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Formula used
Sheet resistance: Rₛ = ρ / tTrace resistance: R = Rₛ × N, where N = L / WFour-point probe: Rₛ = (π / ln 2) × (V / I) × correction factorsVan der Pauw: exp(−πRₐ/Rₛ) + exp(−πRᵦ/Rₛ) = 1Multilayer stack: 1 / Rₛ,eq = Σ(1 / Rₛ,i)How to use this calculator
Select the calculation mode that matches your known data. Enter values and choose matching units. Then review all correction and uncertainty settings.
Use the material preset to load reference resistivity. Adjust values for deposition conditions and purity. Thin-film properties often differ from bulk materials.
Add conductive layers when current flows through stacked films. Enter each layer’s resistivity and thickness. The calculator combines their sheet conductances.
Press Calculate to generate results and calculation steps. Review warnings before relying on any value. Export results for records or later analysis.
Example data
| Example | Known values | Method | Expected result |
|---|---|---|---|
| Copper film | ρ = 1.68 × 10⁻⁸ Ω·m, t = 100 nm | ρ/t | 0.168 Ω/□ |
| Rectangular trace | Rₛ = 0.168 Ω/□, L/W = 10 | Rₛ × L/W | 1.68 Ω |
| Four-point probe | V = 0.077 mV, I = 1 mA | π/ln(2) × V/I | About 0.349 Ω/□ |
| Two equal layers | Each layer = 10 Ω/□ | Parallel conductance | 5 Ω/□ |
Material reference table
Values are representative near room temperature. Actual thin films depend on purity, grain size, processing, and microstructure.
| Material | Resistivity, Ω·m | Temperature coefficient, 1/°C |
|---|---|---|
| Silver | 1.59E-8 | 0.0038 |
| Copper | 1.68E-8 | 0.00393 |
| Gold | 2.44E-8 | 0.0034 |
| Aluminium | 2.82E-8 | 0.00403 |
| Tungsten | 5.6E-8 | 0.0045 |
| Nickel | 6.99E-8 | 0.006 |
| Platinum | 1.06E-7 | 0.00392 |
| Chromium | 1.29E-7 | 0.003 |
| Titanium | 4.2E-7 | 0.0038 |
| Nichrome | 1.1E-6 | 0.0004 |
| Graphite, representative | 3.5E-5 | -0.0005 |
| Indium tin oxide, representative | 0.0001 | 0.0008 |
| Polysilicon, representative | 0.001 | 0.001 |
Frequently asked questions
What does ohms per square mean?
It describes a uniform film’s resistance independent of square size. Every square has equal resistance between opposite sides. Geometry determines how many squares are connected.
How is sheet resistance different from resistance?
Sheet resistance is a material and thickness property. Resistance also depends on conductor length and width. Multiply sheet resistance by the square count.
Why can thin-film resistivity exceed bulk resistivity?
Thin films can contain grain boundaries and defects. Surface scattering also increases electron resistance. Deposition conditions can strongly change measured values.
When should four-point probe corrections be applied?
Corrections matter near sample edges and finite boundaries. They also matter when thickness approaches probe spacing. Use verified factors for the instrument geometry.
What is the Van der Pauw method?
It measures sheet resistance on arbitrary flat samples. Contacts sit around the sample perimeter. The sample should be uniform and simply connected.
How are multilayer films combined?
Conductive layers share current like parallel resistors. Their sheet conductances are added together. The reciprocal gives equivalent sheet resistance.
Does contact resistance affect four-point measurements?
Ideally, voltage probes draw negligible current. This greatly reduces contact-resistance error. Poor contacts can still cause noise and instability.
How is temperature included?
The calculator applies linear and quadratic coefficients. Large temperature ranges may need measured material data. Phase changes invalidate simple polynomial corrections.
How should uncertainty results be interpreted?
The uncertainty estimate uses independent relative contributions. Correlated inputs require a more detailed model. Confidence ranges depend on the selected multiplier.
Assumptions and limitations
The calculator assumes uniform thickness and isotropic conductivity. It treats most geometry models as ideal. Real devices may require finite-element simulation.
Material presets are approximate room-temperature references. Deposited films can differ substantially from bulk values. Use measured data whenever available.
Probe corrections must match the actual sample geometry. The calculator does not derive proprietary instrument factors. Verify critical designs with laboratory standards.