W11_HW3

W11_HW3 - N D = 1x10 16 cm-3 . Assume that the holes are...

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ECE103 (Winter 2011) HW #3 1/27/11 (Will not be collected! OR if turned by Tuesday 2/1, will be graded for extra credits) 1. Pierret, Problem 3.12. 2. Calculate the Si crystal shown below, in which N A = 0 and N D = N 0 e -x/L , with N 0 =1 x 10 16 cm -3 and L = 1 mm. Assume T = 300K. i. Calculate the electric field at x = 1 μ m, assuming that n(x) = N D (x) for x > 0 and N D >> n i , and that E C – E F is determined by n(x) for x > 0. Sketch the energy band edge diagram assuming the Fermi level is constant within the crystal. ii. Calculate J diff and J drift (Give numerical values with units) at x = 1 μ m, and indicate the direction (+x-direction or –x-direction) of each of these components of the current density. Calculate J total = J diff + J drift and explain why your result is sensible (hint: consider the conditions required under equilibrium). 3. Consider an n-type Si crystal of length L (with ends located at x = 0 and x = L) In which
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Unformatted text preview: N D = 1x10 16 cm-3 . Assume that the holes are injected at both ends of the crystal to create steady-state carrier concentrations ∆ p n (x=0) = ∆ p 1 , ∆ p n (x=L) = ∆ p 2 . You may assume that these carrier concentrations correspond to low-level injection. The diffusion coefficient for holes is D p , and the minority carrier life-time is τ p . i. Following the general approach shown in class, derive the differential equation for the non-equilibrium hole concentration ∆ p n (x). ii. Write down the general solution to the differential equation in (a), and using the boundary conditions given obtain the complete solution for ∆ p n (x) in terms of q, ∆ p 1 , ∆ p 2 , L, ∆ p , and τ p . iii. Compute the hole current J p due to diffusion at x = 0. 4. Pierret, Problem 3.20. 5. Pierret, Problem 3.22. 6. Pierret, Problem 3.24....
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This note was uploaded on 04/02/2011 for the course ECE 103 taught by Professor Song during the Spring '11 term at UCSB.

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