Corresponding author: Kira L. Enisherlova ( enisherlova@pulsarnpp.ru ) © 2019 Andrey N. Aleshin, Kira L. Enisherlova.
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Citation:
Aleshin AN, Enisherlova KL (2019) Physicochemical fundamentals of phase formation in silicon layers implanted with oxygen and carbon. Modern Electronic Materials 5(2): 7785. https://doi.org/10.3897/j.moem.5.2.51365

The thermodynamic and kinetic regularities of processes occurring during heat treatment in silicon layers implanted with oxygen and carbon ions have been considered. We have analyzed the regularities of silicon deformation, impurity distribution and defect formation after different annealing modes. Diffusion smearing of implanted impurities in these layers has not been observed during carbon and oxygen implantation. Asannealed carbon does not occupy sites of the silicon lattice, in contrast to the implantation behavior of other impurities, e.g. boron and phosphorus. Phase formation regularities in implanted layers during subsequent heat treatment have been analyzed. Changes in the free energy of the system during heterogeneous and homogeneous precipitate nucleation have been compared. Sequential implantation with carbon and oxygen ions has been found to initiate diffusion flows of carbon and oxygen toward the center of the ion doped layer (the uphill diffusion phenomenon). The possibility of uphill diffusion has been analyzed from the standpoints of the Onsager theory. We show that the contribution of the chemical interaction between oxygen and carbon is far greater than the entropy contribution to the diffusion flux. We have demonstrated the high efficiency of ion doping with oxygen and carbon for gettering of uncontrolled impurities from active regions of silicon structures. The efficiency of this gettering process has been assessed for epitaxial structures in which layers had been grown on silicon wafers implanted with these impurities. Uphill diffusion in the layers after double doping with carbon and oxygen has led to the formation of more defects which may provide for efficient gettering. We have found the optimal oxygen and carbon implantation dose ratio for maximal gettering efficiency.
semiconductors, ion implantation, silicon, defect formation, gettering, gettering centers, diffusion smearing, uphill diffusion
One of the problems solved with the help of advanced semiconductor technologies, e.g. ion implantation is the synthesis of metastable nanosized heterophase structures in a semiconductor matrix. These structures can be synthesized primarily through the formation of binary compositions if the implanted component is an insoluble or low soluble element, e.g. carbon. By choosing implantation temperature and carbon ion flux intensity and making use of impurity coagulation in the matrix, e.g. in copper or silver, one can produce nanosized carbon particles, the socalled carbon onions having a fullerene structure [
The method of gettering by means of ion implantation of usually light elements (С, Не, О) when the getering regions are located as close as possible to active device structures is well known as proximity gettering [
The aim of this work is to generalize all experimental data on phase formation during heat treatment and regularities of diffusion observed in silicon layers implanted with carbon, oxygen and jointly with oxygen and carbon, and to describe the thermodynamics and kinetics of processes occurring in ion doped layers during annealing. Analysis of defect formation processes during annealing of layers implanted with these impurities is also of interest since C and O are the main background impurities in silicon the presence and interaction of which mostly determine the properties of the material. Although ion doped regions are heavily supersaturated, study of phase formation in these layers may provide additional useful information.
We studied the structure and analyzed the concentration profiles of ion implanted impurities in zone melting grown KEF20 silicon wafers with (100) working surface orientations. Ion implantation was carried out in dechanneling mode without target heating, at a 300 keV energy and a 0.1 mA ion beam current so as to avoid specimen heating by the ions. At this energy the mean projected ranges R_{p} of oxygen and carbon ions are almost the same, i.e., 0.68 µm [
The following methods were used in the study:
– to assess the type and degree of deformation in thin surface layers of the asimplanted and asannealed test specimens we used doublecrystal Xray diffraction, taking the diffraction curves;
– the distributions of the implanted impurities in the asimplanted and asannealed specimens were studied using secondary ion massspectrometry (SIMS) on an ISM3F spectrometer;
– regularities of defect formation were analyzed using transmission electron microscopy (TEM);
– gettering efficiency was evaluated for the epitaxial structures by making spherical crosssections, etching defects in the surface layers and calculating the density of defects in the epitaxial films.
Analysis of the diffraction curves for the asimplanted specimens showed that all the experimental versions of ion implantation produced elastic stresses in the specimens and deformed their lattice in surface layers, as indicated by additional peaks in the diffraction curves at lower reflection angles. This peak position suggests an increase in the lattice parameter [
Diffraction curves after ion implantation: (a) O^{+}, dose 6 × 10^{14} 1/cm^{2}; (b) C^{+}, 1.2 × 10^{15} 1/cm^{2}; (c) C^{+}, 6 × 10^{14} 1/cm^{2} + O^{+}, 1.8 × 10^{15} 1/cm^{2}.
Electron microscopic studies expectedly showed that oxygensilicon precipitates formed in the oxygen implanted layers after annealing at 1200 °C. The precipitates had typical shapes and were surrounded by dislocation loops (precipitatedislocation complexes) (Fig.
(a and b) Micrographs of defects in ion implanted silicon layers asannealed at 1200 °C and (c) a schematic of planar defect arrangement in Fig. (b): (a) O^{+}, dose 2.4 × 10^{15} 1/cm^{2}; (b) C^{+}, 2.1 × 10^{15} 1/cm^{2} + O^{+}, 6 × 10^{14} 1/cm^{2}.
Changing the oxygen implantation dose to be at least twice the carbon dose caused the formation of a completely different type of structural defects after postimplantation annealing. A system of perfect loops formed (Fig.
Planar TEM micrograph of silicon surface layer (moving toward the middle of the ion implanted layer, (a–c)) with interstitial dislocation loops after C and O implantation at a carbon to oxygen dose ratio of 1 : 4 followed by annealing at 1200 °C for 2 h.
Study of the implanted impurity concentration profiles in the asimplanted and asannealed specimens showed that after implantation of one impurity the asimplanted and asannealed carbon concentration distributions at different implantation doses are generally similar. Their main distinctive feature was that carbon was localized after annealing in the same spatial regions as before annealing (Fig.
Secondary C ion depth profiles for implanted Si layers (1) before and (2) after annealing at 1200 °C for 4 h: (a) C^{+}, dose 3.0 × 10^{15} 1/cm^{2}; (b) C^{+}, 6 × 10^{14} 1/cm^{2} + O^{+}, 2.4 × 10^{15} 1/cm^{2}.
(1 and 2) C and (3 and 4) O depth profiles in the implanted layer (1 and 3) before and (2 and 4) after annealing at 1200 °C for 2 h. Carbon ion dose 6 × 10^{14} 1/cm^{2} oxygen ion dose 2.4 × 10^{15} 1/cm^{2}.
The main requirements to gettering regions which attract detrimental impurities during heat treatment are as follows:
– stability of spatial dimensions during subsequent heat treatments, i.e., minimum smearing of the ion doped regions during further growth of epitaxial films and device heat treatments, because otherwise there will be the risk of defect propagation to active device regions due to their proximity;
– presence of gettering centers in these regions capable of trapping and pinning uncontrolled metallic impurities. As was shown earlier, the strongest gettering centers are dislocation fragments [
It is believed that growth carbon in single crystal silicon occupies silicon lattice sites. For the temperature in question (T = 1200 °C) the carbon diffusion coefficient is D_{С} = (3.5÷4.86) × 10^{11} cm^{2}/s, its solubility being c^{s}_{C} = 5.4 × 10^{16} cm^{3} [
Electron microscopic studies showed that the regularities of defect formation in oxygen and carbon implanted silicon layers during postimplantation annealing differ dramatically from those of defect formation in layers implanted with conventional impurities, e.g. phosphorus and boron. After boron and phosphorus implantation at the same total doses annealing causes the formation of dislocation loops, mainly interstitial type ones [
Planar carbon interlayers evolved into centers of predominant formation of oxygensilicon precipitates by a heterogeneous mechanism (“hanging” hemispheres in Fig.
Two hemispeheres of SiO_{2} precipitates growing at the walls of planar defects. Ψ is the contact angle and r is the hemisphere radius.
$N=\frac{{N}_{0}}{{x}_{\theta}}\mathrm{exp}\left(\frac{\Delta {G}^{*}}{k{T}_{\mathrm{nucl}}}\right)$ (1)
where x_{θ} is the oxygen concentration in SiO_{2} expressed in atomic fractions, ∆G^{*} is the work of nucleation per unit precipitate, N_{0} is the number of potential precipitate nucleation sites per unit area of the interface, k is the Boltzmann constant and T_{nucl} is the nucleation temperature. ∆G^{*} depends on the change in the free Gibbs free energy ∆G_{V} per unit volume of growing precipitate, the interphase surface tension σ_{αθ} between silicon and precipitates (hereinafter the α and θ phases, respectively) and the contact angle Ψ. The correlation between ∆G^{*} and ∆G_{V} is described by the expression [
$\Delta {G}^{*}=\frac{4\pi {\sigma}_{\alpha \theta}^{3}}{3\Delta {G}_{V}^{2}}\left(2\mathrm{cos}\Psi +{\mathrm{cos}}^{3}\Psi \right)$ (2)
Experimental data allow calculating ∆G^{*}. We accept that the linear dimension of the interface is 200 nm and the number of precipitates on one of its surfaces is 45 (this agrees with our structural examination results). Then N ≈ 1.5 × 10^{11} cm^{2}. We accept N_{0} = 10^{15} cm^{2} which corresponds to the atomic density in the {111} plane. Thus ∆G^{*} = 1.7 × 10^{12} erg at 1200 °C (1 erg = 10^{7} J). According to literary data [
We will now calculate the change in the the Gibbs free energy of the system for precipitate nucleation by a homogeneous mechanism as seems to be the case for precipitate nucleation during annealing of Cz silicon. ∆G_{V} can be estimated by analogy with the Gibbs free energy estimation for solid phase precipitate nucleation during crystallization of a singlecomponent liquid at its crystallization temperature T_{cr}. Then, according to an earlier work [
$\u2206{G}_{V}^{\mathrm{er}}=\frac{1}{\mathrm{\Omega}}\frac{{L}_{\mathrm{m}}}{{T}_{\mathrm{m}}}\left(\frac{{T}_{\mathrm{cr}}}{{T}_{\mathrm{m}}}\right)$, (3)
where Ω is the molar volume of the solid phase, L_{m} is the melting heat and T_{m} is the melting point. For Cz silicon the advantage in the Gibbs free energy for oxygen precipitate nucleation ∆G_{V} will be described by the formula
$\Delta {G}_{V}=\frac{1}{{\nu}^{*}}\frac{Q}{{T}_{\mathrm{m}}}\left(1\frac{{T}_{\text{nucl}}}{{T}_{\mathrm{m}}}\right)$ (4)
where Q is the heat of oxygen dissolution in silicon, Т_{nucl} is the precipitate nucleation and growth temperature, Т_{m} is the silicon melting point, υ^{*} is the volume occupied by one oxygen atom in a SiO_{2} precipitate, υ^{*} ≈ 2/3Ω_{Si} = 3.76 × 10^{23} cm^{3}/at and Ω_{Si} is the volume per one atom in pure silicon. According to an earlier work [
Experiments show that hightemperature annealing of oxygen ion doped layers produces precipitatedislocation complexes that are typical of oxygen. The absence of nucleation centers suggests that these complexes form by a homogeneous mechanism. To check this one should first theoretically confirm that the heat treatment time chosen is sufficient for the formation of the experimentally observed density of defects. During annealing the precipitates grow by enlargement of existing nuclei, but new ones may also form. During the decomposition of a supersaturated solid solution the concentration of precipitates N tends to a certain limit N_{s} determined by a decrease of the chemical driving force of transformation and a decrease of the second phase nucleation rate. We denote the time required for N to reach N_{s} as t_{s}. It is wellknown [
${N}_{\mathrm{s}}={I}_{0}^{3/5}{\left(\frac{4}{3}\pi {D}_{\mathrm{O}}^{3/2}\right)}^{2/5}$ (5)
${t}_{\mathrm{s}}={\left(\frac{4}{3}\pi {D}_{\mathrm{O}}^{3/2}{I}_{0}\right)}^{2/5}$ (6)
where I_{0} is the nucleation rate and D_{О} is the oxygen diffusion coefficient in silicon at the precipitate nucleation and growth temperature. For a homogeneous mechanism the SiO_{2} nucleation rate is described as follows [
${I}_{0}=4\pi Z\frac{{D}_{\mathrm{O}}}{d}{c}_{\mathrm{O}}^{2}{r}_{\mathrm{c}}^{2}\mathrm{exp}\left(\frac{4\pi {\sigma}_{\alpha \theta}{r}_{\mathrm{c}}^{2}}{3kT}\right)\mathrm{exp}\left(\frac{t}{\tau}\right)$ (7)
where Z is the Zeldovich factor, r_{c} is the critical precipitate radius, d is the interatomic distance and с_{О} is the initial concentration of oxygen in silicon. The precipitation rate vs time curve incorporates the incubation time τ of precipitate nucleation. It is commonly believed that this time is far shorter than the precipitate growth time t. The formula of the critical size of a spherical precipitate is as follows [
${r}_{\mathrm{c}}=\frac{2{\sigma}_{\alpha \theta}}{\left\Delta {G}_{V}\right}$ (8)
It is accepted in Eq. (7) that the surface tension is σ_{αθ} = 400 erg/cm^{2} and the Zeldovich factor is ≥ 0.001.
The nucleation parameters obtained from a calculation using the above formulae for different Si–O solid solution supersaturation degrees are summarized in Table
Parameters of the process of precipitate formation by a homogeneous mechanism at various of silicon oxygen supersaturation degrees.
c _{O}, 10^{18} cm^{3}  T _{e}, K  (T_{e} – T_{0})/T_{e}  ΔG_{V}, 10^{10} erg/cm^{3}  r _{c}, 10^{8} cm  I _{0}, cm^{3}∙ c^{1}  N _{s}, cm^{3}  t _{s}, c 

4.4  –  –  –  –  8.42  10^{6}  118.74 × 10^{3} 
5  2092.76  0.296  1.220  6.557  7.599 × 10^{3}  –  – 
6  2161.758  0.319  1.300  –  –  –  – 
7  2223.845  0.338  1.320  –  8.42 × 10^{5}  10^{9}  1187.4 
8  2280.582  0.354  –  –  –  –  – 
9  2333.087  0.369  –  –  –  –  – 
10  2382.146  0.382  1.572  5.087  2.445 × 10^{10}  5 × 10^{11}  – 
20  2428.337  0.393  –  –  8.42 × 10^{10}  10^{12}  11.874 
$\Delta {G}_{V}=\frac{1}{{v}^{*}}\frac{Q}{{T}_{\mathrm{e}}}\left(1\frac{{T}_{0}}{{T}_{\mathrm{e}}}\right)$ (9)
where T_{0} is the temperature of precipitate formation, Т_{e} is the temperature obtained by extrapolation of the oxygen solubility in silicon vs temperature curve (Eq. (10)) to above the melting point. The oxygen solubility in silicon was calculated using the formula [
${c}_{\mathrm{O}}^{s}=1.63\xb7{10}^{21}\mathrm{exp}\left(\frac{99.54\mathrm{kJ}/\mathrm{mol}}{RT}\right)$, (10)
where R is the universal gas constant.
Our calculations confirmed the assumed defect formation mechanism during annealing in the oxygen ion implanted layer. The calculated ∆G_{V} were close to those obtained by calculating the change in the Gibbs free energy for oxygen precipitation by a homogeneous mechanism in Cz silicon during annealing at T = 700 °C.
The correlated behavior of the carbon and oxygen diffusion fluxes allows us to use the Onsager theory [
${j}_{i}=\sum _{k}{L}_{ik}{X}_{k}$ (11)
where L_{ik} is the kinetic coefficient and X_{k} is the generalized thermodynamic force. The matrix L_{ik} of the kinetic coefficients contains the diagonal coefficients L_{ii} describing the effect of the thermodynamic force X_{i} on the flux of the intrinsic property j_{i} and the nondiagonal (crossing) coefficients L_{ik}(i ≠ k) describing the effect of the thermodynamic force X_{i} on the flux of other properties. A fundamental standpoint of the Onsager theory is the equality of the kinetic coefficients L_{ik} = L_{ki}. Hereinafter when referring to the Onsager theory we will use the expression of X_{k} for a system without energy fluxes. Then the generalized driving force of the ith element is written as –∇µ_{k}, where µ_{i} is the chemical potential of any solution component. Therefore the formal expressions describing the mutual effects of the diffusn fluxes of the elements 1 and 2 dissolved in the matrix of the third element can be written as
${j}_{1}={L}_{11}\nabla {\mu}_{1}{L}_{12}\nabla {\mu}_{2}$ (12a)
${j}_{2}={L}_{21}\nabla {\mu}_{1}{L}_{22}\nabla {\mu}_{2}$ (12b)
The connection between the chemical potentials of the components in a solid solution (carbon and oxygen solution in silicon) is described by the Gibbs–Duhem equation [
${c}_{1}\nabla {\mu}_{1}+{c}_{2}\nabla {\mu}_{2}=0$ (13)
where с_{1} and с_{2} are the concentrations of carbon and oxygen, respectively, in atomic fractions.
Set of Eqs (12) can be represented as follows:
${j}_{1}={L}_{11}\nabla {\mu}_{1}\left(1\frac{{c}_{1}}{{c}_{2}}\frac{{L}_{12}}{{L}_{11}}\right)$ (14a)
${j}_{2}={L}_{22}\nabla {\mu}_{2}\left(1\frac{{c}_{2}}{{c}_{1}}\frac{{L}_{12}}{{L}_{22}}\right)$ (14b)
The problem of the mutual effects of the diffusion fluxes can be simplified if one assumes that the diffusion of each of the components obeys Fick’s law, by analogy with ideal solutions. Then the partial diffusion coefficient D_{i} can be represented through the kinetic coefficient L_{ii}
${D}_{i}=\frac{{L}_{ii}}{{c}_{i}}kT$ (15)
where L_{ii}/c_{i} has the meaning of the mobility U_{i}. Thus, finally, set of Eqs (12) takes on
${j}_{1}={D}_{1}^{*}\left(1\frac{{c}_{1}}{{c}_{2}}\frac{{L}_{12}}{{L}_{11}}\right)\nabla {c}_{1}={D}_{1}^{ef}\nabla {c}_{1}$ (16a)
${j}_{2}={D}_{2}^{*}\left(1\frac{{c}_{2}}{{c}_{1}}\frac{{L}_{12}}{{L}_{22}}\right)\nabla {c}_{2}={D}_{2}^{ef}\nabla {c}_{2}$ (16b)
where D^{ef}_{1}and D^{ef}_{2}are the experimentally observed effective diffusion coefficients of the first and second solution components which become negative. It follows from Eqs (16) that uphill diffusion of both the first and the second solution components may occur if the second term in the parentheses is greater than 1. The experimentally revealed diffusion fluxes of carbon and oxygen toward the center of the ion doped layer suggest a strong mutual attraction of carbon and oxygen when the chemical forces (in the case considered these forces are the chemical interaction between oxygen and carbon) are far greater than the entropy contribution to the diffusion flux.
The above set of equations for diffusion fluxes does not allow for the diffusion fluxes of matrix atoms but this is justified for interstitial diffusion. Oxygen diffuses in silicon by an interstitial mechanism and hence the Onsager expression for the diffusion flux is completely correct for this element. Structural studies carried out in this work show that carbon implanted into silicon is in interstitial positions. Therefore the relatively formal Onsager approach is correct in this case. Structural studies of ion doped silicon layers in which carbon and oxygen ions were consistently implanted with doses of 0.6 × 10^{15} and 2.4 × 10^{15} 1/cm^{2} (the total dose is the same as for implantation of solely carbon ions) showed that another type of structure forms in this case. The structure consists of perfect loops decorated with clusterlike features, with the loop density increasing closer to R_{p}. The optimum carbon and oxygen ion dose ratio for this defect formation mechanism is 1 : 4. The formation of a defect structure in the ion doped oxygen and carbon layers is strongly affected by the chemical carbonoxygen bond. This bond is so strong that intrinsic silicon interstitial atoms cannot participate in the formation of clusterlike agglomerations of carbon and oxygen atoms. Instead interstitial silicon atoms form the perfect loops observed.
It follows from the above that the presence of a large number of dislocation loops, the sharp localization of the damaged region and the absence of diffusion smearing of the damaged region at device process annealing steps are quite favorable for efficient gettering. Indeed, studies of epitaxial films grown on substrates after different implantation versions showed that the defect density in the epitaxial films grown on the reference substrates was (8–9) × 10^{3}–5 × 10^{4} cm^{2}. For implantation of sole oxygen there was a weakly resolved layer of discrete defects under the epitaxial film, and the defect etching pattern in the film differed but slightly from that for the epitaxial films grown on the reference substrates. The best result was obtained for implantation of two impurities at a 1 : 4 dose ratio. Then the defect density in the film was 1 × 10 cm^{2}, and the surface layer under the film had a clearly seen narrow layer of gettering centers (Fig.
Analysis of the gettering properties of silicon layers implanted with C and O ions from the standpoints of the thermodynamics and kinetics of the processes occurring there during annealing revealed the following:
– if the layer is implanted with sole carbon, then carbon does not occupy silicon lattice site during annealing, unlike boron, but forms defects of a special type;
– the presence of uphill diffusion in the layers after double implantation with carbon and oxygen ensures the absence of diffusion smearing of the layers during longterm annealing and leads to the formation of a large number of dislocation loops thus making these layers optimal for the formation of efficient gettering regions.