Problem 1: MOS Fundamentals Consider an ideal MOS capacitor maintained

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Problem 1: MOS Fundamentals Consider an ideal MOS capacitor maintained at T = 300 K with the following characteristics:Gate material is p+ polycrystalline-silicon (work function ΦM = 5.15 eV )Substrate is n-type Si, with doping concentration 1018 cm−3 Oxide thickness xo = 2 nm a) What is the flat-band voltage, VFB, of this capacitor? b) Sketch the energy-band diagrams, labeling qVG, qϕs, qVox (no numerical values required), for the following bias conditions: i) flat-band ii) accumulation iii) equilibrium iv) strong inversion c) What is the threshold voltage, VT, of this device? d) Suppose we want to change the gate material to be n+ polycrystalline-silicon (work function ΦM = 4.03 eV). How would we need to change the substrate doping in order to keep VT the same? (A numerical answer is required.)

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Problem 1: MOS Fundamentals Consider an ideal MOS capacitor maintained at

T = 300 K

with the following characteristics:

Gate material is p+ polycrystalline-silicon (work function $Φ_{M} = 5.15 e V$ )
Substrate is n-type $S i$ , with doping concentration $10^{18} {c m}^{- 3}$
Oxide thickness $x_{o} = 2 n m$ a) What is the flat-band voltage, $V_{F B}$ , of this capacitor? b) Sketch the energy-band diagrams, labeling $q V_{G}, q ϕ_{s}, q V_{o x}$ (no numerical values required), for the following bias conditions: i) flat-band ii) accumulation iii) equilibrium iv) strong inversion c) What is the threshold voltage, $V_{T}$ , of this device? d) Suppose we want to change the gate material to be $n +$ polycrystalline-silicon (work function $Φ_{M} = 4.03 e V$ ). How would we need to change the substrate doping in order to keep $V_{T}$ the same? (A numerical answer is required.)