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NSUB_Calculation

# NSUB_Calculation - Square law model with channel length mod...

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Square law model with channel length mod I D-sat term (at pinchoff) + "extra" I D = μ n C ox 2 W L V GS ! V tn ( ) 2 I D ! sat 1 2 4444 3 4444 1 + " V DS ! V eff ( ) [ ]

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Square law model with channel length modulation Fractional extra part is " (V DS -V eff ) Meaning of " : Fractional change in current I D per volt change in V DS Problem: " depends on L Want parameter for SPICE model that works for all L I D = μ n C ox 2 W L V GS ! V tn ( ) 2 I D ! sat 1 2 4444 3 4444 1 + " V DS ! V eff ( ) [ ]
What causes change? Where does " come from? Change in effective channel length L One way to reduce " : longer L Change " L represents smaller fraction

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Revisit modified square law I D = μ n C ox 2 W L V GS " V tn ( ) 2 I D + " I D = μ n C ox 2 W L # " L V GS # V tn ( ) 2 " V DS ! " L ! " I D & I D " I D " V DS
Revisit modified square law I D 1 + " I D I D # \$ % & ( = μ n C ox 2 W L 1 ) " L L # \$ % & ( V GS ) V tn ( ) 2 Rewrite in fractional change terms Use (small x) Relate " L to known L; measured I D ; change in I D I D 1 + " I D I D # \$ % & ( = μ n C ox 2 W L V GS ) V tn ( ) 2 I D 1 2 444 3 444 1 + " L L # \$ % & ( " L = L " I D I D # \$ % & ( 1 1 " x # 1 + x

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" L also given by semiconductor physics ... " L = 2 K S # 0 " V DS qN SUB L " I D I D # \$ % & ( = 2 K S ) 0 " V DS qN SUB Voltage drop " V DS across depleted region " L with doping density N SUB Equate N SUB
NSUB parameter for SPICE

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NSUB_Calculation - Square law model with channel length mod...

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