A silicon pn junction (step junction) has doping densities of NA=5×10¹⁵ cm⁻³ on the p-side and ND=1×10¹⁷ cm on the n-side. Carrier lifetimes are given as τₙ=10⁻⁶s and τₚ=10⁻⁷ s. Assume long diode, i.e. long quasi-neutral regions. calculate the ratio of hole current density to total current density at the depletion region edge, xn, on the n-side.