Hw5_solution_fall09

# Hw5_solution_fall09 - ECE 440 Homework V Due Friday Fall...

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ECE 440 Homework V Fall 2009 Due: Friday, October 09, 2009 Please write your name and net ID on your homework. Show all work leading to your answer. 1. The acceptor 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 posted in the 440 website), and the sample is at thermal equilibrium at 300 K. (a) Determine the diffusion coefficients for majority carriers at points A, B and C, respectively. (b) Find the majority carrier diffusion current densities along the cross sections at points A, B and C, respectively. Indicate not only the magnitude but also the direction. (c) Find an expression for the built-in electric field E (x) at equilibrium over the range from x= 1µm to x=3 µm. (d) Sketch a band diagram such as in Fig. 4-15 over the range from x= 1µm to x=3 µm and indicate the direction of E . X (μm) 0 10 16 /cm 3 N A 10 15 /cm 3 1 2 3 4 5 6 7 8 A B C

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To find the diffusion coefficients, we have to first find the doping concentrations at those points. After we find those values, we can use the Einstein Relationship (4-29) to figure out the diffusion coefficients: (b) Find the majority carrier diffusion current densities along the cross sections at points A, B and C, respectively. Indicate not only the magnitude but also the direction. Before we can calculate the diffusion current densities, we need to find the equation for the majority carriers N A (x) = p(x). diff p p p J qD x = - Remember that the plot shown in the HW is a semilog plot. Therefore, we need to formally calculate the carrier concentration as a position of x, because the slope is different at every point! Luckily, with a mathematical trick and 2 points, we can easily find the equations we need. For the range 1μ m x m , the general form of the solution and our boundary conditions are (note the solution here assumes the general solution is an exponential in order to be consistent with the results obtained in the book, however,
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Hw5_solution_fall09 - ECE 440 Homework V Due Friday Fall...

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