Angle dependence of acoustic phonon-assisted tunneling in a weakly coupled superlattice: Evidence for terahertz phonon amplification

We investigate nonequilibrium acoustic phonon-assisted tunneling in a weakly coupled GaAs /AlAs superlattice (SL). Previously it had been predicted that, in such structures, the conditions for terahertz acoustic phonon amplification can be achieved [B. A. Glavin, V. A. Kochelap, and T. L. Linnik, Appl. Phys. Lett. 74, 3525 (1999)]. We present experimental measurements of the change in current ΔI due to an incident nonequilibrium phonon pulse generated by thermalizing a laser pulse in a metal film. In particular, we measure the dependence on the angle of incidence θ of the phonons relative to the SL growth direction. The results are compared with numerical calculations made using the two-well model. It is found that good agreement between the measurements and calculations can be obtained for all θ if we assume that amplification is occurring for phonons propagating in a direction near θ =0. Due to the amplification of phonons with energy ℏω_q≲Δ, where Δ is the energy drop per period of the SL, the nonequilibrium phonon distribution in the vicinity of the SL is different from the expected Planck spectrum of the phonon source. We show that this can explain the experimental measurements of ΔI at θ =0. We present these results as evidence for phonon amplification in the 400-GHz-1-THz frequency range.