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# hw8 - W vs N d for the junctions described in(a 3 When a...

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ECE 440 Homework VIII Fall 2005 Due: Monday, October 10, 2005 1. An abrupt Si p-n junction has N a = 7x10 16 /cm 3 on the p-side and N d = 2x10 17 /cm 3 on the n- side. (a) Calculate the Fermi level positions at 300 K in the p and n regions. (b) Draw an equilibrium band diagram for the junction and determine the contact potential V o from the diagram. (c) Compare the results of part (b) with V o as calculated from Eq. (5-8). (d) Using Eq. (5-8), calculate and plot V o versus temperature ranging from 300 K to 500 K. 2. Consider the following Si p-n junctions operating at 300 K. (a) Using Eq. (5-8), calculate the contact potential V o for N a = 5x10 14 and 10 19 /cm 3 , with N d = 10 14 , 10 15 , 10 16 , 10 17 , 10 18 , 10 19 /cm 3 in each case and plot V o vs. N d . (b) Plot the maximum electric field E o vs. N d for the junctions described in (a). What levels of N d doping are required so E o can exceed 10 5 V/cm when N a = 2x10 19 /cm 3 ? (c) Plot the width of the depletion region
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Unformatted text preview: W vs. N d for the junctions described in (a). 3. When a prolonged diffusion or a high-energy implantation is conducted to form a p/n junction. The doping profile near the junction is usually graded, and the step-junction approach is no longer suitable to find the relationship between the width of the depletion region and the contact potential. However, the underlying principle used to establish equations 5-13 to 5-23 remains intact, and they can still be used to determine similar equations for the graded junction. Assume that the doping profile varies as N a-N d =Gx where G is 10 20 /cm 4 in a linearly graded junction. (a) Find and plot the electric field, ε (x), for -∞ <x<+ ∞ . (b) Determine the relationship between the width of the depletion region and contact potential for the junction at equilibrium....
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