1030 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



Rewriting the equation for mobility in terms of the coUision frequencies 

 l/r = v-Jl and 1/rop, the power input from the electric field is 



{dS/dOncia = qn^^ = q'E'/m [(l/r) + (l/rop)] 



(A7.26) 

 = qn^/Mvr) [1 + Wlo;)Mv,)] 



where the »2 term is omitted if Vi < Vy. The power delivered by phonons is 



(J8/J/)phonons = 4mc2 {Vi/ ^) [1 - (Vi/VtY] " km/ Lr> 



= (4qc'/noKvi/vT) (A7.27) 



X [1 - {vi/vtY - {hp/4mc')W^o^){v2M]. 



The two coefficients of (i'2/2'i) are both larger than unity according to the 

 analysis given above. We shall introduce the symbols A and B for them: 

 Accordingly 



A = //4p = hp/kT, (A7.28) 



the last equahty following from (A7.19), and 



B = hvl^ mc\ (A7.29) 



If we take hv = k S20°K, m = the electron mass and c = 5 X 10^ cm/ sec, 

 we find 



B = 87. (A7.30) 



As discussed in the text, the losses appear to be larger than can be ac- 

 counted for by these values of m and c. The critical drift velocity used in 

 the fit of Fig. 4 was 2.6 X 10® cm/sec and this corresponds to a value of c 

 of 



c = Vc/l.Sl = 1.72 X W cm/sec (A7.31) 



according to the exact treatment based on the sphere model. (As stated in 

 the text this means an effectiveness of energy interchange about (1.72 X 

 10V5 X 10^)2 = 10 times larger than the simple theory.) 

 Our simplified energy loss equation (A7.27) leads to 



Vc = 2c (A7.32) 



so that we shall take 



c = 1.3 X 10« (A7.33) 



