介质中含孤立发光中心的纳米粒子的辐射寿命概率分布

含发光中心的纳米粒子在介质中随机分布,造成局域介质相对折射率的随机分布,导致了纳米粒子辐射寿命的涨落.分析纳米粒子数量在线度为发射光波长量级的体积内的概率密度,由此得出局域介质相对折射率的概率密度.通过纳米粒子辐射寿命对折射率的依赖关系,得到纳米粒子辐射寿命概率密度的解析表达.在此基础上,分析了Meltzer等人的实验中,含Eu³⁺离子的Y₂O₃粒子在甲醇溶液中辐射寿命的相对偏移量的涨落,并得出辐射寿命的不确定度(均方差)与纳米粒子体积、体积密度等物理量的关系.

Probability Distribution of Luminescence Lifetime of Nanometer Particles Containing Luminescent Ions Embedded in Media

Spontaneous emission rate is not only affected by the properties of the material itself, but also depends on the dielectric properties of the surrounding media. Recently, some work has been carried out to study the dependence of spontaneous emission rates of the luminescent-ion-containing nanometer particles on the refractive index of the media. Based on the free distribution of nanometer particles in media, the pro-bability density of luminescent lifetime is analyzed. Since nanometer particles distribute freely in media, the number of nanometer particles in a given volume surrounding the luminescent center obeys the Poission distribution. The local relative refractive index nr, which is the ratio of media effective refractive index to particle refractive index, is affected by the particle number of nanoparticles within a sphere of radius half of the radiative wavelength. The probability density function of nr can be obtained according to the dependence of nr on the particle number. Based on the relation between nr and luminescence lifetime, the analytical form of probability density function of lifetime is obtained. A calculation has been done based on the parameters given in Meltzer's experiment (Eu3 doped Y2O3 in methanol). The result shows that the relative fluctuation of luminescence lifetime is too small to be observed. However, with increasing size of nanometer particles or density of nanometer particles, the relative fluctuation of lifetime increases greatly and could be observed.