Kramers-Kronig-consistent optical functions of anisotropic crystals: generalized spectroscopic ellipsometry on pentacene
Kramers-Kronig-consistent optical functions of anisotropic crystals: generalized spectroscopic ellipsometry on pentacene
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DOI：
10.1364/oe.16.019770
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发表时间：
2008-11-24
期刊：
影响因子：
3.8
通讯作者：
Schubert, M.
中科院分区：
文献类型：
--
作者：
Dressel, M.;Gompf, B.;Schubert, M.
响应函数的实部和虚部之间的Kramers-Kronig关系在固体物理中被广泛使用，以便在只测量一个分量的情况下计算相应的量。它们是最基本的陈述之一，因为它们只基于物质反应的分析行为和因果性质[物理。修订本104,1760-1770(1956)]。例如，光学损耗可以从所有波长的介电常数的色散中获得，反之亦然[固体光学常数手册，第1卷，第35页]。尽管Kramers-Kronig关系的普遍有效性从未受到质疑，但Kramers-Kronig关系不能简单地应用于各向异性晶体材料，因为来自不同方向的贡献以一种与频率相关的方式混合，这是一个长期存在的问题。在这里，我们提出了一种识别与频率无关的主极化率方向的一般方法，即使在对称性最低的材料中也符合Kramers-Kronig关系。以三斜并五苯单晶表面的广义椭圆偏振光谱为例，计算了其复介电常数，并与沿晶体方向的能带结构计算结果进行了比较。给出了从低对称性晶面的宏观测量到Kramers-Kronig关系沿轴的晶胞微观介电性质的一般公式。(C)2008年美国光学学会
The Kramers-Kronig relations between the real and imaginary parts of a response function are widely used in solid-state physics to evaluate the corresponding quantity if only one component is measured. They are among the most fundamental statements since only based on the analytical behavior and causal nature of the material response [Phys. Rev. 104, 1760-1770 (1956)]. Optical losses, for instance, can be obtained from the dispersion of the dielectric constant at all wavelengths, and vice versa [Handbook of optical constants of solids, Vol. 1, p. 35]. Although the general validity was never casted into doubt, it is a longstanding problem that Kramers-Kronig relations cannot simply be applied to anisotropic crystalline materials because contributions from different directions mix in a frequency-dependent way. Here we present a general method to identify frequency-independent principal polarizability directions for which the Kramers-Kronig relations are obeyed even in materials with lowest symmetry. Using generalized spectroscopic ellipsometry on a single crystal surface of triclinic pentacene, as an example, enables us to evaluate the complex dielectric constant and to compare it with band-structure calculations along the crystallographic directions. A general recipe is provided how to proceed from a macroscopic measurement on a low symmetry crystal plane to the microscopic dielectric properties of the unit cell, along whose axes the Kramers-Kronig relations hold. (c) 2008 Optical Society of America