发光基础概念

• 光是电磁波, 是信息的载体。频率、波长、相位、振幅、偏振、 模式等等 (信息技术基础)
• 光由光子(粒子)构成, 是能量的载体 (能源技术基础)
• 光与物质发生电磁相互作用, 反映物质内部的信息, 并改变物质的属性 (物质科学技术基础) ——李志远(华南理工)
• From a puzzling experimental result to its interpretation, to the development of a general concept, and finally, to the prediction of new phenomena or the development of a new method - this is the line which can be traced in many of his studies. (P.P. Feofilov and the Spectroscopy of Activated Crystals)

吸收和发射

(1) 进一步延伸，如果过来

(2) 以激光介质为例子，可描述为将激光介质中每个吸收光强的粒子视为一个小光删，它将入射到介质中的光挡掉, 而吸收截面就是这个小光删的横截面积。
(3) 微分散射截面：$$\displaystyle\frac{d \sigma}{d \Omega}$$是对散射截面关于空间立体角求导的结果，由于空间立体角无量纲，所以导数依然具有面积的量纲。总的散射截面$$\sigma$$等于微分散射截面$$\displaystyle\frac{d \sigma}{d \Omega}$$对全空间立体角的积分$$\sigma=\displaystyle\int \frac{d \sigma}{d \Omega} d \Omega$$。参考如何理解微分散射截面?-知乎

(1) 无论是吸收系数还是吸收截面，都和波长有关，所以上式其实可以写成
$$I(\nu)=I_{0}(\nu) \exp (-\alpha(\nu) L)$$

(2) [Optically stimulated detrapping during charging of persistent phosphors-OME-2016]文章中的$$p$$ 既不是吸收截面，也不是吸收系数，而是“吸收截面×光通量”；
(3) 温度升高会造成吸收峰的展宽，随着温度的升高，有的激发波长的吸收可能变大了，有的反而变小了。[Andries_CM_2009] (4) 温度升高会造成吸收峰的展宽，可能使得reabsorption增强，QE降低。

Temperature dependent reflection spectroscopy is useful to study: [Thomas Jüstel-PPT]

•  body color shift
•  band gap shift
• QE drop with temperature

朗伯比尔定律

(1) 入射光是平行、单色、垂直入射
(2) 溶液均匀，而且是非散射体系(肉眼看是澄清的)
(3) 溶液中的分子彼此之间没有相互作用(这要求为稀溶液，低于0.01摩尔每升)
(4) 入射光不引起溶液中反应的发生。
(5) 高浓度时，吸光粒子之间的平均距离减小，粒子间的电荷分布相互影响作用，那么吸收系数也会发生变化，导致偏离比尔定律。

$$\log _{10} \displaystyle\frac{I_{t}}{I_{0}}=-K \cdot l \cdot c$$和$$\ln\displaystyle\frac{I}{I_{0}}=-\sigma Ln$$，其实就是左右两侧同时乘以一个常系数。参考换底公式$$\ln x=\log _{e} x=\frac{\log _{10} x}{\log _{10} e}$$

寿命

Mono-exponental decay
(其中$$N^*(t)$$表示激发态粒子的数目)  [Jonas-course-PhD] $$\begin{array}{l} { dN^*(t) }/{ dt }=-\omega^{\text{rad}}_{1\rightarrow 2}(N^*(t)) \\ N^*(t=0)=N_0 \end{array}$$解为$$N^*(t) =N_0\text{exp}({-\omega^{\text{rad}}_{1\rightarrow 2}\cdot t})=N_0\text{exp}({ -t }/{ \tau } )$$所以发光强度随时间的变化关系为$$I(t)= -\displaystyle\frac{ dN^*(t) }{ dt }=\omega_{1 \rightarrow 2}^{\text{rad}}N_0\exp \left(\frac{-t}{\tau}\right)=I_0\exp \left(\frac{-t}{\tau}\right)$$(1) The value of $$\tau$$ depends strongly on the tyle of electronic transition
(2) shows dependence on emission energy(color), like CaS:Eu2+(red, 715 ns) and SrGa2S4:Eu2+(green, 450 ns)
(3) and depens on the medium's refractive index (local field effect), like SrSi2O2N2:Eu2+ and SrGa2S4:Eu2+
(4) 这里的$$\omega_{1 \rightarrow 2}^{\mathrm{rad}}$$包含了通过辐射跃迁回到基态，以及非辐射跃迁回到基态的情况，两种情况可以简单的叠加处理，如果处于激发态的电子没有回到基态(比如被trap捕获)，那么就不是简单的叠加为一个整体的$$\omega$$，大概率是双指数的情况。
(5) 注：我们在推导基于Single barrier model的热稳定性的时候，将和温度有关的非辐射跃迁和温度无关的辐射跃迁几率是直接叠加为一个总的跃迁的，这是默认对应于同一类发光中心，否则的话，就是双指数了。

Bi-exponential decay

$$I(t)=I_{1} \mathrm{e}^{-t / \tau_{1}}+I_{2} \mathrm{e}^{-t / \tau_{2}}$$其中$$\tau_{1}$$和$$\tau_{2}$$适合材料有关的本征的物理量，而$$I_{1}$$和$$I_{2}$$的大小受测试条件影响，只有$$I_{1}/I_{2}$$本身才有物理意义。

The fraction in the total emission intensity assigned to each $$\tau_{i}$$ component: $$f_{i}=\frac{\displaystyle\int I_{i} \mathrm{e}^{-t / \tau_{i}} \mathrm{~d} t}{\displaystyle\int I(t) \mathrm{d} t}=\frac{I_{i} \tau_{i}}{I_{1} \tau_{1}+I_{2} \tau_{2}} \quad(i=1,2)$$双指数衰减是两种独立发光衰减过程的(线性)组合，假设$$I_1$$的发光来自state-1，$$I_2$$的发光来自state-2，对于这两个状态的退激发过程，均同时考虑辐射跃迁和非辐射跃迁。那么在脉冲激发后的瞬间，处在state-1的粒子数目为$$A_1$$，处在state-2的粒子数目为$$A_2$$。

• SrAl2O4:Eu2+,Dy3+在370 nm下的绿光峰寿命，在100 K时是单指数(和稀土本征发光有关)，然后随着温度的升高，变为双指数(增加了一个fast decay component)，新增加的部分作者认为和trapping process有关。注意虽然出现了双指数，但是初始的和稀土本正发光有关的成分的寿命还是保持不变。[Philipe_PRB_2014]
• Eu2+处在两种格位，对应的发光峰有重叠，如果检测重叠区域的发光衰减寿命，那么就会是双指数。
• Eu3+处在两种格位，那么可以通过site-selective spectroscopy来测出不同的单指数衰减的寿命(理想情况)。对于普通的光谱寿命测试，由于激发光的单色性不好(或者说同时覆盖两种Eu3+格位的激发谱)，因此可能得到双指数的衰减，分别对应不同的Eu3+的格位(不同的对称性)，参考文献[JSSC-2005]。
• CaGd2(1-x)Eu2x(WO4)4中，Interestingly, we can consistently fit the thermal behavior of the decay for different dopant concentrations with only two types of Eu ions (i.e. isolated ones and those showing energy transfer), both characterized by their own specific thermal behavior.
低掺杂浓度，Eu2+表现为本征的发光，寿命随温度变化不大，表现为孤立的发光中心，单指数衰减(忽略475 K的情况)；全掺杂，Eu3+表现为都可以实现energy transfer，所以也是单指数衰减；对于中等浓度掺杂，有部分Eu2+表现为孤立发光中心的特点有部分Eu2+表现为可以实现energy transfer的特点。参考[OE-2014]
• Sr1−xEuxGa2S4, 也是低掺杂浓度下，表现为单指数衰减，随着掺杂浓度的升高，出现了双指数衰减的形式，其中一个指数保留了之前单指数衰减时的寿命，另一个指数的衰减寿命更短(对应的是non-radiative decay)，内量子效率也随着fast component decay的出现以及比例的增加而减小。At low concentration (x < 5%), the majority of the dopant ions can be considered as isolated centres, and the decay profile is described by a single exponential decay. For higher dopant concentrations, a second type of configuration is formed for which the lifetime is considerably shorter, presumably due to energy transfer between nearby Eu centres, and locally approaching the situation in EuGa2S4. 对于高掺杂浓度的样品，虽然同时有两种Eu存在，但是在低温下75 K二者表现出差不多的衰减特性，因此寿命测试上不可区分，即都可以用单指数拟合寿命曲线，而且和低浓度掺杂样品在75 K下的寿命差不多。参考[Jonas—OM-2012]。

Molecules数衰减的特点

• Typically, molecules exhibit nicely monoexponential decay. This is because molecules, especially dyes, are more well-behaved
• Molecules can deviate from monoexponential behavior for a few reasons:
• Intramolecular charge transfer
• Excimer formation (excited dimer)
• Solvent effects

Nanomaterials数衰减的特点

Nanomaterials, on the other hand, rarely exhibit well-behaved monoexponential decay. 常见的原因如下

• Quantum dots (QDs) have 1000's of atoms (compared to handful for molecules), thus more states that can lead to compete de-excitation pathways.
• Surface states play a huge role in many QDs for adding emissive and nonemissive pathways. 比如量子点表面没有被钝化(Passivation)，那么处在表面的原子可能有dangling bonds猝灭发光。
• Interplay of bright and dark states is higher.

Tips

• 高掺杂浓度下，重吸收明显，重吸收会导致寿命增加。It is well-known that reabsorption of emission gives rise to a longer decay time.[Andries_CM_2009]
• 低掺杂浓度下的寿命更能反映本征的寿命。 [Andries_CM_2009]
• 寿命也可以描述为发光强度衰减到初始强度$$1/e$$所需的时间。
• 已知在$$t$$和$$t+\Delta t$$时间内有$$\Delta n$$个电子回到基态，这些粒子的寿命就是$$t$$，因此平均的寿命为$$\displaystyle\sum_{t=0}^{\infty} t \Delta n / n_{0}$$，写成积分的形式为(参考[固体发光讲义-许少鸿-P14])$$\text{average lifetime}=\frac{1}{n_{0}} \int_{0}^{\infty} t \alpha n_{0} e^{-\alpha t} d t=\alpha \int_{0}^{\infty} t e^{-\alpha t} d t=\alpha\left[\frac{e^{-\alpha t}}{\alpha^{2}}(-\alpha t-1)\right]_{0}^{\infty}=\frac{1}{\alpha}=\tau$$
• 常见发光中心的寿命[Thomas Jüstel-PPT]

量子效率

(1) at the level of the phosphor (in most cases)
(2) at the level of the luminescent ion.

EQE = ​吸收*IQE, 对荧光粉来说，增加掺杂浓度可以提高吸收的比例，但是IQE会下降(浓度猝灭)，所以there exists a trade-off between the increasing absorption (and emission) and a decrease in the internal quantum efficiency due to concentration quenching. [Philipe_JES_2011]

(1) 最好不要用寿命计算量子效率。
(2) 如果吸收比例很低，那么可能出现内量子效率很高，但是外量子效率很低的情况。
(3) 影响外量子效率的吸收率，不仅与荧光粉材料有关，也和荧光粉的颗粒大小，表面形貌有关，甚至实际中的使用环境也有关。
(4) Even when a material has a high quantum - or conversion - efficiency, the energy efficiency is limited by the Stokes shift.
(5) 量子效率也和激发光的强度有关，参考David-Acs Photonics-2017
(6) Quantum yield and brightness-JL-Peter A. Tanner
(7) QE和QY的差异，不同领域(photoluminescence, photochemistry, photovoltaics)的定义也有差异，参见researchgate的问答以及爱思唯尔的资料

(热)猝灭/热稳定性

Single barrier model  ($$E_{\text{Mott}}$$) 或者 Mott-Seitz model
Expression with Boltzman factor: $$\omega_{1 \rightarrow 2}^{\mathrm{n-rad}}(T)=s\text{exp}(\frac { -E_{\text{Mott}} }{ k_\text{B}T } )$$ Yields (其中$$I_0$$表示的是温度为绝对零度即非辐射跃迁强度为零的情况下的发光强度)
$$I(T)=\frac{\omega_{1 \rightarrow 2}^{\text {rad }} }{\omega_{1 \rightarrow 2}^{\text {rad }} +\omega_{1 \rightarrow 2}^{\text {n-rad }} }I_{0}=\frac { I_0 }{ 1+\frac { s }{ \omega_{1 \rightarrow 2}^{\text{rad}} } \text{exp}(\frac{-E_{\mathrm{Mott}}}{k_{\mathrm{B}} T})}$$ $$T_{0.5}=\frac {E_{\text{Mott}} }{k_{\text{B}}\ln(\frac { s}{\omega_{1 \rightarrow 2}^{\text{rad}} } ) }$$Influence on lifetime: two decay mechanism:$$\begin{array}{l} \displaystyle\frac{d N^{*}(t,T)}{d t}=-\omega_{1 \rightarrow 2}^{\mathrm{rad}}N^*(t,T)-\omega_{1 \rightarrow 2}^{\mathrm{n-rad}}(T)N^*(t,T) \\ N^*(t=0) =N_0 \end{array}$$ Yields:$$N^*(t)=N_0\text{exp}{(-\omega_{1 \rightarrow 2}^{\mathrm{rad}}t-\omega_{1 \rightarrow 2}^{\mathrm{n-rad}}(T)t)}=N_0\text{exp}(-\frac { t }{ \tau^\text{rad} }-\frac { t }{ \tau^{\text{n-rad}}(T) } )=N_0\text{exp}(\frac {-t }{ \tau(T) } )$$Monoexponential decay maintained, but with effective lifetime. 这里的$$\omega_{1 \rightarrow 2}^{\mathrm{rad}}$$和$$\omega_{1 \rightarrow 2}^{\mathrm{n}-\mathrm{rad}}$$的比值也是处在激发态的电子选择辐射跃迁还是非辐射跃迁的概率(比例)。

Temperature dependent lifetime (图片来源)(1) In first order, the decay time of the luminescence is following a similar thermal behavior than the intensity quenching [Philipe_JES_2011]描述的也是上图。
(2) SrAl2O4:Eu2+,Dy3+中，370 nm激发下的蓝光，也有类似现象。This correlation between thermal quenching and luminescence lifetime can be expected, due to the increased probability of nonradiative decay paths at elevated temperature, thus lowering the emission intensity and reducing the luminescence lifetime values.[Philipe_PRB_2014]

Mott的single barrier存在的问题是什么？[Jonas course and PhD]

Struck-Fonger Model

Struck and Fonger have shown that the temperature dependence of a non-radiative process is accurately described by considering ground and excited state vibrational wave function overlap. According to the Struck–Fonger model, the non-radiative process occurs through tunneling (crossover) from a vibrational level of the excited state to a high vibrational level of the ground state. The tunneling rate, i.e., the non-radiative decay rate, depends on the wave function overlap of the vibrational levels involved. The tunneling rate will be faster for a larger overlap between the wave functions and when the vibrational levels are in resonance. [Quenching of the red Mn4+-Light-2018]

Mott-Seitz model和公式Struck-Fonger Model差别(公式差不多)：The two commonly used models are the simple Mott model of the activation energy and the more-sophisticated model of Struck and Fonger using the socalled single-configurational-coordinate model, which describes in a simplified way the interaction between the electronic center and the vibrating crystalline environment. [Springer Handbook of Lasers and Optics edited by Frank Träger]-P676

(1) thermal barrier for trap filling versus thermal barrier for PL

在220 K用435 nm光激发样品，然后测TL，会发现没信号，说明存在thermal barrier for trap filling。注意thermal barrier for trap filling和thermal barrier for PL (导带模型)是不一样的，有联系(后者很大的，前者往往也表现明显)，但是不完全一样，因为临界温度(threshold)不同，前者是220 K，后者350 K，对应的能量显然也不同。[Philipe_PRB_2014]

(2) 另外三幅图来自[Thomas Jüstel-PPT]，他认为100-500 K时是Re-absorption导致了量子效率的下降，继续升高温度，IQE decreases due to IC and/or PI

Thermal energy的三重影响(对Eu2+或者Ce3+掺杂荧光粉) [Philippe_JL_2012]

• 热稳定性和长余辉此消彼长我们常用的硅酸盐、铝酸盐长余辉荧光粉(Eu2+or Ce3+)，在室温下很容易实现可见光下(afterglow upon excitation into the lower 5d states. )的有效trap filling(非常低的温度可能也不行)，这也往往伴随着比较差的热稳定性。筛选Eu2+掺杂的长余辉材料(yellow-to-red emission that can be excited with blue-to-green light)，最好是PL热稳定性差的材料，这样更容易室温下用可见光填充traps，当然热稳定性也不能太差，否则trap filling存储的能量都以非辐射跃迁的形式释放了。[Philippe_JL_2012]
• 缺陷增强热稳定性-1：
K2BaCa(PO4)2:Eu2+通过计算认为绿色的那一段上升(zero thermal quenching)和氧空位有关。Drapping需要的能量大于thermal ionization所需的能量对于良好的热稳定性来说很重要。[夏志国_JACS_2018]
• 缺陷增强热稳定性-2：
Na3-2xSc2(PO4)3: xEu2+荧光粉，高温下会出现的Na+ disorder。Te emission losses induced by nonradiative paths were eﬀectively suppressed by a counter mechanism, which associated structural transformation leads to the formation of defect levels that can act as electron-trapping centres, favouring an energy transfer to the activator (Eu2+), which can counteract the quenching behaviour.[Jonas_NM_2017] 但是复旦大学闫世润老师给出了不同的解释，他认为该荧光粉分热稳定性不好。

(2) Thermal ionization is the thermally activated electron transfer process to the CB.

Tips:
(1) Quenching temperature : defined as the temperature where the emission intensity has dropped by 50 %.

(2) 对于高功率LED来说，荧光粉的热稳定性很重要，因为高功率意味着flux大，荧光粉工作温度高。YAG荧光粉就是热稳定性差，不太适合高功率LED。
(3) f-f emitter热猝灭机理：[Philipe_JES_2011] (3-a) phonon-activated crossing of the excited state and the charge transfer state
(3-b) multi-phonon emission
(4) 荧光粉的热稳定性和掺杂浓度有关，比如YAG:Ce3+，低掺杂浓度下的热稳定性非常好(700 K)，但是实际商用的掺杂浓度其实比较高，而且猝灭温度很低(400 K)就有明显的发光强度的下降(这可以用thermally activated concentration quenching解释)。[Andries_CM_2009] (5) 研究热猝灭原因，最好采用寿命作为研究对象(反映intrinsic quenching)，因为温度影响吸收的强度(the absorption strength is strongly temperature-dependent)，也会影响能量的migration和reabsorption，因此luminescence lifetime measurement are performed to provide better insight into the quenching temperature for Ce3+ emission。[Andries_CM_2009] (6) 低掺杂浓度下YAG:Ce有higher thermal quenching temperature。利用这一点可以制备YAG:Ce半透明(translucent)陶瓷，让掺杂浓度低一点，这样猝灭温度高，而厚的透明陶瓷可以让激发光通过更长的optical pathway，以弥补其相对于高掺杂浓度荧光粉吸收能力的差距。

隧穿(Quantum tunnelling)效应

(1) Temperature Independent Quantum tunnelling

Quantum tunnelling may be temperature independent but is critically dependent on the distance between the hole and trapping center. So one might expect that this plateau will rise as more hole and trapping centers are available, decreasing the average distance between the recombination center (Ce4+) and trapping center (Ln2+); in other words, as the concentration of the dopants increases.

(2) Thermally assisted Quantum tunnelling
Recombination pathway is via an excited state of the trapping center. 如右上图(2)过程，the population of the excited state is by thermal activation, causing the thermally assisted tunnelling to become temperature dependent。有人研究长余辉材料Ce-doped Gd3Al2Ga3O12，发现好几个不同温度的peaks都对应着差不多的trap depth，他们将其归因于electron  stored in oxygen vacancies recombine through a thermally assisted tunnelling mechanism with holes localized at Ce3+ centers residing on Lu sites at different crystallographic distances from the traps.

德拜温度(结构刚性)

Eu2+的发光受配位环境影响。Hence, it is intuitively projected that the loose structural framework of material will accommodate a strong lattice relaxation, which possibly results in the severe luminescence dissipation. This viewpoint makes sense for the analysis in the material incorporated by Ce3+ which owns an analogous 4f-5d luminescence as that of Eu2+, and it rationally interprets the remarkable luminescence performance of Ce3+ in compounds with dense structural frameworks. Also, stemming from this understanding, the strong struc-tural rigidity of lattice is conceived as the prerequisite for Ce3+ to acquire superior transition properties,  and this hypoth-esis has been accepted in the field and adopted to explain the advanced feature of phosphor frequently. 文中作者也举出高效Eu2+发光，但是结构不够刚性的例子。文中，作者还用红外/拉曼光谱、热容测试证实文章材料的没那么刚性。但是最后作者解释Eu2+发光强的原因是，weak electron-vibration interaction is the reason for the generation of narrow-band luminescence, which is essentially attributed to the highly rigid local coordination of Eu2+. This weak electron-vibration interaction also diminishes the nonradiative relaxation probability of excited Eu2+, and in combination with the experimental findings as collected from the X-ray spectroscopy, it proves that the deleterious impact of electron ionization on Eu2+ luminescence is suppressed, which consequently assures the superior luminescence efficiency of Eu2+-doped SMPO material.

光电导/霍尔效应

• 通过光电导，可以看main charge carrier是电子还是空穴，从而证实是荧光粉是hole trapping还是electron trapping。
• 霍尔效应：磁场中运动的载流子受洛伦兹力作用，于是在极板上聚集形成电场(应该是材料放在溶液中？)，电场力与洛伦兹力达到平衡于是两极板间有稳定的电压。测试哪一侧为正极即可判断多数载流子是电子还是空穴。
• 光电导研究Ce3+的比较多，注意
(1) 冯昂说透明陶瓷的，very shallow layer engaged in conductivity。

(2) 制备透明陶瓷，粉末要细。

波长和能量转换&分峰

David的文章中$$\displaystyle\frac{\mathrm{d} \phi(E)}{\mathrm{d} E} \sim \lambda^{2} \displaystyle\frac{\mathrm{d} \phi(\lambda)}{\mathrm{d} \lambda}$$，实际上根据$$\displaystyle \int_{a}^{b} f(x) \mathrm{d} x=\displaystyle \int_{\alpha}^{\beta} f(x(u)) \displaystyle\frac{\mathrm{d} x}{\mathrm{~d} u} \mathrm{~d} u$$，有$$\int_{a}^{b} I(\lambda) \mathrm{d} \lambda=\displaystyle\int_{\alpha}^{\beta} I(\lambda(E)) \frac{\mathrm{d} \lambda}{\mathrm{~d} E} \mathrm{~d} E$$其中$$\lambda(E)=\displaystyle\frac { 1024 }{ E }$$，$$\displaystyle\frac{\mathrm{d} \lambda}{\mathrm{d} E}=-\displaystyle\frac { 1024 }{E^2 }$$，代入之后得。

Periodic table of the "lighting" elements

(1) 低压钠灯：工作时其电弧管内的蒸汽压为0.7～1.5 Pa，光近乎单色，集中在589 nm和589.6 nm，对人眼较敏感的黄光区域，所以发光效率高达150流明/瓦以上，但显色性太差，只用于不需分辨颜色的场合。可作为旋光仪、折射仪、偏振仪等光学仪器中的单色光源。
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