Diamond Surface Research Articles

Bottom-Up Cu Filling of High-Aspect-Ratio through-Diamond vias for 3D Integration in Thermal Management.

Three-dimensional integrated packaging with through-silicon vias (TSV) can meet the requirements of high-speed computation, high-density storage, low power consumption, and compactness. However, higher power density increases heat dissipation problems, such as severe internal heat storage and prominent local hot spots. Among bulk materials, diamond has the highest thermal conductivity (≥2000 W/mK), thereby prompting its application in high-power semiconductor devices for heat dissipation. In this paper, we report an innovative bottom-up Cu electroplating technique with a high-aspect-ratio (10:1) through-diamond vias (TDV). The TDV structure was fabricated by laser processing. The electrolyte wettability of the diamond and metallization surface was improved by Ar/O plasma treatment. Finally, a Cu-filled high-aspect-ratio TDV was realized based on the bottom-up Cu electroplating process at a current density of 0.3 ASD. The average single-via resistance was ≤50 mΩ, which demonstrates the promising application of the fabricated TDV in the thermal management of advanced packaging systems.

Construction of Z-Scheme TiO2/Au/BDD Electrodes for an Enhanced Electrocatalytic Performance.

TiO2/Au/BDD composites with a Z-scheme structure was prepared by orderly depositing gold (Au) and titanium dioxide (TiO2) on the surface of a boron-doped diamond (BDD) film using sputtering and electrophoretic deposition methods. It was found that the introduction of Au between TiO2 and the BDD, not only could reduce their contact resistance, to increase the carrier transport efficiency, but also could improve the surface Hall mobility of the BDD electrode. Meanwhile, the designed Z-scheme structure provided a fast channel for the electrons and holes combination, to promote the effective separation of the electrons and holes produced in TiO2 and the BDD under photoirradiation. The electrochemical characterization elucidated that these modifications of the structure obviously enhanced the electrocatalytic performance of the electrode, which was further verified by the simulated wastewater degradation experiments with reactive brilliant red X-3B. In addition, it was also found that the photoirradiation effectively enhanced the pollution degradation efficiency of the modified electrode, especially for the TiO2/Au/BDD-30 electrode.

Surface potential pinning study for oxygen terminated IIa diamond

Surface potential pinning effect is a general rule in semiconductor materials, which can seriously affect the performance of devices. However, the surface potential pinning effect is often overlooked in the literature when studying diamond devices. In our previous work, we experimentally verified that the oxygen terminal with ketone bonds introduces an acceptor surface state, 2.22 eV above valence band maximum (VBM), into bandgap at diamond surface. Here, we further investigated the contact band diagram between metals (Au, Ag, Pt, W, and Pd) with different work function and oxygen terminated diamond using X-ray photoelectron spectroscopy. Results showed that the contact Fermi level was at 2.38 eV, 2.33 eV, 2.32 eV, 2.28 eV, and 2.29 eV above VBM, respectively. In addition, the similar symmetrical photocurrent-voltage characteristics under positive and negative bias were observed between Au–Ag and Ag–Pt electrodes deposited on the same oxygen terminated diamond plate. And the surface energy band can be restored to the similar level after destroying by hydrogen plasma or polishing. All the data above could be drawn a conclusion that the oxygen-terminal can pin the Schottky barrier height. We believe that the results obtained herein will help in the design and theoretical analysis of diamond Schottky devices.

Effect of Nanoscale W Coating on Corrosion Behavior of Diamond/Aluminum Composites

The stability of diamond/aluminum composite is of significant importance for its extensive application. In this paper, the interface of diamond/aluminum composite was modified by adding nanoscale W coating on diamond surface. We evaluated the corrosion rate of nanoscale W-coated and uncoated diamond/aluminum composite by a full immersion test and polarization curve test and clarified the corrosion products and corrosion mechanism of the composite. The introduction of W nanoscale coating effectively reduces the corrosion rate of the diamond/aluminum composite. After corrosion, the bending strength and thermal conductivity of the nanoscale W-coated diamond/aluminum composite are considerably higher than those of the uncoated diamond/aluminum composite. The corrosion loss of the material is mainly related to the hydrolysis of the interface product Al4C3, accompanied by the corrosion of the matrix aluminum. Our work provides guidance for improving the life of electronic devices in corrosive environments.

Bonding, retention and thermal stability of shallow nitrogen in diamond (100) by low-energy nitrogen implantation

We investigate the sub-surface bonding, retention, and thermal stability of nitrogen in diamond (100) implanted with 200 and 800 eV N2+ at room temperature (RT) and 600 °C at an ion dose of 3.4×1014 ions/cm2. Upon 200 eV N2+ implantation at RT and 600 °C, nitrogen is incorporated in the diamond lattice mainly in a C-N/C=N bond bonding configuration alongside a small CN(nitrile-like) component. 800 eV N2+ implantation at both RT and 600 °C, the implanted nitrogen can occupy multiple bonding configurations, including C-N/C=N and CN(nitrile-like) bonds. Implantation at 600 °C resulted in higher thermal stability of the implanted nitrogen compared to RT implantation due to dynamic annealing assisted defect curing and desorption of weekly bonded species (possibly nitrogen bonded to defects) during the high temperature implantation. The long-range order of the N2+ implanted diamond surfaces was also investigated using low-energy electron diffraction measurements.

Entrapment and thermal stability of low energy Argon implanted into diamond studied by in-situ X-ray photoelectron spectroscopy and thermal programmed desorption

The retention and thermal stability of Ar implanted into polycrystalline diamond surfaces with 700 and 5000 eV Ar ions, with high dose (HD) and low dose (LD) of 1016 and 1014 ions/cm2 at room temperature (RT) and 400 °C were investigated. Upon implantation at 400 °C, the thermal stability of the retained Ar is very high and can exceed 1000 °C, whereas, upon RT implantation at the same energy, it is below ∼800 °C. Ar entrapped in a local high crystalline diamond environment possesses a very high thermal stability compared to when it is entrapped in a graphite/amorphous local carbon environment. Ar thermal desorption occurs via diffusion between local defects, greatly enhanced between 600 and 700 °C. Implantation at 400 °C (at HD) results in two distinct regions: graphitic and highly crystalline diamond with low defect density due to dynamic annealing and direct desorption of Ar entrapped within the graphitic/damaged region during the implantation. Ar entrapped in a high crystalline diamond matrix is under higher compressive stress than in graphitic/amorphous carbon.

Frenkel-Poole Mechanism Unveils Black Diamond as Quasi-Epsilon-Near-Zero Surface.

A recent innovation in diamond technology has been the development of the "black diamond" (BD), a material with very high optical absorption generated by processing the diamond surface with a femtosecond laser. In this work, we investigate the optical behavior of the BD samples to prove a near to zero dielectric permittivity in the high electric field condition, where the Frenkel-Poole (FP) effect takes place. Zero-epsilon materials (ENZ), which represent a singularity in optical materials, are expected to lead to remarkable developments in the fields of integrated photonic devices and optical interconnections. Such a result opens the route to the development of BD-based, novel, functional photonic devices.

Nanothermometry with Enhanced Sensitivity and Enlarged Working Range Using Diamond Sensors

Nanothermometry is increasingly demanded in frontier research in physics, chemistry, materials science and engineering, and biomedicine. An ideal thermometer should have features of reliable temperature interpretation, high sensitivity, fast response, minimum disturbance of the target's temperature, applicability in a variety of environments, and a large working temperature range. For applications in nanosystems, high spatial resolution is also desirable. Such requirements impose great challenges in nanothermometry since the shrinking of the sensor volume usually leads to a reduction in sensitivity.Diamond with nitrogen-vacancy (NV) centers provides opportunities for nanothermometry. NV center spins have sharp resonances due to their superb coherence. NV centers are multimodal sensors. They can directly sense magnetic fields, electric fields, temperature, pressure, and nuclear spins and, through proper transduction, measure other quantities such as the pH and deformation. In particular, their spin resonance frequencies vary with temperature, making them a promising thermometer. The high thermal conductivity, high hardness, chemical stability, and biocompatibility of diamond enable reliable and fast temperature sensing in complex environments ranging from erosive liquids to live systems. Chemical processing of diamond surfaces allows various functionalities such as targeting. The small size and the targeting capability of nanodiamonds then enable site-specific temperature sensing with nanoscale spatial resolution. However, the sensitivity of NV-based nanothermometry is yet to meet the requirement of practical systems with a large gap of a few orders of magnitude. On the other hand, although NV-based quantum sensing works well from 0.3 to 600 K, extending the sensing scheme to high temperature remains challenging due to uncertainty in identifying the exact physical limits and possible solution at elevated temperatures.This Account focuses on our efforts to enhance the temperature sensitivity and widen the working temperature range of diamond-based nanothermometry. We start with explaining the working principle and features of NV-based thermometry with examples of applications. Then a transducer-based concept is introduced with practical schemes to improve the sensitivity of the nanodiamond thermometer. Specifically, we show that the temperature signal can be transduced and amplified by adopting hybrid structures of nanodiamond and magnetic nanoparticles, which results in a record temperature sensitivity of 76 μK/√Hz. We also demonstrate quantum sensing with NV at high temperatures of up to 1000 K by adopting a pulsed heating-cooling scheme to carry out the spin polarization and readout at room temperature and the spin manipulation (sensing) at high temperatures. Finally, unsolved problems and future endeavors of diamond nanothermometry are discussed.

The interfacial reaction between diamond (100) surface and CuNi-based filler alloys containing Cr by first-principles calculations

Brazed diamond tools have the advantages of high holding strength for diamond abrasives, superior grinding performance, formability, etc. The elements used commonly in filler alloys such as Cr, Cu, and Ni have an important impact on the interfacial bond strength and diamond thermal damage. In this work, the interactions between Cu, Ni, and Cr of the filler alloy and the diamond (100) surface were investigated using first-principles calculations. The results indicated that the adsorption energy of Cu adsorbed on the diamond (100) surface was low, suggesting that C atoms are extremely difficult to dissolve into Cu-based filler alloys, which makes Cu-based filler alloys less wettable with diamond. While the adsorption energy of Ni adsorbed on the diamond (100) surface was greater, which may form Ni 3 C weak carbide. Therefore, Ni-based filler alloys are usually wettable with diamonds. However, Ni 3 C of poor stability may decompose C atoms at the interface, which may lead to greater corrosion of diamonds. The adsorption energy of Cr adsorbed on the diamond (100) surface was the highest among Cu, Ni, and Cr, while the co-adsorption of Cr and C can grow into stable carbides. With the extension of time, the carbides can grow to form continuous layers of carbides. The results are generally consistent with the experimental results. • Analysis of graphitization on diamond surfaces using first-principles calculations. • The co-adsorption and deposition processes of Cr and C were investigated, which provided the conditions for the formation of chromium carbides. • Interfacial reaction processes, such as C precipitation and carbides nucleation growth, were investigated at the atomic level using first-principles calculations.

Theoretical study of n-type diamond with Li doping and Li-B co-doping: A density functional simulation

The Lithium-doped and Lithium-Boron (Li-B) co-doped diamonds were investigated by density functional theory to find out potential shallow donor impurities in diamond. In Li doped diamond, only interstitial Li doped diamond shows an effective n-type property with a low ionization energy of 0.04 eV. However, an extremely low solubility was found in diamond. In order to overcome this obstacle, co-doping with boron exhibits a unique advantage. A comprehensive research of different Li-B co-doping structures was conducted. With the help of B atom, the solubility of Li is greatly improved. Moreover, through first-principles calculations, we found for the first time that Lii2-B co-doped diamond has both low formation energy (−6.17 eV) and low ionization energy (0.29 eV). The 2p states of B and 2s states of Li dominate the conduction band minimum (CBM). Li atoms have many adsorption sites on intrinsic and B doped (001) surface of diamond, among which the bridge site of the dimer chain is the most suitable adsorption site for Li. It suggests that through the addition of B, Lii2-B co-doping can be an up-and coming candidate of effective shallow donor impurity in diamond.

Izbor reagensa za modifikaciju spektralnih karakteristika slabo i anomalno luminescentnih dijamanata u procesu rendgenske separacije

The feasibility of targeted modification of the spectral properties of weakly and anomalously luminescent diamonds by modifying reagents containing luminophores based on sulfides and zinc orthosilicate, characterized by medium and low deviation of the luminescence signal from that of natural diamond. It was found that the hydrophobic treatment of inorganic luminophores with potassium butyl xanthate could increase the recovery of anomalous luminescent diamonds in the process of X-ray luminescence separation up to 80%. Organic collectors (optically transparent oil products with high extractability for luminophores and adhesion to diamonds) based on technical-grade diesel fuel and catalytically cracked heavy gas oil are recommended for the luminophorecontaining compositions. The feasibility of reducing the fixation of luminophores on the surface of kimberlite grains using sodium hexametaphosphate, sulfonol, carboxymethylcellulose and liquid glass was demonstrated. The application of these reagents in low-salinity water provides decreasing coating of kimberlite grains with luminophores while maintaining the required concentration of luminophores on the surface of diamonds. Semi-industrial tests with an LS-D-4-03N separator proved the possibility of complete recovery of weakly and anomalously luminescent diamonds after treatment of XRS tailings with the modifying reagents.

Ichetyu Diamonds: Constitution, Surface Film Micromineralization, Genesis

Diamonds from the Ichetyu deposit of disputable genesis have been studied using X-ray diffraction analysis, scanning electron microscopy, cathode-, photo- and X-ray luminescence; spectroscopy of Raman scattering and IR absorption, LA-ICP-MS, isotope mass spectrometry. The crystal morphology of diamonds has been analyzed, the parameters of the forms of their mantle dissolution, the degree and nature of plastic and impact deformations have been determined. Features of the internal structure, luminescent-spectroscopic properties were revealed. The bulk concentration of structural nitrogen, the degree of aggregation of point nitrogen defects, and the temperature of mantle annealing are estimated. The composition of microelements and carbon isotopy were determined. The mineral-phase composition of films on the surface of diamonds has been studied. A conclusion was made about the tuffizite-fluidisite genetic type of the Ichetyu deposit.

Formation mechanism and regulation of silicon vacancy centers in polycrystalline diamond films

Diamond silicon vacancy centers (SiV centers) have important application prospects in quantum information technology and biomarkers. In this work, the formation mechanism and regulation method of SiV center during the growth of polycrystalline diamond on silicon substrate are studied. By changing the ratio of nitrogen content to oxygen content in the growing atmosphere of diamond, the photoluminescence intensity of SiV center can be controlled effectively, and polycrystalline diamond samples with the ratios of SiV center photoluminescence peak to diamond intrinsic peak as high as 334.46 and as low as 1.48 are prepared. It is found that nitrogen promotes the formation of SiV center in the growth process, and the inhibition of oxygen. The surface morphology and photoluminescence spectrum for each of these samples show that the photoluminescence peak intensity of SiV center is positively correlated with the grain size of diamond, and the SiV center’s photoluminescence peak in the diamond film with obvious preferred orientation of crystal plane is higher. The distribution of Si centers and SiV centers on the surface of polycrystalline diamond are further characterized and analyzed by photoluminescence, Raman surface scanning and depth scanning spectroscopy. It is found that during the growth of polycrystalline diamond, the substrate silicon diffuses first into the diamond grain and then into the crystal structure to form the SiV center. This paper provides a theoretical basis for the development and application of SiV centers in diamond.

Rational Design of Diamond Electrodes.

Diamond electrodes stepped onto the stage in the early 1990s for electroanalytical applications. They possess the features of long-term chemical inertness, wide potential windows, low and stable background currents, high microstructural stability at different potentials and in different media, varied activity toward different electroactive species, reliable electrochemical response of redox systems without conventional pretreatment, high resistance to surface fouling in most cases, and possibility of forming composites with different components such as other carbon materials, carbides, and oxidizes. Most diamond electrodes are prepared in microcrystalline or nanocrystalline form using chemical vapor deposition techniques. Starting from diamond films and diamond composites, numerous nanostructured diamond electrodes have also been produced. The features of diamond electrodes are therefore heavily dependent on the growth conditions and post-treatment procures that are applied on diamond electrodes such as introduced dopant(s), surface termination(s), surface functional group(s), added components, and final structure(s). Numerous applications of diamond electrodes have been explored in the fields of electrochemical sensing, electrosynthesis, electrocatalysis, electrochemical energy storage and conversion, devices, and environmental degradation.This Account summarizes our strategies to design different diamond electrodes, including diamond films, diamond composites, as well as their nanostructures. With respect to diamond films, the modulation of their dopant(s) and surface termination(s) as well as the attachment of functional modifier(s) onto their surface are discussed. Electrochemical hydrogenation and oxygenation of diamond electrodes are detailed at an atomic scale. As the examples of designing diamond electrodes at a molecular scale, photochemical and electrochemical attachment of modifier(s) onto diamond electrodes are shown. Moreover, electrochemical grafting of diazonium salts is proposed as a new technique to identify hydrogenated, hydroxylated, and oxygenated terminations of diamond electrodes. The introduction of additional component(s) into a diamond film to form diamond composites is then overviewed, where a hydrogen-induced selective growth model is proposed to elucidate the preparation of diamond/β-SiC composites. Subsequently, the production of various diamond nanostructures from diamond films and composites by means of top-down, bottom-up, and template-free approaches is shown. Electrochemical application examples of diamond electrodes are overviewed, covering direct electrochemistry of natural Cytochrome c on a hydroxylated diamond surface, sensitive electrochemical DNA biosensing on tip-functionalized diamond nanowires, and construction of high-performance supercapacitors using diamond electrodes and redox electrolytes. Our diamond supercapacitors, also named battery-like diamond supercapacitors or diamond supercabatteries, are highlighted since they combine the features of supercapacitors and batteries. Future perspectives of diamond electrodes are outlined, ranging from their rational design and synthesis to their electrochemical applications in different fields.

Raman Study of the Diamond to Graphite Transition Induced by the Single Femtosecond Laser Pulse on the (111) Face.

The use of the ultrafast pulse is the current trend in laser processing many materials, including diamonds. Recently, the orientation of the irradiated crystal face was shown to play a crucial role in the diamond to graphite transition process. Here, we develop this approach and explore the nanostructure of the sp2 phase, and the structural perfection of the graphite produced. The single pulse of the third harmonic of a Ti:sapphire laser (100 fs, 266 nm) was used to study the process of producing highly oriented graphite (HOG) layers on the (111) surface of a diamond monocrystal. The laser fluence dependence on ablated crater depth was analyzed, and three different regimes of laser-induced diamond graphitization are discussed, namely: nonablative graphitization, customary ablative graphitization, and bulk graphitization. The structure of the graphitized material was investigated by confocal Raman spectroscopy. A clear correlation was found between laser ablation regimes and sp2 phase structure. The main types of structural defects that disrupt the HOG formation both at low and high laser fluencies were determined by Raman spectroscopy. The patterns revealed give optimal laser fluence for the production of perfect graphite spots on the diamond surface.

Efficient n-Type Surface Doping in Diamond

Conventional doping in diamond is challenging for its application in electronic devices, which could be overcome by an alternative method of surface-transfer doping. In this study, efficient surface n-type conductivity is obtained on the N-terminated diamond surface doped with decamethylcobaltocene (DMC) and cobaltocene (CoCp2) molecules having low ionization energy values by first-principles calculation. By the surface-transfer doping mechanism, electrons are transferred from the dopants to diamond, and then electron accumulation occurs on the diamond surface. For DMC- and CoCp2-doped diamond surfaces, the areal electron density values are 4.822 × 1013 and 4.519 × 1013 cm–2, and the carrier mobility values are 357 and 108 cm2 V–1 s–1 at 298 K, respectively. Moreover, after DMC and CoCp2 molecular adsorption, the optical absorption coefficient increases in the visible region. This study will promote investigations for two-dimensional electron gas on the diamond surface.

Advanced Mapping of Optically-Blind and Optically-Active Nitrogen Chemical Impurities in Natural Diamonds

Natural diamonds with a rich variety of optically blind and optically active nitrogen impurity centers were explored at a nano/microscale on the surface and in bulk by a number of advanced chemical and structural analytical tools in order to achieve a comprehensive characterization by establishing enlightening links between their analysis results. First, novel compositional relationships were established between high-energy X-ray photoelectron spectroscopy (XPS) and low-energy Fourier-transform infrared vibrational spectroscopy (FT-IR) signals of nitrogen impurity defects acquired in the microscopy mode at the same positions of the diamond surface, indicating the verification XPS modality for qualitative and quantitative FT-IR analysis of high concentrations of nitrogen and other chemical impurity defects in diamond. Second, depth-dependent spatial distributions of diverse photoluminescence (PL)-active nitrogen defects were acquired in the confocal scanning mode in an octahedral diamond and then for the first time corrected to the related Raman signals of the carbon lattice to rule out artefacts of the confocal parameter and to reveal different micron-scale ontogenetic layers in the impurity distributions on its surface. Third, intriguing connections between local structural micro-scale defects (dislocation slip bands of plastic deformation zones) visualized by optical microscopy and Raman microspectroscopy, and related distributions of stress-sensitive PL-active nitrogen impurity defects in the proximity of these planes inside bulk diamonds were revealed. These findings demonstrate the broad instrumental opportunities for comprehensive in situ studies of the chemical, structural, and mechanical micro-features in diamonds, from the surface into bulk.

Selection of Temperature regimes for conditioning and flotation of diamond-bearing kimberlite with compound collectors

The condition for stable fixation of a collector on the surface of diamonds and their flotation is the use of collectors of the optimal fractional composition and the choice of the optimum temperature regime of the process. To determine the parameters of the diamond flotation regime, the regularities of the phase transitions of asphaltene-tar fractions at increasing temperature and diluting F-5 with technical diesel fraction were established. It was demonstrated that increasing the collector temperature leads to the transfer of asphaltenetar fractions to a dissolved and finely dispersed state. To an even greater extent, dissolving asphaltene-tar fractions is facilitated by the addition of medium- and low-molecular weight fractions of oil, for instance, a technical diesel fraction.It was revealed that the KM-10, KM-14, and KM-18 reagents, being compounds of F-5 fuel oil with technical diesel fraction (10–18 % DF), were characterized by optimal viscosity and ability to displace aqueous phase from a diamond surface, thus ensuring stable hydrophobization and high floatability of diamonds. The optimal temperature regime has been selected, which involved maintaining the temperature at the stage of conditioning with the collector at +30–40 °С, at which the maximum selective fixation of compound collectors on the diamond surface, characterized by the value of the limiting wetting angle, was achieved. The flotation tests have confirmed that the best results are achieved at a temperature of +30–40 °С at the conditioning stage and +14–24 °С at the flotation stage. At +24 °С, the best results were obtained for the relatively less diluted KM-10 and KM-14 fuel oils obtained by diluting F-5 fuel oil with a technical diesel fraction at the diluent volume fractions of 10 and 14 %. The diamond recovery achieved in the flotation tests was 3.8–4.5 % higher than when using the traditional collector, F-5 fuel oil. At +14 °С, the highly diluted fuel oil, KM-18 with a volume fraction of 18 % of the technical diesel fraction, demonstrated better collecting abilities.The optimal compositions of the collector and the regimes of feed preparation and flotation were tested at a foam separation unit. The tests showed that it is possible to increase diamond recovery into concentrate by 2.3–4.5 %. The recommendations are provided on the use of thermal conditioning in the foam separation cycle and maintaining the conditioning medium temperature at +30–40 °С and the foam separation temperature at +14–24 °С.

Performance of diamond circular saws with innovative Fe-based binders

The influence of binder composition on the performance of diamond circular saws in cutting reinforced concrete was investigated. Two different approaches were used to improve Fe-based binder to provide high cutting rate and stable wear rate of the tool. The first approach was built upon doping the binder with titanium, a strong carbide-forming component, which allowed producing titanium carbide layer at the diamond–binder interface, thus improving adhesion. The second approach involved complex modification of the binder with nanoparticles of tungsten carbide, hexagonal boron nitride and carbon nanotubes. These dopants improve the mechanical properties of the binders and provide formation of self-assembling protective WC coatings on the diamond surface. To confirm the benefits of binder modification, we tested diamond circular saws equipped with designed binders in cutting reinforced concrete. The tools with basic binder had the lowest cutting speed, higher wear rate and dulling during the test. The modification by addition of titanium allows this problem to be partially solved due to better diamond fixation in the working layer. The complex modification of the binder with nanoparticles demonstrated the best results as it changed its wear mechanism as well as enhanced its mechanical properties. The simultaneous strengthening with WC particles and carbon nanotubes and provoking of wear of binder microvolumes by boron nitride made it possible to maintain high cutting speed and stabilize the tool wear during machining. This work was supported by the Russian Science Foundation, Project No. 17-79-20384.

Probing Spin Dynamics on Diamond Surfaces Using a Single Quantum Sensor

A detailed analysis of the coherence decay of a nanoscale sensor shows that ubiquitous spins on the diamond surface are mobile and reveals the potential of local sensors to investigate the dynamics of complex systems.