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70 60 Theta-ja ( C/ W) 25 mm traces 50 40 30 20 0 20 40 60 80 Ground plane length (mm) 100 120 15 mm traces

FIGURE 17.6 The effective qja of a 12 12 mm Chip scale package (CSP) with 49 thermal balls as a function of the (x,y) length of a continuous thermal plane under the package. Two trace lengths were assumed, showing different amounts of coupling of heat from the traces into the plane.

TABLE 59.1 Typical Thermal Cycle Test Parameters for Second-Level Reliability Qualification Parameter Maximum temperature (Tmax) Minimum temperature (Tmin) Ramp rates from Tmin to Tmax and Tmax to Tmin Dwell time at Tmax and Tmin Value 100 C 0 C 10 C/min. 10 min.

experimental parameters for second-level reliability qualification. Figure 59.3 contains a plot of temperature versus time along with explanations of the key experimental parameters. Data acquisition systems and/or event detectors (commonly referred to as glitch detectors) are employed to monitor resistance and/or scan for intermittent opens in real time. One of the early techniques for assessing solder joint integrity during thermal cycling was to remove parts periodically from the test chamber and measure resistance manually at room temperature. The major risk associated with this technique is that opens are observed only at temperature extremes when the deformations due to CTE mismatch are largest. As the package cools to room temperature, most of the CTE-based deformations that pull cracked surfaces of solder joints are gone and there is a potential for cracked surfaces to be in enough physical contact to provide acceptable continuity. In some cases, the cycle number at which opens are observed at temperature extremes is much shorter than the cycle at which the same opens are observable at room temperature. A schematic of a typical thermal cycling chamber, with the boards installed and connected to a data acquisition system, is shown in Fig. 59.4.

Test Boards Test Devices Thermocouple Wires Temp Control Daisy Chain Resistance Wires Data Logger or Event Detector

With this representation, it is easy to see why (2.1) holds. An arbitrary one form a maps a vector V a to a number via the scalar product V = a V a We can think of this either way: we can visualize vectors as maps that take one forms to the real numbers via the scalar product. More generally, we can de ne a ( p, q) tensor as a function that takes p one forms and q vectors as input and