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Consider the following statements for a metal oxide semiconductor field-effect transistor

(MOSFET):

P: As channel length reduces, OFF-state current increases.

Q: As channel length reduces, output resistance increases.

R: As channel length reduces, threshold voltage remains constant.

S: As channel length reduces, ON current increases.

Which of the above statements is INCORRECT?


1. P and Q
2. P and S
3. Q and R
4. R and S

1 Answer

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Correct Answer - Option 3 : Q and R

Concept:

For VDS < VGS – VT, n-channel enhancement type MOSFET will operate in triode/linear region:

\({I_D} = \frac{{{\rm{W\mu_n }}{C_{ox}}}}{{2L}}\left[ {2\left( {{V_{GS}} - {V_T}} \right){V_{DS}} - V_{DS}^2} \right]\)

For VDS ≥ VGS – VT, the MOSFET will be in saturation with the current given by:

\({I_D} = \frac{{{\rm{W\mu_n }}{C_{ox}}}}{{2L}}\left[ {{{\left( {{V_{GS}} - {V_T}} \right)}^2}} \right]\)

L = Channel length

ConclusionSince the Current is inversely proportional to Channel length, the current will increase as the length will decrease. ∴ Statement P and S are correct.

Resistance:

The current in an NMOS in the linear region is:

\({I_D} = \frac{{{\rm{W\mu_n }}{C_{ox}}}}{{2L}}\left[ {2\left( {{V_{GS}} - {V_T}} \right){V_{DS}} - V_{DS}^2} \right]\)

The transistor operates in the linear region for small values of VDS, i.e. neglecting higher powers of VDS, the above expression can be approximated by:

\({I_D} \approx \frac{{{\rm{W\mu_n }}{C_{ox}}}}{{L}}\left[ {\left( {{V_{GS}} - {V_T}} \right){V_{DS}}} \right]\)

\(R_d=\frac{V_{DS}}{I_{DS}}\)

\(R_d=\frac{1}{\frac{{{\rm{W\mu_n }}{C_{ox}}}}{{L}}\left[ {\left( {{V_{GS}} - {V_T}} \right){V_{DS}}} \right]}\)

\(R_d=\frac{L}{W\mu_nC_{ox}{{{}}}{}\left[ {\left( {{V_{GS}} - {V_T}} \right){V_{DS}}} \right]}\)

ConclusionAs the output resistance is directly proportional to the channel length, it reduces with a decrease in channel length. ∴ Statement Q is incorrect.

Threshold Voltage:

The threshold voltage of a MOSFET is given as:

\({V_T} = 2{\phi _F} - \frac{{{Q_d}}}{{{C_i}}} + {\phi _{ms}} - \frac{{{Q_i}}}{{{C_i}}}\)

From the above expression, we can conclude that the threshold voltage is also dependent on the channel length. ∴ Statement R is incorrect.

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