Radiation emission by ballistic electrons in semiconducting superlattices.

Abstract

An analysis of the radiation emitted by ballistic electrons in semiconducting superlattices is presented. The periodicity of the superlattice becomes effective if the mean free path of the electrons is longer than several times the dimension of the unit cell. The rate of spontaneous emission in a finite superlattice is calculated, with the edges of the system taken into account. It is found that when the superlattice is longer than 10 unit-cell lengths, the dominant electronic transitions are between two different minibands. These transitions are characterized by the conservation of the Bloch momentum of the electron. For shorter superlattices there are also other transitions in which the Bloch momentum is not conserved. Accordingly, there are several emitted wavelengths for each initial energy of the electrons. The preferred direction of emittance is shown to be perpendicular to the motion of the electrons. The high rate of spontaneous emission and the preferred direction of emittance imply the possibility of stimulated emission. On that account, the rate equations for the density of photons and electrons are obtained. With use of these equations, two modes of operations, i.e., traveling-wave amplifier and oscillator, are analyzed. The linear gain of the system is found and shown to be strongly affected by the energy characteristics of the electrons. Calculations of the threshold current for positive gain yield a current of the order of 10 kA/${\mathrm{cm}}^{2}$. This value is considered attainable in ballistic electron structures.