THE FORWARD CHARACTERISTIC OF THE PIN DIODE 095 



where C is a constant representing the slowly varying coefficient of 

 ' 7„) " in (41). We choose C snch that (42) becomes exact at high cur- 

 I _nt density when ^Vp is large 



C = -^^ S- (43) 



7^ - 1 V& + 1 



When we regard the third and fom-th tei-nis of (37) together as a constant 

 jSFc Ave obtain the simplified voltage-current characteristic 



/3F = fn ^ + C j/^ + 0Vo (44) 







In this approximation it is unnecessary to evaluate 7(7) from (31). 



Fig. 3 shows plots of jSV versus I/Io calculated from (44). For plotting 

 the curves the \'alue (' =1.1 was used. To choose a value for 13V c we put 

 7=1, which gives 



1 + fc(7/7oo)- 1 + i^ 



so that 



^Vc -^ HIo/(Ins + Ips)] (4G) 



which has the value 27 in silicon according to the values in (3). The dot- 

 ted line is the asymptote approached by the curve at low current densities 



0V -^ (n ■[ I « h (47) 



This is the characteristic of a simple PA'' junction Avhen 



;Ve retain now to the cjuestion of when the large injection conditions 

 (18) are satisfied. Let us suppose 7 is much less than 7o so that 7 '^ 1, 

 7„/7;, ^ R. It follows from (30) and (23) that 



rio ^ n,, ^ ni[I/(Ins + Ips)f'~ (48) 



Now let us set /?„ » P Avhich gives a condition on the current density 



I » (P/mY (L,s ^ Ips). (49) 



Setting /;„„ » Hp'^, Pu-w » Vn'^ gives 



7 » 7,„ + Ip, . (50) 



Usually P » 7ii so that (49) includes (50). When numbers are put in 



