Discussion
The scaling factor of current density in constant voltage model is :
Answer: C
In the constant voltage model, current density scales by \(\alpha^{2}\).
In the scaling scheme used in VLSI design texts, lateral dimensions shrink by \(1/\alpha\) and supply voltage and oxide thickness by \(1/\beta\). The saturation current scales as \(1/\beta\) (gate capacitance per unit area rises by \(\beta\), voltage squared falls by \(1/\beta^{2}\)), and the area it flows through shrinks by \(1/\alpha^{2}\), so current density scales as \(\alpha^{2}/\beta\).
Constant voltage scaling keeps the voltage fixed, so \(\beta = 1\) and the factor is \(\alpha^{2}\). \(\alpha^{2}/\beta\) is the general expression, not its value in this model. \(1/\alpha^{2}\) is how gate area scales, and 1 would mean no change, which is wrong when current is pushed through a smaller area.
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