Multiphonon Relaxation in Glasses
Multiphonon Relaxation in Glasses
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眼镜中的多声子弛豫
DOI：
10.1007/978-1-4613-3174-2_15
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发表时间：
1980
期刊：
影响因子：
--
通讯作者：
R. Reisfeld
中科院分区：
文献类型：
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作者：
R. Reisfeld
离子在晶体、有机分子和半导体中的多声子弛豫理论在过去的二十年里引起了许多研究者的兴趣。一些评论已经写最近（1-6）处理这些重要的现象。对有机和无机体系中多声子弛豫的统一处理以及对现有理论的批判性评论可以在Englman的一本优秀的书中找到（7）。固体中稀土的激发电子能级通过激发晶格振动（声子）而非辐射地衰减。当激发能级和下一个电子能级之间的能隙大于声子能量时，会发射几个晶格声子来桥接能隙。人们认识到，最具能量的振动是造成非辐射衰变的原因，因为这种过程可以在最低阶保存能量。在玻璃中，能量最大的振动是玻璃网络多面体的拉伸振动，并且表明这些不同的振动在多声子过程中是活跃的（8），而不是RE与其周围配体之间的键的能量较低的振动。后来（9）证明，这些能量较低的振动可能参与了高能振动不能完全桥接能隙的情况。实验结果表明，多声子衰减率的对数与能隙或跨差距的声子数成线性关系。多声子机制的非辐射衰变理论首先由Kubo和Toyozawa（10）提出，他们提出允许这种跃迁的基本机制是由于离子的振动运动引起的Born-Oppenheimer（BO）近似中的校正，该离子的振动运动混合了电子波函数并导致代表零阶BO近似中稳态的跃迁。对于mUltiphonon过程，人们必须进行到更高阶的~ E/hw，以获得电子态之间的真实的跃迁（7）。应当指出，与辐射高阶过程的微小性相比，非辐射高阶过程的微扰程度相当高，从理论处理的角度看，精确计算高阶微扰是非常困难的。然而，~ Hvibr的相当大一部分可以通过”重整化“将其精确地包含在波函数中而作为微扰被消除。“~ Hvibr在重整化后仍然保留的部分是BO校正算子的不可逆性。在计算的最后，仅用一个声子模（1，5，11-13）的相互作用近似。对于小耦合和低温，得到了多声子弛豫率随声子数的分布的类泊松函数（12
The theory of multiphonon relaxation of ions in crystals, organic molecules and in semiconductors has attracted the interest of many researchers during the last two decades. A number of reviews have been written recently (1-6) dealing with these important phenomena. A unified treatment of multiphonon relaxation in both organic and inorganic systems as well as a critical review of the existing theories can be found in an excellent book by Englman (7). Excited electronic levels of rare earths (RE) in solids decay nonradiatively by exciting lattice vibrations (phonons). When the energy gap between the excited level and the next electronic level is larger than the phonon energy several lattice phonons are emitted in order to bridge the energy gap. It was recognized that the most energetic vibrations are responsible for the non-radiative decay since such a process can conserve energy in the lowest order. In glasses the most energetic vibrations are the stretching vibrations of the glass network polyhedron and it was shown that these distinct vibrations are active in the multiphonon process (8) rather than the less energetic vibrations of the bond between the RE and its surrounding ligands. Later (9) it was demonstrated that these less energetic vibrations may participate in cases when the energy gap is not bridged totally by the high energy vibrations. The experimental results reveal that the logarithm of the multiphonon decay rate decreases linearly with the energy gap, or the number of phonons bridging the gap. The theory of nonradiative decay by multiphonon mechanism was first proposed by Kubo and Toyozawa (10) who proposed that the basic mechanism allowing such transitions is the correction in the Born-Oppenheimer (BO) approximation due to vibrational motion of ions which admixes the electronic wave function and causes transitions that represent stationary states in the zero order BO approximation. For mUltiphonon processes one has to proceed to higher order being~ E/hw to get real transitions between the electronic states (7). It should be noted that in contrast to the smallness of the radiative processes of high order, the nonradiative high order processes are quite high.From the point of view of theoretical treatment, it is extremely difficult to calculate accurately the perturbation of a high order. However a considerable part of~ Hvibr can be eliminated as a perturbation by including it exactly in the wave function by a" renormalization." The part of~ Hvibr which still remains after renormalization is the nonadiabacity of the BO correction operator. At the end of the calculation an approximation is made of the interaction with only one phonon mode (1, 5, 11-13). For small coupling and low temperature a Poisson-like function is obtained (12) for the distribution of the multiphonon relaxation rate with the number of phonons