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The die size of the processor refers to its physical surface area size on the wafer. It is typically measured in square millimeters (mm^2). In essence a "die" is really a chip, but it is only referred to in this way when discussing physical chip parameters and manufacturing issues.
The importance of die size is rather obvious: the smaller the chip, the more of them that can be made from a single wafer. A larger die means fewer chips from the same wafer, and thus higher cost overall. A larger die also leads to increased power consumption. The three most important contributing factors to die size are the circuit size in microns, the process technology used, and of course, the design of the processor itself (newer processors are in general larger because they do a lot more). Reducing circuit size in particular is key to reducing the size of the chip. For example, the first generation Pentium used a 0.8 micron circuit size, and required 296 square milimeters per chip. The second generation chip had the circuit size reduced to 0.6 microns, and the die size dropped by a full 50% to 148 square milimeters.
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