3.091 Fall Term 2004 Homework #5 with Solutions October 5 (for weekly quiz on Tuesday, October 12) 1. Chemical analysis of a germanium crystal reveals indium at a level of 0.0003 atomic percent. (a) Assuming that the concentration of thermally excited charge carriers from the Ge matrix is negligible, calculate the density of free charge carriers (carriers/cm 3 ) in this Ge crystal. (b) Draw a schematic energy band diagram for this material and label all critical features. 2. Show that green light ( λ = 5 × 10-7 m) can excite electrons across the band gap of silicon. 3. Determine the amount (in grams) of arsenic required to be substitutionally incorporated into a mole of silicon in order to achieve in it a free-electron density of 5 × 10 17 /cm 3 . 4. (a) Electromagnetic radiation of frequency 3.091 × 10 14 Hz illuminates a crystal of germanium. Calculate the wavelength photoemission generated by this interaction.
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