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 VIn 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