Apparent barrier height

In terms of A and eV, K 0.51- y(A, q = 0.51- /. The result of a direct numerical calculation is illustrated in Fig. 2.7. As shown, the apparent barrier height is almost a constant up to the point the barrier collapses. Actually, when the barrier is very thin, a square barrier following Eq. (2.15) becomes a poor approximation for the effect of the image force. The actual barrier is more slim than the square barrier, and the current is growing even faster. The apparent barrier height should not drop, as in the left edge of Fig. 2.7. Rather, it remains almost constant, as also shown by numerical calculations of Teague (1987) (see Fig. 1.40). 

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The significant variation of the barrier height observed for immersed junctions reflects the experimental difficulties associated with determining the tunneling constant, k. Two key issues are contamination of the junction and uncertainty as to the structural and electronic character of the tip [104], Recent data clearly reveal a dependence of the apparent barrier height on tip-substrate separation [7,92-94,104]. Specifically, the effective barrier is observed to diminish for resistance values below <10 Q as shown in Fig. 

FIG. 15. A comparison between the distance dependence of the tunneling barrier between a jellium tip and substrate immersed in solution versus vacuum under zero bias conditions. The apparent barrier height is derived from the WKB approximation. (From Ref. 110.)... 

Fig. 1.6. Tunneling through a controllable vacuum gap. The exponential dependence / V is observed over four orders of magnitude. On clean surfaces, an apparent barrier height of 3.5 eV was observed. (Reproduced from Binnig et al., 1982a, with permission.)...

Furthermore, Binnig et al. (1984) reported that near the mechanical contact, the observed apparent barrier height increases rather than decreases, as shown in Fig. 2.4. It is due to the attractive force between the tip and the sample, which causes a deformation of the tip and the sample near the barrier region. The same observations were reported earlier by Teague (1978). 

Fig. 2.7. Apparent barrier height calculated from the exact solution. Variation of the apparent barrier height 0.95(

The same phenomenon is observed on other layered materials, for which the deformation perpendicular to the cleavage surface is relatively easy. When the large corrugation amplitudes are observed, the apparent barrier height becomes very low, indicating a nearly synchronous motion of the sample surface with the tip. 

The Pethica mechanism is important in imaging diagnosis. If an abnormally low apparent barrier height and a completely defect-free periodic STM image are observed, the possibility of a Pethica mechanism must be considered seriously. 

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-... 

Fig. 8.7. Apparent barrier height measured on IT-VSCj. At low bias, the tip is in...

Fig. 8.8. Variation of the measured apparent barrier height with distance. Circles are data points. The solid curve is derived from Eq. (8.26). The dashed curve is the actual gap displacement as a function of the measured -piezo displacement. The dotted curve, the fictitious gap displacement in the absence of force, is included for comparison. (Reproduced from Chen and Hamers, 1991a, with permission.)...

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. 

Lang, N. D. (1988). Apparent barrier height in scanning tunneling microscopy. Phys. Rev. B 37, 10395-10398. 

See Atomic metallic ion emission Anomalous corrugation theory 31, 142 breakdown 146 graphite, and 31, 144 Apparent barrier height 63,171 anomalously low 171 attractive force, and 49, 209 definition 7 image force, and 72 repulsive force, and 171, 198, 209 square-barrier problem, in 63 Apparent radius of an atomic state 153 Atom charge superposition I 11 analytic form 111 Au(lll), in 138 in atomic beam scattering 111 Atom-beam diffraction 107 apparatus 109... 

Weimer M, Kramar J, Baldeschwieler JD (1989) Band bending and the apparent barrier height in scanning tuimeling microscopy. Phys Rev B Cond Mat 39 5572-5575... 

A = Angstrom e = charge of an electron E = energy G( = tunnelling conductance I = tunnelling current K = Kelvin V = bias voltage z = tip-sample separation h = Plancks constant/2 r = apparent barrier height O) = vibrational frequency. 

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