CONDUCTIVITY-MODULATED SILICON RECTIFIER 977 



at voltages less than half the breakdown voltage. The magnitude and 

 temperature and voltage dependences of measured diodes do not agree 

 with these theoretical values at room temperatures. 



Recently, Pell*^ has shown that the reverse currents at low temperatures 

 in germanium, and at room temperatures in silicon, are dominated by 

 space-charge generated current. The space-charge generated current 

 density (Isc) is given by 



/,, = qWG M, (2-2) 



where W is the width of space-charge region, G is the generation rate of 

 hole-electron pairs in the space-charge region, and M is the breakdown 

 multiplication {M ~ 1 except near the breakdown voltage). G is given 

 by-^ 



G = '^ , (2-3) 



where iii and pi are the densities of electrons and holes respectively if 

 the Fermi levels were at the energy level of the recombination centers, 

 and r„n and Tpo are the minority carrier lifetimes of electrons and holes 

 respectively in heavily doped p-type and ?i-type silicon. This expression 

 assumes constant generation over the space-charge region. Thus, 



and 



n, = Nc exp ^ (Vr - W) = n, exp ^(F. - Yd, (2-4a) 



pr = N. exp ^ (7. - Vr) = m exp - /3(F. - F,), (2-4b) 



where Vr is the recombination level above the valence band edge T'\ , 

 Vi is the midband intrinsic level, /S = q/kT, Nc and A^„ are the effective 

 densities of states in the conduction and valence bands ^ 2.4 X 10 

 (T'/300)^ Vc is the conduction band edge, k is the Boltzmann's constant, 

 and T is the absolute temperature. 

 Substituting (2-4) into (2-3), one obtains: 



rii 1 



G = 



2V TnOTpO 



cosh 



/3(F. - Vi) + h In "^ 



TnO_ 



(2-5) 



For the diffused silicon junctions under consideration, it has been found' 

 that T„ri equals 1.2 X 10"^ seconds and Tpo equals 0.4 X 10"" seconds. 

 Also, iii = 3.74 X 10'' r^'V''""'' and F.- = 0.54 vohs. Using these 



