Unit-cube expression for space-charge resistance

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 2Kv
d
where K is the permittivity of the semiconductor and v
d
is the limiting drift velocity. The space-charge resistance, R
sc
, due to carrier generated under avalanche condition is derived for p-n junctions. It is found that for parallel-plane structure, R
sc
= 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/W
²
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
²
/G where I and J are the current and current density, respectively. Similar results are obtained for p-n junctions with coaxial-cylinder and concentric-sphere structures. For silicon, the value of G is approximately 40 μmhos. The transconductance of a silicon surface-controlled avalanche transistor in terms of the unit-cube expression is about 12.5 N μmhos.