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Recently, it has become increasingly important to lower the supply voltage of fast access time NOR flash EEPROMs for a low power handheld digital equipment. In order to scale the boosted word-line voltage for reading memory data with low power supply, it is necessary to tighten the erased-Vth distribution. The self-convergence method has been proposed to tighten the Vth-distribution within 2 V. However, it's not available to tighten the width below 1 V due to the high power consumption and long converging time. Therefore, the bit-by-bit weak program after over-erase-verify is needed. This paper shows a problem of the bit-by-bit weak program and proposes a sampling method of weak program for a solution, which can achieve 0.5 V in the Vth-distribution width, resulting in lowering the word-line voltage for less than 1.5 V operation.