four-point probe mapping

**Four-Point Probe Mapping** is a **contact-based technique for measuring sheet resistance or resistivity at multiple locations across a wafer** — using four collinear probes where the outer pair supplies current and the inner pair measures voltage, eliminating contact resistance effects. **How Does Four-Point Probe Work?** - **Configuration**: Four equally spaced probes in a line. Current $I$ flows through outer probes, voltage $V$ measured across inner probes. - **Sheet Resistance**: $R_s = frac{pi}{ln 2} cdot frac{V}{I} approx 4.532 cdot V/I$ (for thin sheets with probe spacing $s ll$ wafer diameter). - **Correction Factors**: Applied for finite sample size, edge proximity, and probe spacing. - **Mapping**: Automated stage moves the probe head across a grid pattern. **Why It Matters** - **Absolute Measurement**: Direct, traceable measurement of sheet resistance — the reference method. - **Contact Method**: Works on any conductive material (unlike eddy current which requires specific materials). - **Production Standard**: Used in every fab for post-implant, post-anneal, and post-deposition monitoring. **Four-Point Probe** is **the gold standard for sheet resistance** — the most direct and widely trusted measurement for conductive layer characterization.