Analyzing MOSFET Statements

We need to evaluate the correctness of the three statements regarding enhancement-type MOSFETs.

Statement 1 Analysis: Threshold Voltage and Drain Current

An enhancement-type MOSFET requires the gate-to-source voltage ($V_{GS}$) to exceed the threshold voltage ($V_T$) to form a conductive channel between the drain and source. Therefore, for $V_{GS} < V_T$, the MOSFET is in the cutoff region, and the drain current ($I_D$) is effectively zero.

Conclusion: Statement 1 is correct.

Statement 2 Analysis: Drain Current Equation

The equation $I_D = k(V_{GS} - V_T)^2$ describes the drain current ($I_D$) in the **saturation region** of an enhancement-type MOSFET, which occurs when $V_{GS} > V_T$ and $V_{DS} \ge V_{GS} - V_T$. This equation is non-linear. However, the statement incorrectly applies this relationship for $V_{GS} \le V_T$. As established in Statement 1, for $V_{GS} \le V_T$, $I_D = 0$ mA.

Conclusion: Statement 2 is incorrect.

Statement 3 Analysis: The 'k' Parameter

The constant '$k$' (often expressed as $K_n = \mu_n C_{ox} \frac{W}{2L}$) is indeed dependent on the physical construction of the MOSFET, including material properties (like carrier mobility $\mu_n$), oxide capacitance ($C_{ox}$), and the device dimensions (width $W$ and length $L$). The formula provided, $k = \frac{I_{D(on)}}{(V_{GS(on)} - V_T)^2}$, is a valid way to calculate '$k$' using a specific known operating point ($I_{D(on)}$ at $V_{GS(on)}$) in the saturation region, assuming $V_{GS(on)} > V_T$.

Conclusion: Statement 3 is correct.

Final Conclusion

Based on the analysis, statements 1 and 3 are correct, while statement 2 is incorrect. Therefore, the correct option includes statements 1 and 3 only.