Four-Probe Method — Experiment

Objective

To measure the resistivity ρ or sheet resistance R_s of a semiconductor or thin film sample using the four-probe method, and to determine the voltage–current relationship accurately.

Theory

The four-probe method eliminates contact resistance by using two outer probes to source current and two inner probes to measure voltage. The formulas differ depending on whether the sample is a thick bulk material or a thin film.

• Bulk Sample (Thick material):
  
  ρ = 2π · s · (V / I)
  where s is probe spacing (m), V the measured voltage, and I the applied current.
• Thin Film Sample:
  
  R_s = (π / ln 2) · (V / I)
  ρ = R_s · t
  where t is the film thickness (m).

Multiple (I, V) readings are recommended to create a linear V–I plot and determine the slope (V/I) using linear regression for accuracy.

Apparatus

• Four-probe head with equal probe spacing.
• DC current source or source-meter.
• High-impedance voltmeter or voltage measurement terminal of a source-meter.
• Sample holder and insulating stage.
• Micrometer for measuring probe spacing s and film thickness t.
• Connection wires and cleaning materials (e.g., IPA).

Procedure

1. Clean the sample surface to ensure good electrical contact with the probes.
2. Place the sample on the insulating stage and gently lower the four probes onto the surface.
3. Measure and record the probe spacing s and the film thickness t if applicable.
4. Set a series of current values (e.g., 4–8 steps). Ensure the current is low enough to avoid heating the sample.
5. For each current value, apply current through the outer probes (1 and 4) and measure voltage across the inner probes (2 and 3). Record (I, V).
6. Repeat the measurement for positive and negative currents, then average the results to minimize thermal EMF errors.
7. Plot V versus I and determine the slope m = V/I using linear fitting for highest accuracy.
8. Use the appropriate formula:
    • For thin films: R_s = (π / ln 2)·(V/I) then ρ = R_s·t
    • For bulk samples: ρ = 2π s · (V/I)
9. Repeat the measurement at multiple positions on the sample to evaluate uniformity.
10. Report uncertainties due to probe spacing, contact issues, sample edge effects, and measurement noise.

Safety and Practical Notes

• Avoid using high currents to prevent sample heating.
• Ensure proper grounding to reduce electrical noise.
• Handle thin films carefully to avoid surface damage.