Accurate band mapping via photoemission from thin films

Abstract

Electron bands in solids can be determined in angle-resolved photoemission experiments from thin films, where the perpendicular wave vector (k Ќ ) uncertainty that characterizes photoemission from bulk crystals is removed. However, the comparison with state-of-the-art quasiparticle band-structure calculations has never been done. In this work we have mapped both initial-state ͑occupied͒ and final-state ͑empty͒ E(k Ќ ) bands along the ⌳ axis of aluminum, from photon-energy-and thickness-dependent quantum-well spectra of aluminum films. For final states the best fit is obtained with inverse low-energy electron diffraction band structure calculations. For initial-state bands of Cu and Al, thin-film data display excellent agreement with bulk quasiparticle theory, suggesting the use of thin films as model systems to investigate fine effects in the crystal band structure. DOI: 10.1103/PhysRevB.69.115422 PACS number͑s͒: 73.20.Ϫr, 79.60.Bm An appropriate description of the electron band structures is of general interest as a fundamental property of crystalline solids that explains most of their observable behavior. Many different spectroscopic techniques probe electronic states, but only photoemission from well-defined crystal surfaces allows the thorough determination of E(k) band dispersions. 1 Angle-resolved, valence-band photoemission spectra are generally dominated by peaks that correspond to the so-called vertical transitions from initial to final bulk states, i.e., those where the wave vector k is conserved in the reduced Brillouin zone. The energy and the wave vector parallel to the surface can be determined with a high accuracy depending on the system resolution. However, the broken symmetry at the surface gives rise to a fundamental uncertainty that affects the perpendicular component of the wave vector k Ќ . Occupied bands are usually mapped assuming free-electron-like final-states to define k Ќ , but the actual final state band structure is often more complex as proved in constant initial-state ͑CIS͒ experiments. Such final states can be determined experimentally by very low-energy electron diffraction͑VLEED͒. 2,3 However, this method is limited to high-enough reflectivity, i.e., electron energies below 30 eV.The k Ќ uncertainty is removed in thin films, where k Ќ is fixed by thickness and boundary conditions at the surface interface. 4 This leads to discrete quantum-well ͑QW͒ states in the photoemission spectra, with peaks at k Ќ (E) values that fulfill constructive interference conditions. 5-10 If the film is not too thin and the crystal structure is the same as in bulk materials, k Ќ (E) values actually sample bulk E(k) bands at discrete k Ќ points. 4 Furthermore, if it is assumed that boundary conditions at the surface and the interface do not change by varying the film thickness, k Ќ (E) can be obtained directly from the so-called QW structure plot, i.e., the QW peak energy distribution as a function of film thickness. 5-10 Thus, the fundamental k Ќ uncertainty in bulk crystal photoemission is tran...

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