Semi-empirical approach to assess externally-induced photoluminescence linewidth broadening of halide perovskite nanocrystals with particle-size distribution

Abstract

Colloidal nanocrystals (NCs) can be used to prepare high-color-purity metal halide perovskites (MHPs) for light-emitting displays. However, the NCs have a finite particle-size distribution, which broadens the linewidth of photoluminescence spectra under strong quantum confinement, and thereby degrades the color purity of the MHPs. This paper presents a simple method to quantify this externally-introduced broadening of linewidth ΓSD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{\\boldsymbol{\\Gamma }}}}}}}_{{{{{{\\bf{SD}}}}}}}$$\\end{document} by combining experimental size-distribution histogram with size-dependent photoluminescence-wavelength (PL-λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{\\boldsymbol{\\lambda }}}}}}$$\\end{document}) curve. We develop a semi-empirical method to estimate the other three contributions to the experimentally-measured full-width at half-maximum, ΓEXP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{\\boldsymbol{\\Gamma }}}}}}}_{{{{{{\\bf{EXP}}}}}}}$$\\end{document}. Namely: the intrinsic linewidth ΓLO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{\\boldsymbol{\\Gamma }}}}}}}_{{{{{{\\bf{LO}}}}}}}$$\\end{document} caused by exciton-longitudinal optical (LO) phonon Fröhlich coupling; the inhomogeneous linewidth Γo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{\\boldsymbol{\\Gamma }}}}}}}_{{{{{{\\bf{o}}}}}}}$$\\end{document} caused by imperfections-related scattering, and the broadening ΓQC\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{\\boldsymbol{\\Gamma }}}}}}}_{{{{{{\\bf{QC}}}}}}}$$\\end{document} due to the quantum-confinement effect. We show that ΓLO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{\\boldsymbol{\\Gamma }}}}}}}_{{{{{{\\bf{LO}}}}}}}$$\\end{document} of a nanocrystal decreases together with the particle size, disappearing at 1.6 nm radius. Finally, we show that ΓLO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{\\boldsymbol{\\Gamma }}}}}}}_{{{{{{\\bf{LO}}}}}}}$$\\end{document} is correlated with the degree of Fröhlich-polaron formation, hence proportional to the long-range LO-phonon-electron coupling.