ee606_s04_hw7 - Homework 7 EE 606 Spring 2004 1 Solve...

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1 Homework 7 EE 606 Spring 2004 1. Solve problems 5.10, 5.11, and 6.8 from the textbook. 2. Work out the following problem …… Depletion Approximation vs. “Exact” Solution of the PN Junction To analyze a semiconductor device, we must solve the continuity equations for electrons and holes, the drift-diffusion equations, which describe how carriers move in response to an electric field, along with Poisson’s equation because when they move, they change the electric field. In general, these equations are too complex to solve analytically (the equilibrium problem is solved in problem 5.14), so we resort to approximations such as the well-known and frequently-used depletion approximation. The depletion approximation is extremely useful, when it is valid, so it is important to understand its limitations. In this exercise, you will compare the results of depletion approximation analyses of PN junctions with the “exact” solution obtained by solving the equations of state directly by numerical simulation using the computer program, ADEPT. 1) A Si step junction maintained at room temperature under equilibrium conditions has a p- side doping density of N A = 2 x 10 15 /cm 3 and an n-side doping of N D = 10 15 /cm 3 , Use the depletion approximation to compute: (a) V bi (b) The depletion layer boundaries, x p , x n , and the depletion width, W (c) The electric field at x = 0 (d) The electrostatic potential at x = 0 (e)
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