Investigation of the electrical properties and carrier concentration in n- and p-doped germanium

Abstract

This study investigates the Hall effect in n- and p-doped germanium samples through experimental measurements of Hall voltage, electrical conductivity, charge carrier mobility, and carrier concentration under varying magnetic fields and temperatures. The experimental setup involved measuring Hall voltage as a function of control current, magnetic field induction, and temperature using a TSE Co, LTD company Hall-effect unit. The linear dependence of the Hall voltage on the magnetic field was confirmed, yielding regression line slopes of b = 0.144 VT⁻¹ ± 0.004 VT⁻¹ for n-germanium and b = 0.125VT⁻¹ ± 0.003VT⁻¹ for p-germanium. Corresponding Hall constants were calculated as R_H  = 4.8×10 m^-3 /C and R_H = 4.17×10 m^-3 /C. Electrical conductivities were determined as σ = 53.6 S/m for n-germanium and σ = 57.14 S/m for p-germanium. The Hall mobilities were found to be μ_H = 0.257±0.005 m² /Vs for n-germanium and μ_H = 0.238±0.005 m²/Vs for p-germanium. Carrier concentrations were n = 13.0×10²⁰ m⁻³ for electrons and n =14.9×10²⁰  m⁻³ for holes. From temperature-dependent measurements, the energy bandgaps were calculated as E_g = 0.50 ± 0.04 eV for n-germanium and Eg = 0.72 ± 0.03 eV for p-germanium. The experimental findings provide comprehensive insights into the electronic properties of doped germanium, highlighting its behavior under magnetic fields and varying temperatures, with precise parameter evaluation crucial for semiconductor applications.