What Is the Four-Point Probe Semiconductor Sheet Resistance & Resistivity Calculator?
The four-point probe method is the industry standard for measuring semiconductor sheet resistance and bulk resistivity.
How Does the Four-Point Probe Semiconductor Sheet Resistance & Resistivity Calculator Work?
Separates current-carrying contacts from voltage sensing contacts, eliminating probe contact resistance errors.
Four-Point Probe Semiconductor Sheet Resistance & Resistivity Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
R_s = rac{pi}{ln 2} rac{V}{I} approx 4.5324 rac{V}{I}, quad
ho = R_s cdot t
Four-point collinear probe sheet resistance and bulk resistivity relations.
How to Use the Four-Point Probe Semiconductor Sheet Resistance & Resistivity Calculator
- Input measured inner voltage in millivolts, applied outer current in milliamps, and wafer thickness in micrometers.
Step-by-Step Example Calculation
Silicon Doped Wafer Characterization
Input Values:
measuredVoltageMv:12.5
appliedCurrentMa:1
waferThicknessUm:450
Worked Steps: Sheet resistance R_s = 56.65 Ω/sq, bulk resistivity ρ = 2.55 Ω·cm, conductivity σ = 0.392 S/cm.
Understanding Your Result
Outputs sheet resistance in Ohms per square (independent of probe spacing for thin films) and bulk resistivity in Ω·cm.
Factors That Affect the Result
- Edge proximity and finite wafer geometry require geometric correction factors near boundaries.
When Should You Use This Calculator?
- Semiconductor fabrication fab metrology, diffusion and ion-implantation dosage verification, and transparent conductive oxide (ITO) testing.
Assumptions & Limitations
- Assumes thin sheet limit (wafer thickness much smaller than probe spacing); uniform doping profile.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard ASTM F84 collinear four-point probe formulation.