Digital Integrated Circuit Design
Working from the fundamentals of transistor-level design and building up to system-level considerations, this text demonstrates how to design state-of-the-art high performance digital integrated circuits.
TABLE OF CONTENTS Digital Integrated Circuit Design
3.7: Appendix
3.7 Appendix
The purpose of this Appendix is to present many derivations for device equations that rely more heavily on device physics knowledge. Specifically, equations are derived for the exponential relationship and diffusion capacitance of diodes, the threshold voltage and triode relationship for MOS transistors, and the exponential relationship and base charge storage for bipolar transistors. In addition, small-signal models for diodes, MOS transistors, and bipolar transistors are given in greater detail. These are subjects that are not used often in digital IC design except at the most advanced level where the circuits are considered from an analog perspective.
DIODE EXPONENTIAL RELATIONSHIP
The concentration of minority carriers in the bulk, far from the junction, is given by equations (3.8) and (3.9). Close to the junction for a forward bias, the minority carrier concentrations are much larger. Indeed, the concentration next to the junction increases exponentially with the external voltage, V D, that is applied in the forward direction. The concentration of holes in excess of equilibrium in the n side next to the junction, p n, is given by (Sze, 1981)
Similarly, the concentration of electrons in excess of equilibrium in the p side next to the junction is given by
As the carriers diffuse away from the junction, their concentration exponentially decreases. The relationship for holes in the n side is
where x n is the distance from the junction into the n region and L p is a constant...
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