Equilibrium Segregation Coefficient Research Articles

Interface and surface segregation of germanium in the SiGe semiconductor

The concentration and distribution of germanium in the silicon crystal or SiGe alloy can play critical roles in affecting the performance of prepared semiconductor devices. We quantitatively investigate the segregation behavior of germanium in silicon and SiGe semiconductor based on molecular dynamics simulation using the Stillinger-Weber (SW) and Tersoff empirical potentials. The value predicted by the SW potential is 0.35 which agrees with some reported experimental results. Both potentials predict that the Ge equilibrium segregation coefficient at the solid/liquid interface of silicon is smaller than one. The germanium atoms tend to segregate to the surface in the SiGe nano structures in order to lower the surface energy. We define the surface segregation coefficient Ks to quantitively describe this behavior. It is found that Ks decreases with the increase of total germanium atomic fraction in the liquid slab. The size dependence of the surface segregation coefficient in the nanodroplet is studied and it scales with 1/R3 linearly. The germanium distribution in the SiGe solid slab and nanoparticle is largely affected by the Ge distribution in the liquid slab and nanodroplet before crystallization.

Numerical Simulation of Flow Field Optimizing the Rotating Segregation Purification of Silicon for SoG-Si

In order to improve the preparation efficiency of high-purity silicon, a new method of rotary segregation purification has been developed to prepare polysilicon. Numerical simulation based on ANSYS19.0 software and water model experiments were used to study the distribution of flow field and optimize the impurity removal process. A numerical simulation model suitable for rotating interface is established. The simulation result is in good agreement with the water model experiment. A vortex flow is found in the middle of the mold when the mold insertion depth is 90 mm. The vortex is conducive to the thinning of the impurity enrichment layer at the solid–liquid interface. With the mold insertion depth increases from 90 to 170 mm, two vortex flows appear in the middle and bottom of the mold, respectively. Moreover, setting the mold rotation rate at 100 rpm can contribute to a more stable flow field and a higher melt flow velocity. When the diffusion layer thickness is less than 0.1 mm, the impurity segregation coefficient can approach close to its equilibrium segregation coefficient, indicating that impurity segregation be effectively enhanced by increasing the rotation rate of mold, strengthening the effect of solidification rate and increasing the rotational speed. Industrial tests were carried out at the 100 kg level. The result shows that the rotary segregation method and equipment can achieve the removal of very low impurity in silicon (99.999 pct), and SoG-Si (99.9999 pct) was obtained. This method provides a new way for silicon purification, and it is believed that better results can be obtained through continuous improvement.

Calculation of Phase Diagrams and First-Principles Study of Germanium Impacts on Phosphorus Distribution in Czochralski Silicon

Phosphorus (P) is one of the most widely used donor dopants for fabricating a low-resistivity silicon (Si) substrate. However, its volatile nature and the relatively small equilibrium segregation coefficient in Si at the melting temperature of Si impede the efficient and effective growth of low-resistivity Czochralski (CZ) Si single crystal. The primary objective of this work is to theoretically perceive the influence of germanium co-doping on the heavily P-doped Si crystal by means of CALculation of PHase Diagrams (CALPHAD) approaches and density functional theory (DFT) calculations. Phase equilibria at the Si-rich corner of the Si-Ge-P system has been thermodynamically extrapolated based on robust thermodynamic descriptions of involved binary systems, where Si-P and Ge-P have been re-assessed in this work. Phase diagram calculation results indicate that at a given P concentration (e.g. 0.33 at.% P) Ge co-doping lowers the solidification temperature of the Si(Ge, P) alloys, as well as the relevant equilibrium segregation coefficients of P in the doped Si. DFT calculations simulated the formation of (i) monovacancy in Si as well as (ii) solutions of Si(P) and Si(Ge) with one dopant substitutionally inserted in 64- and 216-atom Si cubic supercells. Binding energies were calculated and compared for Ge-Ge, Ge-P and P-P bonds positioning at the first nearest-neighbors (1NN) to the third nearest-neighbors (3NN). P-P bonds have the largest bonding energy from 1NN to 3NN configurations. The climbing image nudged elastic band method (CL-NEB) was utilized to calculate the energy barriers of P 1NN jump in the 64-atom Si cubic supercell with/without a neighboring Ge atom. With Ge present, a higher energy barrier for P 1NN jump was obtained than that without involving Ge. This indicates that Ge can impede the P diffusion in Si matrix.

Defect control based on constitutional supercooling effect in cast multicrystalline silicon: Boron-indium co-doping

The impact of constitutional supercooling (CS) on the grain structure of cast multicrystalline silicon (mc-Si) materials was investigated. Indium impurity was chosen as the CS dopant because of its low equilibrium segregation coefficient so that CS effect could be obtained at relatively low doping concentration. Industrial indium (In) doped G2 and boron-indium (B–In) co-doped G5 seed-assisted multicrystalline silicon (mc-Si) ingots were fabricated and characterized. Self-nucleated grains and epitaxial grains could be obtained, respectively, as the result of tuning the doping amount of indium. Constitutional-supercooling-related defects (CSD) were found in the co-doped ingot and could suppress the growth and propagation of dislocation-type defects. As a result, the overall deleterious defect density of B–In co-doped mc-Si wafers was well reduced compared to that of referential B-doped wafers, and the average solar cell performance of B–In co-doped ingots was obviously enhanced.

Numerical analysis of impurity separation from waste salt by investigating the change of concentration at the interface during zone refining process

The waste salt treatment process is required for the reuse of purified salts, and for the disposal of the fission products contained in waste salt during pyroprocessing. As an alternative to existing fission product separation methods, the horizontal zone refining process is used in this study for the purification of waste salt. In order to evaluate the purification ability of the process, three-dimensional simulation is conducted, considering heat transfer, melt flow, and mass transfer. Impurity distributions and decontamination factors are calculated as a function of the heater traverse rate, by applying a subroutine and the equilibrium segregation coefficient derived from the effective segregation coefficients. For multipass cases, 1d solutions and the effective segregation coefficient obtained from three-dimensional simulation are used. In the present study, the topic is not dealing with crystal growth, but the numerical technique used is nearly the same since the zone refining technique was just introduced in the treatment of waste salt from nuclear power industry because of its merit of simplicity and refining ability. So this study can show a new application of single crystal growth techniques to other fields, by taking advantage of the zone refining multipass possibility. The final goal is to achieve the same high degree of decontamination in the waste salt as in zone freezing (or reverse Bridgman) method.

Crack susceptibility of binary aluminum alloys during solidification

Cracking can occur during solidification in welding and casting. The present study attempted to deal with some fundamental questions regarding the susceptibility to cracking during solidification. How does the phase diagram affect the crack susceptibility? Can back diffusion occur in welding? How is the dihedral angle related to bridging between grains? To help answer the questions, the maximum |dT/d(fS)1/2| (T is temperature and fS fraction solid) was calculated, whose validity as the crack susceptibility index was verified recently. To deal with curved solidus and liquidus lines (i.e., variable equilibrium segregation coefficient k), fS was calculated as a function of T by numerical integration instead of by a simple analytical equation for constant k. Based on the secondary dendrite arm spacing λ2 in common Al arc welds and the λ2−tf data of Al alloys (tf is local solidification time), it was shown that back diffusion can occur in Al arc welding. Binary Al alloy systems were investigated over wide ranges of the eutectic temperature TE (229–548 °C) and k (about 0–0.87 at TE). It was shown that with a very low TE the crack susceptibility can still be relatively low if k is very high at TE to increase the effect of back diffusion on crack susceptibility reduction, consistent with the lower crack susceptibility of Al-Mg and even Al-Zn than Al-Cu. With both a very low TE and a very low k at TE, however, the crack susceptibility can be very high, consistent with the severe crack susceptibility of Al-Sn. The effect of the curvature of the liquidus and solidus lines on the crack susceptibility was shown. A possible link between the dihedral angle and bridging between grains was also shown.

Application of porous interface on segregation in Czochralski crystal growth

The aim of this paper is to develop a model for the solute segregation in Czochralski crystal growth based on similarity solution. In this model, the effect of crystal growth rate for the wide range of Schmidt (Sc) numbers on boundary layer is considered. We utilize a variable R=V0/νω which represents the ratio of growth velocity (V0) to stirring velocity (νω). Since both crystal rotation rate and growth velocity are almost varied in order to control the growth process, the parameter R can be used as a scale of optimization for the various growth conditions. The analyses show that the effective segregation coefficient (keff) is related to the parameter R. In the end, the results are utilized in the Czochralski configuration to determine the equilibrium segregation coefficient (k0) and Sc number evaluated and compared with experimental data.

Segregation of Ge in B and Ge codoped Czochralski-Si crystal growth

The segregation of Ge in B and Ge codoped Czochralski (CZ)-Si crystal growth was investigated. The concentration of Ge in heavily Ge codoped CZ-Si was measured by electron probe micro analysis (EPMA) and X-ray fluorescence spectroscopy. The effective segregation coefficient of Ge (keff) was calculated by fitting the EPMA data to the normal freezing equation, and by taking the logarithmic ratio of the Ge concentrations at the seed and tail of the ingots (top to bottom approach). The keff of Ge increased from 0.30 to 0.55, when the initial Ge concentration in the Si melt (CL(o)Ge) was increased from 3×1019 to 3×1021cm−3. To avoid cellular growth, the crystal pulling rate was decreased for heavily Ge codoped crystal growth (CL(o)Ge>3×1020cm−3). The equilibrium segregation coefficient (k0) of Ge was calculated by partitioning theory, and was smaller than the experimentally estimated keff. The variation of keff from k0 was discussed based on Ge clustering in the heavily Ge codoped crystal, which led to changes in the bonding and strain energies caused by the incorporation of Ge into Si.

On the bulk β-Ga2O3 single crystals grown by the Czochralski method

The growth of bulkx β-Ga2O3 single crystals by the Czochralski method is reported and discussed in terms of crucial growth conditions and correlated with basic electrical and optical properties of the obtained crystals. β-Ga2O3 crystals have a tendency to a spiral formation due to free carrier absorption in the near infrared (NIR) wavelength range, which hampers radiative heat transfer through the growing crystal. Moderate or low free electron concentrations (<5×1017cm−3) lead to cylindrical crystals with a high crystallized fraction (g≥0.5). The use of a CO2-containing growth atmosphere provides oxygen partial pressures between 0.8 and 4.4×10−2bar that is sufficient to obtain cylindrical and semiconducting crystals. Doping with Sn increases the free electron concentration in the crystals to high values (~1019cm−3) that lead to an immediate spiral formation, while doping with Mg (>6wtppm) provides insulating crystals with reduced probability of the spiral formation. The estimated Mg equilibrium segregation coefficient across the liquid–solid interface is 0.10–0.12. Annealing of undoped crystals in an oxidizing atmosphere at temperatures ≥1200°C for 20h decreases the bulk free electron concentration by about one order of magnitude, while the crystal surface becomes insulating. However, Mg:β-Ga2O3 crystals are insensitive to annealing in both oxygen- and hydrogen-containing atmospheres. The transmittance spectra showed a steep absorption edge at 260nm and virtually full transparency in the visible and NIR wavelength range for low and moderate free electron concentrations. We also demonstrated the possibility of growing 2in. diameter β-Ga2O3 single crystals by the Czochralski method. The good crystal quality is evidenced by rocking curve FWHM values of below 50". We noted that most dislocations propagate parallel to (100) plane. Further, we also provide thermal properties of the crystals as a function of temperature.

Determinations of equilibrium segregation, effective segregation and diffusion coefficients for Nd+3 doped in molten YAG

In this paper, a new mathematical model has been presented to determine the equilibrium segregation (k0) and effective segregation (keff) coefficients for neodymium (Nd) in YAG crystal grown by Czochralski (CZ) method. Determination of diffusion coefficient (DL) of Nd impurity in molten YAG is also investigated. In this model, utilizing Lambert W-function is a new idea to solve the Scheil equation for calculation of effective segregation coefficient. The Nd concentration in the crystal has been measured by optical absorption method to calculate keff. The analyses show that the keff is related to the growth parameters such as crystal growth rate (ug) and crystal rotation rate (ω), (keff~ug/ω) but it is independent of the Nd concentration in the initial melt (C0). Based on obtained keff and experimental growth data, k0 and DL of Nd in molten YAG have been calculated. For all experiments, the average value of k0=0.216 and DL=1.4×10−6 (cm2/s) are obtained. Our results are corroborated by the theoretical and experimental data from the literature.

Purification of Multicrystalline Silicon by Cold Crucible Directional Solidification and Impurity Distribution

In order to get solar grade silicon, large cold crucible has been used in an induction heat furnace. By controlling the relative location of the crucible and coils, directional solidification was realized. More than 200 kg multi-crystalline silicon ingot was produced in a batch with short work time. The removal rate of most metal impurities was high, typically higher than 99% for transition metals like iron. Non-metallic elements such as boron and phosphorus could not be removed efficiently because of larger equilibrium segregation coefficient. The concentration of phosphorus was one third of the feedstock due to the vaporization in the melting process. The distribution of impurities agreed with the solidification principle. Quartzes and carbon was not used, which ensured silicon prevent from the contamination. Cooperated with other methods, large scale of solar grade silicon was produced.

Characterization of a Czochralski grown silicon crystal doped with 1020 cm‐3 germanium

AbstractA dislocation‐free silicon single crystal doped with 1020 cm‐3 germanium (Ge) has been grown using the Czochralski (CZ) growth technique. The Ge concentration in the seed‐end and tang‐end of the crystal was 8×1019cm‐3and 1.6×1020 cm‐3, respectively. The effective segregation coefficient of Ge, the distribution of flow pattern defects (FPDs) and the wafer warpage have been characterized. Both the effective segregation coefficient and the equilibrium segregation coefficient of Ge in silicon were evaluated. Then, the density of FPDs was traced from seed‐end to tang‐end of the ingot, a suppression of FPDs by Ge doping was shown. That is probably because the Ge atoms consume free vacancies and thus a higher density of smaller voids is formed. Furthermore, the mechanical strength of wafers has also been characterized by batch warpage analysis. The warpage in the seed‐end was larger than that in the tang‐end of the ingot, showing that the mechanical strength of wafers is enhanced by Ge doping. Such improvement is interpreted by an enhanced dislocation pinning effect associated with the enhanced nucleation of grown‐in oxygen precipitates in the Ge‐doped silicon wafers. (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Equilibrium segregation coefficient and solid solubility of B in Czochralski Ge crystal growth

This paper reports reevaluated results of the segregation coefficient of boron (B) and a solid solubility of B at melting point of Ge. The crystal growth was carried out from a B-saturated Ge melt, and a solid solubility of B in Ge crystal was estimated to be 3 ± 0.5 × 10 18 cm − 3 . The effective segregation coefficients of 4 and 2.5 were obtained at pulling rates of 10 and 30 mm/h, respectively. An equilibrium segregation coefficient was estimated to be 6.2 and it was considerably smaller than those reported previously. Therefore, boron atoms in Ge melt easily interact with residual O atoms existing in the Ge melt, resulting in various values reported of the segregation coefficient. A phase diagram of Ge and B at Ge-rich region estimated from obtained experimental results is proposed.

Segregation and Twinning in the Rare-Earth Doped KPb2Cl5 Laser Crystals

Ve present the Er 3+ :KPb 2 Cl 5 lattice parameters thermal expansion and twinning characterization, pure KPb 2 Cl 5 crystals room temperature static dielectric constant measurements, and equilibrium segregation coefficients determination of Er 3+ , Ho 3+ , and Pr 3+ defects in KPb 2 Cl 5 . The two main current limitations which still hinder the development of this crystal as a laser material, namely, the Er 3+ cations segregation and low solubility limit as well as the crystal twinning, are discussed.

Segregation of boron in germanium crystal

A heavily boron (B)-doped germanium (Ge) bulk crystal was grown by the Czochralski method. The B concentrations in the crystal were evaluated by measuring the carrier concentration with the Hall effect and resistance method. Maximum solubility of B into Ge was estimated to be 2.5×10 18 cm −3. The equilibrium segregation coefficient of B in Ge was considered to be 5–6, much smaller than that reported previously.

Ga segregation in Czochralski-Si crystal growth with B codoping

Codoping of gallium (Ga) and boron (B) in a Czochralski-silicon (CZ-Si) crystal has been proposed to be an effective way to improve the homogeneity of resistivity over the length of a simply Ga-doped Si crystal, by increasing the very small equilibrium segregation coefficient of Ga ( k 0=0.008). It was observed that the axial resistivity variation in a Ga- and B-codoped Si crystal was smaller than that in simply Ga-doped Si crystals. The segregation behavior of Ga and B in the codoped CZ-Si crystal growth has been investigated in the present study. The effective segregation coefficient of Ga was kept almost constant when the B concentrations were low, but it increased at higher B concentrations. On the other hand, the effective segregation coefficient of B was kept almost constant when the B concentrations were low; however, it decreased at higher B concentrations. It has been analytically demonstrated that there is strong interaction between Ga and B in a Si crystal, which leads to an increase in the segregation coefficient of Ga in Si crystal growth.

Effective segregation coefficient in cluster crystallization model

An expression for the effective segregation coefficient k eff is derived at the assumption that the crystallization begins in the melt within the supercooled diffusion layer by the formation of complex anion structures (clusters). The dependence of k eff on the equilibrium segregation coefficient k 0, the thickness of the supercooled boundary layer σ and the crystal growth rate V is determined for a low supercooling at the melt–crystal interface. There is no necessity to introduce the concept of the interface segregation coefficient (which is equal to the ratio of the concentration in the crystal to that in the melt at the interface), when the presence of the anion structures in the melt is taken into account. The mutual dependence of V and σ is considered. The formula derived fits well to the experimental data for the range of the low crystal growth rates.

Distribution of aluminum and indium impurities in crystals of Ge-Si solid solutions grown from the melt

The problem regarding the distribution of aluminum and indium impurities in bulk crystals of solid solutions with a variable composition Ge1−x Si x (0 ≤ x ≤ 0.3) is solved in order to establish regularities of the changes in the segregation coefficients of impurities with variations in the composition of the host lattice in the germanium-silicon system. Aluminum-and indium-doped crystals of Ge1−x Si x (0 ≤ x ≤ 0.3) solid solutions with a silicon content decreasing along the crystallization axis are grown by a modified Bridgman method with the use of a silicon seed. The concentration distribution of impurities over the length of the crystals is determined from Hall measurements. It is demonstrated that the experimental data on the concentration distribution of impurities in the crystals are in good agreement with the results obtained from the theory according to which the equilibrium segregation coefficients of impurities vary linearly with a change in the composition of Ge-Si solid solution crystals.

Segregation of Ga during growth of Si single crystal

Segregation phenomenon of Ga in Czochralski (CZ)–Si crystal growth has been investigated. The effective segregation coefficient, k eff, of Ga was obtained for different growth rates by assuming the simple relationship between the concentration of Ga in Si crystal and the bulk Ga concentration in melt. Applying BPS theory to effective segregation coefficients which is valid for the melt-solidified fraction up to 0.38, an equilibrium segregation coefficient of Ga was obtained, k 0=0.0079.

Effect of Thermal Oxidation on the Segregation of Phosphorus Implanted into Silicon

Secondary ion mass spectrometry and numerical simulation are used to investigate phosphorus diffusion and segregation in the SiO2-Si(111) system during the thermal oxidation of phosphorus-ion-implanted silicon layers in dry and humid oxygen between 950 and 1150°C. The results demonstrate that the segregation coefficient of phosphorus in SiO2 and Si depends not only on the oxidation temperature and environment but also on the oxidation time, which is interpreted in terms of the variation in the interfacial density of intrinsic point defects as a result of implantation-damage annealing. A model for the reaction segregation of impurities in the SiO2-Si system is used to evaluate the equilibrium segregation coefficient of phosphorus as a function of temperature: = m s * in dry O2 and = 4.2 × 102exp(−0.22 eV/(kT)) in humid O2.