How many Cr atoms are ionized? (b) Assume that there is just one other dopant species which is...

If not otherwise specified, assume T = 300K and that the material is silicon. 1. In order to create "semi-insulating" GaAs, a 0.5 mm thick wafer (E, = 1.12 eV) is doped with Nc, = 5 x 1018cm-3 of Cr, which has an acceptor level 0.77eV above the valence band. The Fermi level is located 0.435eV above the valence band.
(a) How many Cr atoms are ionized? (b) Assume that there is just one other dopant species which is totally ionized (shallow). What is the type and concentration of that dopant? (c) What would be the resistivity of this wafer? 2. A silicon sample is uniformly doped with Na 2 x 1018cm-3. The sample is 100 pm thick. At one surface (x = 0), carriers are generated by light at a rate of 1018cm-26-1 (note: this is surface generation and is per unit area). There is negligible bulk generation. At both ends, there is a recombination velocity of s = 103 cm/s. Assume r„ = r, = 40ps and T = 3COK. (a) Determine the excess hole concentration as a function of position. (b) Calculate the electron current density at z = 50pm. 3. A silicon BIOS capacitor has a polysilicon gate heavily doped with arsenic such that Ef Et + 0.1eV and an oxide thickness of zor = 2nm. The substrate has very light doping up to a depth of lOnm and then boron doping of No - 101'cm-3 below that point. (a) Calculate the depletion region depth and associated depletion charge at the edge of strong inversion. Use bulk doping in determining op. Hint: Think about the voltage drops in the semiconductor as you would a pn junction with non-uniform doping. (b) If o. = 0.8 V, what mode is the device in and what is the applied bias?
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