van der pauw hall

**Van der Pauw Hall Measurement** is a **technique for measuring sheet resistance and Hall mobility on arbitrarily shaped, flat samples** — requiring only four point contacts on the sample periphery, without needing to know the sample geometry. **How Does Van der Pauw Work?** - **Four Contacts**: Place four small contacts (A, B, C, D) on the sample periphery. - **Two Measurements**: Measure resistance $R_{AB,CD}$ and $R_{BC,DA}$ in two orthogonal configurations. - **Van der Pauw Equation**: $exp(-pi R_{AB,CD} t / ho) + exp(-pi R_{BC,DA} t / ho) = 1$. - **Hall Measurement**: Apply magnetic field perpendicular to sample, measure the Hall voltage for mobility. **Why It Matters** - **Geometry-Independent**: Works on any flat shape — no need for precisely patterned Hall bar structures. - **Universal**: Standard method for measuring epitaxial layers, thin films, and bulk semiconductors. - **Combined**: Yields sheet resistance, resistivity, carrier concentration, and mobility from one sample. **Van der Pauw** is **the Swiss Army knife of electrical characterization** — extracting complete electrical properties from any flat sample with four contacts.