• Analysis of actual energy transfer channels in YVO 4 :Yb 3+ ,Er 3+ UCNP is presented. • Simple (reduced) model for energy transfer processes is proposed. • Pump power dependence of upconversion photoluminescence is yielded. • It is established that multiphonon transitions mainly effect on upconversion nonlinearity. • Theoretical results could be useful in UCNPs characterization by spectroscopic data analysis. We analyzed nonlinear emission properties of oxide nanocrystals YVO 4 doped with Yb 3+ and Er 3+ ions which are one of the most interesting types of upconverting nanoparticles (UCNPs). As is widely believed the deviation of the power-dependent upconversion phosphorescence intensity from a quadratic character is attributed to a saturation effect occurring at the relatively high pump power. In this paper, we focused on studying upconversion nonlinearity at the low pump power when excited states populations are considerably less then ground states populations. The analysis of actual energy transfer channels allowed us to propose a reduced model having simple solutions. The obtained analytic expressions for the dependences of upconversion photoluminescence intensity and its nonlinearity on the pump power revealed that multiphonon transitions are a main factor responsible for the variation of upconversion nonlinearity in a range between 1 and 2. This result could be used in spectroscopic experiments for simple and direct identification of the non-radiative relaxation efficiency in YVO 4 :Yb, Er UCNPs.
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