Short-channel MOS transistor circuits: finding all the DC solutions and input-output characteristics

摘要

Circuits containing short-channel MOS transistors, having multiple DC solutions, are analyzed in this paper. The n-th power law model (Level 6, SPICE) of short-channel MOS transistors is investigated and some of its properties are proved. Two basic questions in the DC analysis and design of the circuits are considered. For the circuits with transistors represented by the n-th power law model, the earlier developed method exploiting the idea of contraction, division and elimination is extended, enabling us to find all the DC solutions. Next, each of the solutions is corrected in succession by means of a controlled SPICE simulation using more accurate BSIM 3v3 model. This two part algorithm for finding all the DC solutions is illustrated via a numerical example. The comparison with other alternative methods, tested on a set of representative circuits, shows that the proposed approach is much more effective, and enables us to analyze larger circuits than the other methods. Another question considered in the paper is how to determine effectively multi-valued input-output characteristics in the circuits containing short-channel MOS transistors. An approach for finding the characteristics is developed and illustrated using a numerical example.