Theory and measurements of harmonic generation in semiconductor superlattices with applications in the 100 GHz to 1 THz range

This manuscript describes harmonic generation in semiconductor superlattices, starting from a nonequilibrium Green's functions input to relaxation rate–type analytical approximations for the Boltzmann equation in which imperfections in the structure lead to asymmetric current flow and scattering processes under forward and reverse bias. The resulting current-voltage curves and the predicted consequences on harmonic generation, notably the development of even harmonics, are in good agreement with experiments. Significant output for frequencies close to 1 THz (7th harmonic) at room temperature, after excitation by a 141-GHz input signal, demonstrate the potential of superlattice devices for gigahertz to terahertz applications.

Figure 1

Comparison of current-voltage curves calculated with the NEGF approach (black dashed), the fit to the hybrid approach formula (blue dot-dashed) of Eq. (3), and the experimental data (red solid). The contact area converting current density into current is $1.26\times {10}^{-12}{\mathrm{m}}^2$.

Figure 2

Diagram of the experimental setup used to measure the current-voltage characteristics (a) and the harmonic power (b).

Figure 3

Ratio of the emitted optical power for the $n\mathrm{th}$ harmonic to the 3rd harmonic nonlinearly generated by a field oscillating 141 GHz. The black solid line has been calculated using our theory and assuming an incident power of $\sim 47\mu \mathrm{W}$, or equivalently, $\alpha =28.3$. From left to right, red circles are the corresponding experimental data for the third, fourth, fifth, sixth, and seventh harmonic. The inset shows the normalized transmission function of the waveguide structure where the superlattice is inserted.

Figure 4

Ratio of the emitted optical power for the $n\mathrm{th}$ harmonic to the 3rd harmonic nonlinearly generated by a field oscillating 141 GHz. Both curves have been calculated using $\alpha =28.3$. The solid (black) curve is identical to the calculation in Fig. 3, except that only odd harmonics are shown for a direct comparison with the dashed (green) line, which has been computed with symmetric input parameters. From left to right, the red circles are the corresponding experimental data for the third, fourth, fifth, sixth, and seventh harmonic. The even harmonics are shown as open circles.