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# hw7s - Question 1 A semiconductor device made of silicon...

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Question 1. A semiconductor device made of silicon has, under thermal equilibrium, an M-shaped electric field distribution as shown in the figure below. E / E max 1 0.5 0 a /2 x a -a - a /2 a) Find N d - N a between x = - a and x = a , as a function of E max b) Find the total potential across the semiconductor as a function of E max with a = 0.1 m c) Find E max and the built-in voltage i d) Plot N d - N a for - a x a and indicate numeric values. Specify whether the different regions are p –type or n -type. a) From poisson’s one dimensional equation: s a d s N N q dx d ) ( E From the diagram above, for 2 a x a , a a x max 2 ) ( E E and N d - N a = qa s max 2 E Similarly, for 0 2 x a , N d - N a = qa s max E for 2 0 a x , N d - N a = ; max qa s E and for a x a 2 , N d - N a = qa s max 2 E . b) The potential equals: dx x x ) ( ) ( E , resulting in: 4 5 ) ( 0 max E a x total .

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hw7s - Question 1 A semiconductor device made of silicon...

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