Formation of electric-field domains inGaAs∕AlxGa1−xAsquantum cascade laser structures

Abstract

The current-voltage $(I\text{\ensuremath{-}}V)$ characteristics of $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum cascade laser structures (QCLSs) are found to exhibit current plateaus with discontinuities for voltages below threshold. The number of current discontinuities is correlated with the number of periods of the QCLS, suggesting the formation of electric-field domains that span the entire structure. A self-consistent calculation of the conduction band profile and corresponding electronic wave functions shows that the low-field domain is related to resonant tunneling between the ground state $g$ in the active region and the lowest energy state in the adjacent, downstream injector ${i}_{1}$. For $x=0.33$ $(x=0.45)$, the high-field domain is formed for resonant tunneling between $g$ and the first (second) excited state ${i}_{2}$ $({i}_{3})$ in the injector region. A comparison of the experimental data with the calculated conduction band profile shows that a significant field inhomogeneity within each period shifts the voltage range, for which the resonance condition is fulfilled, to much lower voltages than expected for a homogeneous field distribution.