1. The problem involves understanding the relationship between Drain Current ($I_D$) and Gate Internal Voltage ($V_{GI}$) for three different transistor models: fdsoi_nmos_idvg_lin, fdsoi_highK_TIO2_idvg_lin, and fdsoi_highK_box_idvg_lin. 2. The graph plots $I_D$ (in Amperes) versus $V_{GI}$ (in Volts) with $V_{GI}$ ranging from 0 to 1.2 V and $I_D$ ranging approximately from $1.0 \times 10^{-4}$ to $2.6 \times 10^{-4}$ A. 3. The three curves represent different device characteristics: - Red solid line: fdsoi_nmos_idvg_lin - Green dashed line: fdsoi_highK_TIO2_idvg_lin - Blue dotted line: fdsoi_highK_box_idvg_lin 4. Observing the graph, the green dashed curve shows the highest drain current for a given gate voltage, followed by the blue dotted curve, and then the red solid curve. 5. This indicates that the fdsoi_highK_TIO2_idvg_lin device has better current conduction properties compared to the other two, likely due to the high-K dielectric material enhancing gate control. 6. No explicit formula is given, but generally, the drain current in MOSFETs in the linear region can be approximated by: $$I_D = \mu C_{ox} \frac{W}{L} \left( (V_{GI} - V_{th}) V_{DS} - \frac{V_{DS}^2}{2} \right)$$ where $\mu$ is mobility, $C_{ox}$ is oxide capacitance per unit area, $W$ and $L$ are channel width and length, $V_{th}$ is threshold voltage, and $V_{DS}$ is drain-source voltage. 7. The differences in $I_D$ among the curves suggest variations in $C_{ox}$ and $V_{th}$ due to different materials and device structures. Final answer: The green dashed line (fdsoi_highK_TIO2_idvg_lin) shows the highest drain current for the same gate voltage, indicating superior device performance among the three.