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

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 \ensuremath{\sim}0.5 K, magnetic inductions from 9.0 to \ensuremath{\sim}15 T, and channel currents up to \ensuremath{\sim}20 \ensuremath{\mu}A. The concentration of two-dimensional electrons was changed from 8.6\ifmmode\times\else\texttimes\fi{}${10}^{15}$ to 4.0\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{m}}^{\mathrm{\ensuremath{-}}2}$. When the measurement is made under the condition that ${\ensuremath{\rho}}_{\mathrm{xx}}$(4/i)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}2}$ \ensuremath{\Omega} holds for the ith quantized Hall plateau, the Hall resistivity ${\ensuremath{\rho}}_{\mathrm{xy}}$ 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${\ifmmode\bar\else\textasciimacron\fi{}}_{H}$(i)=6453.2009\ifmmode\pm\else\textpm\fi{}0.0 022 ${\ensuremath{\Omega}}_{\mathrm{ETL}}$ (0.34 ppm) referred to the ohm as maintained by the Electrotechnical Laboratory in Ibaraki, Japan. The systematic uncertainty associated with ${\ensuremath{\Omega}}_{\mathrm{ETL}}$ 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.