Silicon charge pump operation limit above and below liquid helium temperature

Semiconductor tunable barrier single-electron pumps can produce output current of hundreds of picoamperes at sub ppm precision, approaching the metrological requirement for the direct implementation of the current standard. Here, we operate a silicon metal-oxide-semiconductor electron pump up to a temperature of 14 K to understand the temperature effect on charge pumping accuracy. The uncertainty of the charge pump is tunnel limited below liquid helium temperature, implying lowering the temperature further does not greatly suppress errors. Hence, highly accurate charge pumps could be confidently achieved in a $^4$He cryogenic system, further promoting utilization of the revised quantum current standard across the national measurement institutes and industries worldwide.