Temperature effect on upconversion efficiency for erbium-doped microcrystal material

This paper presents a mathematical model describing the effect of temperature on the upconversion efficiency of the Hexagonal Sodium Yttrium Fluoride (β-NaYF4) doped with trivalent Erbium (Er3+). The upconversion process is described by a set of rate equations to account for the different upconversion mechanisms. The temperature effect appears in the multi-phonon relaxation process that is modeled using the energy gap law equation. This model helps in investigating different host materials by their temperature response to overcome the reduction of efficiency in photovoltaic cells due to temperature rising.