Isotope dependence of the lowest direct energy gap in crystalline germanium

Using optical absorption measurements we establish that the lowest direct energy gap changes with atomic mass number m at the rate dE/dm identical with 0.49 plus or minus 0.03 meV at 2 K, decreasing to 0.11 plus or minus 0.03 meV at 300 K, in both isotopically pure and isotopically disordered germanium. These values are broadly consistent with a simple prediction from the measured temperature dependence of the gap and the known dependence of the lattice on the isotope. We confirm, from optical absorption data, that the lowest indirect energy gap of germanium increases at the rate dE/dm identical with 0.36 plus or minus 0.01 meV, in agreement with recent photoluminescence data.