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I was reading on a book (Thomas Lee, The Design of CMOS Radio Frequency Integrated Circuits) that in a short channel model, since the phenomenon of drift speed saturation is very relevant, it is a mistake to use the classical formula of the drain current of a long channel MOSFET, i.e. this one (we are supposing a MOSFET in pinch - off region):

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It states that in a short channel MOSFET the correct expression becomes this one:

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Then it states that, if VGS - VT is not so high, we may anyway use the first formula; if VGS - VT is quite high, we have to use the second one. I do not understand this last statement: in fact the difference between the two MOSFET is their length, and this determines that, with the same VDS applied, there is a high electric field in a short channel Mosfet (and so, speed saturation) and low electric field in a long channel Mosfet (and so, no speed saturation). Why should the choice of the model depend on VGS - VT?

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  • \$\begingroup\$ What would you answer to the reverse question: why would the same model be valid for the complete range of Vgs - Vt ? Also note that there are MOSFET models for triode mode and weak inversion as well. For example the weak inversion models are valid when Vgs is close to Vt so when Vgs - Vt is near zero. \$\endgroup\$
    – Bimpelrekkie
    Commented Oct 1, 2019 at 9:17
  • \$\begingroup\$ If I recall rightly, at about 2 volts per micron, the FETs move into "drift speed saturation" and the exponent becomes ONE. Thus 0.25 micron technology FETs will leave the square-law mode at a mere 0.5 volt across the source-drain. Does this make sense? \$\endgroup\$
    – analogsystemsrf
    Commented Oct 1, 2019 at 14:40

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