458 BELL SYSTEM TEX IIXIC. 1 L JOIRS. I L 



the capacity of the transition region, wliich wc sliall denote by Ct in this 

 section, does depend on the nature of the transition region and, consecjuentl}', 

 on the \'alue of A'. 



If the sizes of the />-region and ;/-region are hirge compared to the diffusion 

 lengths, we may assume the current at Xa to be substantially Ip only and 

 that at xi , /„ only. The total current entering at Xa can be accounted for 

 as doing three things: (1) neutralizing the electron current flowing into the 

 />-region across Xrp , (2) contributing to the charge in the transition region 

 (this corresponds to the capacity discussed in Section 2) and (3) contributing 

 a current flow to the right across .vr„ . 



We have selected the hole current for analysis because the hole has a 

 positive charge and the connection between the algebra and the physical 

 picture is simplified. For the same reason, the text emphasizes forward 

 current, although the equations are equally applicable to reverse currents. 

 Nothing essential is left out by this process; since the sample as a whole 

 remains uncharged, the current / is the same for all values of .v and if //, is 

 known, then I n — I — I p is also determined. 



4.2 Solution fur Hole Floic into the n-region 



We shall calculate first the hole current I pixm) flowing across .Vm . It is 

 readily evaluated as follows: The value of p{xT„) is given by 



pKXTn) = nte 



(4.1j 



where p,, is the hole concentration in the /^-region for thermal equilibrium. 

 If we apply a small a-c. signal superimposed on a d-c. bias so that 



6(/? = ro + ric""' (4.2) 



where vi is an a-c. signal, assumed so small that linear theory may be em- 

 ployed (i.e. Ti « kT q), then 



Pixm) = (^e^^'^^'Od + {qv,/kT)e''''). 



We resolve this density into a d-c. component po and an a-c. comi)onent p\ 



iwt 



e : 



piXrn) = pn + pV + pi <''"' (4.3) 



where 



Po = Pnie"'""'-!) (4.4) 



/>, = {qPnih/kT)e'">"\ (4.5) 



So long as P(xt„) « it,, , tlie normal concentration of electrons in the 



