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Unformatted text preview: ECE 440 HW6 Solutions Summer 2009 Thu, Jul 16, 2009 1 1. An abrupt Si pn junction has & A = 3 x 10 17 /cm 3 on the pside and & D = 2x10 15 /cm 3 on the nside. (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. (58) and compare the result with that in part (b). The results in part (b) and (c) are identical. In fact (58) 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 (58). 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 highenergy implantation is conducted to form a p/n junction. The doping profile near the junction is usually graded, and the stepjunction 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 513 to 523 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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