### Non Ideal Current -Voltage Effects or Second Order Effects

The following three effects are discussed in this section:

1. Body Effect

2. Channel Length Modulation and

3. Subthreshold Conduction

1. Body Effect:

In our analysis so far we have assumed the following:

The Body and the Source are connected together to the ground in nMOS  Transistor

If the Body voltage VB drops below the Source Voltage, then what happens? Let us analyze.

The Source and Drain still remain reverse biased and the device works normally, but there are some changes in the characteristics of the device.

Let VS=VD=0 and VG is slightly less than the threshold voltage VTH

Under these conditions there exists a depletion layer under the Gate area but it must be noted there is no inversion layer.

Now if the Body voltage VB becomes negative more holes are attracted towards the substrate connection. This leaves a larger negative charge behind and the depletion layer becomes wider.

It may be noted here that the threshold voltage is a function of the total charge in the depletion region. This is possible because the Gate charge mirrors the charge density before the inversion layer is formed.

If the value of VB becomes negative, QD increases and VTH also increases.

This Phenomenon is called as Body Effects

$V_{TH}=V_{THO}+\gamma(\sqrt{2\varnothing_F+V_{SB}}-\sqrt{\left|2\phi_F\right|})$

Where 𝛄 represents body effect coefficient, VSB is the Source - Body potential difference.

Note:

The Body effect happens even if the Source Voltage varies with the Body Voltage.

Body effect is undesirable i.e. change in threshold voltage complicates the design of both analog and digital circuits.

1. Channel Length Modulation:

In the pinch off region the Channel length decreases with decrease in potential difference between the Gate and the Drain.

In other words the actual channel length is a function of VDS.

The equation below gives the relationship between the Drain current ID in saturation region to the channel length modulation coefficient 𝛌.

$I_D\approx\frac12\mu_nC_{OX}\frac WL\left(V_{GS}-V_{TH}\right)^2\left(I+\lambda V_{DS}\right)$

1. Subthreshold Conduction:

MOSFET is said to be ON when the voltage VGS is above the threshold Voltage VTH and turns OFF when the voltage VGS is below the threshold voltage VTH.

But when the VGS ≈ VTH, an inversion layer exists in the MOS transistor which is weak - weak inversion layer.

Because of the presence of the weak inversion layer, there is some small amount of current that flows between Source and Drain ID

It may be noted that there is some finite current ID that flows in the device even when the voltage VGS< VTH.

This finite current ID is found to be exponentially dependent on the Gate Voltage VGS. This phenomenon is called Subthreshold Conduction.

$I_D=I_Oexp\frac{V_{GS}}{\xi V_T}$

Here the value 𝞷>1 is a non ideal factor