An analytical MOS transistor model valid in all regions of operation and dedicated to lowvoltage and lowcurrent applications
 Christian C. Enz,
 François Krummenacher,
 Eric A. Vittoz
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A fully analytical MOS transistor model dedicated to the design and analysis of lowvoltage, lowcurrent analog circuits is presented. All the large and smallsignal variables, namely the currents, the transconductances, the intrinsic capacitances, the nonquasistatic transadmittances and the thermal noise are continuous in all regions of operation, including weak inversion, moderate inversion, strong inversion, conduction and saturation. The same approach is used to derive all the equations of the model: the weak and strong inversion asymptotes are first derived, then the variables of interest are normalized and linked using an appropriate interpolation function. The model exploits the inherent symmetry of the device by referring all the voltages to the local substrate. It is shown that the inversion chargeQ _{inv} ^{′} is controlled by the voltage differenceV _{P} − V_{ch}, whereV _{ch} is the channel voltage, defined as the difference between the quasiFermi potentials of the carriers. The pinchoff voltageV _{P} is defined as the particular value ofV _{ch} such that the inversion charge is zero for a given gate voltage. It depends only on the gate voltage and can be interpreted as the equivalent effect of the gate voltage referred to the channel. The various modes of operation of the transistor are then presented in terms of voltagesV _{P} − V_{S} andV _{P} − V_{D}. Using the charge sheet model with the assumption of constant doping in the channel, the drain currentI _{D} is derived and expressed as the difference between a forward componentI _{F} and a reverse componentI _{R}. Each of these is proportional to a function ofV _{P} − V_{S}, respectivelyV _{P} − V_{D}, through a specific currentI _{S}. This function is exponential in weak inversion and quadratic in strong inversion. The current in the moderate inversion region is then modelled by using an appropriate interpolation function resulting in a continuous expression valid from weak to strong inversion. A quasistatic smallsignal model including the transconductances and the intrinsic capacitances is obtained from an accurate evaluation of the total charges stored on the gate and in the channel. The transconductances and the intrinsic capacitances are modelled in moderate inversion using the same interpolation function and without any additional parameters. This smallsignal model is then extended to higher frequencies by replacing the transconductances by first order transadmittances obtained from a nonquasistatic calculation. All these transadmittances have the same characteristic time constant which depends on the bias condition in a continuous manner. To complete the model, a general expression for the thermal noise valid in all regions of operation is derived. This model has been successfully implemented in several computer simulation programs and has only 9 physical parameters, 3 fine tuning fitting coefficients and 2 additional temperature parameters.
 Title
 An analytical MOS transistor model valid in all regions of operation and dedicated to lowvoltage and lowcurrent applications
 Journal

Analog Integrated Circuits and Signal Processing
Volume 8, Issue 1 , pp 83114
 Cover Date
 199507
 DOI
 10.1007/BF01239381
 Print ISSN
 09251030
 Online ISSN
 15731979
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 MOS transistor
 device modeling
 lowvoltage
 lowcurrent
 Industry Sectors
 Authors

 Christian C. Enz ^{(1)}
 François Krummenacher ^{(1)}
 Eric A. Vittoz ^{(1)}
 Author Affiliations

 1. Electronics Laboratory, Swiss Federal Institute of Technology of Lausanne, ELEcublens, CH1015, Lausanne, Switzerland