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1. Using Equation 7 in the Mathematical Analysis page, you  can find the space charge per unit area, Qs, induced in the silicon substrate. (It will be an  amount equal, but opposite in sign, to the charge induced in the metal gate. ) Find a relationship for the charge Qs to the electric field Es. ( i.e. at x= 0, Y = Ys and E =Es ) And then, using this relationship, how much Qs is expected if the electric field Es (x=0) is 1.5x105 V/cm ? ( esi = 11.9 eo )

2. The total charge per unit area induced in the silicon can be expressed as


Using this equation, plot the characteristic curve ln |Qs(C/cm2 ) |  vs   Ys (V) for p-type Si at 300 K ( Na =4x1015 cm-3 , ni= 1.0x1010 cm-3 ).

1. S.M. Sze, ' Physics of Semiconductor Devices' 2nd Ed. , John Wiley & Sons , 1981, p369.
2. C.G.B. Garrett and W.H. Brattain, 'Physical Theory of Semiconductor Surfaces', Phys. Rev., Vol 99 (376), 1955.