Channel approximation, gradual

The gradual channel approximation (described above) may fail, as the channel length of the FET is shortened. The electrostatics of the FET limit L > 1.5 q in a molecular FET, where the dielectric constant of the gate dielectric layer and semiconductor channel may be similar [22, 23]. This is particularly important in monolayer transistors, as many monolayer FETs studied have been limited to tens of nanometers channel length by the tens of nanometers size of ordered domains, and therefore require thin gate dielectric layers. Only recently (described below) have routes been shown to form more extended ordered molecular monolayers, allowing micron-scale FET channel lengths to be explored. 

Using the gradual channel approximation - the lateral electric field does not significantly influence the perpendicular electric field - the drain current in the accumulation regime reads ... 

Although the gradual channel approximation implies that this expression is only valid in the linear regime ( Vd Vg - Vf ), it is also found to be a reasonable description of the drain current close to saturation ( Vd = Vg — VT). 

Of the three most common channel mobilities, psat is probably used the least. The most serious liability of Psat is that it is evaluated in the post-pinch-off regime of operation where the channel thickness and electric field profile are highly non-uniform, the gradual channel approximation is not valid, and the concept of mobility as a proportionality constant between the electric field and carrier velocity is of questionable viability. However, psat offers several advantages, (i) Vj is not required, and (ii) Pfe is not singular when Vgs = Vx, and (iii) its estimation is relatively insensitive to the magnitude of the source-drain resistance, unlike pes and Pfe... 

For a long channel the jc-component of the electric field can be neglected with respect to its y-component this is also known as the long channel or the gradual channel approximation. Therefore Eq. (16) yields... 

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