NEGATIVE RESISTANCE IN SEMICONDUCTOIl DIODES 



825 



where Ws is u{Ez). In the P-region this space charge is compensated by 

 acceptors to produce a region of uniform field in which ^l* is negative. 

 If the F-region is wide compared to the /-region, then the transit time 

 through it will also be relatively large. As a consecjuence bQ will be 

 transferred quickly into the P-region. From that time on bEm. curves, like 

 those of Fig. 4.3, will show an exponential increase with time and also 

 with distance since for this case of constant u in the P-region, time and 

 distance are linearly related. This will lead to a D{t) of the form 



D{t) = {u,/K)(S- t)exp\^.*p,/K\t, 



(5.9) 



where the absolute value signs emphasize that for this case of negative 

 n* there is a build-up in time. This form of D is always convex upwards 

 and, in fact, if 



,S|M*P3/i^| > 1, 



(5.10) 



it starts ^^^th a positive slope at s = so that the transient voltage 

 actually builds up initially with time. 



Even an initially growing D(t) does not give a negative resistance at 

 low frequencies, however. As shown in Section 2, the dc resistance is 

 simply the integral under the D{t) curve and thus \nll still have a posi- 

 tive value. 



5.2. Convergent Geometry 



It is possible to obtain marked improvement of the D(t) curves without 

 the aid of the negative values of m*- This possibility is based upon con- 

 vergent geometry. A possible case is illustrated in Fig. 5.4. In this case 

 it is supposed that the field in the inner P-region is so large that a sub- 

 stantial reduction in fx* has occurred. As a consequence, the decay of field 

 in this region is relatively slow. Furthermore, since both the dc and 



Fig. 5.4 — A convergent flow structure. 



