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The trapped ions confined in a surface-electrode trap (SET) could be free from rf heating if they stay at the rf potential null of the potential well.We report our effort to compensate three-dimensionally for the micromotion of a single 40Ca+ ion near the rf potential null,which largely suppresses the ions heating and thus helps to achieve the cooling of the ion down to 3.4 mK,which is very close to the Doppler limit.This is the prerequisite of the sideband cooling in our SET.