THEORY OF LIGHT ABSORPTION AND NON-RADIATIVE TRANSITIONS IN F-CENTRES
THEORY OF LIGHT ABSORPTION AND NON-RADIATIVE TRANSITIONS IN F-CENTRES
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DOI：
10.1098/rspa.1950.0184
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发表时间：
1950-01-01
影响因子：
--
通讯作者：
RHYS, A
中科院分区：
文献类型：
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作者：
HUANG, K;RHYS, A
本文根据Franck-Condon原理给出了F心吸收带形状的定量理论。这种处理的基础是两个简化的假设：（a）晶格可以近似地作为一个介电连续体处理;（B）在得到晶格的振动波函数时，F中心的影响可以看作是静电荷分布的影响。在这些假设下，它表明，作为频率和温度的函数的吸收常数可以表示在具有虚部参数的贝塞尔函数。吸收常数的理论曲线在所有温度下都与实验曲线相当。本文还考虑了非辐射跃迁的几率，这与F中心光吸收后所观察到的光电导是很重要的。所给的处理不同于迄今为止的定性考虑在一个重要方面，即，电子和晶格之间的耦合强度被考虑在内。用微扰法得到了讨论所需的F心电子的绝热波函数。激发态F中心通过非辐射跃迁回到基态的概率可以忽略不计;然而，如果激发态与导带的距离不超过0·1 eV，那么类似的跃迁到导带是很重要的。这种转变的温度依赖性是复杂的，但在很宽的温度范围内，类似于e-w/kT。初步估计表明，这一结果与所观察到的光电导电流随温度的急剧下降是一致的。
A quantitative theory for the shapes of the absorption bands ofF-centres is given on the basis of the Franck-Condon principle. Underlying the treatment are two simplifying assumptions: namely, (a) that the lattice can be approximately treated as a dielectric continuum; (b) that in obtaining the vibrational wave functions for the lattice, the effect of theF-centre can be considered as that of a static charge distribution. Under these assumptions, it is shown that the absorption constant as a function of frequency and temperature can be expressed in terms of the Bessel functions with imaginary arguments. The theoretical curves for the absorption constant compare very favourably with the experimental curves for all temperatures. Also considered in the paper are the probabilities of non-radiative transitions, which are important in connexion with the photo-conductivity observed following light absorption byF-centres. The treatment given differs from the qualitative considerations hitherto in one important aspect, namely, the strength of the coupling between the electron and the lattice is taken into account. The adiabatic wave functions for theF-centre electron required for the discussion are obtained by perturbation methods. The probability for an excitedF-centre to return to its ground state by non-radiative transitions is shown to be negligible; similar transitions to the conduction band are, however, important if the excited state is separated from the conduction band by not much more than 0·1 eV. The temperature dependence of such transitions is complicated, but, for a wide range of temperatures, resembles e-w/kT. Tentative estimates show that the result is Consistent with the observed steep drop of the photo-conductive current with temperature.