Quantum-well and modified image-potential states in thin Pb(111) films: an estimate for the local work function

Abstract

Quantum-confined electronic states such as quantum-well states (QWS) inside thin Pb(111) films and modified image-potential states (IPS) above the Pb(111) films grown on Si(111)7×7 substrate were studied by means of low-temperature scanning tunnelling microscopy (STM) and spectroscopy (STS) in the regime of constant current I. By plotting the position of the n−th emission resonances U n versus n 2/3 and extrapolating the linear fit for the dependence U n (n 2/3 ) in the high-n limit towards n = 0, we estimate the local work function for the Pb(111) film: W 3.8 ± 0.1 eV. We experimentally demonstrate that modifications of the shape of the STM tip can change the number of the emission peaks associated with the resonant tunnelling via quantized IPS levels for the same Pb terrace; however it does not affect the estimate of the local work function for the flat Pb terraces. We observe that the maxima in the spectra of the differential tunnelling conductance dI/dU related to both the QWS and the modified IPS resonances are less pronounced if the STM tip becomes more blunt.

Superconducting Long-Range Proximity Effect through the Atomically Flat Interface of a Bi2Te3 Topological Insulator

“…In practice, it is not easy to distinguish between the two conductivity channels. In our system, the topological insulator is covered by the additional layer of Pb, and these two materials have different work functions, which are nearly 4.1 eV for Pb , and 5.3 eV for Bi 2 Te 3 . Thus, the work function for Bi 2 Te 3 is larger, and this is expected to result in the downward band bending at the Bi 2 Te 3 surface.…”

Observation of Hidden Parts of Dislocation Loops in Thin Pb Films by Means of Scanning Tunneling Spectroscopy

“…The pronounced oscillations of U aux as a function of U 0 point to the coherent resonant tunneling through the quantum-well states in a thin metallic film 6−13 (see schematics in Figures 1a and 2a). The quantum-size oscillations of the tunneling conductance can be easily detected in Pb(111) films up to 50 monolayers at liquid nitrogen temperatures 51 and up to 100 monolayers at sub-Kelvin temperatures. 52 It is obvious that the energy of electron localized in a one-dimensional infinite potential well is equal to…”

“…Aperiodic large-scale oscillations of the differential conductance, also called as the Gundlach oscillations 54 or field-emission resonances (FERs), correspond to the resonant tunneling through quasi-stationary states localized above the surface of the sample (see schematics in Figure 1b). The elementary theory based on the quasiclassical approximation for the electron trapped in the triangular potential well returns the following expression 51 for the bias voltage U (n) , corresponding to the n-th FER peak…”

“…The pronounced oscillations of U aux as a function of U 0 point to the coherent resonant tunneling through the quantum-well states in a thin metallic film − (see schematics in Figures a and a). The quantum-size oscillations of the tunneling conductance can be easily detected in Pb(111) films up to 50 monolayers at liquid nitrogen temperatures and up to 100 monolayers at sub-Kelvin temperatures . It is obvious that the energy of electron localized in a one-dimensional infinite potential well is equal to E n ≃ E c + ℏ 2 k ⊥, n 2 /2 m *, where E c is the energy of the bottom of the conduction band in the free-electron-gas approximation; m * is the effective mass of electron in a crystalline sample; n = 1, 2... is the integer index, k ⊥, n = π n / D is the allowed values of the transversed wave vector, and D is the width of the quantum well (i.e., film thickness).…”

“…The local electronic properties of the Pb islands were studied by low-temperature STS in the regime with an active feedback, constant tunneling current I , and variable distance z between the tip and the sample surface. , During the scanning process, the potential of the sample was harmonically modulated, containing dc-component U 0 and ac-component U 1 cos (2π f 0 t ), where f 0 = 7285 Hz and U 1 = 40 mV. The amplitude of the first Fourier component of tunneling current I 1 at the modulation frequency was routinely measured by the lock-in amplifier (Stanford Research, model SR 830).…”