Quantum Hall effect in silicon metal-oxide-semiconductor inversion layers: Experimental conditions for determination of h/e2

Abstract

High-precision measurements of quantum Hall and diagonal resistivities have been made for a number of silicon metal-oxide-semiconductor field-effect transistor samples at temperatures from 1.4 to ∼0.5 K, magnetic inductions from 9.0 to ∼15 T, and channel currents up to ∼20 μA. The concentration of two-dimensional electrons was changed from 8.6×${10}^{15}$ to 4.0×${10}^{16}$ ${\mathrm{m}}^{\mathrm{-}2}$. When the measurement is made under the condition that ${\rho }_{\mathrm{xx}}$<(4/i)×${10}^{\mathrm{-}2}$ Ω holds for the ith quantized Hall plateau, the Hall resistivity ${\rho }_{\mathrm{xy}}$ is verified to be constant, i.e., the value corresponding to h/$e^2$ is unchanged against changes in electron concentration, temperature, magnetic field strength, and channel current, to within one part in ${10}^7$, the accuracy of the present experiment. The tentative result and its one-standard-deviation uncertainty are (i/4)R${¯}_H$(i)=6453.2009±0.0 022 ${\Omega }_{\mathrm{ETL}}$ (0.34 ppm) referred to the ohm as maintained by the Electrotechnical Laboratory in Ibaraki, Japan. The systematic uncertainty associated with ${\Omega }_{\mathrm{ETL}}$ has been found to be open to discussion. The effect of dissipative regions distributed over the electron channel is discussed: It could become appreciable in the determination of h/$e^2$ with an uncertainty of less than a few parts in ${10}^8$. The technique of the present precision measurement can be utilized for experimental studies aimed at solving the most basic problems of transport phenomena at lowest excitations.