Electronic Dilation in Germanium and Silicon

The volume of a semiconductor crystal depends on the occupation of the electronic energy levels. When electrons are excited across the energy gap, the crystal strains itself so as to minimize its free energy. The effect is related directly to the change with pressure of the gap. Experiments have been performed to measure the change in volume associated with the excitation of electron-hole pairs in Ge and Si single crystals. The volume change, instead of being determined by conventional techniques, is related to a stress pulse propagated into the unstrained region of the sample. Carriers are excited by ∼40-nsec bursts of MeV electrons. The combination of thermal expansion and electronic strain in the region of energy absorption causes a stress pulse to propagate into the sample; the pulse is detected by a piezoelectric gauge. As the total incident energy is varied, the density of carriers, and consequently their lifetimes, are changed. The difference between the stress amplitudes produced for carrier lifetimes longer or shorter than a characteristic time allows a determination of the dilation or contraction associated with the excitation of a free carrier pair. The relative volume changes per electron-hole pair measured in this way are 10.3×${10}^{-24\mathrm{}}$ and -2.1×${10}^{-24\mathrm{}}$ for Ge and Si, respectively. The values agree within experimental error with those calculated from published values of the pressure dependence of the energy gaps.