ dx /xo-h/ 



(7) 



= £z)U.-AO. 



