In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer thickness is 100 nm. The permittivities of the semiconductor and the oxide layer are $${\varepsilon _s}$$ and $${\varepsilon _{os}}$$ respectively. Asuuming $${\varepsilon _s}/{\varepsilon _{ox}} = 3$$ , the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is________

A MOSFET in saturation has a drain current of 1 mA for V_DS =0.5V. If the channel length modulation coefficient is 0.05 V^-1, the output resistance (in k$$\Omega $$) of the MOSFET is______

For the NMOSFET in the circuit shown, in the threshold voltage is V_th, where V_th>0. The source voltage V_ss is varied from 0 to V_DD. Neglecting the channel length modulation, the drain current I_D as a function of V_ss is represented by

An ideal MOS capacitor has boron doping concentration of 10¹⁵ cm^-3 in the substrate. When a gate voltage is applied, a depletion region of width 0.5 $$\mu m$$ is formed with a surface (channel) potential of 0.2V. Given that $${\varepsilon _0} = 80854 \times {10^{ - 14}}F/cm$$ and the relative permittivities of silicon and silicon dioxide are 12 and 4, respectively, the peak electric field (in V/ $$\mu m$$ ) in the oxide region is ______