Correlation between emission frequency and location on the wafer for terahertz quantum-cascade lasers

The relative change in the growth rate and thickness of the QCL across the wafer were evaluated by ex-situ spectral reflectivity scans for three wafers A, B, and C. Figure 1(a) depicts the relative change in the growth rate (QCL thickness) with respect to the growth rate (QCL thickness) at the center of the wafer A. The emission frequencies of a number of QCLs fabricated from wafer A (B and C) based on a design for 3.36 THz (3.92 THz), which are located in different regions of the wafer, exhibit a blue shift with a decreasing growth rate from the center to the edge of the wafer. Using Fourier transform-based simulations, we calculated the frequency as a function of the relative thickness of the QCL. By utilizing the dependence shown in Fig. 1(a), the frequency is calculated as a function of the location, which is well reproduced by a power law. This power law describes the correlation between the emission frequency of the QCLs and the location on the wafer as indicated by the dashed lines in Figs. 1(b) and 1(c). The simulated frequencies agree well with the experimental results. Using this universal power law, the covered frequency range for a new wafer can now be predicted, and the suitable position on the wafer from which a THz QCL with an application-defined emission frequency is fabricated can be efficiently determined. Rather than growing several homogeneous wafers with a wafer-to-wafer variation of the nominal active-region thickness, THz QCLs with customized emission frequencies can be efficiently fabricated by making use of this well-defined frequency dependence across the wafer.