The Bonding Unit

Let us now construct a representation of the electronic structure of SiOj. There have been many early studies of Si02, principally aimed at interpreting various experimental spectra these have been reviewed recently by Ruffa (1968, 1970). More recently, studios based upon calculations for large clusters of atoms have been made by Reilly (1970), Bennett and Roth (1971a,b), Gilbert ct al. (1973), and Yip and Fowler (1974). Most recently, a full, self-consistent pseudopotential calculation on quartz was made by trhelikowsky and Schliitcr (1977). Here, we shall 

A bonding unil in Si02, showing the coordinate system and the orbitals that are included. 

This reduces the problem to two equations in two unknowns, as in Eq. (3-11). The eigenvalue for and the eigenvalue from the corresponding treatment of 6, arc 

By analogy with the treatment of the bond orbitals in Chapter 3, we can also write down the corresponding bond orbitals  

Bond orbitals for the SiOj bonding unit. All are doubly occupied. The antibonding combinations A. and A, obtained by reversing the sign of the p states in B and arc empty. 

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If the functional group is a carbon species [i.e. —C=C—, —C=N, —CHO, —COR, —C02H(R)], then a possible disconnection point would be the bond uniting the a-carbon to the functional group carbon, as is found with alkynes (Section 5.3), aldehydes (Section 5.7), ketones (Section 5.8), carboxylic acids (Section 5.11) or their derived esters (Section 5.12.3, p. 695). Alternative disconnection points which would be worth considering are the a, / - and / , y-carbon bonds, in for example aldehydes or ketones. 

Extension of the calculation to the polar counterparts of Si02, such as aluminum phosphate, is also quite direct and can be made without the introduction of any new parameters. The energies of the two hybrids in the bonding unit now differ, - = 21/j, but the hybrid energies arc just those given in Table 2-2. We must generalize the bond orbital by allowing different coefficients for /i,> and j/jj) in Eq. (11-2), and must solve a cubic rather than a quadratic equation. 

Orbitals of the bonding unit when it i.s taken to be straight () = 0), as in /1-cristobalite. This approximation simplifies the understanding of the Si02 spectra. The dark dot at. the center of each combination of orbitals is the oxygen nucleus. 

These considerations argue against the interpretation of the optical spectra in terms of the bonding unit used by Pantclides and Harrison (1976) to obtain parameters W2 and IT,. Nonetheless, we sec by comparison between the bands of Panlilcdes and Harrison and those of Chelikowsky and Schliiter (Fig. 11-9) that the matrix elements of Pantelidcs and Harrison were approximately correct. This was really not accidental since they considered many properties simultaneously and only used optical properties to fix exact final values. In fact, the use of larger... 

Wc can directly calculate the dielectric susceptibility by following the procedure that led to Eq. (4-28) for the dielectric susceptibility of the tetrahedral solids that is, we calculate the polarizability of the bonding unit. We do not introduce a scale factor y therefore, we obtain a direct prediction of the corresponding contribution to the susceptibility. We may expect it to be rather good since scaling is necessary principally in the tetrahedral solids for high-metallicity systems with narrow gaps between bands. 

Within the Si02 bonding unit, only the orbitals B, and B. change when the bonding unit is distorted, and the sum over the energies of the four electrons occupying them gives... 

One other transverse-charge parameter can be evaluated. That parameter, 5p gives the change in dipole in the x-direction due to the change in distance R between the two silicons in the bonding unit (the distance between the oxygen and the Si—Si axis is held fixed). Its evaluation is closely related to the calculation of e leading to Eq. (11-17) and can be written as... 

Another approach to 3D integration is to use wafer bonding to stack die before singulation this approach is referred to as wafer-level 3D. There have been a variety of approaches to wafer-level 3D that have been demonstrated, which can be categorized by the wafer-bonding approach used oxide-to-oxide, copper-to-copper, polymer-to-polymer (or adhesive bonding), and mixtures of these approaches (such as redistribution layer bonding). Each of these four approaches will be introduced in this section, with emphasis placed on their application to 3D. The bond unit processes are described further in Section 15.4.2, and their associated CMP issues are discussed in detail in Section 15.5. 

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