THE FORWARD CHARACTERISTIC OF THE PIN DIODE 689 



where Vo is the forward bias across the junction at x = 0, Vp is the po- 

 tential drop in the middle i-egion, and V^ is the forward bias across the 

 junction at x = w. In this notation F(0) = F,„ + Vp and V(w) = Vy, . 

 The total current density is constant 



In{x) + Ij,{x) = I (10) 



! We shall denote electric current densities by e/„ , dp , so that In , Ip , I 

 have the dimensions of (particles/cm -sec) . At x = and x = w the 

 minority carrier currents must flow into the contacts by diffusion, which 

 gives the boundary conditions 



[Pn+ j 



/n(0) = Ins [^ - l] 



[np+ J 



(11) 



where Ips , Ins are saturation current densities 



J. _ Pn Dp J _ np Dn / V 



^ ps f ) -fns — f {i^^J 



jLip Lin 



The order of magnitude of the saturation current density is given by 



e{Ins + Ips) '^3 X 10~^ amp/cm^ in Si 



based on the typical values of (3). Equations (11) contain the assump- 

 tions of linear recombination and small injection into the contacts as 

 discussed in the introduction. 



In the middle region the current densities satisfy 



, j J.et us assume these equations remain valid in the space charge regions.* 

 ' Since these space charge regions are narrow /„ and Ip can be considered 

 constant and the solution of (13) in the space charge regions is 



^ Up JlOW J 



nix) = /^^^> L^e-'^'-'^' -{- ^ I 



U„ Jo 



X 



(14) 



Dn JOO I 



Shockley, W., B.S.T.J., 28, p. 435, 1949. 



