Abstract
The basic E.K.V. model considered in the previous chapter is not suited for real transistors for it makes use of the “gradual channel” approximation, like the C.S.M. Non-uniform doping, mobility degradation, short channel effects, etc. are ignored. Advanced models like BSIM and PSP, which are primarily circuit simulation tools, take care of these but don’t offer the degree of flexibility that is desirable.
We show in this chapter that as long as the source and drain voltages with respect to the substrate remain constant, DC currents, g m ∕ I D and g d ∕ I D ratios of real transistors, even sub-micron devices, can be reconstructed by means of the basic E.K.V model. Once V S or V D is modified, the parameters must be updated. The model remains unchanged however.
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Notes
- 1.
The currents shown in this figure are reconstructed drain currents obtained by means of the PSP compact MOSFET model. The parameters were extracted from measurements carried out on real physical transistors (courtesy of IMEC). The assumption that reconstructed currents agree fairly well with the physical currents is accepted implicitly. The PSP compact MOSFET model is a product of Philips Semiconductors and Penn State University (now respectively NXP and Arizona State University) (PSP 2006).
- 2.
The identification algorithm can be found in the 0start directory under IdentN.m and IdentP.m. The algorithm makes use of the ‘semi-empirical’ N- and P-channel data listed under n90.mat and p90.mat. The compact model parameters outputted by the identification algorithm are stored under ParamN.mat and ParamP.mat,. These are turned into global variables when running Glob.m (see also Annex 1).
- 3.
The MATLAB file IdentifDemo.m illustrates dynamically the evolution of Fig. 5.3 when the drain voltage symbolized by a vertical landmark is swept from 0 to 1.2 V.
- 4.
The MATLAB IdentifN.m and IdentifP.m files implementing the acquisition algorithm can be found in the Glob directory together with the ‘semi-empirical’ data where from the compact model parameters are extracted. It is possible to retrieve the extraction algorithm with other ‘experimental’ data when desired. To get familiar with the data organization, please consult Annex 1.
- 5.
The Early voltage is defined generally as the voltage where the tangent to the I D (V DS ) characteristic crosses the horizontal axis. The Early voltage considered here is the difference between the aforementioned crossing point and the actual drain-to-source voltage. This makes I D ∕ V A identical to g d . When the Early voltage is large, the two definitions coincide more or less, but this doesn’t hold true with short channel devices. In weak inversion, the zero crossing may be located even to the right of the origin owing to the exponential characteristic of the drain current like in Fig. 5.16. The Early voltage would be negative with the first definition.
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Jespers, P.G.A. (2010). The Real Transistor. In: The g m /I D Methodology, A Sizing Tool for Low-voltage Analog CMOS Circuits. Analog Circuits and Signal Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-47101-3_5
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DOI: https://doi.org/10.1007/978-0-387-47101-3_5
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