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The mechanism of direct bonding at room temperature has been attributed to the short range inter-molecular and inter-atomic attraction forces, such as Van der Waals forces. Consequently, the wafer surface smoothness becomes one of the most critical parameters in this process. High surface roughness will result in small real area of contact, and therefore yield voids in the bonding interface. Usually, the root mean square roughness (RMS) or the mean roughness (Ra) are used as parameters to evaluate the wafer bondability. It was found from experience that for a bondable wafer surface the mean roughness must be in the subnanometer range, preferentially less than 0.5 nm. When the surface roughness exceeds a critical value, the wafers will not bond at all. However RMS and Ra were found to be not sufficient for evaluating the wafer bondability. Hence one tried to relate wafer bonding to the spatial spectrum of the wafer surface profile and indeed some empirical relations that have been found. The first, who proposed a theory on the problem of the closing gaps between contacted wafers was Stengl. This gap-closing theory was then further developed by Tong and Gosele. The elastomechanics theory was used to study the balance between the decrease of surface energy due to the bonding and the increase of elastic energy due to the distortion of the wafer. They considered the worst case by assuming that both wafers have a waviness, with a wavelength (lambda) and a height amplitude h, resulting in a gap height of 2h in a head to head position. This theory is simple and can be used in practice, for studying the formation of the voids, or for constructing design rules for the bonding of deliberately structured wafers. But it is insufficient to know what is the real area of contact in the wafer interface after contact at room temperature because the wafer surface always possesses a random distribution of the surface topography. Therefore Gui developed a continuous model on the influence of the surface roughness to wafer bonding, that is based on a statistical surface roughness model Pandraud demonstrated experimentally that direct bonding between processed glass wafers is possible. This result cannot be explained by considering the RMS value of the surfaces only, because the wafers used show a RMS value larger than 1 nm. Based on the approach exposed in reference six, a rigorous analysis of wafer bonding of these processed glass wafers is presented. We will discuss the relation between the bonding process and different waveguide technologies used for implementing optical waveguides into one or both glass wafers, and give examples of optical devices benefiting from such a bonding process.
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