Unit-Cube Expression for Space-Charge Resistance

Copyright © 1967, American Telephone and Telegraph Company Unit-Cube Expression for Space-Charge Resistance By S. M. SZE and W. SHOCKLEY* (Manuscript received November 17, 1966) A simple analysis shows that the unit-cube conductance is a figure of merit in semiconductor device design theory. The unit-cube conductance, G, is given by 2Kvd where K is the permittivity of the semiconductor and vd is the limiting drift velocity. The space-charge resistance, R,c , due to carrier generated under avalanche condition is derived for p-n junctions. It is found that for parallelplane structure, R,e = 1/GN, where N is the number of unit cubes in the depletion region with cube edge equal to the depletion width or N = A/W2 where W is the depletion width and A the junction area. The disturbance in voltage caused by the space-charge effect is given by I/GN = JW'/G where I and J are the current and current density, respectively. Similar results are obtained for p-n junctions with coaxial-cylinder and concentricsphere structures. For silicon, the value of G is approximately J^O fimhos. The transconductance of a silicon surface-controlled avalanche transistor in terms of the unit-cube expression is about 12.5 N ^mhos. A simple analysis of "avalanche resistance" can be given for the limiting case in which carriers are generated at one boundary surface of the depletion region of a p-n junction and travel across the depletion region with a limiting drift velocity v d . Structures satisfying these conditions can be of the n + pp + form.