Multi-component diffusion theory of quantum well intermixing

Quantum well (QW) intermixing via post-growth annealing enables integration of active and passive components in photonic integrated circuits. QW intermixing generally produces a blueshift of the QW band gap, rendering the intermixed section of a QW transparent to a laser fabricated from a non-intermixed section of the same structure. Experimental studies on Al_1−x−yIn_yGa_xAs/InP QWs have, however, identified structures in which intermixing produces a redshift of the band gap. This redshift is anomalous insofar as it is not explained by previous models of QW intermixing based on Fick’s law. To overcome this limitation we apply a generalized (multi-component) form of Fick’s law to describe inter-diffusion of Ga, In and Al in Al_1−x−yIn_yGa_xAs/InP. Based on the experimental observation that annealing can drive strong Ga and In intermixing but Al diffuses minimally, we demonstrate that intermixing in Al_1−x−yIn_yGa_xAs QWs can be formulated as a coupled inter-diffusion problem characterized by independent Ga- and In-related diffusivities, which increase with increasing strain in the QW, and suppressed Al diffusion. The intermixing is governed by the ratio of these diffusivities, which can drive a counterintuitive process that explains the experimentally observed redshift: namely, diffusion of additional In into the well upon annealing of a structure having equal well and barrier In compositions. The model is validated via comparison to experiment. First, by showing that it can quantitatively describe measured composition profiles. Second, via empirical parameterization of the diffusion coefficients, which we demonstrate as sufficient to quantitatively reproduce the measured QW band gap shift vs. annealing temperature.