Chemical Vapor Deposition System Research Articles

Eight In. Wafer-Scale Epitaxial Monolayer MoS2.

Large-scale, high-quality, and uniform monolayer molybdenum disulfide(MoS2) films are crucial for their applications in next-generation electronics and optoelectronics. Epitaxy is a mainstream technique for achieving high-quality MoS2 films and is demonstrated at a wafer scale up to 4-in. In this study, the epitaxial growth of 8-in. wafer-scale highly oriented monolayer MoS2 on sapphire is reported as with excellent spatial homogeneity, using a specially designed vertical chemical vapor deposition (VCVD) system. Field effect transistors (FETs) based on the as-grown 8-in. wafer-scale monolayer MoS2 film are fabricated and exhibit high performances, with an average mobility and an on/off ratio of 53.5 cm2 V-1 s-1 and 107, respectively. In addition, batch fabrication of logic devices and 11-stage ring oscillators are also demonstrated, showcasing excellent electrical functions. This work may pave the way of MoS2 in practical industry-scale applications.

Cotton fabric surface treatment by plasma-deposited hexamethyldisilazane thin films

In the realm of fabric finishing, achieving the best wettability in cotton fabric is often a desired outcome. To accomplish this, a plasma-enhanced chemical vapor deposition (PECVD) system was used to deposit Hexamethyldisilazane (HMDSN) thin films onto cotton fabric for two different durations: 15 and 30 minutes. Various fabric properties were evaluated to determine the effectiveness of the treatment, including wettability, surface morphology, chemical structure, the effect of deposition on fabric stiffness, and the film fastness on the abrasion and washing. These properties were assessed using SEM, FTIR, and Martindale tester. Results indicated that both treatment durations improved the fabric's wicking ability. However, the film did not have a good fastness on abrasion and washing.

Carbon-nanotube-grafted glass-fiber-reinforced composites: Synthesis and mechanical properties

Glass fibers (GFs) are commonly used as reinforcements for advanced polymer composites. To improve the interfacial shear properties and mechanical properties of GF-reinforced composites (GFRPs), carbon nanotubes (CNTs) are directly grafted onto GFs using chemical vapor deposition (CVD). However, this process requires high temperatures, which causes thermal degradation of GFs, deteriorating their mechanical properties. In this study, a low-temperature CNT-grafting process was investigated using a bimetallic catalyst introduced onto a GF fiber surface via precursor solutions. The mechanical properties of the CNT-grafted GFs fabricated at different CVD temperatures were evaluated; they consistently showed low tensile strengths at temperatures above 400 °C. Subsequently, various CNT-grafted GFRPs were manufactured, and their mechanical properties were characterized. Interestingly, the flexural strengths of the composites increased with maintained tensile strength, despite a deterioration of the CNT-grafted GF reinforcements due to the CVD process. This could be attributed to the improved interfacial shear strength (IFSS) of the CNT-grafted GFs at the fiber level, and the enhanced compressive strength and interlaminar shear strength (ILSS) of CNT-grafted GFRPs at the composite level. Considering the properties of GF through CVD processes, particularly in relation to temperature, and factors such as IFSS, ILSS, tensile, compressive and flexural properties of composite materials, grafting CNTs on GF via a CVD system demonstrated its highest optimality at 450 °C.

Protection of Si Nanowires against Aβ Toxicity by the Inhibition of Aβ Aggregation.

Alzheimer's disease (AD) is a progressive neurodegenerative disease characterized by the accumulation of amyloid beta (Aβ) plaques in the brain. Aβ1-42 is the main component of Aβ plaque, which is toxic to neuronal cells. Si nanowires (Si NWs) have the advantages of small particle size, high specific surface area, and good biocompatibility, and have potential application prospects in suppressing Aβ aggregation. In this study, we employed the vapor-liquid-solid (VLS) growth mechanism to grow Si NWs using Au nanoparticles as catalysts in a plasma-enhanced chemical vapor deposition (PECVD) system. Subsequently, these Si NWs were transferred to a phosphoric acid buffer solution (PBS). We found that Si NWs significantly reduced cell death in PC12 cells (rat adrenal pheochromocytoma cells) induced by Aβ1-42 oligomers via double staining with 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) and fluorescein diacetate/propyl iodide (FDA/PI). Most importantly, pre-incubated Si NWs largely prevented Aβ1-42 oligomer-induced PC12 cell death, suggesting that Si NWs exerts an anti-Aβ neuroprotective effect by inhibiting Aβ aggregation. The analysis of Fourier Transform Infrared (FTIR) results demonstrates that Si NWs reduce the toxicity of fibrils and oligomers by intervening in the formation of β-sheet structures, thereby protecting the viability of nerve cells. Our findings suggest that Si NWs may be a potential therapeutic agent for AD by protecting neuronal cells from the toxicity of Aβ1-42.

Laser-induced transverse voltage effect in c-axis inclined La x Sr1−x TiO3 thin films prepared by MOCVD

Light and thermal detectors based on the laser-induced transverse voltage (LITV) effect have garnered significant interest for their rapid and broad spectral response. In this study, we prepared the La-doped SrTiO3 (STO) epitaxial thin films on the 12° inclined single crystal LaAlO3 (LAO) (100) substrates using our home-designed metal–organic chemical vapor deposition system. Under the illumination of a 248 nm laser, the LITV signals of La x Sr1−x TiO3 films were observed and showed dependence on the La doping level, which can be explained by the changes in the light absorption coefficient, thermal conductivity, and optical penetration depth. The optimized LITV signal was observed with a peak voltage of 23.25 V and a decay time of 106 ns under the laser power density of 1.0 mJ mm−2. The high peak voltage and fast response time of La x Sr1−x TiO3 show great potential in the field of light and thermal detection.

Silicon oxide particles size evolution during CVD graphene growth on Cu substrates

Chemical vapor deposition (CVD) on metal substrates is presently the remarkably route for the synthesis of high-quality continuous graphene films at a large scale. Whereas, during the thermal processing procedure in the quartz tube, the formation of silicon oxide particles would degrade the performance of graphene. To better understand the origin of these particles , a series of CVD graphene growth experiments with were conducted on the Cu substrates. In this paper, we investigated the main component and morphology of the particles by X-Ray photoelectron spectroscopy (XPS), energy dispersive spectrometry (EDS) measurement in scanning electron microscopy (SEM) and revealed that the silicon oxide particles gradually increased in diameter across the graphene films on the Cu surface, which was found to be correlated with the working time of the quartz products. Raman spectroscopy was also applied to prove the drawback consequence of the contamination on the quality of the CVD graphene film. To mitigate this issue, we further propose a modification of the CVD system that a coaxial alumina or BN tube inside the quartz tube to screen the contaminants bringing about improved graphene growth.

Impact of alternating precursor supply and gas flow on the LPCVD growth behavior of polycrystalline 3C-SiC thin films on Si

In this paper, we will provide information on the growth mechanism of 3C-SiC using alternating supply deposition (ASD). SiH4 and C3H8 were introduced successively in a low-pressure chemical vapor deposition (LPCVD) system at 1000 °C, forming a stoichiometric polycrystalline 3C-SiC thin film on Si substrates. We demonstrate the influence of different gas flow rates on thin film properties. In detail, altering the flow rates of the precursors and the carrier gas resulted in changes of the growth rate, the surface roughness, the crystal growth mechanisms as well as the crystal quality. Hydrogen inhibition and passivation are proposed to be the main effects influencing the growth behavior of ASD thin films. Applying ASD to grow 3C-SiC thin films with precursors from low to high flow rates resulted in a transition of different growth mechanisms influencing the surface roughness and grain size. Furthermore, we could prove that ASD is a cyclic step-by-step carbon-assisted redistribution of a prior deposited silicon film. This is shown by contact angle measurements of three differently terminated surfaces during the specific phases of one ASD cycle. High resolution transmission electron microscopy (HRTEM) analysis showed a continuous and homogenous thin film and confirmed the absence of silicon- or carbon-rich layers. ASD enables 3C-SiC thin films with customized properties for tailored micro electromechanical system (MEMS) applications.

In Situ Imaging of Two-Dimensional Crystal Growth Using a Heat-Resistant Optical Microscope.

Revealing low-dimensional material growth dynamics is critical for crystal growth engineering. However, in a practical high-temperature growth system, the crystal growth process is a black box because of the lack of heat-resistant imaging tools. Here, we develop a heat-resistant optical microscope and embed it in a chemical vapor deposition (CVD) system to investigate two-dimensional (2D) crystal growth dynamics. This in situ optical imaging CVD system can tolerate temperatures of ≤900 °C with a spatial resolution of ∼1 μm. The growth of monolayer MoS2 crystals was studied as a model for 2D crystal growth. The nucleation and growth process have been imaged. Model analysis and simulation have revealed the growth rate, diffusion coefficient, and spatial distribution of the precursor. More importantly, a new vertex-kink-ledge model has been suggested for monolayer crystal growth. This work provides a new technique for in situ microscopic imaging at high temperatures and fundamental insight into 2D crystal growth.

Enhanced field emission characteristics of WS2 nano-films by diamond film and Mo film

WS2 is a type of transition metal chalcogenide materials (TMDCs) that exhibits exceptional photoelectric properties. Due to its atomically sharp edges, WS2 has the capability to enhance the electric field around its edges, thus presenting significant potential in field emission applications. In this study, the electron beam vapor deposition (EBVD) system and microwave plasma chemical vapor deposition (MPCVD) system were used to prepare a series of single-layer WS2 films，single-layer diamond films and diamond/WS2 nano-composite films on N-type highly doped Si substrate, and Mo/WS2 nano-composite films were prepared on Al2O3 ceramic substrate. Based on the characterization and analysis of the microstructure and chemical composition of each thin film layer in the above film devices, the field emission (FE) characteristics of each thin film device are compared and studied. The results demonstrate that the maximum FE current density of diamond/WS2 nano-composite film device is 912 μA/cm2, which is 2.7 times of the maximum FE current density of Mo/WS2 nano-composite film device 330 μA/cm2, and 3.4 times of the maximum FE current density of the single-layer diamond thin film device 267 μA/cm2. The single layer WS2 film did not exhibit measurable FE performance. The working principles of thin film field emission devices with various structures are introduced. It is considered that the diamond layer plays the role of electron accelerating layer, which not only effectively improves the FE characteristics of diamond/WS2 nanocomposite film, but also improves the repeatability and long-term stability of diamond/WS2 nanocomposite film FE devices.

Evidence of gas phase nucleation of nanodiamond in microwave plasma assisted chemical vapor deposition

The mechanism of ballas-like nanodiamond formation still remains elusive, and this work attempts to analyze its formation in the framework of activation energy (Ea) of nanodiamond films grown from a H2/CH4 plasma in a 2.45 GHz chemical vapor deposition system. The Ea was calculated from the Arrhenius equation corresponding to the thickness growth rate using substrate temperature (∼1000−1300 K) in all the calculations. While the calculated values matched with the Ea for nanodiamond formation throughout the literature, these values of ∼10 kcal/mol were lower compared to ∼15–25 kcal/mol for standard single crystal diamond (SCD) formation, concluding thus far that the energetics and processes involved were different. Further, the substrate preparation and sample collection method were modified while keeping the growth parameters constant. Unseeded Si substrate was physically separated from the plasma discharge by a molybdenum disk with a pinhole drilled in it. Small quantity of a sample substance was collected on the substrate. The sample was characterized by electron microscopy and Raman spectroscopy, confirming it to be nanodiamond, thus suggesting that nanodiamond self-nucleated in the plasma and flowed to the substrate that acted as a mere collection plate. It is hypothesized then, if nanodiamond nucleates in gas phase, gas temperature has to be used in the Arrhenius analysis. The Ea values for all the nanodiamond films were re-calculated using the simulated gas temperature (∼1500−2000 K) obtained from a simple H2/CH4 plasma model, giving new values within the range characteristic to SCD formation. Based on these findings, a unified growth mechanism for nanodiamond and SCD is proposed, concluding that the rate-limiting reactions for nanodiamond and SCD formation are the same.

Iron oxide-based catalyst of (Fe1-xMgx)O·Fe2O3 with well-dispersed active sites favoring carbon nanotubes growth for high-performance microwave absorption

Traditional catalysts for carbon nanotubes growth require specific substrates to prevent catalyst aggregation, then designing environmentally friendly and efficient catalysts remains enormous challenges. Herein, we developed an iron oxide-based catalyst of (Fe1-xMgx)O·Fe2O3 with catalytic active sites for the low-cost growing of carbon nanotubes (CNT) in chemical vapor deposition (CVD) system. This (Fe1-xMgx)O·Fe2O3 was prepared by solid-phase sintering of iron oxide and magnesium oxide uniformly mixed in mass ratio of 3%∼20 wt% MgO at 1400 °C. The introduction of magnesium oxide possesses some advantages of reducing the decomposition temperature of iron oxide and hindering the aggregation of as-formed Fe catalyst during CVD process. Furthermore, the in-situ growing CNT wrapped up the magnetic (Fe1-xMgx)O·Fe2O3 catalyst to form the 3D CNT/(Fe1-xMgx)O·Fe2O3 with the high-performance of microwave absorption. The maximum absorption of the three-dimensional carbon nanocomposites at 11.8 GHz with a thickness of 2.0 mm is −37.3 dB. The coupling of dielectric loss of CNTs and magnetic loss of (Fe1-xMgx)O·Fe2O3 results in the enhancement of microwave absorption. Therefore, this study provides a low-cost and green route to design the efficient catalyst for carbon nanotubes as well as high-performance absorbing materials.

Electrochemical detection of phenacetin with graphite/boron-doped diamond electrode grown at high methane concentration

We have developed a composite electrode containing boron-doped diamond and high graphite content (HGBDD) by microwave plasma chemical vapor deposition system at high methane concentration. The electrode is applied to test the trace level of phenacetin. Scanning rate studies have exhibited that electrochemical oxidation is controlled by adsorption with scanning speed ranging from 20 to 100 mV s−1, while at a higher scanning rate, electrochemical oxidation is controlled by diffusion process. Voltammetry of phenacetin researched on the HGBDD electrode reveals the redox mechanism of phenacetin, the HGBDD has a high current response with a sensitive detection limit of 0.058 μM and a wide linear detection range of 0.5 μM - 400 μM. The high performance could be attributed to the presence of a higher carrier concentration for HGBDD electrode. Based on the density functional theory caculations, the graphite on the diamond surface could adsorb phenacetin strongly and provide more active sites for the redox reaction. Due to the unique properties of diamond, the electrode shows stability, repeatability, and accuracy for detecting phenacetin.

Toward Controlled Synthesis of 2D Crystals by CVD: Learning from the Real-Time Crystal Morphology Evolutions.

The rich morphology of 2D materials grown through chemical vapor deposition (CVD), is a distinctive feature. However, understanding the complex growth of 2D crystals under practical CVD conditions remains a challenge due to various intertwined factors. Real-time monitoring is crucial to providing essential data and enabling the use of advanced tools like machine learning for unraveling these complexities. In this study, we present a custom-built miniaturized CVD system capable of observing and recording 2D MoS2 crystal growth in real time. Image processing converts the real-time footage into digital data, and machine learning algorithms (ML) unveil the significant factors influencing growth. The machine learning model successfully predicts CVD growth parameters for synthesizing ultralarge monolayer MoS2 crystals. It also demonstrates the potential to reverse engineer CVD growth parameters by analyzing the as-grown 2D crystal morphology. This interdisciplinary approach can be integrated to enhance our understanding of controlled 2D crystal synthesis through CVD.

Synthesis of two-dimensional MoO2 nanoplatelets and its multistep sulfurization into MoS2

To control the growth of layered two-dimensional structures, such as transition metal dichalcogenide materials or heterostructures, understanding the growth mechanism is crucial. Here, we report the synthesis of ultra-thin MoO2 nanoplatelets through the sublimation of MoO3. Rhombus MoO2 nanoplatelets with the P21/c space group were characterized using various microscopic and spectroscopic techniques. Introducing sulfur sources into the chemical vapor deposition system also leads to the formation of monoclinic MoO2 nanoflakes due to the incomplete sulfurization of MoO3. With a gradual increase in the vapor concentration of sulfur, MoO3 undergoes stepwise reduction into MoS2/MoO2 and eventually into MoS2. Additionally, utilizing MoO2 as a precursor for Mo sources enables the formation of monolayer MoS2 single crystals. This work provides an effective approach for growing MoO2 nanoplatelets and elucidates the mechanism behind the stepwise sulfurization of MoO3.

Van der Waals Epitaxial Growth of One-Unit-Cell-Thick Ferroelectric CuCrS2 Nanosheets.

Ferroelectric two-dimensional (2D) materials with a high transition temperature are highly desirable for new physics and next-generation memory electronics. However, the long-range polar order of ferroelectrics will barely persist when the thickness reaches the nanoscale. In this work, we synthesized 2D CuCrS2 nanosheets with thicknesses down to one unit cell via van der Waals epitaxy in a chemical vapor deposition system. A combination of transmission electron microscopy, second-harmonic generation, and Raman spectroscopy measurements confirms the R3m space group and noncentrosymmetric structure. Switchable ferroelectric domains and obvious ferroelectric hysteresis loops were created and visualized by piezoresponse force microscopy. Theoretical calculation helps us understand the mechanism of ferroelectric switching in CuCrS2 nanosheets. Finally, we fabricated a ferroelectric memory device that achieves an on/off ratio of ∼102 and remains stable after 2000 s, indicating its applicability in novel nanoelectronics. Overall, 2D CuCrS2 nanosheets exhibit excellent ferroelectric properties at the nanoscale, showing great promise for next-generation devices.

Structure and properties of Si3N4-based diamond/MoS2-TiN composite films

This study aims to optimize the performance of silicon nitride (Si3N4) ceramic bearings in high-temperature and heavy-duty environments and to address the issues of insufficient lubrication and heat generation in vacuum environments. To this end, we prepared diamond and MoS2-TiN composite films on silicon nitride ceramic substrates using a hot-wire chemical vapor deposition system and a physical vapor deposition system. The experimental results show that increasing the deposition time of the diamond films can significantly improve their hardness and elastic modulus, enhance the bonding of the films with the substrate, reduce the friction coefficient, and increase the thermal conductivity. Furthermore, by appropriately reducing the sputtering power of the MoS2 film, we can effectively minimize damage to the diamond film and further enhance the overall performance of the composite film. This study offers valuable insights for addressing lubrication and heat dissipation challenges in vacuum environments.

Preparation of nanodiamonds based on phase transformation of vertical sheet under atmospheric pressure

A basic and important way to prepare diamond is to make graphite experience the phase transformation under the high-pressure high-temperature (HPHT) condition. However, this method needs stringent equipment and high investment cost. Recently, we proposed a method to prepare the diamond by phase transformation of graphite at atmospheric pressure with monodispersed Ta atoms. It is found that a phase transformation happens to H atoms under atmospheric pressure, but the role of O atoms has not been investigated. Here, we use tantalum wires as Ta source and heat the filaments to prepare vertical graphene containing Ta atoms in hot filament chemical vapor deposition (HFCVD) system. And then the vertical graphene layers are annealed in oxygen-containing environment, and nanodiamonds are obtained by phase transformation from the vertical graphene under atmospheric pressure. The results show that the sample morphologies are the same as the untreated vertical graphene’s, when the annealed ambient air pressure is at 10 Pa and 50 Pa with oxygen atom content of 1.96% and 2.04%, respectively; TEM tests reveal TaC and graphite but no diamond in these samples . Nanodiamond grains with the size range of 2–4 nm are observed in the amorphous carbon region of samples annealed at 100 Pa and 500 Pa air pressure with oxygen atom content increasing to 2.77% and 3.11%, respectively, indicating that oxidation facilitates the phase change from Ta-containing vertical graphene to diamond at atmospheric pressure. When the air pressure of the annealing environment rises to 1000 Pa with the oxygen atom content of 3.54%, the sample is extensively oxidized and the graphite structure is severely damaged,which means that a large number of oxygen atoms tend to disrupt the graphite structure rather than promote the phase change into diamond. These results supply a way to prepare nanodiamond and show the effect of O atoms in the graphite phase transition at atmospheric pressure.

Asymmetric contact-induced selective doping of CVD-grown bilayer WS2 and its application in high-performance photodetection with an ultralow dark current.

Two-dimensional (2D) transition metal dichalcogenides (TMDs) are excellent candidates for high-performance optoelectronics due to their high carrier mobility, air stability and strong optical absorption. However, photodetectors made with monolayer TMDs often exhibit a high dark current, and thus, there is a scope for further improvement. Herein, we developed a 2D bilayer tungsten disulfide (WS2) based photodetector (PD) with asymmetric contacts that exhibits an exceptionally low dark current and high specific detectivity. High-quality and large-area monolayer and bilayer WS2 flakes were synthesized using a thermal chemical vapor deposition system. Compared to conventional symmetric contact electrodes, utilizing metal electrodes with higher and lower work functions relative to bilayer WS2 aids in achieving asymmetric lateral doping in the WS2 flakes. This doping asymmetry was confirmed through the photoluminescence spectral profile and Raman mapping analysis. With the asymmetric contacts on bilayer WS2, we find evidence of selective doping of electrons and holes near the Ti and Au contacts, respectively, while the WS2 region away from the contacts remains intrinsic. When compared with the symmetric contact case, the dark current in the WS2 PD with asymmetric (Au, Ti) contact decreases by an order of magnitude under reverse bias with a concomitant increase in the photocurrent, resulting in an improved on/off ratio of ∼105 and overall improved device performance under identical illumination conditions. We explained this improved performance based on the energy band alignment showing a unidirectional charge flow under light illumination. Our results indicate that the planar device structure and compatibility with current nanofabrication technologies can facilitate its integration into advanced chips for futuristic low-power optoelectronic and nanophotonic applications.

Effect of substrate roughness on the nucleation and growth behaviour of microwave plasma enhanced CVD diamond films – a case study

The influence of substrate surface roughness on the nucleation and growth of diamond films by chemical vapour deposition (CVD) is investigated. Silicon substrates were grinded with six different grit sizes of abrasive papers with a rotating wheel. Si was also etched by Ar+ ions to produce average surface roughness Ra = 11.29 nm on the mirror polished side (Ra = 1.17 nm). A comparison of the results of the effect of substrate roughness, on the growth behaviour of nanocrystalline diamond (NCD) films, by using both the resonant cavity and the linear antenna CVD systems, are presented here. Scanning electron microscopy (SEM) images and Raman spectroscopy reveal that under both the linear antenna and the resonant cavity microwave plasma CVD conditions, grown films are NCD. The diamond nanocrystals sizes vary from 80 to 180 nm, grown by both the reactors after few hours of deposition, irrespective of the substrate roughness, whereas their quality (defined by the relative percentage ratios of the Raman sp3 peak intensity to the non-sp3 peak intensity) varies from 33% to 45%, depending on the substrate surface roughness. Such nanocrystals grew into plate-like flat 1–6 μm size diamond grains after prolonged hours (64–69 h) of CVD growth. It is found specifically that the roughness created by the argon plasma treatment of the silicon substrate surfaces effectively enhances the nucleation and growth behaviour of the diamond films.

(Invited) Growth of Hexagonal Boron Nitride by MOCVD for Electronic and Photonic Applications

Hexagonal boron nitride (h-BN) is a 2-dimensional (2D) layered insulating material. Thanks to its wide bandgap of ~6 eV and high thermal conductivity, h-BN has been widely utilized as an ideal substrate, gate dielectric material, passivation layer, and atomic tunnelling layer for 2D electronic devices. Recently, it has gained more attention as active material for photonics applications due to its potential for stable quantum emitters in the visible spectral range, as well as deep-ultraviolet emitters and detectors due to its exceptionally high internal quantum efficiency despite its indirect bandgap. However, mechanically exfoliated bulk h-BN and h-BN films grown on catalytic metal substrates by conventional chemical vapor deposition (CVD) systems have been mainly used to study the fundamental properties, lacking in scalability for practical implementation of h-BN.Here, we exploit the scalable approach to grow h-BN on various substrates such as sapphire, Si, and GaN, by using metal-organic chemical vapor deposition (MOCVD). A few-layer h-BN films were successfully grown on those substrates. In particular, we successfully accomplished the conformal growth of few-layer h-BN over an array of Si-based nanotrenches with 45 nm pitch and the aspect ratio of ~ 7:1. Moreover, it was found that at a specific MOCVD growth condition, a very unique h-BN film can be grown on GaN substrates, in which few-layer h-BN film is suspended on GaN nanoneedles. The combination of state-of-the-art microscopic and spectroscopic analyses revealed that the suspended h-BN films exhibit unprecedented deep ultraviolet photoluminescence spectra with local variation in band-edge emission. In addition, the h-BN films show unprecedented atomic stacking configuration, the mechanism of which will be discussed with optical and structural characterizations and theoretical calculations.