Characterization of semiconductor properties via Hall effect and 4-wire measurements

Duration

July-August 2025

Institution

Northeastern University Department of Physics

Tags

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Electronics

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Semiconductors

Research Question

The goal of this project was to experimentally determine the fundamental electrical properties (resistivity, carrier type, carrier concentration, and carrier mobility) of a doped silicon wafer. Accurate characterization of these properties is critical for understanding a semiconductor's suitability for specific electronic applications.

Methods & Instrumentation

  • Employed a 4-wire measurement technique to accurately determine the sample's resistivity, effectively eliminating contact resistance errors inherent in standard 2-wire methods

  • Conducted a thermoelectric (Seebeck) test using a localized heat source to initially asses the carrier type, observing voltage shifts consistent with p-type material

  • Calibrated an electromagnet and placed the silicon sample within a perpendicular magnetic field while applying a known current

  • Measured the resulting Hall voltage across the sample as a function of both varying magnetic field strength and reversing field direction

  • Utilized MATLAB and Excel for data collection, processing, and linear regression analysis to extract the Hall slope

  • Applied the Lorentz force right-hand rule to the physical setup and measured voltage polarities to definitively confirm the carrier type

Results & Significance

  • Calculated an average sample resistivity of 58.5 ± 11.3 Ω·cm

  • Determined the carrier concentration to be $$(1.13 \pm 0.28) \times 10^{15} \text{ cm}^{-3}$$ and the carrier mobility to be $$94.6 \pm 29.5 \text{ cm}^{2}/\text{Vs}$$

  • Conclusively identified the sample as lightly doped p-type silicon based on the positive polarity of the Hall voltage, vector analysis, and corroborating thermoelectric tests