Voltages and electric fields of diffused semiconductor junctions

Equations are developed and graphs are presented, showing a functional relationship between electric field and space-charge widening and also between reverse bias voltage and space-charge widening, for diffused diodes. Planar geometry, with the diffusion made from a constant surface concentration (C0) into material of constant impurity density, is assumed. The voltage vs space-charge width relation is presented graphically for the case of silicon. Graphs for other materials are not included, since they would differ from the silicon graphs only by a constant in the voltage axis. These graphs illustrate that for small reverse voltages the junction may be considered as being essentially linear, while for large reverse voltages it may be considered as an abrupt junction. A graph is provided which may be used to gain a qualitative indication of the electric field distribution within the space-charge region. This graph also gives an indication of the transition of junction behavior from nearly linear to nearly abrupt as the reverse voltage is increased.