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# hw7_solutions - ECE 440 Homework VII Solutions Spring 2008...

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ECE 440 Homework VII Solutions Spring 2008 1. Consider a silicon sample at 300 K. Assume that the difference of hole concentration varies linearly with distance. At x=0, the hole concentration is p(0). At x=10 μm, the hole concentration is p(10 μm)= 5x10 14 /cm 3 . If the hole diffusion coefficient, assumed constant, is D p =14 cm 2 /sec, determine the hole concentration at x=0 for the following two diffusion current densities: (a) the diffusion current density at x=0 is found to be J p diff = + 0.19 A/cm 2 and (b) J p diff = - 0.19 A/cm 2 . The expression for the diffusion current is in 4-22b. We can replace the derivative with the slopes of the hole concentration. 0 f 0 f p diff p x x ) p(x ) p(x qD J - - - = Thus, p 0 f diff p f 0 qD ) x (x J ) p(x ) p(x - + = (a) 3 14 19 3 14 10 85 . 5 ) 14 )( 10 6 . 1 ( 10 19 . 0 10 5 ) 0 ( - - - = + = = cm x x x x x p (b) 3 14 19 3 14 10 15 . 4 ) 14 )( 10 6 . 1 ( 10 19 . 0 10 5 ) 0 ( - - - = - + = = cm x x x x x p 2. The donor profile of a silicon sample is shown below. Assume that the majority carrier mobility can be obtained from Fig. 3-23 (or the enlarged graph potsed in the 440 wbsite), and the sample is at thermal equilibrium at 300 K.

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hw7_solutions - ECE 440 Homework VII Solutions Spring 2008...

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