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Complementary Metal (Poly-Si) Oxide (SiO2) Semiconductor (CMOS).

cmos_not cmos_nand cmos_nor


channel width \(W_{\ir n/p}\)
channel length \(L_{\ir n/p}\)
gate oxide thickness \(t_{\ir ox}\)
electron mobility \(\mu_{\ir n} \approx \SI{250e-4}{\meter\squared\per\volt\second}\)
\(\mu_{\ir p} \approx \SI{200e-4}{\meter\squared\per\volt\second}\)
rel. permittivity of gate oxide \(\epsilon_{\ir ox} \approx 3,9\)
dielectric constant \(\epsilon_0 = \SI{8.8541878e-12}{\ampere\second\per\volt\meter}\)
specific oxide capacity \(C'_{\ir ox} = \frac{\varepsilon_{\ir ox} \varepsilon_0}{t_{\ir ox}}\)
oxide capacity \(C_{\ir ox} = C'_{\ir ox} \cdot WL\)
gain (also \(\beta\)) \(K_{\ir n} = \mu_{\ir n} C'_{\ir ox} \frac{W_{\ir n}}{L_{\ir n}}\)
\(K_{\ir p} = (-1) \mu_{\ir p} C'_{\ir ox} \frac{W_{\ir p}}{L_{\ir p}}\)
propagation delay $t_{\ir pHL} \propto \frac{C_L t_{\ir ox} L_{\ir p}}{W_{\ir p} \mu_{\ir p} \varepsilon_{\ir ox} (V_{\ir DD} -

Inverter Power#

Power Consumption of a CMOS Inverter

Dynamic Power Consumption#

\[P_{\ir dyn} = P_{\ir cap} + P_{\ir short}\]

Capacitive Power#

\[P_{\ir cap} = \alpha_{01} f C_L V_{\ir DD}^2\]

Short Circuit Power#

\[P_{\ir short} = \alpha_{01} f \beta_n \tau (V_{\ir DD} - 2V_{\ir th})^3\]