Basic MOS device physics

$I_D$ (drain current)

$I_D$ of NMOS (PMOS는 절댓값)

• channel 형성 : $V_{GS} > V_{th}$
• triode(linear) region : $V_{DS} < (V_{GS}-V_{th})$
  • $I_{D}=\mu_{n} C_{o x} \frac{W}{L}\left[\left(V_{G S}-V_{T H}\right) V_{D S}-\frac{1}{2} V_{D S}^{2}\right]$

• saturation region : $V_{DS} > (V_{GS}-V_{th})$
  • $I_{D, \max }=\frac{1}{2} \mu_{n} C_{o x} \frac{W}{L}\left(V_{G S}-V_{T H}\right)^{2}$

• overdrive voltage (유효 전압) : $V_{GS}-V_{th}$

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$g_m$ (Transconductance)

MOS 소자가 전압을 전류로 얼마나 잘 변환하는가.

• $g_{m}=\left.\frac{\partial I_{D}}{\partial V_{G S}}\right|_{V D S, \text { const. }}$

• $g_m = \mu_{n} C_{o x} \frac{W}{L}\left(V_{G S}-V_{T H}\right)$

• $g_{m}=\sqrt{2 \mu_{n} C_{o x} \frac{W}{L} I_{D}}$

• $g_m = \frac{2 I_{D}}{V_{G S}-V_{T H}}$