A model for distribution of oxygen in multicrystalline silicon ingot grown by directional solidification

A model, including segregation from silicon melt to silicon crystal as well as evaporation from silicon melt to Ar atmosphere, was established for simulating the oxygen distribution in multicrystalline silicon (mc-si) ingot, which shows good agreement with the experimental results. According to this model, the oxygen distribution in the bottom of ingot is mainly determined by the evaporation of oxygen, whereas that in the top of ingot is dominated by the segregation of oxygen. Furthermore, it could be found that the O_i profiles in growth direction of ingots become more and more steeper with the increase of the exponent X.     

Two-dimensional resolution of minority carrier diffusion constants in different silicon materials

Hall measurements are a common method to determine the majority charge carrier diffusion constant. But the diffusion constant of the minority carriers D_n, the more interesting parameter in photovoltaics, is rather hard to detect. In this paper we introduce a method to determine D_n locally resolved and mapped in two dimensions. For that purpose the local diffusion length L_diff, which can be calculated from LBIC (laser beam induced current) measurements, has been combined with the local bulk lifetime τ_b received by μ-PCD (microwave-detected photo conductance decay) measurements. We evaluated the diffusion constants of the minority charge carriers D_n for different p-type silicon materials with a resolution of 100 μm. The measurements were carried out on solar cells before and after remote plasma hydrogen passivation in order to get an impression of the diffusion constant dependency on hydrogen incorporation.     

Characterisation of direct epitaxial silicon thin film solar cells on a low-cost substrate

Direct epitaxial crystalline silicon thin film (CSiTF) solar cells on low-cost silicon sheets from powder (SSP) ribbons have been prepared using rapid thermal chemical vapour deposition (CVD) growth. The characterisation of CSiTF solar cells was investigated by electron and spectrally resolved light beam induced current (EBIC and SR-LBIC, respectively). All EBIC measurements were performed on both the front-side surface as well as on the cross-section of CSiTF solar cells. The electrical recombination was detected by EBIC and compared with their morphologies. The results of EBIC scan show that recombination centres are situated at grain boundaries (GBs); higher the density of grain, higher the recombination activities (higher contrast). Recombination of different intensity (strong and weak) takes place at vertical GBs. Compared with the high recombination at GBs, the contrast in intragrain is low. The dark contrast of the GBs and intragrain defects is clearly reduced near the surface due to the passivation by hydrogen, which indicates that the minority carrier diffusion length decreases gradually with the depth perpendicular to the surface. The diffusion length was determined by SR-LBIC. The results show that the diffusion length distribution is quite inhomogeneous over the whole cell area. A maximum L_eff of about 25 μm and mean values around 15 μm are calculated for the best solar cell.     

Formation and distribution of silicon carbide (SiC) precipitates in industrial directional solidification of mc-Si ingots

Abstract

Silicon carbide inclusions in multicrystalline (polycrystalline) silicon ingots affect the cutting process and quality of silicon wafers. The higher density of SiC inclusions relative to the silicon melt suggests that they should sink, but inclusions were observed at the top, middle and bottom of industrial ingots. More inclusions were observed at the top relative to the middle and bottom of the ingot. Small SiC inclusions were found at the bottom and reticular SiC inclusions at the top of the ingot, suggesting that inclusion growth may occur during growth of the ingot. A mechanism to explain the formation and distribution of SiC in industrial silicon directionally solidified ingots, based on the thermodynamics of SiC, is proposed together with strategies to reduce carbon contamination and improve ingot quality.     

Fast hydrogen diffusion along Σ13 grain boundary of α-Al2O3 and its suppression by the dopant Cr: A first-principles study

To acquire knowledge of the effect of chromium dopant bringing on hydrogen diffusion along grain boundaries (GBs) of α-Al₂O₃, the energetics and mobility of hydrogen along Σ13 GB with and without Cr dopant have been studied via the first-principles calculations with the projector-augmented wave method. The energy barriers for hydrogen diffusion before and after Cr doped on Al-terminated Σ13 GB are determined to be 0.69 eV and 1.09 eV, respectively, which is smaller than or close to the hydrogen bulk diffusion with an activation energy of 1.10 eV. The results suggest that before doping Cr atoms, there is a rapid and easy diffusion channel for hydrogen along the Σ13 GB. However, the calculations show the segregation of Cr atoms to the GB is energetic favorable with a segregation energy of ?0.39 eV/atom, and the existence of Cr can suppress hydrogen diffusion along the Al-terminated Σ13 GB.     

Fluid flow and heat transfer of opposing mixed convection adjacent to downward‐facing,inclined heated plates

Experimental investigations were carried out for opposing mixed convective flows of air adjacent to downward‐facing, inclined heated plates. The experiments covered the ranges of the Reynolds and modified Rayleigh numbers from Re_L=400 to 4600 and Ra_L^*=1.0×10⁷ to 5.4×10⁸, and the inclination angles from θ=15 to 75^° from horizontal. The flow fields over the plates were visualized with smoke. The results showed that a separation of forced boundary layer flow occurs first at the bottom edge of the plate, and then the separation point shifts toward upstream with increasing wall heat flux, and finally, reaches the top edge of the plates. It was found that the separations at the bottom and top edges are predicted with a non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5)=0.35 and 1.0, respectively. The local heat transfer coefficients of the inclined plates were also measured and the results showed that the minimum coefficients appear in the separation region. Moreover, it was revealed that forced, natural, and combined convective flows can be classified by the non‐dimensional parameter (Gr_Lθ^*/Re_L^2.5). © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Pub‐ lished online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20233     

Current–voltage characteristics of electrovoltaic and electrophotovoltaic cells

Electrovoltaic (EV) effect provides a way of generating voltage across an unbiased junction under dark. Electrovoltaic (EV) cell in its simplest form is a device based on n⁺–p–n⁺ (or p⁺–n–p⁺) like structure in which if one p–n junction is subjected to an external forward bias, then, a voltage is developed across the other p–n junction such that the n-side gets a negative polarity with respect to the p-side. Connecting to a load across one of the n⁺–p junctions a bipolar transistor can be operated as a three-terminal EV cell. A new device henceforth known as electrophotovoltaic (EPV) cell wherein EV and PV effects could be expected to work cooperatively was also realized. It is based on a structure which is a combination of n⁺–p–n⁺ EV and n⁺–p–p⁺ photovoltaic (PV) cell structures having a common n⁺–p junction and is able to operate in EV, PV and EPV modes. We have developed one-dimensional physical models of EV and EPV cells and have applied them to explain the observed I–V characteristics of an n–p–n silicon bipolar transistor 2N3055 in EV mode and the EPV cell in EV, PV and EPV modes. While the photovoltaic efficiency η_PV decreases slowly with d/L, where d is the thickness and L is the diffusion length of minority carriers in the base region, the electrovoltaic efficiency η_EV has a strong dependence on d/L and decreases sharply with increase in d/L. Transistor 2N3055 with d/L=0.7 demonstrated η_EV>60%, whereas, our EPV cell with d/L>2.7 had η_EV<3%. However, in the EPV cell, the PV and the EV effects were indeed found to work cooperatively and the output power was enhanced in the EPV mode over the PV mode value although the efficiency η_EPV was less than 4.5%. To achieve substantially high values of efficiencies in EV and EPV modes the EPV cell should be designed to have d/L1.     

Improved photovoltaic method for measurement of minority carrier diffusion length applied to silicon solar cells

The photovoltage spectrum measured on back illuminated silicon solar cells of the (passivated emitor solar cell) (PESC) type without original bottom ohmic electrode is evaluated with the aim to find the diffusion length of minority carriers in bulk of the absorber (L). Two junctions, namely pn⁺ junction of the cell and that spontaneously created on the free surface generally exist in such samples. They give rise to two signals of opposite signs with one point of exact compensation. Six parameters (including L) are needed to characterize the spectrum. Special simple arrangement removes influence of spontaneously created junction on the free surface, which, in this way, reduces the number of parameters needed for fitting to three and enhances reliability of the measurement.     

Constructal flow structure for a single SOFC

This paper presents a model and a structured procedure to optimize the internal structure of a single solid oxide fuel cell (SOFC) so that the power density is maximized. The polarization curve and power density are obtained as functions of temperature, geometry and operating parameters. The internal structure, which accounts for the thickness of the two electrodes and the electrolyte, and the flow channels geometry, has been optimized. The model is developed using a control volume approach, in which, all relevant thermal and electrochemical interactions between adjacent elements are accounted for. The effects of geometry on the compartments temperatures and reactants concentrations in the fuel cell are explored. The optimized internal structure results from optimal balances between the thickness of anode and cathode, L₃ and L₅, shoulder channel aspect ratio, L_t/L_ch, and the total number of fuel and oxidant channels, n_ch. The optima found are sharp and, therefore, important to be identified in actual SOFC design. The variations of power density in the studied ranges of L₃ and L₅, L_t/L_ch, and n_ch were of 11, 5 and 5%, respectively, in the three‐way optimization process, for the anode‐supported single SOFC. Copyright © 2007 John Wiley & Sons, Ltd.     

Natural convection near 4°C in a water saturated porous layer heated from below

This paper reports a numerical study of two-dimensional natural convection in a horizontal porous layer heated from below and saturated with cold water. The density maximum of water at 3.98°C and atmospheric pressure occurs inside the layer, as the top surface is maintained at 0°C and the bottom surface is varied from 4 to 8°C. Three separate series of numerical simulations document the effect of Rayleigh number, bottom surface temperature, and horizontal length of the porous layer on the overall heat transfer rate vertically through the layer. The range of these numerical experiments is 200 < Ra_p < 10000, 0.167 < H/L < 1 and °C < T_H < 8°C, where Ra_p, H/L and T_H are the Darcy-modified Rayleigh number for a fluid with density maximum, the geometric ratio height/length, and the bottom wall temperature. The numerical results agree with published linear stability results regarding the onset of convection.     

Numerical investigation of mixed convection of non-Newtonian fluid in a vented square cavity with fixed baffle

This paper numerically investigates mixed convective heat transfer in a vented square cavity incorporated with a baffle that is subjected to external non-Newtonian fluids (NNFs). Adiabatic conditions are imposed on the top and bottom walls, while cold temperature conditions are applied to the right and left solid boundaries. Heated NNF enters the cavity through the inlet and goes out through the outlet at three different locations, and it passes on a vertical baffle fixed at the base placed at different lengths. To examine the impact of the inlet and outlet positions, three different shapes of the outlet port located on the right wall and the inlet port on the left bottom wall were investigated. The impacts of Reynolds number (Re) of 100 ≤ Re ≤ 1000, Richardson number (Ri) of 0.1 ≤ Ri ≤ 3, power law index (n) of 0.6 ≤ n ≤ 1.4, length of baffle (L_b) of 0.2 ≤ L_b ≤ 0.6 and the outlet hole positions (S) of $0\le S\le 0.9$ on the thermal and flow distributions in the cavity are taken into consideration in this paper. The results demonstrated that the flow's intensity and heat transfer increase with improvement in the Re and n at any baffle length. When the Ri increased from 0.1 to 3, $N{u}_{\mathrm{avg}}$ increased by 23.3% at $n=0.6$, and 13.8% at $n=1.2$. Also, the Ri increment results in the augmentation of the average heat transfer.     

Double‐diffusive natural convection in a partially heated enclosure using a nanofluid

This paper analyzes numerically the effect of double‐diffusive natural convection of a water–Al₂O₃ nanofluid in a partially heated enclosure with Soret and Dufour coefficients. The top horizontal wall has constant temperature T_c, while the bottom wall is partially heated T_h, with T_h > T_c . The concentration in the top wall is maintained higher than the bottom wall C_c < C_h. The remaining bottom wall and the two vertical walls are considered adiabatic. Water is considered as the base fluid. The governing equations are solved by the Penalty Finite Element Method using Galerkin's weighted residual scheme. The effect of the parameters, namely, Rayleigh number and solid volume fraction of the nanoparticles on the flow pattern and heat and mass transfer has been depicted. Comprehensive average Nusselt and Sherwood numbers, average temperature and concentration, and mid‐height horizontal and vertical velocities at the middle of the cavity are presented as functions of the governing parameters mentioned above. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21010     

Thermal transport analysis for natural convection in a porous corrugated rhombic enclosure

A numerical study of fluid flow and heat transfer, applying natural convection is carried out in a porous corrugated rhombic enclosure. A uniform heating source is applied from the bottom boundary wall while the inclined side walls are maintained to a constant cold temperature and the top corrugated wall is retained at insulated condition inside the enclosure. The heat transfer and flow features are presented for a wide spectrum of Rayleigh numbers (Ra), 10⁴ ≤ Ra ≤ 10⁶, and Darcy numbers (Da), 10^?3 ≤ Da ≤ 10^?2. The number of undulations (n) for the top and bottom walls have been varied from 1 to 13 keeping the amplitude of undulation fixed. It is revealed that the characteristics of heat transfer are conceivably modulated by changing the parameter of the undulation number on the enclosure walls, specifically at the bottom and top. The influencing control of n in altering the heat transfer rate is felt maximum on the left wall and minimum for the right wall, and there is a strong interplay between Ra and Da together with n on dictating the heat transfer characteristics. The critical value, where heat transfer rate is observed as maximum is at n = 11 and thereafter the values decrease.     

Interpretation of minority carrier diffusion length measurements in thin silicon wafers

Diffusion length of minority carriers measured in thin wafers reflects not only properties of the material but also the state of its surface and, consequently, becomes an effective quantity L_eff depending on the thickness of the sample. The function describing this dependence is presented here and compared with the data from surface photovoltage experiments. It allows one to find the correct diffusion length from measurement of two samples with different thicknesses.     

Multicrystalline silicon wafers prepared from upgraded metallurgical feedstock

A solution to the problem of the shortage of silicon feedstock used to grow multicrystalline ingots can be the production of a feedstock obtained by the direct purification of upgraded metallurgical silicon by means of a plasma torch. It is found that the dopant concentrations in the material manufactured following this metallurgical route are in the 10¹⁷ cm⁻³ range. Minority carrier diffusion lengths L_n are close to 35 μm in the raw wafers and increases up to 120 μm after the wafers go through the standard processing steps needed to make solar cells: phosphorus diffusion, aluminium–silicon alloying and hydrogenation by deposition of a hydrogen-rich silicon nitride layer followed by an annealing. L_n values are limited by the presence of residual metallic impurities, mainly slow diffusers like aluminium, and also by the high doping level.     

Determination of front surface recombination velocity of silicon solar cells using the short-wavelength spectral response

A method of determination of recombination velocity S_f of minority carriers at the front surface of an n⁺–p–p⁺(p⁺–n–n⁺) silicon solar cell in which the n⁺(p⁺) front emitter is made by diffusion of dopant impurity in the p(n) region is presented. This method uses the short-wavelength spectral response of the cell to determine S_f and is applicable if the front emitter of the cell has a linearly varying built-in field. It was applied to a p⁺–n–n⁺ solar cell that had a Gaussian distribution of the dopant impurity in the p⁺ front emitter up to a depth of 0.078 μm from the surface. Using the spectral response data of cell in 380 nm<λ< 500 nm range S_f was found to have a nearly constant value 6×10⁵ cm s⁻¹ in 400 nm<λ<460 nm range. Below and above this wavelength range the value of S_f was found to be slightly smaller. For comparison the value of S_f was also determined assuming the p⁺ region to be uniformly doped, and this value was found to be significantly smaller than based on the diffused emitter model. The analysis showed that for a diffused junction cell, the assumption that the front emitter is uniformly doped, ignores the presence of the built-in field in the emitter region and leads to overestimation of minority carrier recombination in the emitter. Consequently for a given contribution of the front emitter region to the spectral response of the cell, this assumption underestimates the front surface recombination and determines a smaller value of S_f. On the other hand, the present method can be expected to determine a realistic value of S_f independent of λ for most diffused junction silicon solar cells using the spectral response data in a suitable short-wavelength range since each such cell indeed has a built-in electric field in the emitter region.     

Effect of spatial variation of incident radiation on spectral response of a large area silicon solar cell and the cell parameters determined from it

Effect of spatial variation of incident monochromatic light on spectral response of an n⁺–p–p⁺ silicon solar cell and determination of diffusion length of minority carriers (L_b) in the base region and the thickness of the apparent dead layer (x_d) in the n⁺ emitter from the spectral response have been investigated. Spectral response of a few 10 cm diameter and 10×10 cm² pseudo-square silicon solar cells was measured with the help of a standard silicon solar cell of 2×2 cm² area in 400–1100 nm wavelength range. Different areas (4, 9, 16, 25 and total area 78.6 or 96 cm²) were exposed. The effect of the radial variation of incident radiation was determined quantitatively by defining a parameter f₁ as the ratio of the average intensity falling on the reference cell to that on the exposed area of the test cell. The value of f₁ varied between 1 and 1.15 (1.25) as the exposed area of the cell varied from 4 cm² to 78.6 (96) cm² indicating that the spatial inhomogeneity of intensity increased with the increase in the exposed cell area. Short-circuit current densities, J_sc, computed from spectral response data for AM1.5 spectrum were less compared to the directly measured values by a factor which was nearly equal to f₁. However, radial variation of intensity does not affect the determination of diffusion length of minority carriers in the base region (by the long wavelength spectral response, LWSR method using the measured spectral response data in 0.85<λ<1.05 μm range) and the thickness of the dead layer (by the method of Singh et al. using the data of 0.45<λ<0.65 μm range) significantly.     

Preliminary photovoltaic response from a polymer containing p-vinylenephenylene amine backbone

Optoelectronic properties from a novel polymer, poly(p-phenylene N-4-n-butylphenyl-N,N-bis-4-vinylenephenylamine) (PNB) have been investigated. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels of the material were estimated to be −5.18 and −2.75 eV, respectively, measured with cyclic voltammetry. A single-layer device structure was prepared by spin-coating PNB thin films from a solution on top of an indium–tin oxide (ITO) substrate while aluminum was used as a top electrode. Current density–voltage (J–V) characteristic was measured which showed a typical rectifying behavior. Photovoltaic from a single-layered device was observed under a white arc lamp illumination. This was improved via a double-layer structure comprising vacuum evaporated copper phthalocyanine (CuPc) or N,N′-ditridecylperylene-3,4,9,10-tetracarboxylic diimide (PTCDI-C₁₃) as an additional layer. The open-circuit voltage, short-circuit current and hence the efficiency were improved in the double-layer devices. An ITO/PNB/PTCDI-C₁₃/Al device was estimated to have external quantum efficiency (EQE) around 1% at 330 nm. In a comparison of optical absorption and photocurrent spectra, it was demonstrated that the excitons could be separated and further, generated carriers drifting to the opposite electrodes more efficiently in the double-layer cells.     

Gas-phase saturation and evaporative cooling effects during wet compression of a fuel aerosol under RCM conditions

Wet compression of a fuel aerosol has been proposed as a means of creating gas-phase mixtures of involatile diesel-representative fuels and oxidizer + diluent gases for rapid compression machine (RCM) experiments. The use of high concentration aerosols (e.g., ∼0.1 mL_fuel/L_gas, ∼1 × 10⁹ droplets/L_gas for stoichiometric fuel loading at ambient conditions) can result in droplet–droplet interactions which lead to significant gas-phase fuel saturation and evaporative cooling during the volumetric compression process. In addition, localized stratification (i.e., on the droplet scale) of the fuel vapor and of temperature can lead to non-homogeneous reaction and heat release processes – features which could prevent adequate segregation of the underlying chemical kinetic rates from rates of physical transport. These characteristics are dependent on many factors including physical parameters such as overall fuel loading and initial droplet size relative to the compression rate, as well as fuel and diluent properties such as the boiling curve, vaporization enthalpy, heat capacity, and mass and thermal diffusivities. This study investigates the physical issues, especially fuel saturation and evaporative cooling effects, using a spherically-symmetric, single-droplet wet compression model. n-Dodecane is used as the fuel with the gas containing 21% O₂ and 79% N₂. An overall compression time and compression ratio of 15.3 ms and 13.4 are used, respectively. It is found that smaller droplets (d₀ ∼ 2–3 μm) are more affected by ‘far-field’ saturation and cooling effects, while larger droplets (d₀ ∼ 14 μm) result in greater localized stratification of the gas-phase due to the larger diffusion distances for heat and mass transport. Vaporization of larger droplets is more affected by the volumetric compression process since evaporation requires more time to be completed even at the same overall fuel loading. All of the cases explored here yield greater compositional stratification than thermal stratification due to the high Lewis numbers of the fuel–air mixtures (Le_g ∼ 3.8).     

Integrated study of lead iodide crystal growth and doping processes

Due to its high atomic number, high density and wide band-gap energy, lead iodide is a promising nuclear-radiation detector material. The radiative transition in PbI₂ is mainly due to donor–acceptor pair (D–A) recombination associated with impurities, which suggests improving scintillating performance of lead iodide by doping certain impurities. Before the doping study, high-purity PbI₂ with the least undetermined impurities is obtained by purifying the commercial PbI₂ with zone-refining technique. After well mixed with certain dopants (AgI and LaI₃), the purified PbI₂ is used as starting material for single crystal growth by vertical Bridgman method. Numerical studies are conducted to study temperature fields in both zone-melting and Bridgman furnaces. The solid/liquid interface is determined according to the heat balance on the growth front. The results are found to agree well with experimental measurements. Distribution of impurity concentration in purified ingot is studied experimentally, while that in grown crystal is studied analytically. By comparing analytical solutions with experiments, the effective redistribution coefficients of dopants in lead iodide crystal are determined. We further conclude that diffusion-dominated mechanism of dopant redistribution accounts for the uniform distribution of dopants in crystal, and that the suppression of natural convection in the melt is critical. By integrated study of heat and mass transfer phenomena during purification and growth processes of lead iodide, important information is achieved for the understanding and improvement of hot-zone design in the furnaces as well as for the parametric optimization of both processes.