Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The body effect in MOSFET causes the threshold voltage \(V_{th}\) to increase as source-body voltage \(V_{SB}\) increases. Reason (R): Increasing \(V_{SB}\) resets the surface potential and therefore reduces the barrier for inversion. In the light of the above statements, choose the most appropriate answer from the options given below :

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

In MOSFET body effect: \[ V_{SB}\uparrow \Rightarrow V_{th}\uparrow \] because increasing source-body reverse bias widens the depletion region and makes channel inversion more difficult.

Answer 1

The Correct Option is C

Concept: The body effect (also called substrate bias effect) in MOSFETs refers to the variation of threshold voltage due to the potential difference between source and body. The threshold voltage expression is: \[ V_{th}=V_{th0}+\gamma\left(\sqrt{2\phi_F+V_{SB}}-\sqrt{2\phi_F}\right) \] where:
• \(V_{th0}\) = threshold voltage when \(V_{SB}=0\)
• \(\gamma\) = body effect coefficient
• \(\phi_F\) = Fermi potential
• \(V_{SB}\) = source-to-body voltage From this equation, it is clear that: \[ V_{th}\uparrow \quad \text{as} \quad V_{SB}\uparrow \] The increase occurs because larger reverse bias between source and body widens the depletion region, making inversion more difficult.

Step 1: Analyze Assertion (A). Assertion states: The body effect causes threshold voltage to increase as \(V_{SB}\) increases. From the threshold-voltage equation: \[ V_{th}=V_{th0}+\gamma\left(\sqrt{2\phi_F+V_{SB}}-\sqrt{2\phi_F}\right) \] we observe that: \[ V_{th}\propto \sqrt{2\phi_F+V_{SB}} \] Therefore, when: \[ V_{SB}\uparrow \] the threshold voltage also increases. Hence, Assertion (A) is correct.

Step 2: Analyze Reason (R). Reason states: Increasing \(V_{SB}\) resets the surface potential and reduces the barrier for inversion. This statement is incorrect. Actually:
• Increasing \(V_{SB}\) increases reverse bias between source and substrate.
• The depletion region width increases.
• More gate voltage is required to create inversion.
• Thus, the barrier for inversion increases rather than decreases. Therefore, Reason (R) is false.

Step 3: Determine the correct relationship between Assertion and Reason. We conclude:
• Assertion (A) is correct.
• Reason (R) is incorrect. Hence, the correct choice is: \[ \boxed{(C)\ (A)\text{ is correct but }(R)\text{ is not correct}} \]