Microelectronics

Intuitive Integrated Circuit Electronics by Thomas M. Frederiksen

By Thomas M. Frederiksen

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2 ppm;oC from Fig. 5). 65 ppm;oC. 2. Properties of Laminated Construction In the usual board manufacturing process [10] epoxy resin-impregnated and cured sheets of woven glass fabric (called "prepreg," such as FR-4) are laminated together between sheets of copper to form a core. Signal and power cores are sandwiched together under temperature and pressure. Electrical connections between different planes are formed by drilling holes through the core and copper-plating the hole walls. Circuit lines are made either by additive plating or subtractive etching of the copper sheets.

The structural solution is then performed, resulting in node displacements {D}. 46) Special care must be exercised to correctly calculate stresses along interfaces of two materials; in circuit boards this may correspond to a copper conductor bonded to epoxy glass, with greatly different moduli. 7 shows the stresses along the juncture: (T y and t xy must be continuous across the boundary; however, (Txl should not be equal to (Tx2' If the structure is a strip in the x-direction, subjected to temperature rise, then the unequal expansion properties of the neighboring materials should, in fact, induce normal stresses (T x of opposite sign on two sides of the interface.

71) may be integrated. 6. Energy Methods in Structural Analysis The principle of stationary potential energy requires the variation of the latter to vanish for an elastic body in equilibrium: <5V = O. 72) Under static loading the total potential energy V = U + Q, where U is the strain energy and Q the potential energy of external loads; both are integral expressions over the body. Inserting these into Eq. 72) the differential equation of the problem together with the natural boundary conditions can be extracted [12].

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