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# hw4_sol_09 - ECE 440 Due Friday Homework IV Fall 2009 Print...

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ECE 440 Homework IV Fall 2009 Due: Friday, September 25, 2009 Print your name and netid legibly. Show all work leading to your answer clearly and neatly. Staple multiple pages. 1. A Si bar is 0.2 cm long and 200 µm 2 in cross-sectional area. Find the current at 300 K with 10 V applied to (a) the Si bar is doped with 1x10 17 /cm 3 gallium and (b) the Si bar is doped with 1x10 17 /cm 3 gallium and 2x10 17 /cm 3 arsenic. Refer to Fig. 3-23 or the mobility chart posted online.) (c) The silicon sample is grounded at x=0 and biased at +10 V at x=0.2 cm. Draw the corresponding energy band diagram for case (a). Solution: To find the current, use Ohm’s law. (1) IR V = (2) R V I / = We know bias so we need to find resistance. (3) σ ρ 1 = = A L A L R (4) A p n q L p n ) ( + = μ μ Substituting (13) into (11): (5) A L V p n q I p n + = ) ( μ μ This expression is only valid if the drift velocity of the carriers is below the saturation velocity. For silicon, the saturation velocity is s cm / 10 7 . (6) = s cm v cm V E s V cm 2 μ For Si bar is doped with 1x10 17 /cm 3 gallium. (a) 3 17 10 - = = cm N p A s cm s cm cm V s V cm 7 4 2 10 10 5 . 1 2 . 0 10 300 < × =

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A L V p q I p μ . mA m cm V s V cm C I 48 . 0 200 2 . 0 10 ) 10 1 300 ( 10 6 . 1 2 1 17 19 = × × - - μ (b) 3 17 10 - = - cm N N n A D 3 3 17 20 10 25 . 2 10 10 25 . 2 - × = × = cm p Using Figure (3-23) in S&B we can see that s V cm n 2 400 μ in this case. Check for saturation: s cm s cm cm V s V cm 7 4 2 10 10 2 2 . 0
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hw4_sol_09 - ECE 440 Due Friday Homework IV Fall 2009 Print...

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