Modern IC processing utilizes a technique called oxygen precipitation to getter metallic contami- nants out of a thin layer at the top surface of the wafer. It is in this so-called denuded zone, where the devices are fabricated. Typically, the denuded zone is thin and is characterized by a fairly long lifetime, while the rest of the wafer where oxygen precipitation has taken place exhibits much lower lifetimes. The denuded zone results in device reverse-bias leakage currents that are much reduced. The change in lifetime in the wafer presents an interesting problem for the computation of the current injected downward in a bulk p+-n diode, as sketched in the figure below. SOBOT RY X < < Ln1 -- X >> Ln2 No solem toz enoitq i suntedisalo No p ranno Ystend palub and Volote n Denuded zone TELO (2) mif dong() (5) Oxygen precipitated region DE40 ogerior a vigas ang a) soresb upala pdt datolaylaviatiluu Make the following assumptions. The doping level is the same in both regions of the n substrate. The junction depth of the p+ region and its associated depletion region are much thinner than x, the denuded zone thickness. x, is much shorter than the local diffusion length Lh1. The thickness of the oxygen precipitated region x is much longer than the local diffusion length Ln2- (a) Sketch the shape of the excess hole concentration in the n region in forward bias. (b) Derive an expression for the hole current density injected into the n-type substrate in forward bias in terms of the hole diffusion length in the oxygen precipitated region, Lh2, the denuded zone thickness, x, and the usual parameters.