The bias voltage dependence of the apparent local barrier height (LBH) corresponding to the "work function" on a nanometer-scale was measured by scanning tunneling microscopy on an An (111) surface with an Au tip. There have been reports of the bias voltage dependence of the LBH under constant current (CC) conditions. However, under CC, a change in the bias voltage causes a change in the tip-sample separation. In this situation, the measured results contain both effects (the bias voltage and the separation). Therefore, to accurately measure the effect of the bias voltage on the LBH, the separation effects must be eliminated. We measured the, bias voltage dependence of the LBH at. a constant separation (CS) using the current on the current-voltage (I-V) curve and compared the results with CC.'For CS measurements, in the ohmic range (the I-V curve is linear), the LBH does not depend on the bias voltage within the experimental error. Beyond the ohmic range, the LBH decreases with increased bias voltage. In contrast, CC measurement results are clearly affected by both effects. In the region where the separation effect can be neglected, the CC resultcorresponds to the CS result. (C) 2003 American Vacuum Society.