/) <; .icxcrioxs i\ si:\ii(0\i)rcroRs 459 



// ifj^'ion, the lit\'tiim' r ,, and diffusion roiistaiil J) l<>|- a hole will be sul> 

 stantiall}- unaltered by V- Ai)plicalion of llie hole cuncnl e(|ualion lo the 

 hole density p(.\\ I) i^ix'es 



I„=-qD^^. (4.6) 



Combining this with the reconil)ination e(|uation 



^ = ^"_Zli _ i ^^ = Pn-^P ^ jj^ll (4.7) 



dt Tp q dx Tj, a.r^ 



leads to (he solution 



P = P,^ + /,0 6*^^"~^"^'^^' + ^^gi./ + (.r«-x)a+<W,)l/2/(Dr,)l/2_ (_^_^) 



The quantity \^Dtp is the diffusion length and is denoted by L^. (We shall 

 use subscript p for holes in the ;/-region and 11 for electrons in the /^-region 

 for both L and r.) 



When p is large conii)ared to p,, , but small compared to ;/„ , the ex- 

 pression for p leads to the following formula for ipp : 



^p = ^n + vr. - ikT/q){x - XTn)/Lp + lie ''. (4.9j 



This shows that the d-c. part of ipp varies linearly in the //-region, for large 

 forward currents, and decreases by {kT/q) in each diffusion length Lp . 

 The transition from this linear dependence to an exponential decay for ^pp 

 comes when ifp — ^„ = {kT/q). This behavior of the d-c. part of ^p is useful 

 in connection with diagrams of ^pp versus distance. (See Sections 5 and 6.) 

 The solution just obtained for p gives rise to a current at Xm of 



Ipixm) = —qD 



dp 



dx (4.10) 



= qp,D/Lp + qpxDe'-'iX ^ io:Tp)'"/Lp. 

 The d-c. part is calculated by substituting (4.4) for /^n : 

 /po(-Vr„) = (<//'„/>/Aj(^""°'"- 1) ; 

 = Ip.{e''""' - I) 

 and the a-c. part is similarly obtained from (4.5) for p\ : 



Tpiixr.) ={qPnU^/L,)\e""""'""]{\ + /a;r,y %-, e''^" 

 = (Gp + iSph.e'"' ^Apv.e'"' 



where . I ^, is called the admittance (i)er unit area) for holes diffusing into the 

 //-region; its real and imaginary parts are the conductance and suscept- 



(4.11) 



(4.12) 



