Retrieving the energy band of Cu thin films using quantum well states

Abstract

Angle-resolved photoemission electron spectroscopy (ARPES) measurement was performed on epitaxially grown Cu/Co/Cu(001) films to observe the quantum well (QW) states due to the electron confinement inside the Cu film by the Cu/Co and Cu/vacuum interfaces. By studying the in-plane dispersion of the QW states, we find a nearly isotropic electronic structure in the neck region of the Fermi surface. Based on the quantization condition, we achieve a model-free method for obtaining the copper energy band and the energy contour near the Fermi energy. The result is in good agreement with theoretical calculations of the bulk copper energy band, showing that there is no significant difference in the energy bands between the bulk and thin film copper. This method can be generalized to measure energy bands of other metallic films using the QW states.

Electron–phonon heat exchange in layered nano-systems

“…The principal characteristic of the electron gas is that due to the quantization of the wavevector component perpendicular to the film surfaces the electron gas forms quasi 2D sub-bands, which are specific to a quantum well (QW) formalism. 16,21,22,26 In an accompanying paper we describe the electrons as a 3D Fermi gas. We choose a range of parameters L, T e (electrons temperature), and T ph (lattice temperature) such that the phonon gas has a quasi two-dimensional distribution (for L = 100 nm we took T e, T ph ≤ 0.2 K).…”

“…In the valley regions, in the low temperature limit P ∝ T 3.5 e − T 3.5 ph , whereas on the crests the heat power increases by more than one order of magnitude and P does not obey a simple power law behavior. Such a sharp oscillatory behavior is a characteristic of the QW description of the electronic states in the metallic films 16,21,22,26 and could be useful for applications, like thickness variation detection or surface contamination. Moreover, by varying the thickness of the membrane one might vary dramatically the electronphonon coupling and, through this, the thermalisation or the noise level in the system.…”

“…Such a sharp oscillatory behavior is a characteristic of the QW description of the electronic states in the metallic films 16,21,22,26 and could be useful for applications, like thickness variation detection or surface contamination. Moreover, by varying the thickness of the membrane one might vary dramatically the electronphonon coupling and, through this, the thermalisation or the noise level in the system.…”

“…Below this temperature one may expect a quasi-2D behavior of the phonon system (rigorously, for T T C ), whereas above it (rigorously, at T T C ) a 3D model would suffice. We carry out our analysis employing a QW picture of the metallic film 16,21,22,26 by taking into account the discretization of the components of the electrons wavenumbers perpendicular to the membrane's surfaces, whereas the 3D Fermi gas picture of the electron system is used in an accompanying paper. We work in a temperature range T < 200 mK in which the phonon gas is quasi-2D and we observe that the electron-phonon heat flux P cannot be simply described by a single power-law dependence, P ∝ T ph , in general the heat flux has a very strong oscillatory behavior as a function of d. At certain regular intervals the power flux increases sharply with the film thickness by at least one order of magnitude ( Fig.…”

Van Hove singularities as a result of quantum confinement: The origin of intriguing physical properties in Pb thin films

“…1(b), and the corresponding ARPES intensity map plot as a function of binding energy and wave vector is displayed in Fig. 2 [21,22], the QWSs are free-electron-like and cross the Fermi level. The subbands near the Γ point bend to higher binding energy (band A starts bending at an energy of 0.15 eV while band B starts bending at 0.56 eV).…”