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Fundamentals of the MOSFET Summary of equations for metal-semiconductor work function difference p-type Silicon Aluminum gate: ms m, , n-type Silicon Aluminum gate: Fp 2e Eg n+ polysilicon gate: Eg Fp 2e ms m, , n+ polysilicon gate: Eg Fn 2e m s m s p+ polysilicon gate: p+ polysilicon gate: Eg Fp 2e m s Fn 2e Eg Eg Fn 2e m s 1. Calculate the maximum space charge width given a particular semiconductor doping concentration. Consider silicon at T = 300 K doped to Nd = 1016 cm-3. 2. Consider an oxide-to-p-type silicon junction at T = 300 K. The impurity doping concentration in the silicon is Na = 3x1016 cm-3. Calculate the maximum space charge width in the silicon. 3. Calculate the metal-semiconductor work function difference ms for a given MOS system and semiconductor doping. For an aluminium-silicon dioxide junction, m’ = 3.20 V and for a silicon-silicon dioxide junction, ’ = 3.25 V. We can assume that Eg = 1.12 eV. Let the p-type doping be Na = 3x1014 cm-3. 4. Design the oxide thickness of an MOS system to yield a specified threshold voltage. Consider an n+ polysilicon gate and a p-type silicon substrate doped to Na = 5x1016 cm-3. Assume Q’ss = 1011 electronic charges per cm, ox = 3.9 and ms -1.15 V. Determine the oxide thickness such that VTN = +0.40 V. 5. Repeat problem 4 for the case when the gate material is aluminium ( ms -0.98 V). 6. Calculate the threshold voltage of an MOS system using an aluminium gate. Consider a p-type silicon substrate at T = 300 K doped to Na = 1014 cm-3. Let Q’ss = 1010 electronic charges per cm, tox = 500x10-8 cm, and assume the oxide is silicon dioxide (ms -0.83 V). 7. Design the semiconductor doping concentration to yield a specified threshold voltage. Consider an aluminium-silicon dioxide-silicon MOS structure (ms -0.35 V). The silicon is n type, the oxide thickness is tox = 650x10-8 cm, and the trapped charge density is Q’ss = 1010 electronic charges per cm. Determine the doping concentration such that VTP = 1.0 V.