Thermal-error regime in high-accuracy gigahertz single-electron pumping

Single-electron pumps based on semiconductor quantum dots are promising candidates for the emerging quantum standard of electrical current. They can transfer discrete charges with part-per-million (ppm) precision in nanosecond time scales. Here, we employ a metal-oxide-semiconductor silicon quantum dot to experimentally demonstrate high-accuracy gigahertz single-electron pumping in the regime where the number of electrons trapped in the dot is determined by the thermal distribution in the reservoir leads. In a measurement with traceability to primary voltage and resistance standards, the averaged pump current over the quantized plateau, driven by a 1-GHz sinusoidal wave in the absence of a magnetic field, is equal to the ideal value of ef within a measurement uncertainty as low as 0.27 ppm.