HOT ELECTRONS IN GERMANIUM AND OHM's LAW 1031 



in this section so as to agree with the critical velocities observed in Fig. 2. 

 This leads to a value for B of 



B = k 520°K/^m (1.3 X 10«)2 



(A7.34) 

 = 12.8 



For A we shall take 



A = 520/r (A7.35) 



The only other adjustable parameter is /zq. For this we shall use the value 

 based on Haynes' drift mobility and acoustical scattering. 



^o(r) = ^0 (298°i^)(298°i^/r)3/2 



(A7.36) 

 = 3600 {29S°K/Tyi^ 



This value automatically fits the room temperature data in the Ohm's law 

 range. The T~^'^ dependence then extrapolates it to the other ranges. 

 The steady state condition may then be written in the form 



x2(l + Ay){ABy + Ax"^ - 1) = z^ (A7.37) 

 where 



V, = {2hv/myi^ (A7.38) 



X = v,/v., y = v,/v, = (1 - x-^yi^ (A7.39) 



A = hv/kT = (v./vtY (A7.40) 



B = 12.8 (A7.41) 



z = MO {T)E/2cA''\ (A7.42) 



This form lends itself to calculation of z as a function of x. The drift velocity 

 is then found to be given by 



u = Vd/2c = z/x{l + Ay) 



(A7.43) 

 = [(ABy + Ax' -1)/(1 + Ay)Y'' 



If ^ » 1, there are three distinct ranges of behavior for u versus z: 



Range (/) u = z/A"'' 



For z — > 0, x^ ^ 1/A , y = and consequently, 



u = zA"' = Vd/2c = Mo E/2c (A7.44) 



