For solder this chip, Maxim 1987, on to laptop Hp Compaq NC series, is a square of 6 mm side, 12 pin side, think that you succeed with a soldering iron with fine tip, or it could go one better hotgun?
The lead free? or not, must be many mm? and paste flux soldering?
This same IC was asked about, here on SER, not long ago.. probably for the same application, as there were lots of search results wrt flexing boards making this IC's connections open.
The package of this IC is 40-pin? Thin QFN 6mmx6mm.. there are no leads on this IC package, click image for a larger picture:
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Hot air reflow would be a good approach, but tinning the IC pads and the board pads with leaded solder, then placing/holding the IC in position, should allow someone who's fairly well skilled at soldering to reflow the connections with a low-to-medium heat soldering iron equipped with a fine tip.
Trying to apply/add solder to the individual pads with the IC in place could easily cause shorts/bridges between the contacts, which could require removal of the IC to remove the excess solder.
If the board pads have enough lead solder applied to them, just applying some liquid flux, then positioning the IC and touching the contacts with a fine tip of a soldering iron would likely be a reasonable method of reflowing the connections.
For small components and/or fine pitch ICs, I avoid adding solder with the part in position since it's too easy to apply too much solder.. instead, I try to make sure that the board contacts have enough solder, and after applying liquid flux, it's easier to just reflow the contacts.
My guess is that the board manufacturer uses paste to hold the IC in place, then heats the board. Search "QFN stencil" and "QFN soldering".
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No balls should be needed.. the IC is not BGA, it's QFN.
Hot air would most likely be ideal, but a soldering iron and skill could suffice. This type of repair is best accomplished by someone with skill and experience in SMT repairs.
This is why I recommend liquid flux if enough solder is already in place.. then just touch the contacts and pads, moving around the IC (without trying to add solder).
If the IC has been removed, I would apply a minimal amount of lead solder to the board pads, then with the IC in position (and liquid flux applied), carefully heat the contacts and pads.
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