Physical atomistic kinetic Monte Carlo modeling of Fermi-level effects of species diffusing in silicon (original) (raw)
Related papers
2005
Atomistic process simulation is expected to play an important role for the development of next generations of integrated circuits. This work describes an approach for modeling electric charge effects in a three-dimensional atomistic kinetic Monte Carlo process simulator. The proposed model has been applied to diffusion of electrically active boron and arsenic atoms in silicon. Several key aspects of the underlying physical mechanisms are discussed: (i) the use of the local Debye length to smooth out the atomistic point charge distribution, (ii) algorithms to correctly update the charge state in a physically accurate and computationally efficient way, and (iii) an efficient implementation of the drift of charged particles in an electric field. High concentration effects such as band-gap narrowing and degenerate statistics are also taken into account. The efficiency, accuracy, and relevance of the model are discussed.
Materials Science and Engineering: B, 2005
Continuum downscaling of MOSFET devices requires of ultra-shallow junction formation. Performance of the source and drain from B and As low energy implant and subsequent annealing is seriously affected by the presence of the Si-SiO 2 interface. Dopant loss due to segregation and dopant pileup at the interface during the transient enhanced diffusion (TED) are crucial phenomena for current and future CMOS devices. In this work we have implemented the Oh-Ward model [Y.-S. Oh, D.E. Ward, Tech. Dig. Int. Electron Devices Meet. 1998 509] for the dopant behaviour at the interfaces integrated in an atomistic kinetic Monte Carlo simulator. Dopant traps at the interface can capture from or emit to either side of the interface. Furthermore, segregation of dopants and saturation of the interface by the presence of other species are also included. As a test of the model, low energy implants through a screen oxide have been simulated. When annealing these very shallow implants, a pileup at the interface is observed. The mechanisms involved in this process, as well as its dependence on the implant dose and energy are discussed.
Atomistic simulations in Si processing: Bridging the gap between atoms and experiments
Materials Science and Engineering: B, 2005
With devices shrinking to nanometric scale, process simulation tools have to shift from continuum models to an atomistic description of the material. However, the limited sizes and time scales accessible for detailed atomistic techniques usually lead to the difficult task of relating the information obtained from simulations to experimental data. The solution consists of the use of a hierarchical simulation scheme: more fundamental techniques are employed to extract parameters and models that are then feed into less detailed simulators which allow direct comparison with experiments. This scheme will be illustrated with the modeling of the amorphization and recrystallization of Si, which has been defined as a key challenge in the last edition of the International Technology Roadmap for Semiconductors. The model is based on the bond defect or IV pair, which is used as the building block of the amorphous phase. The properties of this defect have been studied using ab initio methods and classical molecular dynamics techniques. It is shown that the recombination of this defect depends on the surrounding bond defects, which accounts for the cooperative nature of the amorphization and recrystallization processes. The implementation of this model in a kinetic Monte Carlo code allows extracting data directly comparable with experiments. This approach provides physical insight on the amorphization and recrystallization mechanisms and a tool for the optimization of solid-phase epitaxial-related processes.
Atomistic analysis of defect evolution and transient enhanced diffusion in silicon
Journal of Applied Physics, 2003
Kinetic Monte Carlo simulations are used to analyze the ripening and dissolution of small Si interstitial clusters and ͕113͖ defects, and its influence on transient enhanced diffusion of dopants in silicon. The evolution of Si interstitial defects is studied in terms of the probabilities of emitted Si interstitials being recaptured by other defects or in turn being annihilated at the surface. These two probabilities are related to the average distance among defects and their distance to the surface, respectively. During the initial stages of the defect ripening, when the defect concentration is high enough and the distance among them is small, Si interstitials are mostly exchanged among defects with a minimal loss of them to the surface. Only when defects grow to large sizes and their concentration decreases, the loss of Si interstitials through diffusion to the surface prevails, causing their dissolution. The presence of large and stable defects near the surface is also possible when the implant energy is low-small distance to the surface-but the dose is high enough-even smaller distance among defects. The exchange of Si interstitials among defects sets a interstitial supersaturation responsible for the temporary enhancement of the diffusivity of interstitial diffusing dopants. The transitory feature of the enhancement is well correlated to the extinction of the Si interstitial defects.
Atomistic Modeling of Complex Silicon Processing Scenarios
MRS Proceedings, 2000
The level of sophistication reached by today's Si device fabrication technologies has called for new modeling and simulation schemes, capable of handling the wide variety of interaction mechanisms that govern the complex phenomena that can occur at the atomic level. The kinetic Monte Carlo (KMC) technique seems particularly apt for this task. It takes as input basic materials parameters, derived from ab-initio calculations or from experiments, and is capable of carrying out a detailed simulation up to the dimensions and time scales of current ULSI Si device manufacture. In addition, it can accommodate and efficiently simulate complex interactions between multiple dopant and defect types. We explain the approach and show examples of application in both materials processing and device fabrication. Finally, we present the use of some artificial intelligence techniques (namely, genetic algorithms) that look most promising as methodologies that can easy and efficiently be employed to build the extensive KMC parameter database.
Atomic scale models of ion implantation and dopant diffusion in silicon
Thin Solid Films, 2000
We review our recent work on an atomistic approach to the development of predictive process simulation tools. First-principles methods, molecular dynamics simulations, and experimental results are used to construct a database of defect and dopant energetics in Si. This is used as input for kinetic Monte Carlo simulations. C and B trapping of the Si self-interstitial is shown to help explain the enormous disparity in its measured diffusivity. Excellent agreement is found between experiments and simulations of transient enhanced diffusion following 20±80 keV B implants into Si, and with those of 50 keV Si implants into complex B-doped structures. Our simulations predict novel behavior of the time evolution of the electrically active B fraction during annealing.
Modeling of defects, dopant diffusion and clustering in silicon
Journal of Computational Electronics, 2014
Ion implantation is a very well established technique to introduce dopants in semiconductors. This technique has been traditionally used for junction formation in integrated circuit processing, and recently also in solar cells fabrication. In any case, ion implantation causes damage in the silicon lattice that has adverse effects on the performance of devices and the efficiency of solar cells. Alternatively, damage may also have beneficial applications as some studies suggest that small defects may be optically active. Therefore it is important an accurate characterization of defect structures formed upon irradiation. Furthermore, the technological evolution of electronic devices towards the nanometer scale has driven the need for the formation of ultra-shallow and low-resistive junctions. Ion implantation and thermal anneal models are required to predict dopants placement and electrical activation. In this article, we review the main models involved in process simulation, including ion implantation, evolution of point and extended defects and dopant-defect interactions. We identify different regimes at which each type of defect is more relevant and its inclusion in the models becomes crucial. We illustrate in some examples the use of atomistic modeling techniques to gain insight into the physics involved in the processes as well as the relevance of the accuracy of models.
Monte Carlo Simulation of Electron-Electron Interactions in Bulk Silicon
Scientific Computing in Electrical Engineering, 2020
We have developed a novel Monte Carlo (MC) algorithm to study carrier transport in semiconductors in the presence of electron-electron scattering (EES). It is well known that the Boltzmann scattering operator for EES is nonlinear in the single-particle distribution function. Numerical solution methods of the resulting nonlinear Boltzmann equation are usually based on more or less severe approximations. In terms of the pair distribution function, however, the scattering operator is linear. We formulate a kinetic equation for the pair distribution function and related MC algorithms for its numerical solution. Assuming a spatially homogeneous system we derived a two-particle MC algorithm for the stationary problem and an ensemble MC algorithm for the transient problem. Both algorithms were implemented and tested for bulk silicon. As a transient problem we analyzed the mixing of a hot and a cold carrier ensemble. The energy of the hot ensemble relaxes faster with EES switched on. The cold ensemble is temporarily heated by the energy transferred from the hot ensemble. Switching on the electric field rapidly is known to result in an velocity overshoot. We observe that EES enhances the overshoot. The stationary algorithm was used to calculate the energy distribution functions at different field strengths.
Atomistic Modeling of Point and Extended Defects in Crystalline Materials
MRS Proceedings, 1998
Atomistic process modeling, a kinetic Monte Carlo simulation technique, has the interest of being both conceptually simple and extremely powerful. Instead of reaction equations it is based on the definition of the interactions between individual atoms and defects. Those interactions can be derived either directly from molecular dynamics or first principles calculations, or from experiments. The limit to its use is set by the size dimensions it can handle, but the level of performance achieved by even workstations and PC's, together with the design of efficient simulation schemes, has revealed it as a good candidate for building the next generation of process simulators, as an extension of existing continuum modeling codes into the deep submicron size regime. Over the last few years it has provided a unique insight into the atomistic mechanisms of defect formation and dopant diffusion during ion implantation and annealing in silicon. Object-oriented programming can be very helpful in cutting software development time, but care has to be taken not to degrade performance in the critical inner calculation loops. We discuss these techniques and results with the help of a fast object-oriented atomistic simulator recently developed.
First-principles-based predictive simulations of B diffusion and activation in ion implanted Si
2000
We present a kinetic Monte Carlo model for boron diffusion, clustering and activation in i o n implanted silicon. The input to the model is based on a combination o f experimental data and ab i n i t i o calculations. The model shows that boron diffusion and activation are low while vacancy clusters are present in the system. As the vacancy clusters dissociate, boron becomes substitutional and the active fraction increases rapidly. At the same time, the total boron diffusion length also increases rapidly while interstitial clusters ripen. The final burst of boron diffusion occurs a s the large interstitial clusters d i s s o l v e , but most of the transient diffusion of the implanted boron has already taken place by this time. We show that these results are in excellent agreement with experimental data on annealed dopant profiles and dopant activation as a function of annealing time.