Frequency dependence of acoustic phonon-assisted tunnelling in semiconductor superlattices

In recent experiments [1,2] we have shown that the change in tunnel current, ∆I(V), through a GaAs/AlAs SL produced by a non-equilibrium acoustic phonon pulse has a maximum at a bias voltage V which varies linearly with the characteristic temperature of the phonon distribution. The form of ∆I(V) is in reasonable agreement with calculations by Glavin et al. [3]. While the experiments clearly show that ∆I(V) is dependent on the dominant phonon frequency, information on the spectral halfwidth ∆ω (HWHM) of the SL detector is limited by the broad distribution of incident phonons and we can only conclude that h∆ω ≤ k T B , where kBT is the energy halfwidth of the thermal source. A narrower band source would be needed to measure ∆ω. In the present work we have investigated the halfwidth theoretically by looking at the current changes produced by quasi-monochromatic phonon beams using a model similar to that of ref. [3]. The effect of bias on the SL is to produce an energy separation ∆ between the quasibound states in neighbouring quantum wells. The frequency, ωmax, of the peak in ∆I increases with ∆ as expected and is also sensitive to the angular range, 0<θ<θmax, of the incident phonons. Fig. 1 shows ∆I as a function of ε ω = h for ∆=2meV and for different values of θmax. ∆ω /ωmax increases from ~0.2 to ~0.35 with increasing θmax, and so q|| max (q|| = qsinθ), while the peak, ωmax, moves to lower frequencies. If level broadening can be neglected, ∆ω /ωmax should be reduced towards the lower value by quantising magnetic fields, ∞ωc ≠∆, EF, provided q|| max ~1/lB < ∆/∞s [4] (lB is the magnetic length and s is the TA sound velocity) both of which are readily achievable. We also note that the dominant assisted tunnelling process contributing to ∆I is stimulated phonon emission [2,3] and, since the sizes of the signals seen in the experiments are approximately thirty times larger than those expected, we believe that phonon amplification may be taking place. This should also result in a significant reduction in the spectral linewidth.