LO-Phonon Band Filling by Means of Charge Carriers Accelerated in Electric Fields

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Non-thermal phonons attract increasing attention in the theory of electron and hole dynamics in crystals subjected to high electric fields. Of special interest is the population inversion of the bands of lattice vibrations, e.g., increasing number of longitudinal optical (LO) phonons relative to the lower-energy (transverse optical — TO, longitudinal acoustic — LA, or transverse acoustic — TA) modes. Inversion is the necessary condition for constructing the phonon-difference laser [1] — the device harnessing lattice vibrations for midor far-infrared light generation. The term of phonon laser is sometimes misused for designation of ultrasound generator based on stimulated emission and reflection of mechanical waves [2]. We are interested in such situations when a higher-energy phonon mode transforms to the lower-energy one, and the difference of phonon energies gives rise to photon emission. Seeking to reveal the conditions of creating the phonon-difference laser, we investigate the changes of phonon distributions among the LO and lower bands under influence of charge carriers accelerated in high electric fields. We use Monte Carlo (MC) method for modeling the carrier and lattice dynamics. Simulation includes charge carrier scattering on LO and LA phonons, piezoelectric and impurity ion potentials. Among the examined crystals (Si [3], GaN [4], InSb [5], and others [6]), the covalent-bond n-type Si crystals are particularly interesting because LO phonons are accumulated there predominantly due to the g-type electron umklapp (electron transfer between the equivalent valleys). The process is characteristic of many other indirect-gap semiconductors. In the direct-gap polar semiconductors, LO