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Heat spreads laterally through a spreader at roughly 45 degrees, so a 3 mm copper lid over a 13 mm die presents about 19 mm of area to the heatsink — nearly twice the flux reduction. Beyond that the spreading resistance of the material itself limits any further benefit.
Heat spreading
spreader side = die side + 2 x thickness x tan(45 degrees); flux reduction = spreader area / die area
Beyond about a 45 degree spread cone the extra area receives little heat, because in-plane conduction resistance dominates. Thicker copper helps more than wider copper.
Copper conducts about twice as well (390 versus 200 W/m·K), which matters most in the spreading layer where flux density is highest.