978 



THE BELL SYSTEM TECHNIC'AL JOUU.NAL, JULY 1U57 



numbers, (2-6) becomes: 



1.25 X 10'« 



(; = — 



;^oo 



g20.8(l-30O/r) 



'osh 



.8.02 (^)(r,.- 0.54) 



0.55 



(2-6a) 



aiitl 



where 



a = G:miV,M\T, Vr), 



(7:51)0 (» r) — 



1.25 X 10 



16 



cosh [38.62(T^ - .54) - 0.55]' 



and 



f{T, Vr) 



(2-6b) 



(2-7a) 

 (2-7b) 



' rp \3;2 



J \ 20.8(1-300/7') 



In (2-6b), G-m{yr) is the generation rate for a recombination level at 

 Vr equal to 300° K, and f{T, T,) is the temperature variation of G for a 

 recombination level at 1', normaHzed to :^00° K. 



Curves of /(T, Vr) are gi\-en in Fig. 1 for several \alues of W with a 

 curve g{T) which is the temperature variation of the reverse saturation 

 current (/o). Table I gives values for Gm for various Vr . 



In the reverse biased diffused junctions made with high resistivity ma- 

 terial, the junction may be considered abrupt. Therefore, the width (IF) 

 of the space-charge region, when the junction is rtn-erse biased to a volt- 

 age V, is given by 



ir = 



:V 



1/2 



:2qN 



= 3.14 X urirp,,) 



1 2 



cm 



(2-8) 



where the units after the first equal sign are electrostatic, and k is the di- 

 electric constant. In the second expression, 1' is in volts, and pp , the base 

 material resistivity, expressed in ohm-centimeters. Thus, 



/,,. = 4 X 10"''G';uH,(r,.)/(7', l',.)[rpj' - amperes-cnF 



(2-9) 



It is seen that /«< varies theoretically as the square root of the reverse 

 voltage for values of V less than h Va , the breakdown voltage, in which 

 range avalanche multiplication is negligible. The (luantity /,,. varies in- 

 versely with Na^^' and will be large for high \'oltage de\'ices with small 

 Na . The Isc at 300° K for a rectifier with 40 ohm-centimeter base ma- 



