Determine the channel half-width for an n-channel silicon FET having Gate-to-Source voltage, $$V_{GS} = \frac{V_p}{4}$$, where $$V_p$$ is the Pinch-off voltage and drain current, $$I_d = 0$$. (Consider (a) Donor Concentration $$N_D = 10^{15}$$ electrons/cm$$^3$$ (b) Channel half-width for $$V_{GS} = 0 V$$ is 3 $$\mu$$m).

A

$$2.25 \mu m$$

B

$$3 \mu m$$

C

$$1.5 \mu m$$

D

$$0.75 \mu m$$