## Enhancement Mode Operating regions

Regions of operation

The output characteristics of MOSFET are as shown below with Gate to source voltage kept constant.

Characteristics of enhancement MOSFET

There are mainly three regions of operation in MOSFET as it is evident from output characteristics shown above listed as

1. Cut off region
2. Ohmic region (or) Triode region
3. Saturation region

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The equation for drain current in terms of Vgs and Vds is given as

Where

K’n = is Transconductance of the device given by K’nµn * Cox

µn is the mobility of electrons

Cox is the capacitance of oxide layer per unit area of oxide layer given by Cox = εox / tox

εox is the dielectric constant of oxide layer

tox is the thickness of oxide layer

W is the lateral width of oxide layer

L is the effective length of oxide layer

Vt is threshold voltage

Cut off region: This is the region of output characteristics where Vgs < Vt in which drain current is almost Zero. This is also called Sub threshold region. In this region drain current is of the order of Nano amperes. Threshold voltage of MOSFET which is the onset voltage at which drain current starts flowing is a function of source to body voltage (VSB).

Where, are constants and VSB is the source to body voltage.

The Body terminal of the MOSFET is generally shorted to source, If it is not the case the threshold voltage can be controlled by Source to body voltage. In turn the drain current can be controlled by varying VSB as drain current is a function of threshold voltage. Hence the substrate terminal acts as a second gate terminal to control the drain current.

Ohmic region: This is the region of output characteristics in which Vgs > Vt i.e channel is induced and Vds << Vgs-Vt the equation for Ids can be reduced to

Where the term

can be neglected as per the assumption. From the equation it is obvious that the drain current Ids α Vds and hence obeys ohms law. The On resistance of the MOSFET can be calculated as follows

MOSFET can be used as a variable resistor when operated in this region. The On resistance of the MOSFET is of the order of 2 to 3 kilo ohms.

Further as we increase drain to source voltage the linear relation between drain current and drain to source voltage no longer holds and drain current varies in a parabolic fashion. This is the transition region between Ohmic and saturation region.

Saturation region: When Vds = Vgs – Vt the channel gets pinched off at drain end and the drain current reaches a maximum value, further increase in Vds does not have any effect on drain current theoretically. The saturation drain current is given by

So the incremental saturation drain resistance of MOSFET should be ideally infinite as ∆Ids = 0 amps for a finite nonzero ∆Vds and Rinc = ∆Vds / ∆Ids = ∞.

But practically as explained before due to channel length modulation Vds does affect Ids. So the equation can be modified as follows

Assuming linear relationship between change in length and Vds i.e ∆L/L= λ*Vds where λ is technology parameter also known as channel length modulation factor and has units of. Hence

Therefore the incremental saturation resistance of MOSFET can be derived as

Which is finite and of the order of tens of kilo ohms.

The transfer characteristics of Enhancement type MOSFET in saturation region Vds > Vgs – Vt is given above.

The parabolic dependence of Id on Vds in saturation region is obvious from the equation of drain current from the above derivation. The drain current is zero for Vgs < Vt as there exists no channel to conduct drain current.