Particle Size Distribution (PSD) is the statistical characterization of particle contamination that reports defect counts binned by size rather than as a single total number — providing the forensic fingerprint needed to identify contamination sources, select appropriate filtration, calculate true yield impact, and distinguish systematic process problems from random background contamination on semiconductor wafer surfaces.

The Power of Distribution Over Total Count

A wafer with 100 particles at 30 nm and a wafer with 100 particles at 200 nm both report "100 LPDs" as a single number — yet they represent completely different contamination scenarios with different yield impacts, different sources, and different remediation strategies. PSD resolves this ambiguity.

Standard Size Bin Structure

Inspection tools (KLA Surfscan, Hitachi SSIS) report LPDs in logarithmically spaced size bins: <30 nm, 30–45 nm, 45–65 nm, 65–90 nm, 90–130 nm, 130–200 nm, 200–400 nm, >400 nm. Each bin count feeds downstream yield analysis platforms (Klarity Defect, Galaxy) for spatial and statistical processing.

Source Identification via PSD Signature

Normal background contamination follows an approximate power-law distribution: N(d) ∝ 1/d³ — many small particles, few large ones, appearing as a straight line on a log-log PSD plot.

Deviations signal specific sources:

• Spike at 50–100 nm: Slurry agglomerates or filter bypass — abrasive particles that escaped filtration
• Spike at 200–500 nm: Robot end-effector particles — mechanical contact debris
• Elevated large particles (>1 µm) only: Macro-contamination event — spill, human entry, equipment failure
• Uniform elevation across all bins: Chemical bath degradation or ambient cleanroom issue

Killer Defect Density Calculation

Not all particle sizes kill devices. PSD enables calculation of killer defect density D_k by convolving the PSD with the critical area map of the device: D_k = Σ(N_i × A_crit_i), where A_crit_i is the fraction of die area sensitive to particles in size bin i. This converts particle counts into a predicted yield number.

Filtration Engineering

PSD from incoming chemical analysis determines filter pore size selection. If a process chemical shows elevated particles at 50 nm, a 10 nm nominal rated filter is specified. Over-filtering adds cost and pressure drop; PSD-guided selection optimizes the filter network.

Particle Size Distribution is the forensic spectrum of contamination — transforming a raw particle count into a diagnostic fingerprint that identifies the source, predicts the yield impact, and guides the corrective action.