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 cm²/s, its solubility being c^s_C = 5.4 × 10¹⁶ cm^-3 [12]. Thus carbon should be extremely stable against diffusion degradation processes which is favorable for gettering. Analysis of the evolution of the implanted impurity concentration profiles after annealing obtained by SIMS confirmed that the carbon implanted layers did not undergo diffusion smearing (the main peak of the as-annealed carbon concentration profiles was at the same depth as R_p). The as-annealed carbon concentration in that region was even somewhat higher than the as-implanted carbon concentration (Fig. 4a). The second carbon concentration peak produced by heat treatment located at ~400 nm (Fig. 4a) was most likely caused by trapping of carbon atoms by vacancies close to the surface. (Implantation induced vacancies and interstitial silicon atoms are known to locate in different spatial regions of the silicon matrix: vacancies concentrate closer to the surface while interstitial atoms accumulate at depths greater than R_p [13]). However experiments showed that carbon does not occupy silicon lattice sites after annealing. This was indicated by the absence of additional peaks in the X-ray diffraction curves after annealing. This behavior of implanted carbon differs from that of implanted boron most atoms of which occupy silicon lattice sites after annealing [14, 15] leading to the formation of lattice stresses due to the difference in the ion radii of boron and silicon [16]. But if carbon is in interstitial positions it should have a much higher diffusion rate than that for a vacancy mechanism [12]. This however is not in agreement with experimental results for carbon ion doped layer profiles. The origin of this discrepancy can be clarified by TEM examination of defects in ion doped layers and studies of carbon diffusion after double doping.

Electron microscopic studies showed that the regularities of defect formation in oxygen and carbon implanted silicon layers during post-implantation 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 [14, 15]. In our experiments single ion doping with either oxygen or carbon did not produce loops that form as a result of the coagulation of interstitial silicon atoms during annealing. However heat treatment induced relaxation occurred by different mechanisms for carbon and oxygen implantation. Oxygen atoms that could not diffuse from the ion implanted layer formed standard precipitates with oxygen that were surrounded by dislocation loops (Fig. 2a) while carbon occupied lattice sites and formed planar hexagonal structures (Fig. 2b, c). The contrast observed at different defect plane tilting relative to the electron beam suggests that this defect produced stronger elastic stress fields compared with those of similarly sized standard stacking faults. Thus one can assume that this defect was formed by atoms differing in size from the matrix ones. Furthermore the change in the contrast due to specimen tilting suggests the presence of elastic stress fields forming in the silicon matrix when there is an extra plane embedded in the silicon lattice. One can therefore conclude that the hexagonal features are planar agglomerations of carbon atoms located in lattice pores parallel to the {111} planes. From the structural viewpoint these carbon atom agglomerations are similar to stacking faults.

Planar carbon interlayers evolved into centers of predominant formation of oxygen-silicon precipitates by a heterogeneous mechanism (“hanging” hemispheres in Fig. 2b, c). This precipitate nucleation mechanism is possible due to the interaction between carbon and oxygen atoms. Solute oxygen in silicon was attracted to carbon interlayers which locate, as shown above, mainly near R_p and participated in the formation of oxygen-silicon precipitates. Thus a diffusion flux of oxygen atoms was directed from the peripheral regions of the ion implanted layer toward the center of the carbon distribution profile, tending to compensate the oxygen loss caused by the precipitate nucleation. The chemical interaction between carbon and oxygen atoms also attracted carbon to the center of its concentration profile. This latter process led to the observed slight growth of the as-annealed carbon concentration near R_p (Fig. 4a). One can indirectly estimate the strength of the carbon-oxygen bond for heterogeneous precipitate nucleation on planar hexagonal carbon interlayers by comparing the change in the Gibbs free energy of the system between two precipitate nucleation mechanisms, i.e., the heterogeneous and homogeneous ones. For the heterogeneous precipitate nucleation on hexagonal interlayers considered herein the shapes of the precipitates are not spherical, and the deviation from a spherical shape can be described with the contact angle Ψ (Fig. 6). The number of precipitates N per unit area of the interface is described as follows [17]:

$N=\frac{N_0}{x_{\theta }}\exp \left(-\frac{\Delta G^{*}}{k{T}_{\mathrm{nucl}}}\right)$ (1)

where x_θ is the oxygen concentration in SiO₂ expressed in atomic fractions, ∆G^* is the work of nucleation per unit precipitate, N₀ 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 [17]

$\Delta G^{*}=\frac{4\pi {\sigma }_{\alpha \theta }^3}{3\Delta G_V^2}\left(2-\cos \Psi +{\cos }^3\Psi \right)$ (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 × 10¹¹ cm^-2. We accept N₀ = 10¹⁵ 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 [18, 19] σ_αθ = 360÷500 erg/cm². Accepting σ_αθ = 400 erg/cm² and Ψ = 60° one can calculate ∆G_V: ∆G_V = -9.9 × 10¹⁰ erg/cm³ (-9.9 kJ/cm³).

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 single-component liquid at its crystallization temperature T_cr. Then, according to an earlier work [20] the advantage in the free energy per molar volume of the solid phase is

$∆G_V^{\mathrm{er}}=-\frac{1}{\mathrm{\Omega }}\frac{L_{\mathrm{m}}}{T_{\mathrm{m}}}\left(-\frac{T_{\mathrm{cr}}}{T_{\mathrm{m}}}\right)$, (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 SiO₂ precipitate, υ^* ≈ 2/3Ω_Si = 3.76 × 10^-23 cm³/at and Ω_Si is the volume per one atom in pure silicon. According to an earlier work [18], Q = 16.53 × 10^-13 erg/at (99.54 kJ/mol). Calculations showed that for homogeneous SiO₂ precipitate nucleation (for simplicity we will accept that only a single type of oxygen precipitate forms in layers implanted with solely oxygen ions) at 700 °С ∆G_V = -1.74 × 10¹⁰ erg/cm², and at 800 °С ∆G_V = -1.5 × 10¹⁰ erg/cm². Thus for heterogeneous precipitate nucleation (carbon implantation) the change in the Gibbs free energy of the system is far greater than that for homogeneous oxygen precipitate nucleation in Cz silicon, G_Vhom = -(1.5÷1.74)¹⁰ erg/cm³ and ∆G_Vhet = -9.9 × 10¹⁰ erg/cm³.

Experiments show that high-temperature annealing of oxygen ion doped layers produces precipitate-dislocation 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 well-known [21] that N_s and t_s can be calculated using the following semi-empirical expressions:

$N_{\mathrm{s}}=I_0^{3/5}{\left(\frac{4}{3}\pi D_{\mathrm{O}}^{3/2}\right)}^{-2/5}$ (5)

$t_{\mathrm{s}}={\left(\frac{4}{3}\pi D_{\mathrm{O}}^{3/2}{I}_0\right)}^{-2/5}$ (6)

where I₀ 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 SiO₂ nucleation rate is described as follows [18]:

$I_0=4\pi Z\frac{D_{\mathrm{O}}}{d}{c}_{\mathrm{O}}^2{r}_{\mathrm{c}}^2\exp \left(-\frac{4\pi {\sigma }_{\alpha \theta }{r}_{\mathrm{c}}^2}{3kT}\right)\exp \left(-\frac{t}{\tau }\right)$ (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 [22]:

$r_{\mathrm{c}}=\frac{2{\sigma }_{\alpha \theta }}{\left|\Delta G_V\right|}$ (8)

It is accepted in Eq. (7) that the surface tension is σ_αθ = 400 erg/cm² 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 1. These data suggest that at 1200 °C it is possible to achieve a precipitate density of 10⁹–10¹¹ cm^-3. This requires oxygen concentrations of one and a half order of magnitude higher than the oxygen solubility in silicon at Т = 1200 °C (с_O^s = 4.81 × 10¹⁷ cm^-3). These oxygen concentrations can be achieved at the oxygen implantation doses used in this experiment. (Note that in this case we mean that the oxygen concentration is the averaged oxygen concentration in the ion doped layer with a thickness of the order of 2∆R_p, where ∆R_p is the struggling of the oxygen concentration profile). For example, for oxygen ion implantation at 300 eV and R_p = 0.68 µm, ∆R_p = 150÷170 nm which corresponds to an oxygen concentration of (5–6) × 10¹⁹ cm^-3. For these high supersaturation degrees Eq. (4) should be transformed to

$\Delta G_V=-\frac{1}{v^{*}}\frac{Q}{T_{\mathrm{e}}}\left(1-\frac{T_0}{T_{\mathrm{e}}}\right)$ (9)

where T₀ 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 [18]

$c_{\mathrm{O}}^s=1.63·{10}^{21}\exp \left(-\frac{99.54\mathrm{kJ}/\mathrm{mol}}{RT}\right)$, (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 [23, 24] for describing the uphill diffusion of carbon. According to Onsager the flow j of the i-th property depends linearly on all the thermodynamic forces acting in the system:

$j_i=\sum _k{L}_{ik}{X}_k$ (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 non-diagonal (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 i-th 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 [19]

$c_1\nabla {\mu }_1+c_2\nabla {\mu }_2=0$ (13)

where с₁ and с₂ 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^ef₁and D^ef₂are 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 × 10¹⁵ and 2.4 × 10¹⁵ 1/cm² (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 cluster-like 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 carbon-oxygen bond. This bond is so strong that intrinsic silicon interstitial atoms cannot participate in the formation of cluster-like 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) × 10³–5 × 10⁴ 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. 7).