THEORY OF THE SWEPT INTRINSIC STRUCTURE 1243 



Outline of the Following Sections 



Sections II through V deal with the ideal ease of equal hole and elec- 

 tron mobilities. Here the problem is somewhat simplified and the physics 

 easier to visualize because of the resulting symmetry. In Section VI, 

 the general case of arbitrary mobilities is solved by an extension of the 

 methods developed for solving the ideal case. The technique is to deal 

 not with the hole and electron flow densities but with two linear com- 

 binations of hole and electron flow densities that have a simple form. 



Section II deals with the basic relations and in particular the formula 

 for recombination in an intrinsic region for large disturbances in carrier 

 density. The nature and range of validity of the various approximations 

 are discussed. Section III derives the field distribution in regions where 

 recombination is small compared to pair generation. Section IV treats 

 the recombination region and the smooth joining of the recombination 

 and no-recombination solutions. Section V considers the role of chffusion 

 in current flow and the situation at the junctions where the field and 

 carrier concentration abruptly become large. The change in form of 

 the solution near the junctions is shown to be represented by a basic in- 

 stability in the governing differential equation. Section VI extends the 

 results to the general case of unequal mobilities. Section VII deals with 

 the still more general case where there is some fixed charge in the "in- 

 trinsic" region. If the density of excess chemical impurities is small com- 

 pared to the intrinsic carrier density, the solution remains unchanged in 

 the range where recombination is important. In the no-recombination 

 region the solution is given b}'' a simple first order differentiatial equation 

 which can be solved in closed form in the range where the carrier flow is 

 by drift. The fixed charge may have a dominant effect on the space 

 charge even when the excess density of chemical impurities is small com- 

 pared to the density n, of electrons in intrinsic material. Consider, for 

 example, a junction between an extrinsic P region and a weakly doped 

 n region having an excess density N = Nd — Na oi donors. In the limit, 

 as the reverse bias is increased and the space charge penetrates many 

 difi"usion lengths into the n region, the field distribution becomes linear, 

 corresponding to a constant charge density equal to 



m + Vn^ + 8 n.-^jeV^i'] 



where Li is the diffusion length in the weakly doped n type region and £ 

 is the Debye length for intrinsic material. For germanium at room tem- 

 perature £,/Li is the order of 10~^ Thus, in this example, a donor density 

 as low as lO" cm~^ will have an appreciable effect on the space charge. 



