A Device Model for Analog VLSI Circuits
This paper presents a new formulation of a CMOS device model. The model is primarily intended for analog circuit analysis. Exponential (subthreshold) and square-law (above threshold) behavior is modeled, with a smooth and accurate threshold transition. The new formulation is based on three independent physical process parameters: Na – bulk doping concentration, Qss – fixed oxide charge, and μ0 – effective carrier mobility. The mutual independence greatly simplifies the use of the model for prediction and for understanding the significance of process changes. This contrasts with the present standard practice of using, for example, the threshold voltage, Vt, as a model parameter. A change in Vt must be due to a change in the flatband voltage, which depends on Cox, φms, and Qss, or the Fermi potential which depends on Na and ni. Changes to these parameters in turn imply changes in the value of other model parameters such as β (μ × Cox) or γ (body effect). Thus, it is not physically realistic to change Vt while implicitly holding β or γ constant. This mistake is often made by users of models, such as SPICE, which permit changing Vt directly. The model has a simple closed form and therefore is well-suited to circuit simulation. Its incorporation into the anaLOG circuit simulator is described. Finally, two examples of the use of the model for devices from a 1.2um and a 0.8um process are given. In the course of reviewing the theoretical and empirical origins of the parameters for the standard device models, some anomalies were uncovered. These are discussed, and more accurate parameter values are derived. Some of these more accurate values would likely be useful in other models. By far the most important inaccuracy is the accepted value of the intrinsic carrier concentration in silicon (ni). The widely accepted value (as uniformly used in SPICE models, for example) of ni is 1.45× 1010cm−3 at 300oK. The accurately measured value is 0.99976× 1010. In a typical case, this 45% error in ni from its correct value changes Vt from 0.602 to 0.623. A 20mV change in Vt represents, for a transistor operating in subthreshold, an approximately 70% change in current, and thus can have a significant effect on the behavior of many analog circuits. The accurate value of ni has been known by people working on CCD’s and by people developing silicon-based solar cells, however the information has not been noticed by the CMOS device and circuits community. Quite a lot of time has been spent making “adjustments” for the resulting mismatch between “theory” and observation of device behavior. DRAFT: First published: July 1997 Current version: 2.4 29 April 2014. 12:47. DRAFT: First published: July 1997 Current version: 2.4 29 April 2014. 12:47.