7.2 The MOSFET Models

Table of Contents - Glossary - Study Aids - ¬ ­ ®
In this Section

  1. Description of the three models
  2. Comparison of the three models
  3. The linear model
  4. The quadratic model
  5. The variable depletion layer model
Reading: Neamen 10.3.3, 10.3.4 pp 457-465

Next: 7.3 Threshold voltage calculation and threshold voltage adjustment

7.2.1 Description of the three models

Three models for the MOSFET are presented below: the linear model, the quadratic model and the variable depletion charge model. All three models provide expressions for the drain current as a function of the gate-source and the drain-source voltage.

The simplest model of the three, the linear model, is based on the assumption that the drain-to-source voltage is small so that the charge density in the inversion layer is constant.

The quadratic model includes the gradual change of the charge in the inversion layer between the source and the drain due to the fact that the channel voltage varies from the source voltage to the drain voltage.

The variable depletion layer model includes in addition to the gradual change of the inversion layer charge the variation of the charge in the depletion layer between the inversion layer and the substrate. This model is required to understand the body or substrate bias effect.

7.2.2 Comparison of the three models

A numeric comparison of the three MOSFET models is offered here to get a better feel for the differences between the models. While the quadratic model is most common since it contains most features without being complex, the linear model makes it easier to understand the basic operation of the device (eventhough its actual use is limited) while the variable depletion layer model is more complex and more accurate.

Click here to compare the quadratic and the variable depletion layer model.

7.2.3 The linear model

Required background: Carrier transport, carrier mobility and inversion layer charge

The linear model describes the behavior of a MOSFET biased with a small drain-to-source voltage. As the name suggests, the MOSFET, as described by the linear model, acts as a linear device, more specifically a linear resistor whose resistance can be modulated by changing the gate-to-source voltage. In this regime the MOSFET can be used as a switch for analog signals or as an analog multiplier.

The general expression for the drain current equals the total charge in the inversion layer divided by the time the carriers need to flow from the source to the drain:

where Qinv is the inversion layer charge per unit area, W is the gate width, L is the gate length and tr is the transit time. If the velocity of the carriers is constant between source and drain, the transit time equals: where the velocity equals the product of the mobility and the electric field: The constant velocity also implies a constant electric field so that the field equals the drain-source voltage divided by the gate length. This leads to the following expression for the drain current: We now make an assumption about the inversion layer charge density, namely that it is constant between source and drain and that the charge density in the inversion layer is given by the product of the capacitance per unit area and the gate-to-source voltage minus the threshold voltage: The charge is zero if the gate voltage is lower than the threshold voltage. Replacing the inversion layer charge density in the expression for the drain current yields the linear model:

Note that the capacitance in the above equations is the gate oxide capacitance per unit area. Also that the drain current is zero if the gate-to-source voltage is less than the threshold voltage. The linear model is only valid if the drain-to-source voltage is much smaller than the gate-to-source voltage minus the threshold voltage. This insures that the velocity, electric field and inversion layer charge density are indeed constant between the source and the drain.

An example of the linear Current-Voltage characteristics of a MOSFET is shown in Fig. 7.2.1.


mfliniv.xls - mflinv1.gif

The figure illustrates the behavior of the device in the linear regime: While there is no drain current if the gate voltage is less than the threshold voltage, the current increase with gate voltages larger than the threshold voltage. The slope of the curves equals the conductance of the device which increases linearly with the applied gate voltage. It is in the linear mode of operation that the MOSFET can be used as a voltage controlled resistor.

7.1 ¬ ­ ® 7.2.4
© Bart J. Van Zeghbroeck, 1996, 1997