Population Inversion Induced by Resonant States in Semiconductors

We present a theoretical prediction of a new mechanism for carrier population inversion in semiconductors under an applied electric field with suitable field strength. The mechanism is originated from a coherent capture-emission-type inelastic scattering of resonant states. We support our theory with concrete calculations for shallow acceptor resonant states in strained p-Ge where a lasing in THz frequency region has been recently observed. Unlike in an ordinary heterostructure laser where carrier population inversion is achieved by injection of electrons and holes into an active region [1], in unipolar-type lasers population inversion can be created by different mechanisms. Examples are p-Ge laser under crossing electric and magnetic fields [2] and quantum cascade laser [3], which are based on k-space population inversion between subbands. We will prove in this Letter that a novel unipolar-type population inversion can be realized when the streaming motion of carriers emerges in semiconductors at low temperatures where both elastic impurity scattering and acoustic phonon scattering are weak. We will demonstrate in quantitative details that our suggested mechanism is realistic. Based on a uniaxially strained p-Ge in which shallow acceptors induce resonant states [4,5], a terahertz laser has been fabricated recently [6], and the radiation emission is due to optical transitions between the resonant states and the localized acceptor (Ga) states. Up to now, the mechanism of lasing has remained a puzzle. Our theory will explain the physical origin of the population inversion which leads to the lasing. The study of lasing is a separated issue, and will be presented elsewhere. We consider a model system of charge carriers interacting with optical phonons under an electric field E applied along the z axis. A carrier acquires energy from the field and drifts in k space until its energy exceeds ¯ hv0. This can happen if E $ ¯