MOS transistor current response

One of the most important property of a MOS transistors to get a very good handle is its current response. The dependence of the current passing through MOS transistor on the Gate to Source voltage (Vgs) and Drain to Source voltage (Vds).

Following is a fairly popular graph of I v/s V curves of a MOS transistor. Along with the image is shown the setup to achieve the measurements for this I v/s V graph.

Figure 1. NMOS Drain current v/s Drain to Source Voltage at various Gate to Source Voltages.

Figure 2. Spice setup to achieve NMOS I v/s V curves.

Figure 1 depicts two distinct regions of the curve. Linear region and saturation region. In reality there are three regions in this curve: cutoff region, linear region or often referred to as triode region and saturation region. For simplicity most of the curve only shows linear region and saturation region.

These three regions on the curves correspond to the three modes of operation of a MOS transistor. We all know that MOS transistor has three modes cutoff, linear and saturation. Cutoff region on the curve lies very near the origin of the graph.

The curves in figure 1, are achieved through setup in figure 2. You control both Vgs and Vds through variable voltage sources and although it is not shown explicitly in figure 2, you measure Ids passing through transistor.

When gate to source voltage Vgs is less than Vth, the inversion channel has not been formed. Lets recap a bit here for proper reference. In an NMOS transistor, when gate voltage is increase to more than zero, the positive holes in the p substrate are pushed away from the gate by electric field of the same charge(same charge repels eachother).

Figure 3. NMOS transistor modes.

The field at gate not only pushes away the same charge, but also attracts opposite charge electrons near the gate. In p-substrate there are always minority carrier electrons are present. As they are minority they’re not many of them available and the gate field needs to be strong enough to accumulate enough of minority carriers near the gate such that this accumulated set of electrons can effective flow as material current. This happens when gate to source voltage reaches Vth. Until then transistor just doesn’t conduct irrespective of drain to source voltage and it is in cutoff mode

Once gate to source voltage reaches Vth, the inversion channel forms. Now the inversion channel is a lateral channel which could extend from the gate to source and how much it extends towards the drain, really depends on drain voltage. If drain to source voltage Vds is less than (Vgs-Vth), which really means if gate to drain voltage is higher than Vth[ Vds < Vgs – Vth => Vth < Vgs – Vds => Vth < Vgd], the channel extends all the way from source to drain and is called fully formed.

When channel is fully formed, MOS transistor acts like a resistor with linear characteristics. Meaning the current flowing through transistor Ids, linearly varies with Vds, which can be seen in the linear region portion of the curves. This part is often called ohmic region because transistor acts as a ohmic resistor. The reason why transistor behaves linearly in this region, is that the mechanism by which the current travels through transistor in this region is same as in any other resistor.

You can see in the graph that in linear region, Ids increases almost linearly with Vds. Also notice that Ids also depends on the Vgs and increasing Vgs also increases Ids, while maintaining the Ids to Vds relationship.

As you keep increasing Vds, Vds becomes equal to Vgs – Vth, and eventually when Vds becomes more than Vgs – Vth, the channel pinches off at gate to drain junction. This happens because Vgd becomes less than Vth now[ Vds > Vgs – Vth => Vth > Vgs – Vds => Vth > Vgd => Vgd < Vth]. At this stage current flowing mechanism changes inside transistor. There is no more fully formed channel now. This means it doesn’t behave like a resistor anymore and Ids doesn’t change linearly with Vds now.

What happens in this region is that electrons now travel through inversion channel, until the channel ends, and then it travels through depletion region to cross the gate to drain junction. You imagine as if electron dispersion happens and the crossing of electrons through gate to drain junction happens with influence of a different kind of field compared to fully formed channel(attempt at explaining this phenomenon in simple terms). Because of this change in mechanism, current no longer depends on Vds. It still is modulated by Vgs as Vgs dictates how much charge is concentrated in inversion channel at gate to source junction. Please provide your feedback through comments.


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