(4.15) 



NEGATIVE RESISTANCE IN SEMICONDUCTOR DIODES 817 



lilt ion. Each of the dashed lines represents the decay of 8E as measured in 

 a moving coordinate system: Thus wo consider 8E measiu'ed at a position 

 x(so + 0; this is a position that moves with the dc velocity 7/. This BE 

 is evidently expressed in terms of dE(x, t) by writing x = x(so -\- /): 



dE in moving system = 8E„Xso , t) = dE[x(so + t), t]. (4.14) 



The differential equation for SE^ is 



(d/dt) 8Em = (d8E/dt), + (d8E/dx)tdx/dt, 



= {d8E/dt), + {d8E/dx)tU, 



= - {u8p + p8u)/K + (8p/K)u, 



= -{pn*/K)8E = -v8E, 



where the quantity 



V = pn*/m (4.16) 



is an effective dielectric relaxation constant being the differential con- 

 ductivity pn* divided by the permittivity K. 



E\'idently j/ is a function of position x only and may be expressed as 

 v(s) through the dependence of x upon s. Thus we may write 



(d/dt)8EUso , t) = -v(so + t)8E^(so , t) (4.17) 



which has a solution 



8E^iso, t) = 5^„(.So, 0) exp [-g(so + + ^(^o)], (4.18) 



where 



g{so + t) = [ v{s) ds. (4.19) 



Js' 



The lower Hmit s' is chosen for convenience so as to avoid singularities in 

 g{s). This integration shows that 8Em decays exponentially as the elec- 

 trical field would decay in a material whose dielectric relaxation constant 

 changed -snth time just as v changes as observed on the moving plane. 



Fig. 4.3 shows on the dashed lines the decay of 8Em on the moving 

 planes. Since 8Em is zero to the left of the initial pulse in Fig. 4.2(a), it 

 remains zero on all moving planes which follow the pulse of 8Qo . This 

 justifies the statement made earlier. The solid curves labelled /i , t-i etc. 

 show the spatial dependence of 8E for times ti , ^2 , etc. after the charge 

 8Q1 is added. 



The values of the transient voltage v(t) at time ti , for example, is the 



