在晶体中，离子要在光谱范围内有发射，它的最低激发态应该低于导带较多。基质的禁带也应该较宽(所以一般是透明的，并且只能用紫外激发)。否则激发时，电子就可能直接到达导带或由激发态通过热激活而进入导带，之后的发光就不能保证一定是该中心的发光，而可能是复合发光，例如是导带电子和某种受主俘获的空穴的复合。这种情况虽然少见，但却不能排除。(《固体发光讲义》)
如何看懂能带图
参考：知乎-如何看懂能带图
直接带隙和间接带隙
- 直接带隙(GaAs, GaN, InN, InP)—导带底和价带顶在\(k\)空间中的同一位置，电子要跃迁到导带上产生导电的电子和空穴只需要吸收能量，而且更大的概率将能量以光子的形式释放出来。直接带隙半导体适合用于发光。吸收系数大，所以可以做成薄膜太阳能电池CdTe.
- 间接带隙(Si, Ge, AlAs, GaP)—导带底和价带顶在\(k\)空间中的不同位置，从一个状态到另一个状态必须改变动量(有声子参与)，而且大概率将能量释放给晶格，转化为声子的能量。声子提供的能量很少，little impact on the energy balance; but provide the required change of electron momentum. 声子参与的这个过程 are poaaible, but occur at much lower rate; therefore, the absorption coefficient is much reduced. Temperature has a big influence on absorption, because temperature affects the phonon populations. 由于间接带隙半导体的吸收系数小，所以silicon layer in photodiode and solar cell need to be thicker(几百微米)。
- 直接带隙半导体内电子和空穴很容易复合，虽然不一定发光，但是这是高效发光的前提条件。物理上也可用recombination lifetime复合寿命来表征。容易复合，也就是载流子的寿命更短。如用作LED芯片发光的GaN，载流子寿命为纳秒级。
- 硅是间接带隙，载流子寿命在微秒级别，发光效率低到根本不能用来发光。想让间接带隙材料发光，可以采用掺杂引入客发光体。
布洛赫波(Bloch Wave)波和稀土能级的Bloch state
- 在固体物理学中，Bloch Wave是周期性势场(如晶体)中粒子(一般为电子)的波函数。
- 价带和导带能级是delocalized Bloch state。
- 激发价带的电子到导带，使得价带留下一个空穴(a real hole in VB)，a hloe that can accept an electron.
- energy levels of Ln impurities—localized Bloch state.
- 65d1，那么这个激发态不能被看作是a hole state that can be filled by an electron. One can only treat it as a real hole state after the electron has been completely removed from the Ln, 也就是说激发出去的电子变成delocalized 然后Eu2+也转变为真正的Eu3+。参考
直接确定impurity level position
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光学带隙(optical bandgap)和电子学带隙(electronic/ transport bandgap)
(1) 来自band gap的维基百科
In materials with a large exciton binding energy, it is possible for a photon to have just barely enough energy to create an exciton (bound electron–hole pair), but not enough energy to separate the electron and hole (which are electrically attracted to each other). In this situation, there is a distinction between "optical band gap" and "electrical band gap" (or "transport gap"). The optical bandgap is the threshold for photons to be absorbed, while the transport gap is the threshold for creating an electron–hole pair that is not bound together. The optical bandgap is at lower energy than the transport gap.
(2) Electrical band gap is the minimal energy required to create an electron hole pair in a semiconductor, whereas optical band gap is the exciton energy which determines the onset of vertical interband transitions.
2O中，激子结合能分分别为\(\text{4 meV}\)和\(\text{10 meV}\)，激子在室温下(\(k_{\text{B}}T \approx \text{26 meV} \)
(1) 光学带隙和电子学带隙的经验公式： As a rule of thumb we will assume that \( E_{\mathrm{VC}}=1.08 E^{\mathrm{ex}} \approx \text{4.9 eV}\) (i.e., the binding energy of the electron-hole pair in the exciton is about \( 8\%\) of the exciton creation energy) ，\( E^{\mathrm{ex}}\)右上角的\(\mathrm{ex}\)表示的是exciton参考[Dorenbos_CM_2005] 这个是仅仅针对宽带隙的材料？
4基质发射的390 nm对应的激发峰(吸收峰)能量即为光学带隙，于是可以算出电子学带隙。参考[]
禁带宽度的测量和计算
来源小木虫(1) 带隙的理论计算；(2) 电学变温实验测量 (3) 紫外吸收谱；(4) 光电效应；(5) 光激发普；(6)Auger谱。
利用DFT可以计算带隙，但是误差很大，所以要开发不同方法矫正。，比如 To reduce the self-interaction error of DFT in band gap calculations, we used the Heyd–Scuseria–Ernzerhof (HSE) hybrid functional approach to evaluate the band gap and to compare with the PBE functional approach. [夏志国]
材料带隙测试精度本来就不高，这个和材料晶格以及所含的杂质有关，光学的方法对杂质非常敏感，因此不同人对同一材料的不同样品测出来就会有一定差别，想特别精确测量没有实际意义，即使精确测量，也是你这一个样品而已，换个样品可能就不是这个值了。
各种测试手段都有局限性，有的只是测试材料表面，不能代表材料的整体特性。光学的方法简单，是比较公认的方法；光电子谱不太准，终态不是电中性。利用电学方法测量带隙只是针对本征半导体，非本征半导体测到的是激活能。而且测量本征半导体要利用变温实验，然后用阿伦尼乌斯方程拟合计算。
绝缘体的测试：对于high bandgap materials (大于6 eV)，比如二氧化硅，氧化铝，then you need a vacuum UV (or synchroton) setup which may be more complex.
基质变化对发光的影响
3+掺杂CaTiO3中，interband absorption/transition导致了O2--to-Ti4+ electron transfer (LMCT)，然后a host electron−hole recombination Ti3+-to-O- takes place and its energy is nonradiatively transferred directly to the 1D2 level of Pr3+, which finally emits in red. 基质少许组分的变化或者处理工艺的变化are expected to produce local defects, which can modulate the electron−hole recombination energy in their proximities and, as a consequence, the selective energy transfer from the host to the 1D2 level of close Pr3+ ions.
Localization/Delocalization
参考：
固体发光材料—P118
New localized/delocalized emitting state of Eu2+ in orange-emitting hexagonal EuAl2O4
Persistent Emission of Narrowband Ultraviolet-B Light upon Blue-Light Illumination