ECE 440 Homework IX Spring 2006 Due: Wednesday, March 08, 2006 1. 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 3x10 20 /cm 4 in a linear 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. 2. An abrupt Si p-n junction has the following properties at 300 K: p-side n-s i d e A = 10-4 cm 2 N a = 1x10 17 /cm 3 N d = 1x10 16 /cm 3 τ n = 1 μs τ p = 10 μs μ
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