HOT ELECTRONS IN GERMANIUM AND OHM's LAW 1023 



and the actual drift velocity is 



Vd(Ec) = 0.785 X 1.84c = 1.45c. (A6.18) 



If we introduce Ec into the steady state equation (A6.9), and express 

 Ve/vT as a mobility ratio, we obtain 



(mo/m)' - (mo/m)' = (E/Eef. (A6.19) 



We give this equation in order to show the similarity of the Maxwellian 

 distribution case to the cruder case considered next. 



A similar treatment may be given for a hypothetical distribution of elec- 

 trons such that all have the same energy S and speed v. The effective mo- 

 bility of such a distribution is^ 



(A6.20) 



M = (^V^) (1 + (3) d(nT/dCnv) 



= 2qt/?)vm = TT^''^ hoVt/2v. 



The steady state equation deduced from (A6.19) and (A6.4) is 



(v/2vl) [Wlvl) - 1] = (37r/64) (noE/cf (A6.21) 



For high fields we find that this steady state condition gives 



Vd = iW^Y" {cfjioEy^ = 1.01 (cfjioEyi\ (A6.22) 



a value somewhat smaller than that obtained from the Maxwellian approxi- 

 mation. This leads to a critical field of 



E, = (7r/3)i/2 ^/^^ = 1 03 c/no (A.623) 



at which Vd given by (A6.22) extrapolates to give the same value as fioE. 

 We may use this distribution and make it give identical results with the 

 Maxwellian distribution. If we use the steady state condition for low fields, 

 we find V = 2^'^ Vt and 



M = MO = VVS MO = 0.625 MO. (A6.24) 



In terms of this /io, the steady state equation becomes 



(MiW [(m'oM' - 1] = {E/E:y. (A6.25) 



with 



El = {S/Sy c/fjLo = 1.63 c/fj^. (A6.26) 



It is evident that if we chose modified values of c and i so as to make 

 Hoi^') become equal to /xo and eI{c, t') = Ec{c, I), then the monoenergetic 

 22 See E and H in S problem 8 page 293. m 



