Point Defects and Their Interaction

Wagner, Carl

doi:10.1146/annurev.ms.07.080177.000245

Cited by 18 publications

(3 citation statements)

References 34 publications

(37 reference statements)

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“…Nevertheless, vacancies are still randomly distributed on a liquid surface as a structural imperfection in a short-range order ( Wagner, 1977 ). The highly isotropic noncrystalline structure of the liquid surface allows homogeneous nucleation of 2D materials on these defect sites.…”

Section: Surface-engineered Substratementioning

confidence: 99%

Controllable growth of two-dimensional materials on noble metal substrates

2021

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Summary Chemical vapor deposition (CVD) is a promising approach for the controllable synthesis of two-dimensional (2D) materials. Many studies have demonstrated that the morphology and structure of 2D materials are highly dependent on growth substrates. Hence, the choice of growth substrates is essential to achieve the precise control of CVD growth. Noble metal substrates have attracted enormous interest owing to the high catalytic activity and rich surface morphology for 2D material growth. In this review, we introduce recent progress in noble metals as substrates for the controllable growth of 2D materials. The underlying growth mechanism and substrate designs of noble metals based on their unique features are thoroughly discussed. In the end, we outline the advantages and challenges of using noble metal substrates and prospect the possible approaches to extend the uses of noble metal substrates for 2D material growth and enhance the structural controllability of the grown materials.

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Section: Surface-engineered Substratementioning

confidence: 99%

Controllable growth of two-dimensional materials on noble metal substrates

2021

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“…Defects form in almost all conditions and strongly affect the structural, elastic, optical and electronic properties of crystalline and amorphous systems. [1,2,3] The physical properties arising from the presence of defects are notoriously difficult to attribute to individual species experimentally; unless the defects are present in very high concentrations, most often one has to infer their structure and energy states by secondary means (see e.g. Refs.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium point defect and charge carrier concentrations in a material determined through calculation of the self-consistent Fermi energy

Buckeridge

2019

Computer Physics Communications

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Classification: 16.1 Structure and properties, 23 Statistical Physics and Thermodynamics Nature of problem: To determine the self-consistent Fermi energy and equilibrium defect and carrier concentrations given a set of point defect formation energies in a crystalline system, assuming the constraint of charge neutrality. Solution method: The concentrations of each defect in each charge state are calculated, as are the free carrier concentrations. These concentrations are functions of the Fermi energy. The code, using an interative search algorithm, determines the Fermi energy that satisfies the charge neutrality constraint (the self-consistent Fermi energy). The defect and carrier concentrations at that Fermi energy are then reported, as well as the Fermi energy itself. Restrictions: Thermodynamic equilibrium is assumed. The defect formation enthalpies and electronic density of states of the pristine system must be known. Additional comments: The concentrations of defects can be fixed to a particular value, thus modelling 'frozen-in' defects formed by e.g. kinetic processes. This procedure is facilitated by the related program, FROZEN-SC-FERMI, which is identical to SC-FERMI apart from the additional defect concentration fixing routine. Running time: Less than one second.

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“…The EM also depends on the structural properties of the interconnects after the fabrication process. A metal lattice vibrates at any temperature above 0 K [86]. The atomic vibrations change the metal atoms positions from their equilibrium and cause electron scattering.…”

Section: The Electromigration Phenomenonmentioning

confidence: 99%

Study of electromigration in integrated circuits at design level

Nunes¹

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Electromigration damage in interconnects is a well-known bottleneck of integrated circuits, because it causes reliability problems. Operation at high temperatures and current densities accelerates the damage, increasing the interconnect resistance and, therefore, reducing the circuit lifetime. This issue has been accentuated with the technology downscaling. To guarantee the interconnect reliability and, as a consequence, the integrated circuit reliability, traditional methods based on the so-called Blech Effect and on the maximum allowed current density are implemented during interconnect design. These methods, however, do not take into account the impact of the electromigration on the circuit performance.In this work the traditional approach is extended and a method to evaluate the effect of the electromigration in an integrated circuit performance is developed. The method is implemented in a tool which identiĄes the critical interconnect lines of an integrated circuit and suggests the proper interconnect width based on different criteria to mitigate the electromigration damage and to increase the reliability. In addition, the variation of performance parameters of the circuit as an interconnect resistance changes is determined.The tool is incorporated into the design Ćow of the integrated circuit and uses the data from design kits and reports directly available from the design environment.An accurate analysis of the temperature distribution on the interconnect structure is essential to a better assessment of the interconnect reliability. Therefore, a model to compute the temperature on each metallization level of the interconnect structure is implemented.The temperature distribution on the metallization layers of different technologies is investigated. It is shown that the temperature in the Metal 1 of the Intel 10 nm can increase by 75 K, 12 K higher than in the Metal 2. As expected, the layers that are closer to the transistors undergo a more signiĄcant temperature increase.The tool is applied to evaluate the interconnects and the robustness of different circuits, namely a ring oscillator, a bandgap voltage reference circuit, and an operational ampliĄer, against electromigration. The operational ampliĄer, in particular, is thoroughly studied.The proposed methodology identiĄes critical interconnects which under electromigration cause large variations in the performance of the circuit. In a worst-case scenario, the cutoff frequency of the circuit varies by 65% in 5 years of operation. An interesting Ąnding is that the proposed methodology identiĄes critical interconnects which would not be identiĄed by the traditional criteria. These interconnects have current densities below the limit recommended by the design rules. Nevertheless, one of such an interconnect leads to a variation of 30% in the gain of the operational ampliĄer. In summary, the proposed tool veriĄed that from the 20% paths with a critical current density, only 3% degrades signiĄcantly the circuit performance.This work brings the study of the reli...

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Point Defects and Their Interaction

Cited by 18 publications

References 34 publications

Controllable growth of two-dimensional materials on noble metal substrates

Controllable growth of two-dimensional materials on noble metal substrates

Equilibrium point defect and charge carrier concentrations in a material determined through calculation of the self-consistent Fermi energy

Study of electromigration in integrated circuits at design level

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