454 BELL SYSTEM TECH MCA L JOCRXAL 



the total voltage drop. For this purpose we treat ipp — ^n as constant over a 

 range of integration from x = —L„ to x = -\-Lp obtaining 



= I.ie^"'^^"''' - IJ 



where 



/. = gq{L,. + L,) (3.12) 



is the current density corresponding to the total rate of generation of hole- 

 electron pairs in a volume L,, + Lp thick. We next consider 5^«p + 5^r„ 

 shown in Fig. 5c, where, as the subscript R implies, these are thought of as 

 resistive terms and are given by the integrals 



8ip, 



Rp 



+ B<pKn = - / d<fp - / d>f„ = / Ip dx/qfip + / /„ dx/qubn. 



Jxa •'0 Jza •'0 



The denominators are both approximately qtxip + bn) which occurs in the 

 integral for Ro . Furthermore, for most of the first range Ip = I and for 

 most of the second /„ = /. Near .v = 0, /;, or In must be at least 1/2. Hence 

 it is evident that dtpHp + Vk« cannot be much less than IRo . We shall repre- 

 sent it by IRi where Ro < 2Ri < 2Ro . 



In terms of Ry and h , the relationship between current and voltage 

 becomes 



dip = 8^Rp + 5sr«„ + 5v-y = i?i/ + — In ( 1 + - j . (3.13) 



This corresponds to an ideal rectifier in series with a resistance Ri . The 

 junction will, therefore, be a good rectifier if the second term represents a 

 much higher resistance. 



We shall compare the two resistances for the case corresponding to A' « 1. 

 For this case, we have p = —ax and n = +o.v except in the narrow range 

 \x\ < La = ni/a. The integral Rq can be approximated by integrating 

 dx/(T for .V outside of the range ±La using the approximation ±a.v for 

 p and n and approximating the integral from —L„ to +/.„ by 2/.<,,V (in- 

 trinsic). This procedure gives 



Ri = / dx/q^xax -\ ° + / dx/qubax 



(3.14) 



= ■^(l-\'\)\nix,/La) 

 qHUi \ b/ 



where it is supposed that -Xa = xt and that In {xb/L^ is large compared to 



2f(j) _(- 2 -(- 1 'b). The evaluation of /,p and /.„ for use in /., is more involved 



