particle size distribution
**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.