Force in tunneling barrier measurements

For a large number of materials, the stability condition, Eq. (8.26), is satisfied. In addition, in most cases, the STM images are taken under attractive-force conditions. The dramatic amplification effect does not occur. However, the effect of force and deformation is still observable. By measuring the apparent barrier height using ac method, based on Eq. (1.13), 

A systematic study was conducted on clean Si(lll) surface with a clean W tip (Chen and Hamers, 1991). The entire curve of the dependence of the measured apparent barrier height, Eq. (8.27), with z-piezo displacement, was recorded. The experiment was performed under the condition that a clear 7X7 pattern was observed, which indicated that both the tip (near the apex atom) and the sample were clean. By carefully moving the tip back and forth, so as not to press into the sample surface too deeply, the entire process is completely reversible. The experimental barrier height measurements were performed using an ac modulation method, by applying a small 0.05 A modu- 

The observed variation of apparent barrier height can be understood quantitatively by assuming that the force follows a Morse curve. Thus, the 

The solid curve in Fig. 8.8 is drawn with 7=0.95 and assuming the actual apparent barrier height is 3.5 eV throughout the entire region. The accurate fit indicates that the model is reasonable. 

The normal tip-sample distance in STM experiments can be obtained accurately from this experiment. In Fig. 8.8, the equilibrium distance, where the net force is zero, is taken as the origin of z. As shown for the case of aluminum, because the attractive force has a longer range than the repulsive force, the absolute equilibrium distance between the apex atom and the counterpart on the sample surface is slightly less than the sum of the atomic radii of both atoms, which is about 2 A. The normal topographic images on Si(lll) are usually taken at / =1 nA, corresponding to a distance of 3 A from the equilibrium point, or 5 A from nucleus to nucleus. 

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