Using a Natural Ratio to Compare DC and AC Resistances

Area of Science:

• Electrical Engineering
• Metrology
• Solid State Physics

Background:

• Accurate resistance standards are crucial for electrical metrology.
• Existing standards often rely on specific material properties or complex setups.
• Bridging traceability between calculable capacitors and quantum Hall effect standards presents a challenge.

Purpose of the Study:

• To design and demonstrate a silicon wafer-based resistor for both DC and AC resistance measurements.
• To derive a theoretical resistance ratio independent of sample resistivity and thickness.
• To establish a potential link between different resistance traceability chains.

Main Methods:

• Application of the van der Pauw method and the Thompson-Lampard theorem.
• Development of a silicon wafer resistor with specific geometric considerations.
• Performing DC and AC (1 kHz) simulations and experimental measurements.
• Utilizing a calculable capacitor and quantum Hall effect for traceability.

Main Results:

• A constant resistance ratio of (π/ln2)² ≈ 20.5 was theoretically derived.
• DC simulations showed agreement with the theoretical ratio within 0.035%.
• Experimental DC and AC measurements confirmed the ratio within 0.23% (±0.06% uncertainty).

Conclusions:

• The developed silicon wafer resistor provides a stable and reproducible resistance standard.
• The derived ratio offers a method for comparing different resistance traceability chains.
• This work contributes to advancing electrical metrology and resistance standardization.