Spectral Overlap Limits Optical Gain in Quantum Heterostructure Photonic Devices

Population inversion in quantum heterostructures underpins light generation in a wide range of photonic devices, including quantum cascade lasers and intersubband emitters. It is commonly assumed that increasing carrier density enhances inversion and optical gain; however, this trend can reverse at elevated densities due to many-body interactions. Here, we investigate this behavior using a controlled doping series in terahertz quantum cascade lasers combined with self-consistent nonequilibrium Green's function simulations. We show that Coulomb-induced quasiparticle broadening increases with carrier density and competes directly with the intrinsic energy separation of the active states, reducing the spectral selectivity of optical transitions. We introduce a dimensionless spectral-overlap parameter, Γ_avg/Δ, where Γ_avg represents the interaction-induced optical linewidth and Δ is the interlevel energy separation, and demonstrate that gain across distinct device architectures follows a common trend with a maximum near Γ_avg/Δ ≈ 1. Beyond this point, spectral overlap suppresses inversion and limits optical gain. These results reveal a density-driven crossover in which many-body broadening sets a fundamental spectral limit on optical gain in quantum-confined photonic systems. The Γ_avg/Δ parameter provides a universal design metric for identifying inversion limits and optimizing performance in quantum heterostructure light-emitting devices.