810 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1954 



Q = -10. (3.39) 



The calculations indicate that attenuation can be controlled to a 

 considerable degree while maintaining the desired phase shift. 



3.2. Justification of Consequences (1), (2) and (3) 



In germanium at room temperature the product np is about 10 

 under equilibrium conditions. At the first junction of Fig. 3.1 it is 10 ", 

 implying a forward bias^ " of (kT/q) 2.3 X 5. In order to maintain this 

 forward bias a flow of electrons must be furnished to A^. There are sev- 

 eral ways of accomplishing this. In the first place, the reverse bias 

 across Si drawls a reverse current of thermally generated electrons from 

 P2 . This current can be controlled by controUing the lifetime and 

 temperature in the P2 region. Alternatively, electrons may be injected 

 into P2 ; some of these will diffuse to S2 and arrive at N. Still another 

 means of controlling the bias across *Si is to make contact to .V itself. 

 Since only the dc bias need be controlled, the series resistance across A^ 

 itself is unimportant; the source should be of high impedance. 



The decrease in density of 10 across the junction in carrier concentra- 

 tion implies a potential difference of 9.2 {kT/q). Most of this potential 

 difference occurs where the carrier concentration is negligible. Hence 

 the space charge theory may be applied. Furthermore, the acceptor con- 

 centration is much higher than the donor concentration. Hence the 

 space charge extends chiefly into the donor region and we may write 



A7i = {2TrqNd/K)W^ (3.40) 



for the relationship between width W of the space charge region and 

 voltage drop AF. 



If this voltage drop has an ac component, then a charging current will 

 be required to change W. This current is determined by the admittance 



coC = w/c/47rTF (3.41) 



of the space charge region. 



At the same time injected hole and electron currents flow across the 

 junction. The admittance associated with the hole current is approxi- 

 mately 



A = {iw/Df" cTpi , (3.42) 



where o-pi is the hole conductivity just inside the n-layer. ' Actually, as 

 discussed below, the admittance is somewhat higher. 



