150 BELL SYSTEM TECH X ILAL JUL' RS A L 



where Xp < and .v„ > are the ends of the sj)ace-charge layer in the p- 

 and ^-regions. The gradient of potential at x = must be equal for the two 

 layers leading to 



— ppXj, = HnXn (2.51) 



so that if the total width of the space charge layers is IT = .v„ — .v^, , it 

 follows that 



Xp -= —)iJV/(nn + pp) and .v„ = pp\V/(nn + pp). (2.52) 



The potential difference across the layer, which is xph — ^a is 

 h - ^a = {2Trq/K){ppx\ + n,/n) = [2Trq ppUn/Kipp + ;/,0]n'' (2.53) 

 If pp » )in this reduces to 



4'b — ^a = 2Trq UnW /k (2.54) 



the formula given by Schottky, which should be appreciable in this case, 

 for which all the voltage drop occurs in the //-region. 

 The capacity for the abrupt transition will be 



C = K/iwW (2.55) 



where \V is obtained by solving (2.53). For this case (l/Cf should plot as a 

 straight line versus \pb — 4^a '• 



- = ISiriPp + n,)/KqPp uM, - iA„). (2.56) 



3. Oeneral Conclusions Concerning the Junction Characteristic 



In this section we shall consider direct current flow through the junction 

 and shall derive the results quoted in Fig. 1 relating the current distribution 

 to the characteristics of the junction. We shall suppose that holes and elec- 

 trons are thermally generated in pairs at a rate g and recombine at a rate 

 rup so that the net rate of generation j)er unit volume is 



(net rate of generation) = ,(,' — nip, » 



wliich \-anishes at equilibrum. Obviously, g = ni'i . If relatively small con- 

 centrations bp and bn of holes and electrons are present in e.xcess of the 

 equilibrium values, the net rate of generation is 



5j, = 5/, ^ g - rill + bii)(p -f bp) = -nibp - rpbii (3.1) 



Tliis is equivalent to sa\-iiig thai excess holes in an //-tyj)C semiconductor, 



