Modelling of the grain size probability distribution in polycrystalline nanomaterials

Theoretical analyses have always resulted in nanomaterials’ grain size probability distribution being of varied form: approximately either lognormal, Rayleigh, normal, Weibull, etc. The isotropic Hillert’s model of grain growth which is more suitable for soap froth has been frequently used to establish these distributions with the hope of approximating experimental observations. Observed grain growth in nanomaterials shows departures from the Hillert’s model.In the present paper, the probability distribution of grain size in nanomaterials is dealt with. Use is made of a modified model of grain growth in polycrystalline nanomaterials developed recently by the authors. The modified model accounts for grain growth caused by curvature driven grain boundary migration and grain rotation-coalescence mechanisms. Since the grain size in the aggregate is random, the stochastic counterpart of the expression governing the incremental change in individual grain size is obtained by the addition of two fluctuation terms.The integro-differential equation governing the development of the probability density function of the grain size is obtained which is the generalised Fokker–Planck–Kolmogorov equation. Numerical solution to the integro-differential equation is obtained.Results from analytical modelling of grain size probability distribution in polycrystalline nanomaterials are different if the effect of grain rotation-coalescence mechanism on grain growth process is taken into account and, further, due to the addition of the fluctuation terms. Results also depend on the nature of the fluctuation term, which is a material property as the fluctuation in grain sizes varies from one material to another. It is shown that many of the major attributes of grain growth, such as self similarity (probability density approaching a stationary one), can be predicted by the solution of the Fokker–Planck–Kolmogorov equation.     

Determination of bulk and interface density of states in polycrystalline silicon thin film transistors

The aim of our investigation is to determine the bulk and interface density of states in excimer laser annealed polycrystalline silicon thin film transistors (polysilicon TFTs). The exponential energy distribution of the band tail states in the bulk of the polysilicon layer is obtained from analysis of the space charge limited current in n⁺-i-n⁺ structures. The density of traps at the gate oxide/polysilicon interface and the slope of the exponential band tail states in a thin layer adjacent to the channel/gate oxide interface are extracted from low-frequency noise measurements. The experimental results indicate that the degree of disorder is improved in the upper part of the polysilicon layer due to its columnar growth.     

On the quasi-stationary grain size distribution from two Gamma size distributions in three-dimensional grain growth

Two different grain structures of which the grain size distribution could be well described by the Gamma distribution were generated by the combination of the Laguerre tessellation and Monte Carlo technique. Monte Carlo simulation shows that the three-dimensional grain growth process can evolve to the quasi-stationary state. The quasi-stationary grain size distribution could be well fit by the Gamma distribution with different parameters. The results in literature from various simulation methods support this point.     

A simulation study of the effect of the diverse valence-band offset and the electronic activity at the grain boundaries on the performance of polycrystalline Cu(In,Ga)Se2 solar cells

The paper presents a two-dimensional simulation study of a polycrystalline Cu(In,Ga)Se₂ (CIGS) solar cell with various shapes of grains inside the CIGS absorber layer. The grain boundaries (GBs) with a diverse valence-band offset (VBO) and the density of defect states (N_tA) are considered so as to evaluate their effects on the performance of the CIGS cell. The numerical simulations show that a CIGS cell with column-like grains can achieve a high conversion efficiency (η), while the η of a CIGS cell with diamond-like grains is low if the VBO at the GBs exceeds 0.4 eV. The VBO at which the η of the CIGS cell with diamond-like grains peaks is found at 0.20-0.27 eV. A favorable VBO mainly depends on the shape of the grains, but it also depends on the N_tA. The simulations of the CIGS cells in the substrate and superstrate configurations showed that their performances change if the VBO is varied. This result also implies that the configuration of the CIGS cell is important and the substrate configuration with larger grains in the space-charge region has a considerable advantage if the VBO ranges from 0 eV to 0.2 eV.     

Effects of aging temperature and grain size on the formation of serrated grain boundaries in an AISI 316 stainless steel

The effects of aging temperature and grain size on the formation of serrated grain boundaries have been investigated in an AISI 316 stainless steel. Grain size increased slightly over aging temperature ranges of 650–870 °C, resulting in predominantly serrated grain boundaries. However, when the temperature exceeded 880 °C, the grain size significantly increased, and grain boundary serration was not observed. The initial grain size also had an influence on the occurrence of grain boundary serration. For specimen having a large initial grain size of about 200 μm, no serrated grain boundary formed after aging treatment at 760 °C. Serrated grain boundaries were observed when “normal” initial grain sizes 55 μm were employed. It was found that the frequency of low angle boundaries markedly increased as the initial grain size increased from 55 to 200 μm. From the results obtained, it is possible to describe that the grain boundary serration could be considered as a spontaneous reaction that aims to reduce the total free energy of the system, and form a new interface of lower free energy. We proposed that the competition between grain growth and grain boundary serration during aging treatment reduces the total free energy of the alloy system: at temperatures exceeding 880 °C, the dominant process is the grain growth, while grain boundary serration predominates over the range of 650–870 °C.     

Effect of grain size on the hydrogen-assisted cracking in duplex stainless steels

The embrittlement behavior of 2205 duplex stainless steels with two different grain sizes in 26 wt% NaCl (pH 2) under cathodic potential were investigated by slow strain rate testing. The electrochemical permeation technique was used to characterize the permeation rate and effective diffusivity of hydrogen. The results indicated that both the effective diffusivity and the susceptibility of hydrogen embrittlement were lower for the finer grain size specimen. Ultimate tensile strength (UTS) and uniform elongation (UEL) decrease linearly with decreasing logarithm of strain rate. The dependence of UTS and UEL on the logarithm of strain rate was higher for the finer grain specimen. The microstructural examination revealed that internal cracks resulted from hydrogen embrittlement of the ferrite phase under cathodic charging conditions were arrested by austenite in duplex stainless steels.     

Direct growth of large grain polycrystalline silicon films on aluminum-induced crystallization seed layer using hot-wire chemical vapor deposition

Large grain polycrystalline silicon (poly-Si) films on glass substrates have been deposited on an aluminum-induced crystallization (AIC) seed layer using hot-wire chemical vapor deposition (HWCVD). A poly-Si seed layer was first formed by the AIC process and a thicker poly-Si film was subsequently deposited upon the seed layer using HWCVD. The effects of AIC annealing parameters on the structural and electrical properties of the poly-Si seed layers were characterized by Raman scattering spectroscopy, field-emission scanning electron microscopy, and Hall measurements. It was found that the crystallinity of seed layer was enhanced with increasing the annealing duration and temperature. The poly-Si seed layer formed at optimum annealing parameters can reach a grain size of 700 nm, hole concentration of 3.5 × 10¹⁸ cm^− 3, and Hall mobility of 22 cm²/Vs. After forming the seed layer, poly-Si films with good crystalline quality and high growth rate (> 1 nm/s) can be obtained using HWCVD. These results indicated that the HWCVD-deposited poly-Si film on an AIC seed layer could be a promising candidate for thin-film Si photovoltaic applications.     

Efficiency improvement of multicrystalline silicon solar cells after surface and grain boundaries passivation using vanadium oxide

The aim of this work is to investigate the effect of vanadium oxide deposition onto the front surface of multicrystalline silicon (mc-Si) substrat, without any additional cost in the fabrication process and leading to an efficient surface and grain boundaries (GBs) passivation that have not been reported before. The lowest reflectance of mc-Si coated with vanadium oxide film of 9% was achieved by annealing the deposited film at 600 °C. Vanadium pentoxide (V₂O₅) were thermally evaporated onto the surface of mc-Si substrates, followed by a short annealing duration at a temperature ranging between 600 °C and 800 °C, under O₂ atmosphere. The chemical composition of the films was analyzed by means of Fourier transform infrared spectroscopy (FTIR). Surface and cross-section morphology were determined by atomic force microscope (AFM) and a scanning electron microscope (SEM), respectively. The deposited vanadium oxide thin films make the possibility of combining in one processing step an antireflection coating deposition along with efficient surface state passivation, as compared to a reference wafer. Silicon solar cells based on untreated and treated mc-Si wafers were achieved. We showed that mc-silicon solar cells, subjected to the above treatment, have better short circuit currents and open-circuit voltages than those made from untreated wafers. Thus, the efficiency of obtained solar cells has been improved.     

Predicting recrystallized grain size in friction stir processed 304L stainless steel

A major dilemma faced in the nuclear industry is repair of stainless steel reactor components that have been exposed to neutron irradiation. When conventional fusion welding is used for repair, intergranular cracks develop in the heat-affected zone(HAZ). Friction stir processing(FSP), which operates at much lower peak temperatures than fusion welding, was studied as a crack repair method for irradiated 304 L stainless steel. A numerical simulation of the FSP process in 304 L was developed to predict temperatures and recrystallized grain size in the stir zone. The model employed an Eulerian finite element approach,where flow stresses for a large range of strain rates and temperatures inherent in FSP were used as input. Temperature predictions in three locations near the stir zone were accurate to within 4%, while prediction of welding power was accurate to within 5% of experimental measurements. The predicted recrystallized grain sizes ranged from 7.6 to 10.6 μm, while the experimentally measured grains sizes in the same locations ranged from 6.0 to 7.6 μm. The maximum error in predicted recrystallized grain size was about 39%, but the associated stir zone hardness from the predicted grain sizes was only different from the experiment by about 10%.     

Simulation studies on the effect of a buffer layer on the external parameters of hydrogenated amorphous silicon p-i-n solar cells

Device modeling of p-i-n junction amorphous silicon solar cells has been carried out using the amorphous semiconductor analysis (ASA) simulation programme. The aim of the study was to explain the role of a buffer layer in between the p-and i-layers of the p-i-n solar cell on the external parameters such as dark current density and open circuit voltage. Investigations based on the simulation of dark I–V characteristics revealed that as the buffer layer thickness increases the dark current for a given voltage decreases.     

Influence of the second-phase particle size on grain growth based on computer simulation

A three-dimensional Monte Carlo simulation method for grain growth in two-phased materials is set up, basing on a micro-physical analysis of the interaction between the second-phase particle and the grain boundary. Two-phased systems containing second-phase particles with the same quantity but different sizes are designed, and the complete processes of grain growth are simulated. The influences of the particle size on grain growth are observed and studied quantitatively.     

纳米复合永磁体的成分、晶粒尺寸与各向异性

以Nd2Fe14B/α—Fe为例，研究了晶粒之间交换耦合相互作用对纳米复合永磁体有效各向异性的影响。纳米复合永磁体的有效各向异性常数可用软—软、硬—硬、软—硬三种不同晶粒界面对应有效各向异性常数的统计平均值表示。计算结果表明：材料的有效各向异性常数Keff随软磁性相成分的增加而降低；在相成分比例一定的条件下，随软、硬磁性相晶粒尺寸比值的增加而增加。     

Micro-structures of BF2- and As-implanted polycrystalline silicon thin films of various thicknesses and heat treatments

Characterization of annealed BF₂⁺- and As⁺-doped polycrystalline silicon (polysilicon) films is presented. Effects of heat treatment, doping concentration, and thickness of film on the grain size and mobility of polysilicon films are investigated and discussed. By using transmission electron microscopy (TEM), it is found that the grain size, effective carrier concentration, and carrier mobility of a polysilicon thin film increases with increasing film thickness. Our results show that a high concentration of As dopant could enhance the recrystallization of the polysilicon films. Heavily As⁺-doped samples were seen to have a relatively larger grain size compared to the lightly doped film. The maximum grain size of about 278 nm can be realized in a polysilicon film with 150 nm in thickness. In contrast, the B dopant has a negligible effect on the recrystallization of polysilicon films. With increasing film thickness and thermal annealing temperature, a high performance polysilicon film with high mobility and grain size can be obtained.     

Microcrystalline silicon carbide thin films grown by HWCVD at different filament temperatures and their application in n-i-p microcrystalline silicon solar cells

To optimize the performance of microcrystalline silicon carbide (µc-SiC:H) window layers in n-i-p type microcrystalline silicon (µc-Si:H) solar cells, the influence of the rhenium filament temperature in the hot wire chemical vapor deposition process on the properties of µc-SiC:H films and corresponding solar cells were studied. The filament temperature T_F has a strong effect on the structure and optical properties of µc-SiC:H films. Using these µc-SiC:H films prepared in the range of T_F = 1800-2000 °C as window layers in n-side illuminated µc-Si:H solar cells, cell efficiencies of above 8.0% were achieved with 1 µm thick µc-Si:H absorber layer and Ag back reflector.     

On the variation of grain size and fractal dimension in an austenitic stainless steel

Samples of an AISI type 316L stainless steel were subjected to different treatments to promote changes in their microstructure. The specimens were heated in a box furnace set at four different temperatures for 30 min and cooled in air to room temperature by placing them in water after the cycle was completed. The samples were prepared following standard metallographic procedures, the microstructure was revealed with an electrolytic etchant, and the average grain size in each sample was determined by the mean line intercept technique. Images from the microstructures were digitized and fed into a personal computer for their fractal analysis by box counting. Two different approaches were used to obtain the fractal dimension of the structure, yielding to similar values in both cases. It was found that the fractal dimension of the microstructure increased with the reduction in grain size.     

High-throughput screening of critical size of grain growth in gradient structured nickel

Nanocrystalline metals with high Gibbs free energy have a strong tendency towards thermally driven grain growth,thus understanding the critical size or temperature of grain growth is vital for their applications.The investigations of thermal stability were usually conducted on the materials with a homo-geneous structure;however,these methods are time-consuming and expensive.In the present work,we reveal a high-throughput experimental strategy to characterize the size-dependent thermal stability via annealing the gradient structured Ni.Employing this method,the critical size of grain growth(dc)at a given annealing temperature was rapidly determined.The critical size of grain growth was～95 nm when annealed at 503 K for 3 h,which is consistent with the value reported in the homogeneous structured Ni.Furthermore,this critical size was found to be identical in three types of gradient structured Ni,i.e.,independent on the gradient structure.Our present work demonstrates a high-throughput strategy for exploring the critical size of grain growth and size-dependent thermal stability of metals.     

Opto-electronic properties of rough LP-CVD ZnO:B for use as TCO in thin-film silicon solar cells

Polycrystalline Boron-doped ZnO films deposited by low pressure chemical vapor deposition technique are developed for their use as transparent contacts for thin-film silicon solar cells. The size of the columnar grains that constitute the ZnO films is related to their light scattering capability, which has a direct influence on the current generation in thin-film silicon solar cells. Furthermore, if the doping level of the ZnO films is kept below 1 × 10²⁰ cm^− 3, the electron mobility can be drastically enhanced by growing large grains, and the free carrier absorption is reduced. All these considerations have been taken in account to develop ZnO films finely optimized for the fabrication of microcrystalline thin-film silicon solar cells. These TCO allow the achievement of solar cell conversion efficiencies close to 10%.     

Crystal plasticity-based modelling of grain size effects in dual phase steel

With decreasing grain size, the strength of steel increases due to the well-known Hall–Petch type effects, which is generally neglected in the classical crystal plasticity-based models. In the present work, the classical crystal plasticity-based model has been modified to incorporate the grain size effect. Validation of the present model was carried out with the published experimental results of a dual phase steel and, it was found to be possible to predict the grain size effects quite accurately using the model. The proposed model was used to carry out a parametric study for effects of grain size and was further used to predict the influence of grain size on cross effects during orthogonal loading.