MOSFET Parameter K Calculation Explained

This question asks us to calculate the device parameter 'K' for a MOSFET, given specific operating conditions. MOSFETs (Metal-Oxide-Semiconductor Field-Effect Transistors) are fundamental semiconductor devices where the current flow is controlled by an input voltage. The relationship between the input voltage and the output current isn't always straightforward (it's non-linear), and this parameter 'K' is crucial in defining that behavior.

Understanding the MOSFET Relationship

The behavior of a MOSFET, particularly the output current ($I_D$), is related to the voltage applied between the gate and source ($V_{GS}$) and the threshold voltage ($V_{th}$). The device parameter 'K' quantifies this relationship. Based on the provided options and the typical formulas, we can infer the relationship used here is:

$ I_D = K (V_{GS} - V_{th})^2 $

Where:

• $I_D$ is the Drain Current (output current).
• $V_{GS}$ is the Gate-Source Voltage (input voltage).
• $V_{th}$ is the Threshold Voltage.
• $K$ is the device parameter we need to find.

Note: A common formula includes a factor of 1/2, but deriving the provided answer requires using the formula above.

Identifying Given Values

Let's list the values provided in the question:

• Input voltage ($V_{GS}$) = 6 V
• Output current ($I_D$) = 10 mA
• Threshold voltage ($V_{th}$) = 4 V

First, we need to convert the output current from milliamperes (mA) to amperes (A):

$ I_D = 10 \text{ mA} = 10 \times 10^{-3} \text{ A} $

Calculating MOSFET Parameter K

To find 'K', we need to rearrange the formula:

$ K = \frac{I_D}{(V_{GS} - V_{th})^2} $

Now, substitute the given values into the rearranged formula:

1. Calculate the overdrive voltage ($V_{GS} - V_{th}$):

   $ V_{GS} - V_{th} = 6 \text{ V} - 4 \text{ V} = 2 \text{ V} $

2. Square the overdrive voltage:

   $ (V_{GS} - V_{th})^2 = (2 \text{ V})^2 = 4 \text{ V}^2 $

3. Calculate K using the formula:

   $ K = \frac{10 \times 10^{-3} \text{ A}}{4 \text{ V}^2} $

4. Perform the division:

   $ K = 2.5 \times 10^{-3} \text{ A/V}^2 $

Therefore, the calculated value for the MOSFET parameter 'K' is $2.5 \times 10^{-3} \text{ A/V}^2$. This matches the first option.