98G THE BELL SYSTEM TECHNICAL JOUENAL, JULY 1957 



where 7?, and n are the mstantaneous concentrations of holes and elec- 

 trons, respectively. When a PN junction is forward biased, holes and 

 electrons are injected into the space-charge region which has been re- 

 duced in width. Some of these carriers diffuse through the space charge 

 region and give rise to the normal diffusion current when the excess 

 minority carriers recombine with majority carriers in field free regions. 

 The other carriers recombine according to (4-1) in the space-charge re- 

 gion giving rise to what is called the space-charge generated current. In 

 the reverse biased junction, the current is due to carriers generated in the 

 space-charge region; whereas, in the forward biased junction, the current 

 is due to recombination of carriers. The quantity U is large in the space- 

 charge region since both p and n are large in this region. In the field free 

 regions, however, one of these quantities is usually small and the product 

 deviates only slightly from rii . 



The space-charge generated current, Igc , is given approximately by:'" 



V 

 2qWn, ^"^^^2 ,,,, (4-2) 



where Vb is the built-in potential of the junction, and /(6) is discussed 

 in Reference 12 and is approximately 1.5 for recombination centers near 

 the intrinsic level as is the case for the diodes under consideration. For 

 shallower recombination levels the function f(b) is much smaller and de- 

 pends strongly upon the forward applied voltage. 



For the forward-biased junction, the space-charge region is narrow, 

 the concentration gradient can be considered linear and W is given by 

 the following expression: 



W = 4.35 X io'(lj^^\ ' cm, (4-3) 



where Fjunction is the total potential across the junction in volts and a 

 is the concentration gradient at the junction in cm^^ These are given 

 by: 



' junction ' built-in ' 



= kT/q In (NANn/nf) - V (4-4) 



= 0.792 - V. 



Also, a = — ^ 6-^^/"°' for diffused junctions, (4-5) 



'VirDt 



where Cc = surface concentration of diffusant = 3 X 10 cm , 



