(A5.4) 



HOT ELECTRONS IN GERMANIUM AND 0HM*S LAW 1019 



where Py corresponds to neglecting the energy change of the electron on 

 coUision. This approximation is not good enough for the first term in (A5.1) 

 which involves P^ — Pa. In order to evaluate this first term we note that 

 the relationships 



Pa = Py[\ - {PoPy/2Pl)] (A5.3a) 



Pp = Py[l + (PoPy/2Pl)] (A5.3b) 



may be derived up to the first order in Pq. This permits us to write 



Pi dP^ - Pi dPa = (i) d [{P^ - Pa){^P\)] 



= d[P,P\/P\] = 4.{PoP\/P\) Py dPy . 



Hence 



(58) = 2{cPoP\/P\) - cP\l2kT. (A5.5) 



The second term is proportional to the (average change in momentum)^ 

 for colUsion by angle B. It thus corresponds to energy which would be trans- 

 ferred to an initially stationary mass M^mhy the colliding electron pro- 

 vided we take 



M = kT/c\ (A5.6) 



That this mass is much greater than the electron's mass may be seen in 

 terms of v, the velocity of a thermal electron: 



mv\/2 = kT. (A5.7) 



From this we obtain 



M = mivi/cy/2 = 170w (A5.8) 



at room temperature where Vi — 10 cm/sec while c = 5.4 X 10 cm/sec. 

 The first term may then be interpreted as follows: 



2cPoP\/P\ = 2c''mP\/Pl = 2{kTm/M){P\/P\) (A5.9) 



If this is averaged over all angles 6, the Py/Pi term becomes 2; the energy 

 gain is then just that picked up by a mass m colliding with a mass M moving 

 with a Maxwellian distribution at temperature T as may be seen as fol- 

 lows: For this case the velocity Vm of M parallel to the line of centers on 

 collision imparts an added velocity 2vm to the electron and, on the average, 

 an energy 



(i)m {{2vMy) = 2m {v^m) = 2 mkT/M (A5.11) 



