THE FORWARD CHARACTERISTIC OF THE PIN DIODE 



701 



If we eliminate / from equations (24) we get 



J . Ir h cosh O) + 1 nr 2 



olps + J r+l " ''^ 



+ 7 

 which can be solved for ^ 



Ir cosh CO + 6 



1 b + 1 



(72) 



y _ Ir cosh CO + ^ To — 7 

 ^ ~ 7;:. 6 + 1 /?7- - ^ 



where 



pi' 



70 = 



6 cosh cj + 1 



cosh CO + 5 

 Substituting (73) into (70) gives the equation satisfied by y 



Ry' cosh CO + 1\ , ^ / [(7/700)' - 1]' 



7 r> o , — T ) (7 - 70) = 7 



Ry"^ + cosh CO / " ' "' /oo ^7^ + cosh co 

 ■where loo is a characteristic (particle) current density 



(73) 



(74) 



(75) 



J^ 00 — -' o 



CO 



sinh 



CO 



cosh u -\- h 

 h + 1 



(76) 



Now the solution of (75) has two branches which as / -^ approach 

 N'alues given by 



a) 

 b) 



7 -^ 70 



Ry" cosh CO + 1 

 Ry- + cosh CO 



(77) 



As I increases the first branch remains positive and approaches 700 as 

 / — > 00 . The second branch becomes negative and approaches —700 . 

 Therefore, we choose that branch which satisfies 



7(0) = 70 = 



b cosh CO + 1 



6+ 1 



y(cc) =y^= {h/Rf" 



7 > 



(78) 



( )n this Ijranch 7 always lies between 70 and y^ , and 7 never approaches 

 the quantity in (77b). Therefore we replace Ry by b (as if 7 = 700) in 



II 



