1005 



Since theory shows that t varies as r~\ the mobihty should vary as T~ . 

 This prediction is in good agreement with experimental findings over the 

 range of conditions for which the dominant scattering processes are those 

 considered here. 



Next we consider the effect of very large fields. Under these conditions 

 an electron drifting in the direction of the field with drift velocity Vd acquires 

 energy from the field at an average rate 



{dZ/dl)c^no toB = VaqE. (3.26) 



If this power is large enough, the electrons will be unable to dissipate energy 

 sufficiently rapidly to the phonons that they can maintain their normal tem- 

 perature. As a result their average energy mounts, after the field is initially 

 appHed, until they can furnish energy to the phonons fast enough to main- 

 tain a steady state. Under these conditions the sum of the two rates is zero 



{d&/dl)axio to B -\- {dS^/dl)dMo to phonons = 0. (3.27) 



If the field is high enough, there may be no steady state solution. This 

 can occur if the ability of the phonons to remove energy decreases with 

 increasing energy. Such cases play an essential role in the theory of dielectric 

 breakdown.* In them it is concluded that electrons will gain sufficient energy 

 from the field so that they can produce secondary electrons which repeat the 

 process thus producing avalanches. For the cases with which we are con- 

 cerned, theory indicates that the energy losses increase rapidly with the 

 energy of the electron while the power input decreases because of decreasing 

 mobility so that a steady state will thus occur. 



In order to estimate the drift velocity for the steady state we must intro- 

 duce expressions for the two powers involved. For this purpose we assume 

 that an electron has on the average a speed Vi and we calculate the power 

 to phonons as the average energy loss per collision for this velocity times 

 the rate of collision, Vi/t For vi » Vt , we can neglect the effect of motion of 

 the M spheres and thus obtain from (3.19) 



(^SM)phonons = -(z;i/^) mhl/M. (3.28) 



The mobility will be less because of the higher collision rate so that the drift 

 velocity in the field will be approximately 



Vd = {qf/mv,)E. (3.29) 



The power furnished by E will be 



idZ/dl)a.e toB== (q''C/mvi)E?. (3.30) 



8 See the references to Frohlich and Seitz in Section 1. 



