1248 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1956 



The data of Burton, Hull, Morin, and Severien* shows that a typical 

 value of the ratio of Tpo and r„o is about 10. This means that the varia- 

 tion in r with carrier concentration will be less than 10 per cent provided 

 St is about -ikT from So . In what follows we shall assume that this is so. 

 Then we have the mass action law (2.12) with r a constant, which could 

 be measured by one of the standard technicjues involving small dis- 

 turbances in carrier density. The general case of variable t is considered 

 briefly at the end of Section IV. 



Outline of the Solution 



To conclude this section, we discuss briefly the form of the equations 

 and the solution in different parts of the intrinsic region. First consider 

 (2.6) for the current in the ideal case of equal mobilities. In Sections III 

 and V we shall show that throughout almost all of the intrinsic region the 

 current flows mainly by pure drift so we can take I = asE. The reason 

 for this is as follows. The quantity £ is so small that the diffusion term 

 remains negligible unless the second derivative of E becomes large — so 

 large in fact that the E versus x curve bends sharply upward and both 

 the drift and diffusion terms become large compared to the current /. 

 This is the situation at the junction where / is the small chfference be- 

 tween large drift and diffusion terms. Thus (2.6) has two limiting forms: 



(1) Except at the junctions the current is almost pure drift so 7 = 

 asE is a good approximation. In Section III we derive an upper limit 

 for the error introduced by this approximation and show how the 

 approximate solution can be corrected to take account of the diffusion 

 term. 



(2) At the junction, the drift term becomes important and the 

 current rapidly becomes a small difference between its drift and diffusion 

 terms and the solution approaches the zero current solution, for which 

 sE = £^ (fE/dx^. In Section V we derive an approximate solution that 

 joins onto the I = asE solution near the junction and then turns con- 

 tinously and rapidly into the zero current solution. We shall call this the 

 junction solution. 



The abrupt change in the solution from (1) to (2) near the junction 

 is shown to be related to a basic instability in the differential equation. 

 This makes it impractical to solve the equations on a machine. 



When the applied bias is large compared to the built-in voltage drop, 

 the junction region will be of relatively little interest so the I = asE 

 solution can be used throughout. 



In the region where / = <tsE there are two overlapping regions in 

 which the equations assume a simple form. These are the following: ' 



^ Burton, Hull, Morin and Severiens, J. Phys. Chem., 57, p. 853, 1953. 



