# sol6 - ECE 440 HW6 Solutions Summer 2009 Thu 1 1 An abrupt...

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Unformatted text preview: ECE 440 HW6 Solutions Summer 2009 Thu, Jul 16, 2009 1 1. An abrupt Si p-n junction has & A = 3 x 10 17 /cm 3 on the p-side and & D = 2x10 15 /cm 3 on the n-side. (a) Calculate the Fermi level positions in the p and n regions at 300 K. P region: N region: (b) Draw an equilibrium band diagram for the junction and determine the contact potential V from the diagram. First draw the Fermi level straight across (the sample is in equilibrium). Then, draw E c and E v in both the p and n regions based on the calculations in part (a). V can be determined graphically. (c) Calculate V from Eq. (5-8) and compare the result with that in part (b). The results in part (b) and (c) are identical. In fact (5-8) can be derived from the equations in part (a) fairly simply. ECE 440 HW6 Solutions Summer 2009 Thu, Jul 16, 2009 2 (d) Calculate and plot V versus temperature ranging from 200 K to 500 K. Because both V and n i depend on T, this plot can be somewhat difficult to construct. One can either take sample points (at least three) and interpolate between those points or approximate n i (T) and plug that into equation (5-8). Here is the Matlab code to make a plot of V vs. T. (When making this plot, one can make the approximation that m n and m p do not depend on temperature.) >> T = 200:500; >> ni = (1.5*10^10).*(T./200).^(3/2).*exp(-1.11/(2*(8.62.*10^-5))*(1./T- 1/200)); >> V0 = 8.62*10^-5 * T .* log( 2*10^17*7*10^16./ ni.^2); >> plot(T,V0) and the corresponding plot is: ECE 440 HW6 Solutions Summer 2009 Thu, Jul 16, 2009 3 2. 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 & a-& d =Gx where G is 3x10 20 /cm 4 in a linear junction....
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sol6 - ECE 440 HW6 Solutions Summer 2009 Thu 1 1 An abrupt...

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