Channel-Length Modulation (CLM) is a non-desirable second-order effect in MOSFETs, which increases the drain voltage (Ids) when the drain voltage (Vds) also increases.
Channel Lenght Modulation is caused by a reduction or shortening of the effective length of the inverted channel region resulting in an increment of the drain-source current (Ids). The channel length modulation is together with the Body effect the most common and frequent undesirables effects in MOSFETs devices.
In this post, we are going to consider an NMOS device operating in the saturation region, but it is equivalent to PMOS devices. In summary, there are 3 relevant second-order effects on MOSFET devices: channel-length modulation, body effect and subthreshold conduction. All these topics are covered in chapter 2 of Razavi’s book/bible.
We all have in mind the equation of the drain-source current at the saturation region:
where λ is a parameter or coefficient related to the channel-length modulation, often neglected for simplicity.
Let’s start with the ideal situation…
Here Ids is independent of Vds at the saturation region.
The channel is pinched off at the drain end. So any variation in the drain voltage Vds doesn’t change the shape of the inverted region (dark black).
In the following ideal plot, the current (Ids) is independent of drain-source voltage (Vds) as it can be seen, the current (Ids) traces a nice straight horizontal line. This is an ideal case.
But in reality, when Vds increases, the current also does. In the following curve, the CLM effect is exaggerated only to be more visual. It can be seen the small ramp in the saturation region.
The effective channel length of the transistor is reduced when Vds increases. Therefore, the pinched-off point is moved away from the drain, towards the source, because the electron field of the drain pushes it back. As a consequence, the uninverted region expands toward the source. The reverse bias region takes an asymmetrical shape and is separated from the drain, as depicted in the following figure.
As a result
The resistance of the channel decreases due to a decrease in the effective length of the channel, causing an increase in the drain current (Ids).
Because the resistance is proportional to the length of the channel, the output resistance of the nmos device is also marginally decreased.
We can see the shortening of the channel on the drain current equation for a MOS device in the saturation region:
The reduction of the length leads to a higher current. This equation can be rearranged in function of the parameter lambda (λ).
As a consequence, the transconductance gm equation now becomes more complex:
The channel-length modulation is considered a “short-channel effect”, which becomes more and more relevant in the new advanced nodes with shorter MOSFET lengths.
Channel-length modulation intensifies when:
- source-to-drain separation is shorter
- drain junction is deeper
- oxide insulator is thicker
Analogy in BJTs Transistors: Early effect
An analogous phenomenon occurs in bipolar devices, a similar increase in current is seen with increased collector voltage due to base-narrowing, known as the Early effect.
This analogy in the current has influenced the use of the term “Early effect” for MOSFETs as well, as a synonym for “channel-length modulation“.