midterm103_2009_solutions

midterm103_2009_solutions - substrate doping of 10 17 cm-3...

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ECE 103 Midterm (Fall 2009) Assume silicon, room temperature, complete ionization. 1. (20 pts) An abrupt n + -p junction with N d = 10 20 cm -3 and N a = 10 17 cm -3 is forward biased at 0.5 V. (a) Draw the band diagram, label n and p regions, show the direction of current flow. What is the current type (electron or hole, drift or diffusion) in the p- type region just outside the depletion region? (b) Calculate the depletion charge capacitance per unit area. Solutions: (a) Current flow --------------------------- Æ Electron diffusion is the type of current in the p-region outside the depletion region. (b) 97 . 0 56 . 0 41 . 0 2 ln = + = + = q E n N q kT g i a bi ψ V 078 . 0 ) 5 . 0 ( 2 = = a bi si d qN W ψε μ m 7 10 33 . 1 × = = d si d W C ε F/cm 2
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2. (30 pts) Consider an MOS device with 20 nm thick gate oxide and uniform p-type
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Unformatted text preview: substrate doping of 10 17 cm-3 . The flat band voltage is -0.98 V. There is no interface charge in the oxide. (a) What is the threshold voltage for strong inversion? (b) Draw the band diagrams at the flat band condition and at the threshold condition. (c) Calculate the total MOS capacitance (per area) at the threshold condition. Solutions: (a) 42 . ln = = i a B n N q kT V V 98 . = fb V 83 . 97 . 84 . 98 . ) 2 ( 2 2 = + + = + + = ox B a si B fb t C qN V V V. (b) (c) 104 . ) 2 ( 2 = = a B si dm qN W m si dm ox W C C + = 1 1 min F/cm 7 min 10 63 . = C 2...
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midterm103_2009_solutions - substrate doping of 10 17 cm-3...

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