Tunneling interferometry and measurement of the thickness of ultrathin metallic Pb(111) films

Abstract

Spectra of the differential tunneling conductivity for ultrathin lead films grown on Si(111)7 × 7 single crystals with a thickness from 9 to 50 monolayers have been studied by low-temperature scanning tunneling microscopy and spectroscopy. The presence of local maxima of the tunneling conductivity is typical for such systems. The energies of maxima of the differential conductivity are determined by the spectrum of quantum-confined states of electrons in a metallic layer and, consequently, the local thickness of the layer. It has been shown that features of the microstructure of substrates, such as steps of monatomic height, structural defects, and inclusions of other materials covered with a lead layer, can be visualized by bias-modulation scanning tunneling spectroscopy.

Nonuniform Quantum-Confined States and Visualization of Hidden Defects in Pb(111) Films

“…The growth of Pb on the Si(111)7×7 surface at room temperature is known to occur through the Stranski-Krastanov mechanism: first a disordered wetting Pb layer with the thickness of the order of 1 nm is formed, then two-dimensional Pb islands with the upper facets corresponding to the (111) plane start to grow. It was shown [2]- [9] that the local tunneling conductance G depends on U 0 in non-monotonous way (Fig. 2b).…”

“…Since the interval ∆E between the neighbour maxima at the G(U 0 ) dependence is equal to 185 meV ( Fig. 2b) and the Fermi velocity is equal to v F ≈ 1.8 · 10 8 cm/s [2,9], one could estimate the local thickness of this island d π v F /∆E 19 nm or approximately 70 monolayers. The local thickness of the Pb island in the area I exceeds the local thicknesses in the areas II and III by one and two monolayers, respectively.…”

“…2a). Since in the regions where the dislocation line is parallel to the surface such dislocation line has to be either an edge dislocation Taking into account that E F = ( 2 /2m * ) (3π 2 n) 2/3 in the model of free electron gas [21], the bottom of the conduction band in the area IV should be shifted down at the value of the order of δE 0 ∼ 2E F /(3N ) = 90 meV in order to ensure the constancy of the Fermi level, where m * is the effective mass which is close to the mass of free electron for Pb films in the (111) direction [9], E F 9.47 eV is the Fermi energy for bulk Pb [21], N 70 is the number of the monolayers in the considered area. Since δE 0 is close to the half of ∆E, the relocation across the invisible part of the dislocation loop should be accompanied by a sharp change in brightness for the maps of the tunneling conductance.…”

“…Provided that f 0 significantly exceeds the threshold frequency of the feedback loop (∼ 200 Hz), the modulated potential applied to the sample should not result in the appearance of any artifacts on the topographic images. Such technique [9] allows us to synchronously obtain both topographic images in the regime of constant average current I 0 and the dependence of G on the lateral coordinates x and y at the given value U 0 .…”

“…The visualization of atomic structure of the lower interface under metallic layer was demonstrated in [4] and this effect is based on the dependence of ϕ 2 on the lateral coordinates. The possibility to visualize defects such as monoatomic steps in the substrate and the inclusions of other materials under metallic layer, which were invisible in a topographic image, was shown in [9]. The estimates indicate that the thickness of a monolayer d M L for the Pb(111) surface is equal to 0.285 nm, the Fermi wavelength λ F is equal to 0.394 nm, therefore the ratio λ F /d M L is close to 4/3 [5].…”