A.1.2.4 Speed and Scaling

A rough estimate of the switching speed can be obtained in terms of transconductance and gate capacitance:

$$\ensuremath{g_{\mathit{m}}}\xspace = \ensuremath{\beta }\xsp... ...V_{\mathit{GS}}}\xspace -\ensuremath{V_{\mathit{T}}}\xspace ) ,$$ (A.15)

$$\tau \approx \frac{\ensuremath{g_{\mathit{m}}}\xspace }{\ens... ...V_{\mathit{GS}}}\xspace -\ensuremath{V_{\mathit{T}}}\xspace ) .$$ (A.16)

Thus, when the gate length is reduced by a scaling factor $1/\ensuremath{\kappa }\xspace$ the speed improves as $1/\ensuremath{\kappa }\xspace ^2$, This relation is valid only as long as (A.12) is valid, i.e., for long-channel devices.

What can be concluded from this is not, as it may seem, a way for technology scaling, but simply the proof that long-channel devices operated as switches (like in digital circuits) are inferior to short-channel devices, which are consequently used in virtually all digital VLSI circuits.