ece340Spring04HW12Sol - ECE 340 1 Homework XII Due Friday...

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ECE 340 Homework XII Spring 2004 Due: Friday, April 02, 2004 1. For a p + -n silicon junction, N a =10 17 /cm 3 in the p-side and N d =10 15 /cm 3 in the n-side. Determine the depletion capacitance per unit area of cm 2 at –4 V. Solutions: 17 15 0 21 0 2 10 10 ln 0.0259ln 0.695 (1.5 10 ) ad i NN kT VV qn × == = × 00 2( ) ) 11 pn rr d WW qN N q N εε + ⎛⎞ ++ =+ = ⎜⎟ ⎝⎠ 19 14 15 92 0 1.6 10 11.8 8.85 10 10 4.22 10 / 2( ) 2 (0.695 4) j d r C Fcm AW ε −− ×× × = = × + 2. A Schottky barrier is formed between a metal having a work function of 4.7 eV and n-type Si (electron affinity = 4 eV). The donor doping in the Si is 4x10 17 /cm 3 . (a) Draw the equilibrium band diagram showing numerical values for qV o and schottky barrier, q φ n . (b) Draw the band diagram with 0.5 V forward bias. Repeat for 3V reverse bias. For all three diagrams, determine and show the proper widths of the depletion region. Solutions: (a), At equilibrium: 17 3 41 0 d Nc m , ln 0.443 d Fs i i N kT E Ee V −= = ( )( ) [ / 2 ] 4 0.55 0.443 4.107 sg F s i qq E E E q e V χ Φ= + = + = ( ) (4.7 4) 0.7 Bm q e V Φ= Φ− = − = 0 4.7 4.107 0.593 ms =Φ −Φ = = 6 0 2 4.40 10 d V Wc m qN × (b), At forward bias: Free Space Energy E c E F E v 4 qe V = 4.7 m V 0 0.593 qV eV = 4.107 s V Φ = 0.7 B V Φ = E Fm W
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0 0.593 0.5 0.093 f VVV V =−= − = 0 6 2( ) 1.74 10 f d VV Wc m qN ε == × At reverese bias: 0 0.593 3 3.593 r V =+= += 5 0 ) 1.08 10 r d m qN + × 3. Assume that a p + -n diode with a uniform cross section area, A, is built with an n region width A smaller than a hole diffusion length ( A < L
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This note was uploaded on 01/28/2010 for the course ECE 440 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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ece340Spring04HW12Sol - ECE 340 1 Homework XII Due Friday...

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