Simple, approximate formulas are developed to calculate the mean gain and excess noise factor for avalanche photodiodes using the dead-space multiplication theory in the regime of small multiplication width and high applied electric field. The accuracy of the approximation is investigated by comparing it to the exact numerical method using recursive coupled integral equations and it is found that it works for dead spaces up to 15% of the multiplication width, which is substantial. The approximation is also tested for real materials such as GaAs, InP and Si for various multiplication widths, and the results found are accurate within ∼ 15% of the actual noise, which is a significant improvement over the local-theory noise formula. The results obtained for the mean gain also confirm the recently reported relationship between experimentally determined local ionization coefficients and the enabled non-local ionization coefficients.
Synthesized nanoparticles with strong luminescence in the second near-infrared window show great potential for applications in biomedical imaging and diagnosis. Nanoscale dimensions and tunable optical properties can enable nanoparticles to operate as fluorescent probes in the imaging of tumors and lymphatic tissues. Lanthanide-doped rareearth fluoride nanoparticles with photoluminescence tuned to the second near-infrared window can circumvent many of the issues currently limiting the clinical utility of fluorescence imaging technology and show promise as tools for the early detection of cancer. We report on the synthesis and characterization of colloidal LiYF 4 nanoparticles doped with erbium. The nanoparticles were synthesized through a coprecipitation method using rare-earth chlorides, LiOHꞏH 2 O, and NH 4 F as precursors. 1-octadecene was used as a high-temperature solvent, and oleic acid was used as an organic capping agent. The reaction took place under the protection of nitrogen atmosphere. The size, morphology, and colloidal stability of the nanoparticles were determined using data obtained from transmission electron microscopy, dynamic light scattering, and zeta potential techniques. Optical characterization data were collected using NIR absorption spectroscopy and fluorescence spectroscopy. The Er 3+ -doped LiYF 4 nanoparticles show NIR-II emission peaks at 1001 nm, 1490 nm, 1531 nm, and 1558 nm upon NIR-II excitation at 972 nm. The excellent luminescence in the NIR-II range makes them a strong candidate for bioimaging applications.
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