Diffusion Of Phosphorus In Silicon Research Articles

Retarded boron and phosphorus diffusion in silicon nanopillars due to stress induced vacancy injection

Phosphorus and boron diffusion in silicon at temperatures between 900 and 1050 °C was studied both in bulk and nanostructured samples by means of scanning spreading resistance microscopy. The dopant diffusion from highly doped silicon substrates into 300–1200 nm diameter natural silicon nanopillars is clearly retarded compared to dopant diffusion in the bulk material. A three-dimensional solution of Fick’s equation enables a better understanding of dopant diffusion processes in silicon nanostructures, including all participating point defects. The observed decrease of diffusivity by 20%–50% can be explained by the injection of vacancies at the sidewalls of the pillar. The results do not provide any evidence on a possible change in point defect properties or fundamental diffusion processes in silicon nanostructures with respect to bulk silicon.

Engineering of the spin on dopant process on silicon on insulator substrate

We report on a systematic analysis of phosphorus diffusion in silicon on insulator thin film via spin-on-dopant process (SOD). This method is used to provide an impurity source for semiconductor junction fabrication. The dopant is first spread into the substrate via SOD and then diffused by a rapid thermal annealing process. The dopant concentration and electron mobility were characterized at room and low temperature by four-probe and Hall bar electrical measurements. Time-of-flight-secondary ion mass spectroscopy was performed to estimate the diffusion profile of phosphorus for different annealing treatments. We find that a high phosphorous concentration (greater than 1020 atoms cm−3) with a limited diffusion of other chemical species and allowing to tune the electrical properties via annealing at high temperature for short time. The ease of implementation of the process, the low cost of the technique, the possibility to dope selectively and the uniform doping manufactured with statistical process control show that the methodology applied is very promising as an alternative to the conventional doping methods for the implementation of optoelectronic devices.

Model of phosphorus diffusion in silicon for highly doped solar cell emitter layer

Purpose The purpose of this paper was the development of a model enabling precise determination of phosphorus concentration profile in the emitter layer of a silicon solar cell on the basis of diffusion doping process duration and temperature. Fick’s second law, which is fundamental for describing the diffusion process, was assumed as the basis for the model. Design/methodology/approach To establish a theoretical model of the process of phosphorus diffusion in silicon, real concentration profiles measured using the secondary ion mass spectrometry (SIMS) method were used. Samples with the phosphorus dopant source applied onto monocrystalline silicon surface were placed in the heat zone of the open quartz tube furnace, where the diffusion process took place in the temperature of 880°C-940°C. The measured real concentration profiles of these samples became template profiles for the model in development. Findings The model was developed based on phenomena described in the literature, such as the influence of the electric field of dopant ionized atoms and the influence of dopant atom concentration nearing the maximum concentration on the value of diffusion coefficient. It was proposed to divide the diffusion area into low and high dopant concentration region. Originality/value A model has been established which enabled obtaining a high level of consistency between the phosphorus concentration profile developed theoretically and the real profile measured using the SIMS method. A coefficient of diffusion of phosphorus in silicon dependent on dopant concentration was calculated. Additionally, a function describing the boundary between the low and high dopant concentration regions was determined.

Efficient implementation of multiple drive-in steps in thermal diffusion of phosphorus for PERC solar cells

N-type phosphorus diffusion in silicon using phosphorus oxychloride, POCl3, has been widely used in the production of p-type silicon solar cells. The thermal diffusion process in a furnace generally involves two steps: pre-deposition and drive-in. The phosphorous doping by thermal diffusion often shows high surface concentrations, leading to an increase in charge recombination, which should be inhibited in order to fabricate high efficiency silicon solar cells. In this study, we investigate the influence of 3 drive-in steps at sequentially increasing temperatures during the POCl3 diffusion on the emitter performance. As a result, it was found that the kink region was made shorter while maintaining surface concentration for a good metal contact without losing its passivation quality. This result is attributed to the higher active dopant concentration of the 3 drive-in step samples, leading to a lower series resistance and higher fill factor in the PERC solar cells. The results show that slight changes in the PSG process conditions can contribute to the improvement of high efficiency solar cells.

First-principles study of hydrogen-enhanced phosphorus diffusion in silicon

We present a first-principles study on the interstitial-mediated diffusion process of neutral phosphorus (P) atoms in a silicon crystal with the presence of mono-atomic hydrogen (H). By relaxing initial Si structures containing a P atom and an H atom, we derived four low-energy P-H-Si defect complexes whose formation energies are significantly lower than those of P-Si defect complexes. These four defect complexes are classified into two groups. In group A, an H atom is located near a Si atom, whereas in group B, an H atom is close to a P atom. We found that the H atom pairs with P or Si atom and changes the nature bonding between P and Si atoms from out-of-phase conjugation to in-phase conjugation. This fact results in the lower formation energies compare to the cases without H atom. For the migration of defect complexes, we have found that P-H-Si defect complexes can migrate with low barrier energies if an H atom sticks to either P or Si atom. Group B complexes can migrate from one lattice site to another with an H atom staying close to a P atom. Group A complexes cannot migrate from one lattice site to another without a transfer of an H atom from one Si atom to another Si atom. A change in the structure of defect complexes between groups A and B during the migration results in a transfer of an H atom between P and Si atoms. The results for diffusion of group B complexes show that the presence of mono-atomic H significantly reduces the activation energy of P diffusion in a Si crystal, which is considered as a summation of formation energy and migration barrier energy, leading to the enhancement of diffusion of P atoms at low temperatures, which has been suggested by recent experimental studies.

MODELING OF MOS TRANSISTOR WITH BUILT-IN CHANNEL PREPARED BY USING PHOSPHORUS DIFFUSION IN SILICON FROM PHOSPHORIC ANODIC OXIDE FILMS

Currently, there is not enough information in literature about MOS transistors with built n-type channel simulation. The article suggests a model of MOSFET with integrated n- type channel, prepared by using phosphorus diffusion in silicon from phosphoric anodic oxide films, based on threshold voltage. Model parameters were calculated for the specific case - capacitance of gate dielectric, transconductance, drain current. It is shown that this model even in a simplified form gives a sufficient agreement with experimental data.

The Mechanism of Enhanced Diffusion of Phosphorus in Silicon During Rapid Photothermal Processing of Solar Cells

In this paper, we have presented the experimental results of phosphorus diffusion in silicon for the cases of rapid thermal processing (RTP) and rapid photothermal processing (RPP). In the case of the RPP, other than thermal energy, the vacuum ultraviolet photons are used as an additional source of energy. We have investigated the secondary-ion-mass-spectroscopy impurity profiles at different concentrations of P in Si. Based on our own experimental results and the data published in the open literature, we have provided an explanation of the enhanced diffusion both for the RTP and RPP cases. The thermal factor leads to the excitation (vibration) of atoms and quantum energy to the electron system excitation. As compared with the pure thermal process, the quantum-energy contribution provides a reduced activation energy and a higher diffusion coefficient.

Phosphorus Oxide Assisted n-type Dopant Diffusion in 4H-Silicon Carbide

AbstractPhosphorus is an important n-type dopant for both silicon and silicon carbide. Although solid-state diffusion of phosphorus in silicon has been well documented and experimentally proven, not much is known about phosphorus solid-state diffusion in silicon carbide, especially at lower temperatures. A convenient source of phosphorus for solid-state diffusion in silicon carbide is phosphorus oxide. The possibility of using phosphorus oxide as a dopant source for silicon carbide is investigated by considering the probable reactions between silicon carbide and phosphorus oxide at temperatures below 1700 K using published thermodynamic data. By considering the standard free energies of reactions, it can be shown that phosphorus can be introduced in silicon carbide at temperatures below 1700 K using phosphorus oxide. A successful development of low temperature dopant incorporation in silicon carbide would reduce the need for high temperature processes and prevent process-induced thermal degradation of critical device structures such as the oxide-semiconductor interface. Experimental results showing phosphorus impurity incorporation and activation in 4H-SiC are presented.

Activation volume for phosphorus diffusion in silicon and Si0.93Ge0.07

The hydrostatic pressure dependence of the diffusivity of P in compressively strained Si0.93Ge0.07 and unalloyed Si has been measured. In both cases the diffusivity is almost independent of pressure, characterized by an activation volume V* of (+0.09±0.11) times the atomic volume Ω for the unalloyed Si, and (+0.01±0.06) Ω for Si0.93Ge0.07. The results are used in conjunction with the reported effect of biaxial strain on diffusion normal to the surface to test the prediction for an interstitialcy-based mechanism of Aziz’s phenomenological thermodynamic treatment of diffusion under uniform nonhydrostatic stress states. The prediction agrees well with measured behavior, lending additional credence to the interstitial-based mechanism and supporting the nonhydrostatic thermodynamic treatment.

Set of equations for stress-mediated evolution of the nonequilibrium dopant-defect system in semiconductor crystals

A set of equations describing a stress-mediated evolution of the nonequilibrium dopant-defect system has been derived and analyzed. Together with coupled diffusion of dopant atoms and point defects, we consider the drift of all mobile species in different charge states, namely vacancies, self-interstitials, and pairs “dopant atom–point defect”, in the field of stress. It has been shown that stresses may affect the diffusion of dopant atoms mainly in two ways: (1) directly, due to the drift of the pairs in the field of stress; (2) indirectly, by the formation of nonuniform defect distribution due to the drift of point defects. On this basis, various features of doping processes, such as phenomena of “uphill” impurity diffusion near the surface (within the framework of the first or second mechanisms) and the peculiarities of high concentration phosphorus diffusion (due to the second mechanism), can be explained. Numerical computations of high concentration phosphorus diffusion in silicon and transient-enhanced diffusion of ion-implanted arsenic have been carried out, and parameters of diffusion have been extracted. The calculated dopant profiles agree well with the experimental data. The set of equations obtained is applicable to modeling of diffusion in the layers with nonuniform stress distribution arising due to high concentration of dopant atoms, lattice mismatch, etc.

First-principles study of phosphorus diffusion in silicon: Interstitial- and vacancy-mediated diffusion mechanisms

A vacancy-mediated diffusion mechanism has been assumed in traditional models of P diffusion in Si. However, recent experiments have suggested that for intrinsic P diffusion in Si, the interstitial-assisted diffusion mechanism dominates. Here, we describe first-principles calculations of P diffusion in Si performed to study interstitial- and vacancy-mediated diffusion mechanisms. Special care is taken with regard to structural minimization, charge state effects and corrections. We calculated the defect formation energies and migration barriers for the various competing P–interstitial diffusion mechanisms, as well as P–vacancy diffusion energetics in different charge states. For P–interstitial diffusion, we find overall diffusion activation energies of 3.1–3.5 eV for neutral and +1 charge states, in close agreement with experiments at intrinsic conditions. For P–vacancy diffusion, our calculation is in agreement with previous calculations in the neutral case, but suggests that only P+V= plays a role in the heavily doped n region while the interstitial mechanisms may dominate in near-intrinsic regions.

A model of high-and low-temperature phosphorus diffusion in silicon by a dual pair mechanism

A model of phosphorus diffusion in silicon was developed on the basis of a dual pair mechanism; according to this model, the contribution of the impurity-vacancy (PV) and impurity-self-interstitial (PI) pairs to diffusion is accounted for directly in terms of the phosphorus diffusion coefficient. A violation of thermodynamic equilibrium in relation to native point defects occurs as a result of diffusion of the PI neutral pairs. At the high-temperature diffusion stage, the phosphorus diffusion is described by a single diffusion equation with the diffusion coefficient dependent on both the local and surface phosphorus concentrations; whereas at the next (occurring at lower temperatures) stage, the phosphorus diffusion is described by two diffusion equations for the total concentrations of the components containing phosphorus and self-interstitials. An anomalously high rate of the low-temperature diffusion is ensured by excess self-interstitials accumulated in the doped layer during the preceding high-temperature diffusion. The model makes it possible to quantitatively account for the special features of the phosphorus diffusion in a wide range of the surface concentrations at both the high (900–1100°C) and lower (500–700°C) temperatures.

Simulation of High-Concentration Phosphorus Diffusion in Silicon Taking into Account Phosphorus Clustering and Pile-Up

We have simulated the transient enhanced diffusion (TED) of high-concentration phosphorus (P) in silicon during post-implantation annealing. Based on the models for P diffusion, for TED by self-interstitial clusters, and for end-of-range (EOR) dislocations as both a sink for and source of self-interstitials, a unified simulation is done, taking into account P clustering and P pile-up. P clustering is taken into account only beneath EOR dislocations, and P pile-up is estimated by a diffusion-segregation term in the diffusion equations. We have satisfactorily fitted P depth profiles at high doses (∼1015 cm-2) in a wide range of annealing conditions (700–1000°C).

Experimental Study of Self-Diffusion in Silicon Using Isotopically Enriched Structures

ABSTRACTSelf-diffusion in silicon has been studied using epitaxially grown isotopically enriched structures under nonequilibrium concentrations of intrinsic point defects created by thermal oxidation and nitridation. Comparison of identical anneals for self, antimony, and phosphorus diffusion in silicon enables us to determine bounds on the fractional contributions of microscopic mechanisms for Si self-diffusion in the temperature range 800–1100°C. We obtain direct experimental evidence for a dual vacancy-interstitial mechanism of self-diffusion in silicon and show that the fractional contribution of each mechanism has a weak dependence on temperature.

Enhanced diffusion and improved device performance using dual spectral source rapid thermal processing

In this study, we used a vacuum ultraviolet (VUV) radiation source in conjunction with tungsten halogen lamps based rapid thermal processing (RTP) system. The two light sources were arranged in different configurations to study the phosphorus diffusion in silicon. The high energy VUV photons in conjunction with infrared and visible photons resulted in enhanced diffusion and improved the bulk properties of silicon substrate. An improvement in the leakage currents of the diodes made from VUV irradiated wafers is observed. A qualitative explanation of the results based on the role of high energy photons in RTP is presented. High energy photons from VUV region to about 800 nm results in a decrease in the bond dissociation energies of the molecules, since they are in electronic excited states. Higher activation of dopants and reduction in activation energies is observed. The minority carrier lifetime measurements show that there is an enhanced phosphorus gettering and overall reduction of the recombination-generation centers in silicon.

Nitridation‐Retarded Diffusion of Phosphorus in 〈100〉 Silicon

Diffusion of phosphorus in silicon in an ambient of pure , pure , and mixtures of and has been investigated to study the effect of the direct nitridation reaction on the diffusivity. The diffusion coefficient of phosphorus can be expressed as a function of the partial pressure of and temperature as In addition, the ratio of the interstitial concentration under nitridation conditions to the concentration under inert conditions is also determined as

Time-integration and iterative techniques for semiconductor diffusion modeling

We investigate numerical integration, preconditioning, iterative solution and multigrid strategies for a class of reaction-diffusion systems used for modeling nonequilibrium phosphorus diffusion in silicon. These problems typically yield stiff systems of equations, and their efficient numerical simulation requires the use of stable integration strategies along with fast, robust algebraic system solvers. We compare the numerical performance of semi-implicit Runge-Kutta methods in conjunction with several standard nonsymmetric iterative solvers and multigrid methods. Our results demonstrate that block-diagonal preconditioning with node-based assembly of the discrete system dramatically improves the performance of iterative solvers. Numerical studies also reveal some interesting new aspects regarding the choice of integration schemes when using iterative methods to solve the linear systems. Unlike the case of direct solvers, where higher-order integration methods typically yield higher computational efficiency, the use of iterative solvers can significantly change or even reverse this trend.

Anomalous Diffusion of Phosphorus in Silicon by Pair Diffusion Model and Decrease in Quasi Vacancy Formation Energy

Anomalous Diffusion of Phosphorus in Silicon by Pair Diffusion Model and Decrease in Quasi Vacancy Formation Energy

Oxynitridation‐Enhanced Diffusion of Phosphorus in Silicon

Diffusion of phosphorus in silicon in an ambient of pure , pure , and mixtures of and has been investigated to study the effect of the oxynitridation reaction on the diffusivity. With a thin layer on the silicon wafer and a low phosphorus concentration, the diffusion coefficient of phosphorus can be expressed as a function of the partial pressure of and temperature asAt the same time, the ratio of the interstitial concentration under oxynitridation conditions to the concentration under inert conditions can be expressed asBy using P diffusion as an interstitial monitor, the data (Ref. 1) of oxynitridation‐enhanced B diffusion are analyzed and the fraction of boron diffusion which occurs through the interstitial mechanism is calculated to be 0.88.

Simulation of Phosphorus Diffusion in Silicon Using a Pair Diffusion Model with a Reduced Number of Parameters

In this work, we describe a general model for dopant diffusion via dopant‐defect pairs containing all possible charge states of species under the assumption of local equilibrium for electronic processes, but not for chemical processes. We present a method by which the unknown parameters can be reduced efficiently. With the aid of this method all the backward reaction rate coefficients can be replaced by the forward reaction rate coefficients and two new parameters. Introducing the intrinsic diffusion coefficient, one of the two new parameters can be replaced, too. Thus, we have only one constant parameter instead of all backward reaction rate coefficients, and additionally the model automatically yields the correct results in the intrinsic case. In our model we use the barrier energy for the Frenkel pair mechanism and the point defect parameters which we have determined from gold diffusion experiments previously. We present several simulations of phosphorus diffusion and compare the results with experiments published in the literature. Very good agreement between simulations and experiments has been obtained. As a result we suggest a complete set of parameters for phosphorus diffusion in silicon for the temperature range from 900 to 1200°C.