DESIGN THEORY OF JUNCTION TRANSISTORS 1285 



and across which there is a small electrostatic potential. The potential 

 difference across the region exists primarily because of the difference in 

 energy levels between the conduction band in which the mobile electrons 

 exist and the valence bond band in which the mobile holes move. The 

 potential difference depends on the densities of holes and electrons in 

 the p and n regions, but it cannot exceed the energy gap or difference 

 in band levels, so long as the junction is at equilibrium. 



If a reverse voltage is applied to a junction, the applied voltage ap- 

 pears principally across the depletion region, where it strengthens the 

 electric field by widening the barrier region so as to bring more fixed 

 donor and acceptor charges into the field. It is obvious that the depletion 

 region has a capacitance, since an electric field exists across it. This 

 capacitance decreases with increase of reverse voltage, since the capaci- 

 tance is charged not by bringing mobile carriers to fixed electrodes but 

 rather by widening the region to include new fixed charges from the 

 semiconductor regions on each side. 



Both emitter and collector capacitances may be calculated easily 

 for the principal cases of published engineering interest, the graded 

 transition and the abrupt or step transition. For graded transitions, the 

 depletion layer is in a region of linearly changing fixed charge density 

 (zero at the center of the layer). The step junction has the barrier layer 

 almost entirely in either a p or an n region of uniform fixed charged 

 density since the fixed charged density in the other region is usually so 

 large that the field effectively terminates at its surface. 



The general expression for barrier capacitance is 



c = '^ 



where Xm is barrier thickness and the other symbols have conventional 

 meanings. In the case of graded junctions, this becomes 



^ 2 \SKeyJ 



where a is the rate of change of fixed charge density in charges per cm' 

 per cm. For step junctions, the relation is 



/q{Na - Na)y" 



/ qjNa - Na) V 



\ 2/c€of: / 



where (Nd-Na) is the fixed charge density in the low charge density region, 

 ordinarily the base region in transistors. The potential Vc is the electro- 

 static potential across the depletion layer and under bias conditions is 



