van der pauw structure
**Van der Pauw structure** measures **sheet resistance of thin films** — a four-point probe configuration that eliminates contact resistance effects, providing accurate resistivity measurements for semiconductor films, metals, and other conductive layers.
**What Is Van der Pauw Structure?**
- **Definition**: Four-point probe method for sheet resistance measurement.
- **Shape**: Arbitrary shape (often square or cloverleaf) with four contacts at periphery.
- **Advantage**: Eliminates contact resistance from measurement.
**How It Works**
**1. Current Injection**: Apply current between two contacts (e.g., I₁₂).
**2. Voltage Measurement**: Measure voltage between other two contacts (e.g., V₃₄).
**3. Resistance Calculation**: R = V₃₄ / I₁₂.
**4. Sheet Resistance**: Use Van der Pauw formula to extract Rₛ.
**Van der Pauw Formula**
exp(-πR_A/R_s) + exp(-πR_B/R_s) = 1
Where R_A and R_B are resistances measured in perpendicular configurations.
**Why Van der Pauw?**
- **Accurate**: Eliminates contact resistance errors.
- **Versatile**: Works for arbitrary sample shapes.
- **Standard**: Widely used in semiconductor industry.
- **Simple**: Four contacts, straightforward measurement.
**Requirements**
**Contacts**: Small, at sample periphery.
**Uniformity**: Sample should be uniform thickness.
**Isolation**: No holes or voids in sample.
**Symmetry**: Better accuracy with symmetric shapes.
**Applications**: Sheet resistance measurement of doped silicon, metal films, transparent conductors, graphene, other 2D materials.
**Variations**: Greek cross (more accurate), cloverleaf (compact), square (simple).
**Tools**: Four-point probe stations, semiconductor parameter analyzers, automated test systems.
Van der Pauw structure is **the standard for sheet resistance measurement** — by eliminating contact resistance, it provides accurate resistivity characterization essential for semiconductor process control and materials research.