NEGATIVE RESISTANCE IN SEMICONDUCTOR DIODES 809 



value of the algebraic expressions lies between 2 for 7 = and 1 for 

 Y = 00 . 



It is instructi^'e to express the real part of tlie ex})oiieiit in terms of 

 a and ^1 . This is done as follows: 



a - a(l + iyf- = --q - id^. (3.28) 



This can be solved for r] and (1 + ^7)"': 



7/ = («- + diY' - a, (3.29) 



(1 + iyf" = [(a- + d,Y' + ie,]/a. (3.30) 



From there it is seen that for a fixed value of ^1 , the attenuation can be 

 greatl}^ reduced by increasing a. Unfortunately, this requires very large 

 changes in concentration. For example with ^1 = 37r/2 and a = ^1 , the 

 value of 7} is reduced to r; = 0.414 di . However, the value of potential 

 difference is 



qAV/kT = St, (3.31) 



giving 



N,,/N,2 = 10'. (3.32) 



For the case shown in Fig. 3.1, a = 1.15 and for 9i = 57r/4 = 3.9 we 

 obtain 



n = 2.95 = Ine 19.5 (3.33) 



This is an improvement of about 1 factor of e in the exponential com- 

 pared to having AT' = 0. The value of (8 is 



/3 = 0.082 X exp (-i 218°), (3.34) 



and this leads to 



Z = (C0C2)"' (-0.05 - i 1.0G5). (3.35) 



Thus at the operating frequency, the diode appears to be a capacitor 

 with a negative Q of 21. 



Increasing the concentration change to a factor of 100, so that a = 

 2.3, gives 



ri = 2.25, (3.36) 



/3 = 0.18 < - 220°, (3.37) 



Z = (cuCs)"' (-0.11G - f 1.14), (3.38) 



