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Of course for mosfet
I guess since you are asking narrow channel
instead of short channel, you are asking what is the
effect of small channel width (w).
If you decrease too much the channel width too much, your effective threshol voltage will increase
a little bit. This is due to the following reason, when you draw the layout of the transistor, you have extra
poly exceeding the diffusion area. Now underneath of this extra part, when the mosfet is turned on, some charge is collected that are stolen from the channel. If the effective area of the channel with respect to this area is small (which happen for small w values), some of the channel charge is stolen by this portion instead of helping the channle to invert (which is equivalent to increase threshol voltage.)
Now short channel is another story
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