Recent Cases

This is a summary of the case law from 1965

Thin film growth and band lineup of In2O3 on the layered semiconductor InSe

Thin films of the transparent conducting oxide In2O3 have been prepared in ultrahigh vacuum by reactive evaporation of indium. X-ray diffraction, optical, and electrical measurements were used to characterize properties of films deposited on transparent insulating mica substrates under variation of the oxygen pressure. Photoelectron spectroscopy was used to investigate in situ the interface formation between In2O3 and the layered semiconductor InSe. For thick In2O3 films a work function of φ = 4.3 eV and a surface Fermi level position of EF−EV = 3.0 eV is determined, giving an ionization potential IP = 7.3 eV and an electron affinity χ = 3.7 eV. The interface exhibits a type I band alignment with ΔEV = 2.05 eV, ΔEC = 0.29 eV, and an interface dipole of δ = −0.55 [email protected]

Laterally inhomogeneous surface-potential distribution and photovoltage at clustered In/WSe₂(0001) interfaces

Small increments of indium were evaporated at 300 and 100 K onto the van der Waals (0001) surface of p-type WSe₂ crystals. The interface formation was investigated in vacuo with x-ray photoemission spectroscopy, ultraviolet photoemisson spectroscopy, soft-x-ray photoemission spectroscopy, and low-energy electron diffraction. Additional scanning tunneling microscopy (STM), scanning electron microscopy (SEM), and microprobe measurements were performed ex situ. For deposition at 300 K a nonreactive interface is formed and the indium layer grows in the Volmer-Weber growth mode. The size and distribution of the In clusters for specific coverages were determined ex situ by STM and SEM. The band bending of 0.55 eV, as determined from binding-energy shifts of the substrate emissions, is far below the expected Schottky-limit value of 1.1 eV. The observed surface-photovoltage (SPV) shifts of the substrate emission lines are smaller (up to 0.2 eV) than those from the adsorbate lines. The maximum adsorbate SPV shift of 0.6 eV at 150 K exceeds the measured band bending, indicating that the band bending beneath the In clusters must be larger than between them. At a sample temperature of 100 K, In forms atomically flat layers (Frank–van der Merwe growth) allowing the determination of the actual band bending of 0.9–1.0 eV below the In-covered surface. For these conditions, the SPV is only 0.1 eV due to an electrical leakage current. During warmup to 300 K, a transition to the clustered interface occurs. For this interface, the band bending below the indium clusters could also be determined from temperature-dependent SPV measurements. The determined barrier height of 1.04 eV is in good agreement with the value measured at the unclustered interface

Electronic band structure of single-crystal and single-layer WS₂: Influence of interlayer van der Waals interactions

The valence band structure of the layered transition metal dichalcogenide WS₂ has been determined experimentally by angle resolved photoelectron spectroscopy and theoretically by augmented spherical wave band structure calculations as based on density functional theory. Good agreement between experimental and calculated band structure is observed for single crystal WS₂. An experimental band structure of a single layer was determined from an electronically decoupled film prepared on a single crystalline graphite substrate by metal-organic van der Waals epitaxy. The polarization dependent photoemission selection rules of the single layer film are appropriate for a free standing film. The experimental single layer band structure shows some differences compared to band structure calculations using bulk atomic positions within the layer. We conclude that relaxation of the single layer occurs as a consequence of the missing interlayer interactions leading to close agreement between electronic structure of the single layer and single crystal. As a consequence of the missing interlayer interactions the valence band maximum for the single layer is located at the K point of the Brillouin zone

The Fermi energy in oxides: assessing and understanding the limits using XPS

The Fermi energy in semiconductors can often be freely controlled across the whole energy gap by doping. This is not the case in oxides, where different mechanisms exist, which can limit the range of the Fermi energy. These limits can be caused by i) dopants having deep rather than shallow charge transition levels, ii) self-com­pen­sation where the Fermi energy dependence of the defect formation energy leads to spontaneous formation of compensating defects, iii) the change of the oxidation state of either the cations or the oxygen. The latter is particularly relevant for compounds with transition metal or rare earth cations and has been recently demonstrated to explain the low water splitting efficiency of hematite [1]. Please click Additional Files below to see the full abstract

Electronically Decoupled Films of InSe Prepared by van der Waals Epitaxy: Localized and Delocalized Valence States

Submonolayer to several monolayer thick films of the layered semiconductor InSe were deposited on highly oriented pyrolytic graphite by van der Waals epitaxy and probed by energy dependent angle resolved photoelectron spectroscopy. The layers show a transition from two-dimensional bands with atomiclike states to molecularlike states localized along the c direction normal to the surface. The extended band structure showing band dispersion was observed for thicker films

Analytical Study of Solution-Processed Tin Oxide as Electron Transport Layer in Printed Perovskite Solar Cells

Solution‐processed tin oxide (SnO$_{x}$ ) electron transport layers demonstrate excellent performance in various optoelectronic devices and offer the ease of facile and low cost deposition by various printing techniques. The most common precursor solution for the preparation of SnO$_{x}$ thin films is SnCl$_{2}$ dissolved in ethanol. In order to elucidate the mechanism of the precursor conversion at different annealing temperatures and the optoelectronic performance of the SnO$_{x}$ electron transport layer, phonon and vibrational infrared and photoelectron spectroscopies as well as atomic force microscopy are used to probe the chemical, physical, and morphological properties of the SnO$_{x}$ thin films. The influence of two different solvents on the layer morphology of SnO$_{x}$ thin films is investigated. In both cases, an increasing annealing temperature not only improves the structural and chemical properties of solution‐processed SnO$_{x}$, but also reduces the concentration of tin hydroxide species in the bulk and on the surface of these thin films. As a prototypical example for the high potential of printed SnO$_{x}$ layers for solar cells, high performance perovskite solar cells with a stabilized power conversion efficiency of over 15% are presented

Spectroscopic investigation of the deeply buried Cu In,Ga S,Se 2 Mo interface in thin film solar cells

The Cu In,Ga S,Se 2 Mo interface in thin film solar cells has been investigated by surface sensitive photoelectron spectroscopy, bulk sensitive X ray emission spectroscopy, and atomic force microscopy. It is possible to access this deeply buried interface by using a suitable lift off technique, which allows to investigate the back side of the absorber layer as well as the front side of the Mo back contact. We find a layer of Mo S,Se 2 on the surface of the Mo back contact and a copper poor stoichiometry at the back side of the Cu In,Ga S,Se 2 absorber. Furthermore, we observe that the Na content at the Cu In,Ga S,Se 2 Mo interface as well as at the inner grain boundaries in the back contact region is significantly lower than at the absorber front surfac

User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

Dangling Bond Defects on Si Surfaces and Their Consequences on Energy Band Diagrams: From a Photoelectrochemical Perspective

Using silicon in multijunction photocells leads to promising device structures for direct photoelectrochemical water splitting. In this regard, photoelectron spectra of silicon surfaces are used to investigate the energetic condition of contact formation. It is shown that the Fermi‐level position at the surface differs from the values expected from their bulk doping concentrations, indicating significant surface band bending which may limit the overall device efficiency. In this study, the influence of different surface preparation procedures for p‐ and n‐doped Si wafers on surface band bending is investigated. With the help of photoemission and X‐ray absorption spectroscopy, Si dangling bonds are identified as dominating defect centers at Si surfaces. These defects lead to an occupied defect band in the lower half and an unoccupied defect band in the upper half of the Si bandgap. However, partial oxidation of the defect centers causes a shift of defect bands, with only donor states remaining in the Si bandgap. Source‐induced photovoltages at cryogenic temperatures indicate that partial surface oxidation also decreases the recombination activity of these defect centers. It is shown that defect distribution, defect concentration, and source‐induced photovoltages need to be considered when analyzing Fermi‐level pinning at Si surfaces