In analog applications such as current mirrors or active loads, it is important for the transistor to have a large output resistance. Such circuits emulate a current source or current sink, and the Norton resistance of such a circuit should be large for ideal behavior.
The output resistance, usually denoted by rO, is a measure of how much drain-to-source voltage change is necessary to cause a given change in transistor output current when the transistor is in active mode. This resistance depends upon VGS, of course, because the channel conductivity depends upon the number of carriers within it, and that increases with gate voltage. However, rO also varies with VDS.
The reason a change in drain bias changes the resistance is that the channel exists only when the oxide field is sufficient to form a channel. At the source itself the oxide field is dependent upon the voltage drop VGS, which in active mode is above the threshold voltage, and so a channel forms. However, near the drain the oxide field depends upon VGD, and the applied drain voltage VDS makes VGD smaller than VGS because VDS brings the drain closer in voltage to the gate than is the source. The field in the oxide above the channel interpolates between these two values. In the ohmic or triode mode, a channel exists all the way from source to drain. But in the active mode, the drain voltage is high enough that somewhere between the source and drain the oxide field becomes too low to form a channel. The channel ends and dumps its carriers into the bulk semiconductor to finish their trip toward the drain without a channel. The termination of the channel is called the pinch-off point and it moves toward the source as the drain voltage increases. The channel becoming shorter as drain bias increases, the resistance between source and pinch-off point drops, so there results a lowering of output resistance with increase in drain bias. This phenomenon is called either channel-length modulation or the Early effect.
According to a simple empirical model patterned after the bipolar model for output resistance, the output resistance is given by:
where λ is called the channel-length modulation parameter with dimensions V−1 and 1/λ plays the role of the Early voltage VA found in the bipolar model. The current IDS(VGS, VDS) is the drain current evaluated at the selected gate and drain voltages. It should be noted that this formula for output resistance is largely a fiction of hand analysis, and cannot be trusted. For example, the figure shows a tentative attempt to establish λ for a rather old 3/4μm technology. A single value for λ provides only a crude indicator of the slope of these curves in active mode.
To illustrate that λ is a function, not a constant, the lower figure shows measured values of VA=1/λ for a 0.18μm MOSFET process at a bias in the active mode of VGD=VGS−VDS=0 V. Here, VA = 1/λ increases by an order of magnitude as the channel becomes stronger. The need to employ a variety of λ-values is even greater in today's technology where λ is a function of device geometry in three dimensions (not just channel length, although this is important) and bias voltages. In practice, a particular value is calculated for each situation using a numerical model of the transistor or is measured directly.
Generally speaking, the output resistance of MOSFETs is low, and where high resistance is necessary, special circuit techniques involving multiple transistors are implemented to increase the effective resistance.