Constant Growth Rate Research Articles

Optimal strategies for collective defined contribution plans when the stock and labor markets are co-integrated

This paper investigates a collective defined contribution (CDC) pension fund scheme in continuous time, where members' contributions are fixed in advance, and benefit payments depend on the final salary rate. We take account of the co-integration between labor income and the stock market by letting the difference between logs of labor and dividends follow a mean-reverting process. Further, labor income is also a product of aggregate labor income and member's idiosyncratic shocks whose constant growth rate is unknown. It can be modeled by a continuous-time two-state hidden Markov chain. Further, the pension fund can be invested in the financial market consisting of one risky asset and one risk-free asset to enhance profits. After using Hamilton-Jacobi-Bellman (HJB) equations, the closed-form solutions for the optimal asset allocation and the benefit payment policies are obtained to maximize the social welfare and the terminal surplus wealth. Numerical examples are also conducted to illustrate the sensitivity of parameters on the optimal strategies.

The Efficacy of Open Performance Review and Appraisal System on Teachers’ Work Performance in Tanzania. A Case of Selected schools of Vwawa, Iyula and Msangano Secondary Schools in Mbozi District

This study mainly sought to determine the effectiveness of the Open Performance Review and Appraisal System (OPRAS) on Teachers' work performance in the selected secondary schools of Vwawa, Iyula and Msangano in Mbozi district council. The study was also driven by the following main objective, which includes; how the practice of OPRAS has improved the work performance of secondary school teachers in Mbozi district council. A mixed research approach both qualitative and quantitative approach with 93 respondents was employed. Questionnaires and interviews were used to obtain data. Quantitative data was analyzed through descriptive statistics where inferences were presented in the form of frequencies and percentiles. Qualitative information was also analyzed through thematic and content analysis and presented in the form of concepts and narrations. Although Mbozi district has been effectively implementing OPRAS for the past 15 years, active data show that the district has a stable progression performance rate of 30.1 % since 2018 to date. The key variable that was tested was increased teacher commitment. Considerably, this has been established due to constant growth rates of indicators of performance against the performance of teachers from 2018 to 2023. The study recommended that the government should set and engage a realistic budget for training, and empowerment workshops and highly capacitate the Office of the public communications for the purpose of intensifying communication and feedback in public organizations including secondary schools

The advancement of EVA polymerization kinetics and development of high-performance EVOH polymerization process

Ethylene-vinyl alcohol copolymer (EVOH) is a material with excellent barrier properties, produced via the radical copolymerization of ethylene and vinyl acetate in solution, followed by alcoholysis in methanol with NaOH as a catalyst. It is widely used in packaging and medical materials. However, balancing the barrier properties and processability remains challenging. Currently, multi-scale research methods using density functional theory (DFT) to explore polymerization mechanisms and obtain kinetic data, combined with process simulation methods to develop high-performance EVOH polymerization process, are gaining attention. Therefore, this study employs DFT and transition state theory (TST) methods to study the kinetics of chain growth and chain transfer reactions of radicals at first, yielding the average chain growth and chain transfer rate constants for copolymerization reactions. Then, based on these rate constants, process simulations were used to model the ethylene–vinyl acetate solution copolymerization reactor, developing polymerization process for EVOH with high barrier properties as well as EVOH with both high barrier properties and good processability. These findings provide suggestions and guidance for EVOH production and application.

Phosphate-Driven Interfacial Self-Assembly of Silk Fibroin for Continuous Noncovalent Growth of Nanothin Defect-Free Coatings.

Silk fibroin is a fiber-forming protein derived from the thread of Bombyx mori silkworm cocoons. This biocompatible protein, under the kosmotropic influence of potassium phosphate, can undergo supramolecular self-assembly driven by a random coil to β-sheet secondary structure transition. By leveraging concurrent nonspecific adsorption and self-assembly of silk fibroin, we demonstrate an interfacial phenomenon that yields adherent, defect-free nanothin protein coatings that grow continuously in time, without observable saturation in mass deposition. This noncovalent growth of silk fibroin coatings is a departure from traditionally studied protein adsorption phenomena, which generally yield adsorbed layers that saturate in mass with time and often do not completely cover the surface. Here, we explore the fundamental mechanisms of coating growth by examining the effects of coating solution parameters that promote or inhibit silk fibroin self-assembly. Results show a strong dependence of coating kinetics and structure on solution pH, salt species, and salt concentration. Moreover, coating growth was observed to occur in two stages: an early stage driven by protein-surface interactions and a late stage driven by protein-protein interactions. To describe this phenomenon, we developed a kinetic adsorption model with Langmuir-like behavior at early times and a constant steady-state growth rate at later times. Structural analysis by FTIR and photoinduced force microscopy show that small β-sheet-rich structures serve as anchoring sites for absorbing protein nanoaggregates, which is critical for coating formation. Additionally, β-sheets are preferentially located at the interface between protein nanoaggregates in the coating, suggesting their role in forming stable, robust coatings.

Importance of zero cross-point (Cp = 0) control between the vacancy and interstitial Si atom concentration curves to obtain a perfect Si ingot using Si melt growth

The cross-point (Cp), which appears in the vacancy (CV) and interstitial Si atom (CI) concentration curves, is a simple controlling factor for ingot growth and provides a final goal to obtain a defect-free Si ingot using general Si melt growth. The importance of Cp is demonstrated using the noncontact crucible method (NOC), which has a relatively small temperature gradient due to an ingot grown inside the melt. The control of temperature gradient G at a constant growth rate v is simple for the actual ingot growth; thus, the present simulated results are expressed by G at a constant v. The concentration at the Cp point becomes smaller as G becomes smaller and finally becomes zero (Cp = 0), in which CV and CI are practically zero (CV=CI=0). The estimated G and temperature T at Cp = 0 for v = 0.000144 cm s−1 are 6.3, 12.5, and 18.5 K cm−1 and 1216 K (943 °C), 1354 K (1081 °C), and 1371 K (1098 °C), corresponding to each combination. At 1216 K, G should be precisely controlled within 6.3 ± 3 % K cm−1 in the region substantially close to Cp = 0 to maintain the remaining concentration of point defects substantially lower than 1.0 × 1013 cm−3. G should be changed during growth from larger G to smaller G, such as 6.3 K cm−1, to efficiently grow the ingot within the limited time. The changing point, x of G, is an important key parameter for the timing variation, where x denotes the normalized distance from the growing interface. The initial G is large; thus, the changing point of G approaches the growing interface. The growth condition necessary to obtain a defect-free Si ingot can be demonstrated using the Cp = 0 point, which is fully compatible with the perfect critical point where CV and CI are practically zero. The present results are mainly considered using the CV and CI concentration curves. However, these results largely help understand the approximate trend of G and v for the growth of defect-free ingot and the relation between Cp and the commonly used critical point between CV and CI.

High cell density culture of microalgae in horizontal thin-layer algal reactor: Modeling of light attenuation and cell growth kinetics

This study delved into the light intensity effects and light attenuation modeling in high cell density culture (HCDC) of green alga Neochloris oleoabundans. The research primarily focused on how different light intensities influence cell growth in terms of cell division and cell mass, and the biochemical composition within the cells. Recognizing the need to avoid overestimating light path by excluding data point in the data zone where the light intensity was zero, we proposed and verified a novel modified Beer-Lambert model, which was superb in fitting experimental data and predicting light attenuation in both low and high cell density cultures. Taking advantage of the prediction power of the modified Beer-Lambert model, we devised an approach to maintain constant mean light intensity (Imean) and by adjusting the incident light intensity (I0). The results indicate that at an Imean of approximately 66.67 μmol/m2/s and 6 mm culture thickness, maximum volumetric and areal biomass productivities of 2.72 g/L/day and 16.32 g/m2/day, respectively, were achieved. Whereas the highest biomass concentration of 28.20 g/L was produced in 20 days at Imean 50 μmol/m2/s. Photoinhibition to cell division become evident at I0 750 μmol/m2/s and above. Using the data generated at constant Imean in the constant specific growth rate range, superb fitting to the Monod model with a R2 of 0.9910 was demonstrated, highlighting the importance of generating reliable data for the modelling of the kinetics of photoautotrophic growth of microalgae, which had considered to be challenging.

Reproducible high-quality perovskite single crystals by flux-regulated crystallization with a feedback loop

Controlling the linear growth rate, a critical factor that determines crystal quality, has been a challenge in solution-grown single crystals due to complex crystallization kinetics influenced by multiple parameters. Here we introduce a flux-regulated crystallization (FRC) method to directly monitor and feedback-control the linear growth rate, circumventing the need to control individual growth conditions. When applied to metal halide perovskites, the FRC maintains a stable linear growth rate for over 40 h in synthesizing CH3NH3PbBr3 and CsPbBr3 single crystals, achieving outstanding crystallinity (quantified by a full width at half-maximum of 15.3 arcsec in the X-ray rocking curve) in a centimetre-scale single crystal. The FRC is a reliable platform for synthesizing high-quality crystals essential for commercialization and systematically exploring crystallization conditions, maintaining a key parameter—the linear growth rate—constant, which enables a comprehensive understanding of the impact of other influencing factors.

Operando Characterization and Molecular Simulations Reveal the Growth Kinetics of Graphene on Liquid Copper During Chemical Vapor Deposition.

In recent years, liquid metal catalysts have emerged as a compelling choice for the controllable, large-scale, and high-quality synthesis of two-dimensional materials. At present, there is little mechanistic understanding of the intricate catalytic process, though, of its governing factors or what renders it superior to growth at the corresponding solid catalysts. Here, we report on a combined experimental and computational study of the kinetics of graphene growth during chemical vapor deposition on a liquid copper catalyst. By monitoring the growing graphene flakes in real time using in situ radiation-mode optical microscopy, we explore the growth morphology and kinetics over a wide range of CH4-to-H2 pressure ratios and deposition temperatures. Constant growth rates of the flakes' radius indicate a growth mode limited by precursor attachment, whereas methane-flux-dependent flake shapes point to limited precursor availability. Large-scale free energy simulations enabled by an efficient machine-learning moment tensor potential trained to density functional theory data provide quantitative barriers for key atomic-scale growth processes. The wealth of experimental and theoretical data can be consistently combined into a microkinetic model that reveals mixed growth kinetics that, in contrast to the situation at solid Cu, is partly controlled by precursor attachment alongside precursor availability. Key mechanistic aspects that directly point toward the improved graphene quality are a largely suppressed carbon dimer attachment due to the facile incorporation of this precursor species into the liquid surface and a low-barrier ring-opening process that self-heals 5-membered rings resulting from remaining dimer attachments.

Quantitative Assessment of Drug Efficacy and Emergence of Resistance in Patients with Metastatic Renal Cell Carcinoma Using a Longitudinal Exposure-Tumor Growth Inhibition Model: Apitolisib (Dual PI3K/mTORC1/2 Inhibitor) Versus Everolimus (mTORC1 Inhibitor).

Cancer remains a significant global health challenge, and despite remarkable advancements in therapeutic strategies, poor tolerability of drugs (causing dose reduction/interruptions) and/or the emergence of drug resistance are major obstacles to successful treatment outcomes. Metastatic renal cell carcinoma (mRCC) accounts for 2% of global cancer diagnoses and deaths. Despite the initial success of targeted therapies in mRCC, challenges remain to overcome drug resistance that limits the long-term efficacy of these treatments. Our analysis aim was to develop a semi-mechanistic longitudinal exposure-tumor growth inhibition model for patients with mRCC to characterize and compare everolimus (mTORC1) and apitolisib's (dual PI3K/mTORC1/2) ability to inhibit tumor growth, and quantitate each drug's efficacy decay caused by emergence of tumor resistance over time. Model-estimated on-treatment tumor growth rate constant was 1.7-fold higher for apitolisib compared to everolimus. Estimated half-life for loss of treatment effect over time for everolimus was 16.1 weeks compared to 7.72 weeks for apitolisib, suggesting a faster rate of tumor re-growth for apitolisib patients likely due to the emergence of resistance. Goodness-of-fit plots including visual predictive check indicated a good model fit and the model was able to capture individual tumor size-time profiles. Based on our knowledge, this is the first clinical report to quantitatively assess everolimus (mTORC1) and apitolisib (PI3K/mTORC1/2) efficacy decay in patients with mRCC. These results highlight the difference in overall efficacy of 2 drugs due to the quantified efficacy decay caused by emergence of resistance, and emphasize the importance of model-informed drug development for targeted cancer therapy.

An enhanced hybrid model for batch sugar crystallization based on the pattern recognition for overall heat transfer coefficient using a machine learning approach

AbstractA hybrid model is developed and evaluated to simulate the heat and mass transfer in the crystallization unit of a sugar factory. While the mass transfer is modeled by using the kinetic growth rate model, the heat transfer is simulated by applying the energy balance to the model. Here, the overall convection heat transfer coefficient of the crystallizer's heat exchanger is considered as a temperature‐dependent function. As this makes the governing equations more realistic, it can help to increase the model accuracy. Additionally, a thorough examination of key practical equations and principles governing the sugar crystallization process is presented. A regression learner method is applied to extract the pattern of the overall heat transfer coefficient. According to our results, the regression learning model successfully predicts the heat transfer coefficient with an average 7% deviation from experimental results. For the hybrid model, an average deviation of about 10% is observed. The crystallizer's behavior is somehow linear, indicating a constant growth rate of sugar crystals. Furthermore, the heat transfer in the crystallizer is improved by increasing the working temperatures.Practical applicationsThe method and obtained results of this work could be used in the following practical purposes: to find the optimum working temperatures of crystallizers used in sugar industry and to predict total working time of batch crystallizers versus working parameters.

Synthesis of Gold Clusters and Nanoparticles Using Cinnamon Extract-A Mechanism and Kinetics Study.

In this work, UV-Vis spectrophotometry, High Resolution Scanning Transmission Electron Microscopes and selected experimental conditions were used to screen the colloidal system. The obtained results complement the established knowledge regarding the mechanism of nanoparticle formation. The process of gold nanoparticles formation involves a two-step reduction of Au ions to Au(0); atom association and metastable cluster formation; autocatalytic cluster growth; ultra-small particle formation (1-2 nm, in diameter); particle growth and larger particles formation; and further autocatalytic crystal growth (D > 100 nm). As a reductant of Au(III) ions, a cinnamon extract was used. It was confirmed that eugenol as one of the cinnamon extract compounds is responsible for fast Au(III) ion reduction, whereas cinnamaldehyde acts as a gold-particle stabilizer. Spectrophotometry studies were carried out to track kinetic traces of gold nanoparticle (D > 2 nm) formation in the colloidal solution. Using the Watzky-Finke model, the rate constants of nucleation and autocatalytic growth were determined. Moreover, the values of energy, enthalpy and entropy of activation for stages related to the process of nanoparticle formation (Index 1 relates to nucleation, and Index 2 relates to the growth) were determined and found to be E1 = 70.6 kJ, E2 = 19.6 kJ, ΔH1 = 67.9 kJ/mol, ΔH2 = 17 kJ/mol, ΔS1 = -76.2 J/(K·mol), ΔS2 = -204.2 J/(K·mol), respectively. In this work the limitation of each technique (spectrophotometry vs. HRSTEM) as a complex tool to understand the dynamic of the colloidal system was discussed.

Comparison of the bioaccumulation and biosorption of copper ions by Rhizopus delemar and Candida lipolytica

In this study, the bioaccumulation of Cu(II) ion by Rhizopus delemar and Candida lipolytica was investigated and the bioaccumulation and biosorption of Cu(II) ions by Candida lipolytica compared. The specific growth rate and the maximum microorganism concentration of both microorganisms increased with increasing initial molasses concentration whereas decreased with increasing initial Cu(II) ion concentrations up to 250 mg/L. Accoding to Monod equation, the maximum specific growth rate and saturation constant for C. lipolytica and R. delemar were determined as 0.335 h−1-32.330 g/L and 0.406 h−1-24.182 g/L, respectively. The bioaccumulation efficiencies of R. delemar and C. lipolytica were determined as 74.18% and 67.30% in the presence of 50 mg/L Cu(II), respectively. At pH 4.0, the maximum biosorption rate (4.72 mg/g min) and the biosorbed Cu(II) ion concentration (49.0 mg/L) were obtained for C. lipolytica and these values increased with increasing Cu(II) concentration. Cu(II) biosorption by C. lipolytica fitted well to the Langmuir isotherm model and pseudo-second-order kinetic model and maximum adsorption capacity was found as 114.942 mg/g. The bioaccumulated Cu(II) was found to be 21.5 mg/g whereas the amounts of biosorbed Cu(II) were calculated as 53 mg/g by C. lipolytica at a concentration of 100 mg/L of Cu(II).

The Effect of La on the Surface Properties of Plasma Nitrided CoCrCuFeNi High-Entropy Alloys at 440 Degrees Celsius

This paper investigates the effect of the element La on plasma nitriding of the CoCrCuFeNi high-entropy alloy (HEA) at 440 °C for 8, 16, and 24 h. The phase composition, morphology, and hardness distribution of the nitrided layer are characterized using XRD, optical microscopy, and a microhardness tester. Furthermore, the corrosion resistance is tested using an electrochemical workstation. The study evaluated the friction and wear performance using a testing machine and scanning electron microscope. The thickness of the effective hardening layer after 16 h of treatment with La was similar to that after 24 h of treatment without La. The addition of La significantly increased the growth rate constant of the effective hardening layer from 0.53 × 10−14 m2/s to 0.72 × 10−14 m2/s. In addition, an expanded FCC phase with greater interplanar spacing can be formed on the surface of the sample by introducing La into the plasma nitriding process. This indicates that the expanded FCC phase, with a higher concentration of interstitial nitrogen atoms, can effectively improve the corrosion resistance of the specimen surface. The corrosion rate of the specimen surface was reduced by 27.5% and the wear rate was reduced by 41.7% after 16 h of treatment with the addition of La compared to 24 h of nitriding without the addition of La. It has been shown that the addition of La to the plasma nitriding process results in a higher quality nitrided layer in a shorter time and also demonstrates that La has the potential to optimize the surface properties of plasma nitrided HEAs.

A dual-gain scaling approach to event-triggered adaptive tracking for large-scale nonlinear systems via output feedback

A novel non-backstepping output feedback control approach, called as the dual-gain scaling approach, is proposed by combining the extended Lyapunov matrix inequalities with dual-domination idea. This approach provides partially decentralised adaptive output feedback controllers with three event-triggered mechanisms to achieve the global practical tracking of a family of uncertain large-scale nonlinear systems subject to unknown control coefficients and strongly interconnected nonlinearities with output-polynomial growth rate. The dual gains are embedded in the observers and controllers, which can effectively compensate for time-varying control coefficients and unknown constant growth rate multiplied by output-polynomial function. Three different threshold schemes including fixed threshold, relative threshold and time-varying threshold are introduced to save communication resources. The stability analysis shows that the solutions of the closed-loop system are globally uniformly bounded and the tracking error converges to a preset compact set after a finite time; also, there will be no zeno behaviour in the closed-loop response.

Effects of different light wavelengths on Bacillus subtilis and Bacillus velezensis, two biocontrol agents isolated from the maize phyllosphere.

In previous studies, two strains isolated from the maize phyllosphere were identified as Bacillus subtilis (EM-A7) and Bacillus velezensis (EM-A8) and selected as potential biocontrol agents against Exserohilum turcicum. This study aimed to assess the ability of EM-A7 and EM-A8 to form biofilm and have antagonistic activity under varying light conditions. LED sources were custom-designed so that each corresponded to a given spectrum at a specific photosynthetically active photon flux density. Significant differences were observed in growth parameters (generation time and constant growth rate) under different LED sources. Blue light inhibited the growth of both strains. Red increased k rate in EM-A8, while the g values increased in EM-A7. Red and white light generally increased biofilm formation, and blue light inhibited it. EM-A7 and EM-A8 significantly reduced their ability to swim under blue LED, but it was not affected by red, green, or white light. The ability to swarm was negatively affected. Fungal growth decreased significantly compared to the control when the bacterium growing on the same plate had been previously incubated under red and white light or in the dark. These results indicate that different light wavelengths clearly influenced the aspects assessed in B. subtilis and B. velezensis, with the effects of blue light being overall negative and those of red and white overall positive. Given that, all these factors can be important for the establishment and survival of Bacillus strains on leaves, as well as for their effectiveness against pathogens, light could be a significant factor to consider in the design of biocontrol strategies.

Application of anaerobic digestion model No. 1 on thermophilic anaerobic digestion with microbial immobilization media for biogas production from sugarcane vinasse

Anaerobic Digestion Model no.1 (ADM1) for the "Mixed Reactor Compartment" of AQUASIM with modified kinetic parameters was proven to be effective in predicting the behavior of thermophilic anaerobic digestion of sugarcane vinasse in a continuous stirred tank reactor (CSTR) equipped with unwoven textile as the microbial immobilization media. The modified kinetic parameters implied higher microbial growth rate constants in the CSTR with microbial immobilization media than the CSTR without media. The 16 s rRNA assay confirmed the inferences on the physical interpretation of the kinetic parameters. Microbial immobilization media shifted the initially homogeneous microbial composition in the CSTR’s bulk liquid into methanogenic dominance in the biofilm attached to the media and acidogenic dominance in the liquid bulk after 90 days of operation. The remarkable finding of this study was that the segregated microorganisms indicated a beneficial micro-environment for both acidogenic and methanogenic populations to have favorable conditions for each of them. ADM1 well predicted the effect of this segregation with modified kinetic parameters and confirmed by the 16 s rRNA assay on the reactor’s liquid and biofilm samples.

A multi-criteria drought resistance assessment of temperate Acer, Carpinus, Fraxinus, Quercus, and Tilia species

A rapidly warming climate with growing frequency of hot droughts urges Central Europe’s forestry sector to adapt to increasing climatic stress. One option is to choose native minor timber species with assumed higher stress tolerance; yet, information on the drought resistance of many species is scarce. We examined the drought resistance of adult trees of Norway maple (Acer platanoides), European hornbeam (Carpinus betulus), Common ash (Fraxinus excelsior) and Little-leaved lime (Tilia cordata) at leaf, branch, stem and root levels, combining studies on leaf water status, branch xylem hydraulics, fine root vitality and radial stem growth, for deriving an evidence-based drought resistance ranking of the species. Results were compared to Sessile oak (Quercus petraea), a fairly drought-resistant major timber species. All species showed constant growth rates despite increasing climatic aridity, indicating low climate vulnerability. Foliage loss after the severe 2018/19 drought increased in the sequence Quercus < Fraxinus < Acer < Tilia < Carpinus. The water potential at leaf turgor loss (PTLP) was no suitable indicator of the species’ climate-sensitivity of growth or drought-induced foliage loss. The growth performance of Tilia demonstrates that some angiosperm trees can achieve a fairly high degree of drought resistance through plant-internal water storage and high leaf tissue elasticity, despite a small hydraulic safety margin and high PTLP. Drought resistance as deduced from growth performance and defoliation after severe drought decreased in the sequence Quercus > Fraxinus & Acer > Tilia > Carpinus. We conclude that Acer, Carpinus, and Tilia (and Fraxinus, despite being often Hymenoscyphus-infected) are suitable timber species for Central Europe’s forestry sector in a drier and warmer climate.

A non-singular fractional-order logistic growth model with multi-scaling effects to analyze and forecast population growth in Bangladesh

This paper is primarily concerned with data analysis employing the nonlinear least squares curve fitting method and the mathematical prediction of future population growth in Bangladesh. Available actual and adjusted census data (1974–2022) of the Bangladesh population were applied in the well-known autonomous logistic population growth model and found that all data sets of the logistic (exact), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach, and logistic multi-scaling approximation fit with good agreement. Again, the existence and uniqueness of the solution for fractional-order and Hyers-Ulam stability have been studied. Generally, the growth rate and maximum environmental support of the population of any country slowly fluctuate with time. Including an approximate closed-form solution in this analysis confers several advantages in assessing population models for single species. Prior studies predominantly employed constant growth rates and carrying capacity, neglecting the investigation of fractional-order methods. Thus, the current study fills a crucial gap in the literature by introducing a more formal approach to analyzing population dynamics. Therefore, we bank on the findings of this article to contribute to accurate population forecasting and planning, national development, and national progress.

Electromigration enhanced growth kinetics of intermetallics at the Cu/Al interface

The growth kinetic behaviors of the Cu/Al system under current were investigated. The current was shown to significantly promote the growth of the intermetallic (IMC) layer. The growth rate constant of the Al4Cu9 layer under current was approximately 3.26 times higher than that processed without current. Moreover, the current direction leads to a significant difference in the growth rate of the IMC layer, which was attributed to the electromigration effect. Based on the traditional thermal-activated theory and electromigration theory, an electromigration and thermal dual-activated growth kinetic model incorporating the contributions of Joule heat and the nonthermal effect was constructed. The growth kinetic behaviors of the Al4Cu9 layer were investigated by applying this model. The calculated growth activation energies under different current densities were almost constant and close to 130 kJ/mol. The experimental data were applied to verify the model, and the results showed that the model was in good agreement with the experimental results.

Ultrahigh density InGaN/GaN nanopyramid quantum dots for visible emissions with high quantum efficiency

In this study, the selective area epitaxy (SAE) of InGaN/GaN nanopyramid quantum dots (QDs) on a block copolymer patterned (BCP) GaN template using metalorganic chemical vapor deposition is reported. The pattern transfer process and SAE process are developed to enable a ultrahigh density of 7–9 × 1010 cm−2 QD formation with a feature size of 20–35 nm. The growth mechanism and geometrical properties of the QDs were investigated by scanning electron microscopy and cross-sectional transmission electron microscopy, showing the nanopyramid QD structure with InGaN grown on semipolar {101¯1} planes. The optical characteristics of the nanopyramid QDs were examined by microphotoluminescence measurements. We observed QD emission centered at 488 and 514 nm, depending on the growth temperature employed. These emissions were found to be longer wavelength than those from a planar quantum well structure. This can be attributed to the combined effects of higher indium incorporation along the semipolar plane and a larger InGaN thickness. Furthermore, we also found that the QD emission intensity increases as the number of InGaN layers increases without wavelength shift, indicating a constant growth rate and indium incorporation along the semipolar plane after the formation of the nanopyramid structure. The internal quantum efficiency is estimated to be over 60% by comparing the photoluminescence (PL) intensity of QDs at low temperature and room temperature. PL emission wavelength shows an 11 nm blue shift, while the full width at half maximum decreases from 68 (351 meV) to 56 nm (303 meV) from room temperature to low temperature. By employing BCP lithography and SAE technique, we successfully demonstrated that ultrahigh density, small size InGaN/GaN nanopyramid QDs with visible emission were achieved, which could be a potential active region for QD light-emitting diodes and/or lasers.