p-n JINCTIO.XS l\ SEMlCONDfCTOKS 



439 



•I- 



o^ = y 



p = ni_e kT 



[a] INTRINSIC 





(b) p-TYPE 





q (v^-^) 



+ + + + 



q(^^-yn) 



n = n, e ;,j 



(C) n-TYPE WITH 

 INJECTED HOLES 



>?: 



Fig. 2 — Electrostatic potential i/-, Fermi level <p and quasi Fermi levels ifp and <p,,. 

 (In order to show electrostatic potential and energies on the same ordinates. the ener- 

 gies of holes, which are minus the energies of electrons, are plotted upwards in the figures 

 in this paper.) 



acteristic of a pure sample. For an impurit}- semi-conductor we shall have, 

 as shown in (b), 



p = HiC 



ci{<P-v)lkT 



n = UiC 

 where q is the electronic charge. Accordingly, 



P = ([[Nd - Xf + 2;7, sinh \q(^ - ^p)/'kT]}. 



(a) 

 (b) 



(2.2) 



(2.3) 



When the hole and electron concentrations do not have their equilibrium 

 values, because of hole or electron injection or production of hole-electron 

 pairs by light, etc., it is advantageous to define two non-equilibrium quasi 

 I'ermi levels <pp and -^n by the equations 



Hie 



<i(ipp''ip)lkr 



(a) 



„Q<.'p-<Pn)lkT 



(2.4) 



Hie"' ""' (b) 



as indicated in Fig. 2 (c). In terms of ip,, and ip„ , the hole and electron cur- 

 rents take the simple forms: 



I J, = -q[DVp + M/'V^l = -qf^p^^p (2.5) 



In — bqiDVii — iJiiiVxp] = —qb/jLuVipn (2.6) 



