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Zusammenfassung Unter dem Begriff der Auflösung wird für gewöhnlich das kleinste messbare Merkmal eines Messsystems verstanden. In der dimensionellen Computertomografie hingegen haben sich in den vergangenen Jahren mehrere Auflösungskonzepte etabliert, die aufgrund der fehlenden Normung zueinander im Kontrast stehen. In diesem Beitrag werden die drei häufigsten Konzepte, die Voxelgröße, die Ortsauflösung und die metrologische Strukturauflösung in Kürze vorgestellt. Anschließend wird eine Abgrenzung zwischen den Konzepten getroffen und ein Integration der bestehenden Konzepte in ein gemeinsames Amplituden-Wellenlängen Diagramm diskutiert.

X-ray computed tomography (XCT) is a fast-growing technology for dimensional measurements in industrial applications. However, traceable and efficient methods to determine measurement uncertainties are not available. Guidelines like the VDI/VDE 2630 Part 2.1 suggest at least 20 repetitions of a specific measurement task, which is not feasible for industrial standards. Simulation-based approaches to determine task specific measurement uncertainties are promising, but require closely adjusted model parameters and an integration of error sources like geometrical deviations during a measurement. Unfortunately, the development of an automated process to parameterize and integrate geometrical deviations into XCT models is still an open issue. In this work, the whole processing chain of dimensional XCT measurements is taken into account with focus on the issues and requirements to determine suitable parameters of geometrical deviations. Starting off with baseline simulations of different XCT systems, two approaches are investigated to determine and integrate geometrical deviations of reference measurements. The first approach tries to iteratively estimate geometric deviation parameter values to match the characteristics of the missing error sources. The second approach estimates those values based on radiographs of a known calibrated reference object. In contrast to prior work both approaches only use a condensed set of parameters to map geometric deviations. In case of the iterative approach, some major issues regarding unhandled directional dependencies have been identified and discussed. Whereas the radiographic method resulted in task specific expanded measurements uncertainties below one micrometre even for bi-directional features, which is a step closer towards a true digital twin for uncertainty estimations in dimensional XCT.

The electronic and structural properties of the Ge/GeO2 interface are addressed through a density functional simulation scheme which includes the use of hybrid functionals for achieving accurate band gaps, band offsets and defect levels. The present work discusses the germanium dangling bond levels, the thermodynamics of GeOx, the stability of the oxygen vacancy across Ge/HfO2 interfaces, the atomic structure of GeOx, electron and hole trapping in GeOx, and the band alignment at the Ge/GeO2 interface. (C) 2011 Elsevier B.V. All rights reserved.

An atomistic model of substoichiometric germanium oxide is generated through ab initio molecular dynamics. The resulting structure shows a predominance of threefold coordinated Ge and O atoms. We also generate substoichiometric models through bond-switching Monte-Carlo simulations, which preserve the fourfold Ge and the twofold O coordinations. These differing structures are energetically competitive. Alignment of their electron densities of states to that of GeO"2 reveals that the band-gap reduction is similar for both structures, mainly occurring through a shift of the valence band edge.

The electronic and structural properties at the Ge/GeO2 interface are addressed through a density-functional simulation scheme, which includes the use of hybrid functionals for achieving defect levels and band gaps comparable to experiment. The present work discusses the determination of the germanium dangling bond levels, the band alignment in a model structure of the Ge/GeO2 interface, the thermodynamics of GeOx, the stability of the oxygen vacancy across Ge/GeOx/HfO2 stacks, the structural and electronic properties of GeOx, and its ability to trap electrons.

Using density functional calculations, we studied substoichiometric Ge oxides through a series of crystalline models representing the various oxidation states. We evaluated deviations with respect to a bond-energy description in terms of penalty energies for intermediate oxidation states of Ge. Corresponding bond length variations and band gaps are also given. The calculated penalty energies are significantly lower than for Si indicating higher stability of the substoichiometric phase at Ge/GeO2 interfaces compared to Si/SiO2 interfaces. (C) 2009 Elsevier B.V. All rights reserved.

An atomistic model of the Ge-GeO2 interface has been generated through first-principle methods based on density functional theory. The interface model consists of amorphous GeO2 connected to crystalline Ge through a substoichiometric oxide region showing regular structural parameters. Structural and electronic properties are compared to available experimental data and studied as they evolve across the Ge-GeO2 interface. (C) 2009 Elsevier B.V. All rights reserved.

The Ge core-level shift across the Ge/GeO2 interface is determined within semilocal and hybrid density functional schemes. We first assess the accuracy achieved within these theoretical frameworks by comparing calculated and measured core-level shifts for a set of Ge-based molecules. The comparison with experimental data results in rms deviations of 0.19 and 0.09 eV for core-level shifts calculated with semilocal and hybrid density functionals, respectively. We also compare calculated core-level shifts at the Ge(001)-c(4 x 2) surface with high-resolution x-ray photoemission spectra finding similar agreement. We then turn to the Ge/GeO2 interface, which we describe with atomistic superlattice models showing alternating layers of Ge and GeO2. The adopted models include a substoichiometric transition region in which all Ge atoms are fourfold coordinated and all O atoms are twofold coordinated, as inferred for Si/SiO2 interfaces. Since the calculation of core-level shifts involves charged systems subject to finite-size effects, we use two different methods to ascertain the core-level shift Delta E-XPS between the oxidation state Ge-0 and Ge+4 across the interface. In the first method, core-hole relaxations are first evaluated in bulk models of the interface components and then complemented by the initial-state shift calculated across the interface, while the second method consists of direct interface calculations corrected through classical electrostatics. Using the more accurate hybrid functional scheme, we obtain a shift Delta E-XPS of 2.7 +/- 0.1 eV. This value is significantly lower than experimental data, which typically fall around 3.3 eV or higher, but the underestimation is consistent with that found for the valence band offset of the same model. This leads to the conclusion that the adopted model structures yield an incorrect description of the interface dipole and emphasizes that Ge/GeO2 interfaces possess different structural properties than their silicon counterparts.

Using a density-functional scheme, we study the migration of a single O atom in a (110) plane between two adjacent bond-center sites in bulk Si. The minimum energy migration path is found through the nudged elastic band method within a generalized gradient approximation for the electronic structure. The energy barrier is then also evaluated within a hybrid functional scheme. We achieve for the transition barrier a best estimate of 2.3 eV in the generalized gradient approximation and of 2.7 eV in the hybrid functional scheme, both in fair agreement with the commonly accepted experimental value of 2.53 eV. The transition is characterized by a saddle point which does not occur at the midpoint between the two bond-center sites and by a pattern of displacements extending up to the second nearest-neighbor Si atoms. The atomistic mechanism of oxygen migration is analyzed from three complementary viewpoints involving the evolution of the structure, the Wannier centers, and the single-particle energies and wave functions. The diffusion process can be separated into two distinct parts. In one part, the exchange of the Si atoms in the first-neighbor shell of the diffusing O atom occurs through the formation of a threefold coordinated O center and an overcoordinated Si atom. In the other part, the Si-Si bond flips its position through the creation of occupied and unoccupied Si dangling bonds which give rise to states in the band gap.

Reference EPFL-ARTICLE-171597doi:10.1063/1.3571449View record in Web of Science Record created on 2011-12-16, modified on 2017-05-12

The stability of oxygen vacancies across the Ge–HfO2 interface is studied through semilocal and hybrid density-functional calculations. On the semiconductor side, the formation energies are obtained for substoichiometric GeOx of varying x through the use of a bond-energy model. On the hafnium oxide side, the interface is modeled through bulk models with aligned band structures. Formation energies are compared for different charge states and Fermi energy levels. The oxygen vacancy is found to be most stable in the interfacial germanium oxide layer for both p-type and n-type doping. This favors the formation of substoichiometric GeOx, consistent with experimental observations.

Through hybrid density functional calculations, we compare the Ge-Ge bond energy with the formation energy of a valence alternation pair as the O concentration varies across the Ge/GeO2 interface. First, hole trapping energies are calculated for three atomistic models with different O concentrations: bulk Ge with isolated O atoms, amorphous GeO, and amorphous GeO2 with an O vacancy. The reaction is then broken down in three steps involving the breaking of a Ge-Ge bond, charge transfer processes involving dangling bonds, and the formation of a threefold coordinated O atom. The energy of each elemental reaction is estimated through suitable model calculations. The charge transition levels resulting from this analysis agree with those obtained for the atomistic models. Our estimates indicate that hole trapping at low O concentrations occurs at no energy cost for p-type germanium owing to the formation of threefold-coordinated O atoms. Applied to n-type Ge, our analysis indicates that electron trapping in dangling bonds obtained from the breaking of Ge-Ge bonds is unfavorable. The formation energy of a valence alternation pair is evaluated and discussed in relation to previous results. (C) 2011 Elsevier B.V. All rights reserved.

Model structures of substoichiometric germanium oxide generated by ab initio molecular dynamics reveal a rich variety of bonding configurations, including threefold coordinated Ge and O atoms which correspond to valence alternation pairs. A sizable fraction of twofold Ge atoms carrying unoccupied dangling bonds is also found. The present structures are prone to electron capture. The electrons are trapped in additionally formed Ge-Ge bonds. The associated defect levels fall within the Ge band gap and could explain the poor performance of n-type Ge devices. (C) 2010 American Institute of Physics. [doi : 10.1063/1.3486175]

Using hybrid density functional calculations, we investigate possible origins for the large variation of band offsets measured at Ge/GeO2 interfaces. We consider atomistic model interfaces with both amorphous and crystalline oxides, in which the bond density reduction accounts for the mass densities of the two interface components. To the extent that all the Ge atoms are fourfold coordinated and all the O atoms are twofold coordinated, the band offsets are found to remain constant within 0.1 eV. We then investigate the role of valence alternation pairs consisting of negatively charged Ge dangling bonds and positively charged threefold coordinated O atoms, which have been suggested to occur in sizeable concentrations in substoichiometric germanium oxide. A valence alternation pair is introduced in one of the atomistic models and is found to affect the band alignment by contributing to the interface dipole. The calculated band offsets shift by 0.7 eV for an areal concentration of valence alternation pairs corresponding to one pair per 8 Ge interface atoms. These pairs would act as fixed charges and are not expected to directly contribute to the defect density in the germanium band gap. The occurrence of such bonding patterns offers a possible explanation for the large range of valence band offsets measured at this interface. (C) 2011 Elsevier B.V. All rights reserved.

Electron and hole trapping in substoichiometric germanium oxides are investigated through the use of hybrid density functionals. We consider disordered model structures generated by Monte-Carlo bond switching and by ab initio molecular dynamics (MD). The Monte-Carlo model consists of fourfold coordinated Ge atoms and of twofold coordinated O atoms, and does not show trap levels neither for electron nor for holes. At variance, the MD model shows threefold coordinated O and Ge atoms forming valence alternation pairs and is found to present trap states for both carriers. The trapping states correspond to the formation and breaking of Ge-Ge bonds. The associated defect levels are determined within a band diagram of the Ge/GeO2 interface. (C) 2011 Elsevier B.V. All rights reserved.

Band offsets of the Ge/GeO2 interface are calculated through a hybrid density functional scheme. We first generate a model of disordered GeO2 through ab initio molecular dynamics to describe the oxide component. For addressing the interface, we then consider an atomistic model in which amorphous GeO2 is connected to crystalline Ge through a suboxide transition region showing regular structural parameters. The band offsets are obtained through the application of an alignment scheme, which reproduces the experimental band gaps of the interface components. The calculated valence band offset of 3.7 eV favors the low-energy side of the range of measured offsets.

International audience; This mini-review is intended as a short introduction to electron flow in nanostructures. Its aim is to provide a brief overview of this topic for people who are interested in the thermodynamics of quantum systems but know little about nanostructures. We particularly emphasize devices that work in the steady-state, such as simple thermoelectrics, but also mention cyclically driven heat engines. We do not aim to be either complete or rigorous, but use a few pages to outline some of the main ideas in the topic.