Doping changes the Fermi energy of a semiconductor. Consider silicon, with a gap of 1.11 eV between the top of the valence band and the bottom of the conduction band. At 300 K the Fermi level of the pure material is nearly at the midpoint of the gap. Suppose that silicon is doped with donor atoms, each of which has astate 0.16 eV below the bottom of the silicon conduction band, and suppose further that doping raises the Fermilevel to 0.13 eV below the bottom of that band (see the figure below). For (a) pure and (b) doped silicon, calculate the probability that a state at the bottom of the silicon conduction band is occupied. (c) Calculate the probability that a donor state in the doped material is occupied. Conduction band :T:::::_:::::: I \" Fermi N Donor LileV level level (a) Number n Unme Conduction band Fermi Donor 1.11 eV level level Valence band (a) Number Units (b) Number Units (c) Number Units VPure silicon at room temperature has an electron number density of about 5.00 x 101> m and an equal density of holes in the valence band. Suppose that one of every 107 silicon atoms is replaced by a phosphorus atom. (a) Which type will the doped semiconductor be, n or p? (b) What charge carrier number density will the phosphorus add? (c) What is the ratio of the charge carrier number density (electronsin the conduction band and holes in the valence band) in the doped silicon to that in pure silicon? The density of silicon is 2.33 g/cm* and its molar mass is 28.086 g/mol (a) (b) Number n Units v (c) Number n In a particular crystal, the highest occupied band is full. The crystal is transparent to light of wavelengths longer than 246 nm but opaque at shorter wavelengths. Calculate the gap between the highest occupied band and the next higher (empty) band for this material. Number u Units v