✅ドレイン電流（非飽和領域）

$$
I_D = \mu \cdot C_{\text{ox}} \cdot \frac{W}{L} \left[(V_{GS} - V_T)V_{DS} - \frac{V_{DS}^2}{2}\right]
$$

✅ゲート酸化膜容量

$$
C_{\text{ox}} = \frac{\varepsilon_0 \cdot \varepsilon_{\text{ox}}}{t_{\text{ox}}}
$$

$$
C_{\text{ox}} = \frac{8.854 \times 10^{-14} \cdot 3.9}{270 \times 10^{-8}} = 1.279 \times 10^{-7} \ \mathrm{F/cm}^2
$$

$$
I_D = \frac{1}{2} \mu \cdot C_{\text{ox}} \cdot \frac{W}{L} (V_{GS} - V_T)^2 (1 + \lambda V_{DS})
$$

$\lambda$：チャネル長変調（channel length modulation）係数
- $\lambda = 0$ なら理想飽和
- $\lambda > 0$ なら$I_D$が$V_{DS}$でわずかに増える（非理想）

$$
I_D = \frac{1}{2} \mu \cdot C_{\text{ox}} \cdot \frac{W}{L} (V_{GS} - V_T)^2
$$

$$
g_m = \frac{\partial I_D}{\partial V_{GS}} = \mu \cdot C_{\text{ox}} \cdot \frac{W}{L} (V_{GS} - V_T)(1 + \lambda V_{DS})
$$

$$
g_m = 2 \mu C_{\text{ox}} \frac{W}{L} (V_{GS} - V_T)
$$

$$
g_d = \frac{\partial I_D}{\partial V_{DS}} = \lambda \cdot I_D
$$

$$
r_o = \frac{1}{g_d}
$$