MOS Current

Drain current

In static conditions the only current flowing in the MOSFET is the drain current . The gate current is null due to the oxide isolating the gate.

In our analysis of a nMOS we make simplifying assumptions such as:

• The hole current is negligible in all relevant operating conditions
• The reverse saturation current of the pn junctions is neglected (can be added later)
• Generation and Recombination phenomena are negligible #todo CHECK

With these assumptions is completely related to the electron transport along the channel

The effective mobility characterizes the electron transport in the channel, is lower than the bulk mobility, is affected by the surface roughness at the interface between oxide and substrate and depends on the the vertical electrical field induced by the gate oxide.

We calculate entering the drain along the y axis, exploiting the invariance of the device along z and the definition of electron charge per unit area: #todo add correct link

Neglecting the generation and recombination of electrons and assuming static conditions, the drain current is constant along y and integrating through the channel:

The channel potential is known at the extremities of the channel, being:

the integral becomes

Now we need to substitute the electron charge in the integraltodo insert link to previous note

In saturation when

Subthreshold current

The residual current below threshold is significant in the scaling process, because it controls the static power dissipation. Experimentally is exponentially dependent on and nearly insensitive to ()

We try to find an analytic formula: for the MOS system is in weak inversion, the total semiconductor charge is:

In this case the depletion charge dominates over the inversion charge, the square-bracketed term can be linearized around as:

So the first term corresponds to the depletion charge, hence the second represent the residual inversion charge in weak inversion. This can be used to calculate the subthreshold drain current, by substituting it in the formula, obtaining

Below the strong inversion condition, is independent from the channel potential, and can be taken out of the integration To find the as a function of , we need some more calculations. The is obtained from the Surface Potential Equation, linearizing it around the strong inversion condition since we are near threshold and neglecting the electron charge, obtaining at first order

Substituting it in the drain current, assuming the current independent from and neglecting the term under the square root the resulting subthreshold drain current is

The quality of the transistor turn-off is given by the Subtreshold Swing S defined as

S should be as small as possible to have a fast switch off of the device. The increase in temperature leads to a decrease of and an increase of S, which both result in a higher leakage subthreshold The swing depends on , that should be less than 1.5, represents a limit for the slope, even in the best case scenario () the slope is limited to

todo add transcharacteristics