Starting with the definition of unity-gain frequency, as given by Equation (7.97), neglect the overlap capacitance, assume \(C_{g d} \cong 0\) and \(C_{g s} \cong\) \(\left(\frac{2}{3}\right) W L C_{\text {ox }}\), and show that

\(f_{T}=\frac{3}{2 \pi L} \cdot \sqrt{\frac{\mu_{n} I_{D}}{2 C_{\mathrm{ox}} W L}}\)

Since \(I_{D}\) is proportional to \(W\), this relationship indicates that to increase \(f_{T}\), the channel length \(L\) must be small.