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O. I. Velichko

Publications and source records attributed to O. I. Velichko.

At least 19 recordsLinked to original sources
arXiv2019

A comprehensive model of high-concentration phosphorus diffusion in silicon

A comprehensive model of high-concentration phosphorus diffusion has been developed and simulation of phosphorus diffusion from a constant source (phosphosilicate glass) at a temperature of 890 Celsius degrees for 14.25 min. has been carried out. Such doping processes are widely used in manufacturing modern solar cells. The proposed model combines the ideas of the drift of silicon self-interstitials in the field of elastic stresses with the concept of the formation of negatively charge clusters of impurity atoms. The calculated phosphorus concentration profile is in good agreement with the experimental one.

cond-mat.mtrl-sci↗
arXiv2015

Interstitial diffusion of arsenic in silicon

The mechanism underlying the long-range interstitial migration of nonequilibrium impurity interstitial species is used to simulate arsenic redistribution in ion implantation. An excellent agreement of the calculated arsenic concentration profiles with experimental data allows one to assume that the migration of nonequilibrium arsenic interstitial atoms makes a significant contribution to the formation of a low concentration region on thermal arsenic diffusion. The arsenic concentration profile calculated for a temperature of 1050 Celsius degrees within the framework of this assumption agrees well with the experimental one. A number of parameters describing arsenic diffusion at 1050 and 1108 Celsius degrees have been obtained.

cond-mat.mtrl-sci↗
arXiv2015

On concentration dependence of arsenic diffusivity

An analysis of the equations used for modeling thermal arsenic diffusion in silicon has been carried out. It was shown that for arsenic diffusion governed by the vacancy-impurity pairs and the pairs formed due to interaction of impurity atoms with silicon self-interstitials in a neutral charge state, the doping process can be described by the Fick's second law equation with a single effective diffusion coefficient which takes into account two impurity flows arising due to interaction of arsenic atoms with vacancies and silicon self-interstitials, respectively. Arsenic concentration profiles calculated with the use of the effective diffusivity agree well with experimental data if the maximal impurity concentration is near the intrinsic carrier concentration. On the other hand, for higher impurity concentrations a certain deviation in the local regions of arsenic distribution is observed. The difference from the experiment can occur due to the incorrect use of effective diffusivity for the description of two different impurity flows or due to the formation of nonuniform distributions of neutral vacancies and neutral self-interstitials in heavily doped silicon layers.

cond-mat.mtrl-sci↗
arXiv2015

Different shapes of impurity concentration profiles formed by long-range interstitial migration

A model of interstitial impurity migration is proposed which explains the redistribution of ion-implanted boron in low-temperature annealing of nonamorphized silicon layers. It is supposed that nonequilibrium boron interstitials are generated either in the course of ion implantation or at the initial stage of thermal treatment and that they migrate inward and to the surface of a semiconductor in the basic stage of annealing. It is shown that the form of the "tail" in the boron profile with the logarithmic concentration axis changes from a straight line if the average lifetime of impurity interstitials is substantially shorter than the annealing duration to that bending upwards for increasing lifetime. The calculated impurity concentration profiles are in excellent agreement with the experimental data describing the redistribution of implanted boron for low-temperature annealing at 750 Celsius degrees for 1 h and at 800 Celsius degrees for 35 min. Simultaneously, the experimental phenomenon of incomplete electrical activation of boron atoms in the "tail" region is naturally explained.

cond-mat.mtrl-sci↗
arXiv2014

Radiation-enhanced diffusion of impurity atoms in silicon layers

Modeling of the phosphorus radiation-enhanced diffusion in the course of implantation of high-energy protons into an elevated-temperature silicon substrate and during its treatment in a hydrogen-containing plasma with addition of a diffusant has been carried out. It follows from the results obtained that the radiation-enhanced diffusion occurs by means of formation, migration, and dissociation of "impurity atom -- silicon self-interstitial" pairs being in a local thermodynamic equilibrium with substitutionally dissolved impurity atoms and nonequilibrium point defects generated due to external irradiation. The resulting value of the average migration length of nonequilibrium silicon self-interstitials decreases from 0.19 micrometer for proton energy of 140 keV to 0.09 and 0.08 micrometer for energies of 110 and 80 keV, respectively. The decrease of the average migration length with the proton energy can be due to the interaction of silicon self-interstitials with the vacancies generated at the surface or with the defects formed in the phosphorus implanted region. Based on the pair diffusion mechanism, a theoretical investigation of the form of impurity profiles that can be created in thin silicon layers due to the radiation-enhanced diffusion was carried out. It is shown that depletion of the uniformly doped silicon layer occurs during plasma treatment except for the silicon -- insulator interface where a narrow region with a high impurity concentration is formed. The results of calculations give a clear evidence in favor of further investigation of various doping processes based on the radiation-enhanced diffusion, especially the processes of plasma doping, to develop a cheap method for the formation of strictly assigned impurity distributions in the local semiconductor domains.

cond-mat.mtrl-sci↗
arXiv2014

Analytical solution of diffusion equation for point defects

The analytical solution of the equation describing diffusion of intrinsic point defects has been obtained for a one-dimensional finite-length domain. This solution is intended for investigating and modeling the changes in defect distributions during fabrication of semiconductor devices with layer-type structures. With this purpose, the Robin-type boundary conditions were imposed on both edges of the domain. Using the solution obtained, the calculations of distributions of point defects for different boundary conditions and different defect migration lengths have been carried out. For the case of generation of nonequilibrium point defects due to implantation of hydrogen ions, the influence of the surface on the concentration and spatial distribution of nonequilibrium point defects was investigated depending upon the implantation energy.

cond-mat.mtrl-sci↗
arXiv2013

Simulation of hydrogen diffusion and boron passivation in crystalline silicon

The model of hydrogen migration and of the reactions of hydrogen atoms with electrically active impurity, developed earlier, has been applied to simulate hydrogen diffusion and passivation process during plasma deuteration of silicon substrates doped with boron. The calculated deuterium concentration profiles agree well in the length of the passivated region with the experimental data obtained on treatment in hydrogen plasma at a temperature of 200 Celsius degrees for 5, 10, and 15 minutes. On the other hand, to achieve a good fit to the abruptness of the calculated profiles between the passivated and unpassivated regions, it is necessary to suppose that the values of the parameters that describe the absorption of hydrogen interstitials by electrically active dopant atoms decrease with increase in the depth of the passivated region. For example, nonuniform spatial distributions of nonequilibrium point defects generated during plasma treatment can lead to a spatial dependence of hydrogen absorption.

cond-mat.mtrl-sci↗
arXiv2011

Modeling of the transient interstitial diffusion of implanted atoms during low-temperature annealing of silicon substrates

It has been shown that many of the phenomena related to the formation of "tails" in the low-concentration region of ion-implanted impurity distribution are due to the anomalous diffusion of nonequilibrium impurity interstitials. These phenomena include boron implantation in preamorphized silicon, a "hot" implantation of indium ions, annealing of ion-implanted layers et cetera. In particular, to verify this microscopic mechanism, a simulation of boron redistribution during low-temperature annealing of ion-implanted layers has been carried out under different conditions of transient enhanced diffusion suppression. Due to the good agreement with the experimental data, the values of the average migration length of nonequilibrium impurity interstitials have been obtained. It has been shown that for boron implanted into a silicon layer preamorphized by germanium ions the average migration length of impurity interstitials at the annealing temperature of 800 Celsius degrees be reduced from 11 nm to approximately 6 nm due to additional implantation of nitrogen. The further shortening of the average migration length is observed if the processing temperature is reduced to 750 Celsius degrees. It is also found that for implantation of BF2 ions into silicon crystal, the value of the average migration length of boron interstitials is equal to 7.2 nm for thermal treatment at a temperature of 800 Celsius degrees.

cond-mat.mtrl-sci↗
arXiv2011

Simulation of ion-implanted boron redistribution under different conditions of the transient enhanced diffusion suppression

It has been shown by means of impurity diffusion simulation that ion-implanted boron redistribution at the annealing temperatures 800^{\circ}C and lower is governed by the long-range migration of nonequilibrium impurity interstitials regardless of the methods used for the transient enhanced diffusion suppression. The relative amounts of impurity atoms, which are being transferred to the transient interstitial position, have been determined and time-average migration lengths of nonequilibrium boron interstitials have been obtained.

cond-mat.mtrl-sci↗
arXiv2011

Modeling of ion-implanted atoms diffusion during the epitaxial growth of the layer

The equation of impurity diffusion due to formation, migration, and dissolution of the pairs "impurity atom - intrinsic point defect" taking into account the nonuniform distributions of nonequilibrium point defects and drift of the pairs in the field of elastic stresses is presented in the coordinate system associated with the moving surface of the growing epitaxial layer. The analytical solution of this equation for the low fluence ion implantation has been obtained.

cond-mat.mtrl-sci↗
arXiv2011

Change in the microscopic diffusion mechanisms of boron implanted into silicon with increase in the annealing temperature

A two stream model of boron diffusion in silicon has been developed. The model is intended for simulation of transient enhanced diffusion including redistribution of ion-implanted boron during low temperature annealing. The following mechanisms of boron diffusion were proposed, namely: the mechanism of a long-range migration of nonequilibrium boron interstitials and the mechanism due to the formation, migration, and dissolution of the "impurity atom - silicon self-interstitial" pairs. Based on the model, simulation of the redistribution of boron implanted into silicon substrates for annealing temperatures of 800 and 900 Celsius degrees was carried out. The calculated boron concentration profiles agree well with the experimental data. It was shown that for a temperature of 800 Celsius degrees the transport of impurity atoms occurred due to the long-range migration of nonequilibrium boron interstitials generated during cluster transformation or dissolution. On the other hand, it was found that at a temperature of 900 Celsius degrees the pair diffusion mechanism played a main role in the significant transient enhanced diffusion. A number of parameters describing the transport of nonequilibrium boron interstitials and transient enhanced diffusion of substitutionally dissolved boron atoms were determined. For example, it was found that at a temperature of 900 Celsius degrees the time-average enhancement of boron diffusion was approximately equal to 44 times. The results obtained are important for the development of methods of transient enhanced diffusion suppression keeping in mind the scaling of the dimensions of silicon integrated microcircuits.

cond-mat.mtrl-sci↗
arXiv2010

Simulation of Boron Diffusion during Annealing of Silicon Substrates Undergone a High Fluence Ion Implantation

A theoretical investigation of the microscopic mechanisms provided the transient enhanced diffusion of boron atoms during rapid thermal annealing of silicon substrates doped by high fluence ion implantation was carried out. To compare the mechanisms a model of the transient enhanced diffusion due to migration of the pairs "boron atom - silicon interstitial" was developed. It is supposed that during annealing dissolution of the clusters incorporated boron atoms occurs. During cluster dissolution, a fraction of boron atoms occupies a substitutional position, whereas other atoms become interstitial. It was shown from the comparison of the shape of calculated boron concentration profile after annealing with the experimental data that at a temperature of 850 Celcius degrees and below the nonequilibrium boron interstitials are responsible for the transient enhanced diffusion. On the other hand, at a temperature of 850 Celcius degrees and above a major contribution to the transient enhanced diffusion is provided by the pairs "boron atom - silicon interstitial".

cond-mat.mes-hall↗
arXiv2009

Simulation of interstitial diffusion of ion-implanted boron

A model of the interstitial diffusion of ion-implanted boron during rapid thermal annealing of silicon layers previously amorphized by implantation of germanium has been proposed. It is supposed that the boron interstitials are generated continuously during annealing due to dissolution or rearrangement of the clusters of impurity atoms which are formed in the ion-implanted layers with impurity concentration above the solubility limit. The local elastic stresses arising due to the difference of boron atomic radius and atomic radius of silicon also contribute to the generation of boron interstitials. On the basis of the model proposed a simulation of redistribution of ion-implanted boron during rapid thermal annealing with duration of 60 s at a temperature of 850 degrees Celsius has been carried out. The calculated profile of boron distribution after thermal treatment agrees well with the experimental data that confirms the adequacy of the model. A number of the parameters of interstitial diffusion have been derived. In particular, the average migration length of nonequilibrium boron interstitials is equal to 12 nanometers. It was also obtained that approximately 1.96 % of boron atoms were converted to the interstitial sites, participated in the fast interstitial migration, and then became immobile again transferring into a substitutional position or forming the electrically inactive complexes with defects of crystal lattice.

cond-mat.mtrl-sci↗
arXiv2008

Solution of the nonstationary diffusion equation for interstitial impurity atoms by the method of Green functions

On the basis of the Green function method, analytical solutions of the diffusion equation which describes nonstationary migration of nonequilibrium interstitial impurity atoms have been derived. It is supposed that the initial distribution of nonequilibrium impurity interstitials is formed due to ion implantation and, therefore, is described by the Gaussian function. The condition of the constant concentration of impurity interstitials (the Dirichlet boundary condition) or reflecting boundary condition was imposed on the surface of a semiconductor. The Dirichlet boundary condition was also enforced for the concentration of impurity interstitials in the infinity, i.e., in the bulk of a semiconductor. On the basis of the solutions derived the redistribution of ion-implanted boron in silicon substrate during low-temperature thermal treatment has been simulated. The calculated profile of boron atoms after annealing agrees well with experimental data. It means that the analytical solutions derived can be used both for verifying the numerical results and for modeling the long-range migration of nonequilibrium impurity interstitials during low-temperature thermal treatments.

cond-mat.mtrl-sci↗
arXiv2008

Analytical solution of the equations describing interstitial migration of impurity atoms

An analytical solution of the equations describing impurity diffusion due to the migration of nonequilibrium impurity interstitial atoms was obtained for the case of the Robin boundary condition on the surface of a semiconductor. The solution obtained can be useful for verification of approximate numerical solutions, for simulation of a number of processes of interstitial diffusion, and for modeling impurity diffusion in doped layers with the decananometer thickness because in these layers a disequilibrium between immobile substitutionally dissolved impurity atoms, migrating self-interstitials, and migrating interstitial impurity atoms can take place. To illustrate the latter cases, a model of nitrogen diffusion in gallium arsenide was developed and simulation of nitrogen redistribution from a doped epi-layer during thermal annealing of GaAs substrate was done. The calculated impurity concentration profile agrees well with experimental data. The fitting to the experimental profiles allowed us to derive the values of the parameters that describe interstitial impurity diffusion.

cond-mat.mtrl-sci↗