Surface second harmonic generation

Surface second harmonic generation is a method for probing interfaces in atomic and molecular systems. In second harmonic generation (SHG), the light frequency is doubled, essentially converting two photons of the original beam of energy E into a single photon of energy 2E as it interacts with noncentrosymmetric media. Surface second harmonic generation is a special case of SHG where the second beam is generated because of a break of symmetry caused by an interface. Since centrosymmetric symmetry in centrosymmetric media is only disrupted in the first (occasionally second and third) atomic or molecular layer of a system, properties of the second harmonic signal then provide information about the surface atomic or molecular layers only. Surface SHG is possible even for materials which do not exhibit SHG in the bulk. Although in many situations the dominant second harmonic signal arises from the broken symmetry at the surface, the signal in fact always has contributions from both the surface and bulk. Thus, the most sensitive experiments typically involve modification of a surface and study of the subsequent modification of the harmonic generation properties.

History Second harmonic generation from a surface was first observed by Terhune, Maker, and Savage at the Ford Motor Company in 1962, one year after Franken et al. first discovered second harmonic generation in bulk crystals. Prior to Terhune's discovery, it was believed that crystals could only exhibit second harmonic generation if the crystal was noncentrosymmetric. Terhune observed that calcite, a centrosymmetric crystal which is only capable of SHG in the bulk in the presence of an applied electric field which would break the symmetry of the electronic structure, surprisingly also produced a second harmonic signal in the absence of an external electric field. During the 1960s, SHG was observed for many other centrosymmetric media including metals, semiconductors, oxides, and liquids. In 1968, Bloembergen et al. showed that the second harmonic signal was generated from the surface. Interest in this field waned during the 1970s and only a handful of research groups investigated surface SHG, most notably Y. R. Shen's group at University of California at Berkeley. During the 70s and 80s, most of the research in this field focused on understanding the electronic response, particularly in metals. In 1981, Chen et al. showed that SHG could be used to detect individual monolayers, and since then, much research has gone into using and understanding SHG as surface probe of molecular adsorption and orientation. SHG was later extended to vibrational sum frequency generation spectroscopy (VSFG) and further extended to heterodyne-detected VSFG (HD-VSFG).

Excitation of second harmonic signal Just as bulk second harmonic generation, surface SHG arises out of the second-order susceptibility tensor χ(2). While the χ(2) tensor contains 27 elements, many of these elements are reduced by symmetry arguments. The exact nature of these arguments depends on the application. When determining molecular orientation, it is assumed that χ(2) is rotationally invariant around the z-axis (normal to the surface). The number of tensor elements reduces from 27 to the following 7 independent quantities: χZZZ, χZXX = χZYY, χXZX = χYZY, χXXZ = χYYZ, χXYZ = −χYXZ, χXZY = −χYZX, χZXY = −χZYX. Second Harmonic Generation further restricts the independent terms by requiring the tensor is symmetric in the last two indices reducing the number of independent tensor terms to 4: χZZZ, χZXX (equivalently χZYY), χXXZ (equivalently χXZX, χYZY, χYYZ), χXYZ (equivalently χXZY, −χYXZ, −χYZX). In order for χZXY = −χZYX to hold under this final condition, both terms must be 0. The four independent terms are material dependent properties and can vary as the external conditions change. These four terms give rise to the second harmonic signal, and allow for calculation of material properties such as electronic structure, atomic organization, and molecular orientation. Detailed analysis of the second harmonic generation from surfaces and interfaces, as well as the ability to detect monolayers and sub-monolayers, may be found in Guyot-Sionnest et al.

Applications

Interface structure

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