Use the depletion approximation to analytically solve the Poisson equation in 1-D for a PN junction in equilibrium. Assume a uniform doping profile with . Plot the potential and the field versus position. Use Newton's method to solve the Poisson equation in equilibrium for the same diode as described above. Graph the results on the same axes as the results from the depletion approximation. Can you notice the difference? Extra credit. Use your simulator to calculate the potential and field for more realistic Gaussian-type dopant distributions. Use typical values for maximum doping concentration and straggle.