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A monolithic integrated circuit has its circuit elements fabricated in or on one semiconductor die. Their connections are essential: an unconnected collection of transistors does not implement the intended electrical circuit.

An original ideal example separates function from fabrication. Connect two resistors, $R_1=10\mathrm{k\Omega }$ above $R_2=20\mathrm{k\Omega }$, in a series circuit across an ideal $3\mathrm{V}$ voltage source. With no load electric current drawn from their meeting point, Ohm's law and the Kirchhoff cycle law giveThese equations apply to either a discrete circuit or an idealized monolithic integrated circuit realizing those same electrical resistances. Integration changes construction; the electrical circuit equations still determine the output. A real load, unwanted capacitance or finite resistor tolerance changes the ideal calculation. Manufacturing many functions together also couples their fate: a fatal defect can discard an entire semiconductor die, motivating the Poisson defect yield model.

Consider a deliberately simplified model: fatal defects form a spatially uniform Poisson point process with intensity $D$ per unit area. A semiconductor die of area $A$ works exactly when it contains no fatal defect. Its defect count $N$ has a Poisson distribution with expected value $DA$, hence its probability of working, called its yield, isThe product $DA$ is dimensionless. The formula concerns fatal defects, not every visible imperfection. Spatial uniformity, independent defect counts in disjoint areas, and failure from even one fatal defect are model assumptions. Clustering, shared processing failures, repairable regions and defects that affect only some functions can invalidate them. This is a chosen probability model, not historical yield data.

Choose $D=0.005{\mathrm{mm}}^{-2}$. For semiconductor die areas $25$, $100$ and $200{\mathrm{mm}}^2$, the model gives $Y=e^{-0.125}=0.882497$, $e^{-0.5}=0.606531$ and $e^{-1}=0.367879$. Doubling the area squares the yield: $Y(2A)=Y(A{)}^2$. This follows either from the exponential function or by splitting the larger area into two disjoint parts and using independence. More functions on one semiconductor die can save assembly while making the no-defect requirement harder to satisfy.

A piece of semiconductor carrying a fabricated device or integrated circuit, ordinarily separated from a larger semiconductor wafer. One package can contain multiple semiconductor dies; the package boundary and the semiconductor die boundary are different concepts.