Consider a hypothetical layer of silicon that has an n-type impurity concentration of 10¹⁷ cm⁻³ at the top surface, and in which the impurity concentration decreases exponentially with distance into the silicon. Assume that the concentration has decreased to 1/e of its surface value at a depth of 0.5 μm, and that the impurity concentration in the sample before the insertion of the n-type impurities was 10¹⁵ cm⁻³ p-type. Determine the depth below the surface of the pn junction that results and determine the sheet resistance of the n-type layer. Assume a constant electron mobility of 800 cm²/V-s. Assume that the width of the depletion layer is negligible.