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MOS器件物理

General considerations

MOS symbols

MOS symbols

MOS as a switch

Need to know the threshold voltage \(V_{th}\).

MOS as a VCCS

MOS is also a voltage-controlled current source (VCCS).

Need to derive the I/V characteristics.

MOS I/V characteristics

Threshold voltage

When \(V_{G} = 0\), the MOS is off.

When \(V_{G}\) increases to a sufficiently positive value, the surface is "inverted" and the MOS is on.

The value of \(V_{G}\) at this point is called the threshold voltage \(V_{th}\). If \(V_{G}\) rises further, the charge density in channel continues to increase (\(I_D\) increases).

\[ V_{TH} = \Phi_{MS} + 2\Phi_{F} + \frac{Q_{dep}}{C_{ox}} \\ \]
\[ C_{ox} = \frac{\epsilon_{ox}}{t_{ox}} \]
  • \(\Phi_{MS}\): work function difference between the gate and substrate
  • \(\Phi_{F}\): Fermi level
  • \(Q_{dep}\): Charge density in the depletion region
  • \(C_{ox}\): Gate oxide capacitance per unit area

Important note about \(V_{th}\)

For NMOS

the higher the substrate doping, the higher the \(V_{th}\).

For a given process under given temperature, \(V_{th}\) is almost constant.

I/V characteristics in triode region

\[ I_D = \mu_n C_{ox} \frac{W}{L} \left[ (V_{GS} - V_{TH})V_{DS} - \frac{V_{DS}^2}{2} \right], \quad V_{DS} \le V_{GS} - V_{TH} \]

Observations: \(I_D \propto W\)

In triode region

\(I_D\) is influenced by both \(V_{GS}\) and \(V_{DS}\).

\(W/L\) is called "aspect ratio", a design parameter.

\(\mu_n C_{ox}\) is a process parameter.

I/V pic

Application of NMOS in Triode region

\[ I_D \approx \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{TH})V_{DS}, \quad if \ \ \frac{V_{DS}}{2} \ll V_{GS} - V_{TH} \]
\[ R_{on} = \frac{V_{DS}}{I_D} = \frac{1}{\mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{TH})} \]

img

深线性区（\(V_{DS}\)非常小），MOS管可以当成压控电阻，注意MOS管是压控器件

I/V characteristics in saturation region

\[ I_D = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{GS} - V_{TH})^2 = \frac{1}{2} \mu_n C_{ox} \frac{W}{L} (V_{OD})^2, \quad V_{DS} \ge V_{GS} - V_{TH} \]

\(V_{OD} = V_{GS} - V_{TH}\) is called "overdrive voltage".

\[ V_{OD} = \sqrt{\frac{2I_D}{\mu_n C_{ox} \frac{W}{L}}} \]

saturation region

Application of MOS in saturation region

当\(V_{DS}\)较大时，\(I_D\)不会随\(V_{DS}\)变化（非常缓慢），因此：

Saturated MOS can be used as voltage-controlled current source (VCCS).

NMOS I/V characteristics summary

summary

intuition