Abstract

The rate of the multiphonon relaxation of the 1s(T₂) level in Se⁺ donors in silicon is estimated. The calculation comprises the initial approach to the problem, in which the most simplified form of wave functions is used. To evaluate the transition probability, the Pässler expression known from publications is used [R. Pässler, Czech. J. Phys. B 24, 322 (1974)]. This expression was derived in terms of the so-called static approximation. The deformation potentials of optical and acoustic phonons were determined by the fitting procedure using published data on the luminescence spectrum of Se⁺ donors at the 1s(T₂)–1s(A₁) transition and Franck–Condon principle. Evaluation for the relaxation rate of 10³ s^–1 turned out to be five orders of magnitude smaller than the rate corresponding to the experimentally measured lifetime. The cause of disagreement with the experiment is the excessively simplified model, which does not taking into account several factors, the main one being the presence of quasi-local oscillatory modes. Analysis of the luminescence spectrum based on the mentioned transition leads to the conclusion that the energies of such oscillatory modes lie in the range from 26 to 61 meV. To attain satisfactory agreement with the experiment, the model should be made more complex taking into account the interaction with these modes.

中文翻译：

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硅中单电离硒供体1 s（T 2）态的多声子弛豫。

摘要

估算了硅中Se ⁺供体中1 s（T ₂）能级的多声子弛豫速率。计算包括解决问题的初始方法，其中使用了最简化形式的波动函数。为了评估过渡概率，使用了出版物中已知的Pässler表达式[R. 捷克共和国的派斯勒。J.物理 乙24，322（1974）]。该表达式是根据所谓的静态逼近得出的。光学和声学声子的形变电势通过拟合程序，使用关于Se ⁺供体在1 s（T ₂）-1 s时发光光谱的公开数据确定（A ₁）过渡与弗兰克-康登原理。10 ³ s ^–1的弛豫速率的评估结果比对应于实验测量的寿命的速率小五个数量级。与实验不一致的原因是模型过于简化，该模型未考虑多个因素，主要因素是存在准局部振荡模式。基于所述跃迁的发光光谱的分析得出这样的结论，即这种振荡模式的能量在26至61meV的范围内。为了与实验取得令人满意的一致性，应考虑与这些模式的交互作用，使模型更复杂。