Problem 3 (15 points): An MOS capacitor is made from a 200 nm thick layer of silicon dioxide. The work functions of the metal and the semiconductor are the same. After specialized radiation treatment, the oxide layer traps charge with a surface concentration of OT = 4 × 10−9 C/cm2 . Calculate the effect of these trapped charges on the flat band voltage (VFB) of the MOS capacitor if the charge distribution in the oxide depends on the position linearly, starting from 0 C/ cm3 at the metal-oxide surface and increasing to 0.0004 C/ cm3 at the oxidesemiconductor surface. Give your answer in volts.

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?