Amol,
We pulled off this "hybrid profile" with a leaded solder paste. We recently got our tensile test report results, and our Pb-Free BGA / Pb Paste sample broke off during tensile tests at the pad/substrate interface, and not the joint. This indicates that our profile was kick ass!
The hybrid profile is simple. Ensure a TAL where liquidus is 217*C of at least 30 seconds and a peak around 230-235-ish. It helped that we used a "transitional" lead paste containing flux similar to their Lead-Free formula. Several paste manufacturers now offer this. Your time above 183*C will be a little on the high side. Be mindful of your low mass chip components. The one negative result we had on this hybrid profile was "charred looking" burned-off flux on the 0805 components.
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