ece340Spring04HW15sol

# ece340Spring04HW15sol - ECE 340 Homework XV Due Friday...

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ECE 340 Homework XV Spring 2004 Due: Friday, April 23, 2004 1. Aluminum and polysilicon are commonly used as gate metals for the MOS structure in silicon. Assume that platinum is used as the gate metal. Reconstruct a diagram similar to Figure 6-17 showing the variation of the metal-semiconductor work function potential difference Φ ms with substrate doping concentration. The work function of Pt is 5.7 V and the electron affinity of silicon is 4.0 V. Show your work and draw to scale with accuracy. Solutions: For n-type silicon: ln 5.7 4.0 0.55 0.0259ln 1.15 0.0259ln 2 g dd ms m s m si ii i E NN kT n qn n n χ ⎛⎞ Φ= Φ− + − = − + = + ⎜⎟ ⎝⎠ For p-type silicon: ln 5.7 4.0 0.55 0.0259ln 1.15 0.0259ln 2 g aa ms m s m si i E kT p n n + + + + = Plots based on these two equations: 2. (a) Find the voltage V FB required to reduce to zero the negative charge induced at the semiconductor surface by a sheet of positive charge Q ox located x’ below the metal. (b) In the case of an arbitrary distribution of charge ρ

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ece340Spring04HW15sol - ECE 340 Homework XV Due Friday...

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