INTRODUCTION

Starting from the 1990s, silicon-on-insulator (SOI) structures occupied a firm place in modern electronics as an alternative to monolithic silicon substrates in creation of very large-scale integration circuits in view of the whole spectrum of their advantages due to the smaller silicon volume, the possibility of isolation of separate elements of integrated circuits, the decrease in parasitic currents, the elimination of latch-up, etc. [1]. However, modern trends in development of electronics require creation of structures containing silicon and insulating layers of only several nanometers in thickness. Further use of such structures in silicon technology can be complicated by a decrease in the thermal stability of the films with a nanometer thickness. This is due to the fact that a decrease in the silicon layer thickness to several nanometers is accompanied by an increase in the contribution of a surface to the properties of the silicon layer. As a result, it can lead to a change in the average coordination number of silicon atoms and the average angle between Si–Si bonds. Because of this, with a decrease in the layer thickness, the binding energy per 1 silicon atom can change. This effect can strongly vary with an increase in temperature; namely, it can be accompanied by a change in the melting point of the bulk crystal.

In experiments, thermal instability of SOI films with a nanometer thickness was observed in [2–5] after high-vacuum annealing. In particular, in [5], agglomeration of the SOI films with a thickness of 1.1 to 1.5 nm was observed after annealing at as low as approximately 570°С. With an increasing film thickness to 3 to 6 nm, the temperature at which silicon drops were formed at the SiO2 surface rose to 825 to 850°C, correspondingly. In [6], it was established that the sizes of silicon drops formed as a result of agglomeration depend on the SOI film thickness. Their height and lateral sizes increase with an increasing silicon layer thickness. Nuryadi et al. [6] related this dependence to thermal processes, since the temperature of formation of drops increases with an increasing film thickness.

In the literature, there have been repeated attempts to theoretically describe the change in melting point with a decreasing particle size. In 1908, Pavlov developed a thermodynamic model, which for the first time predicted a decrease in the melting point with a decrease in the particle size [7]. In 1910, Lindemann [8] proposed a melting model based on an approach grounded on the dynamic changes in the crystal lattice with an increasing temperature; viz., the average amplitude of thermal oscillations in the lattice increases with an increasing temperature. The Lindemann criterion was formulated, which says that the ratio of the average amplitude of thermal oscillations of atoms to the interatomic distance in a solid at the melting temperature is constant [8]. Since atoms at a surface are more weakly bonded, under real conditions, this can lead to larger amplitudes of oscillations than those of the atoms in the bulk of the particle or a thin film at the same temperature. In other words, according to the Lindemann criterion, the process of melting of a solid should start from the surface. For nanometer-thick layers it can be accompanied by a general decrease in the melting point of the film, since the contribution of surface atoms becomes quite large.

The models by Pavlov [7] and Lindemann [8] did not take either the crystal shape or the matrix in which it is placed into account or the media it borders. In 1948, Reiss et al. [9] proposed a thermodynamic model of melting, which considered not only the crystal shape, but also its shape and conditions at the interfaces. In particular, the features of change in the melting point of spherical crystals with small sizes, thin extended films, and thin threads were theoretically studied. In the context of the proposed model, it was established that the melting point of the spherical particle decreases with a decrease in its diameter. For a thin film, the effect of film thickness on the melting point is ambiguous, since the melting point can both increase and fall depending on the chemical nature of the substance the film borders.

A model that considers the change in the melting point of nanoparticles as their size is decreased and connects this change with an increase in the amplitude of atomic oscillations and taking account of the interaction between the atoms in the nanoparticle and atoms at the surface or in the surrounding matrix was proposed in [10]. Shi [10] demonstrated that, for spherical nanoparticles, the conditions for both a decrease and increase in the melting point with a decrease in the particle size or film thickness can also be created.

Summing up, analysis of the literature data reveals that a decrease in the crystal dimensions can have an ambiguous effect on the change in its thermal stability. Therefore, the aim of the present study was to investigate the thermal stability and structural changes in nanometer-thick silicon-on-insulator films under the conditions of high-temperature annealing in an oven at normal atmospheric pressure.

EXPERIMENTAL

Experimental samples were prepared by the DeleCut technique on the silicon-on-insulator (SOI) and silicon-on-sapphire (SOS) processing line of the Rzhanov Institute of Semiconductor Physics [1]. As the initial material, single-crystalline n-type (100)-oriented Si wafers with the resistivity of 4.5 Ω cm were used. First, in the first wafer, a SiO2 layer with a thickness of ~300 nm was grown by thermal oxidation in a dry oxygen atmosphere at T = 1100°C. The second wafer, on which a protective 20-nm-thick layer was preliminarily grown in a dry oxygen atmosphere at Т = 900°C, was then implanted with hydrogen \({\text{H}}_{2}^{ + }\) ions with an energy of 120 keV to dose of 2.7 × 1016 cm−2. After implantation of hydrogen ions, the protective SiO2 layer was removed by the solution HF : H2О = 1 : 100. The first wafer was then bonded on its oxidized side with the implanted side of the second wafer and splitting was carried out along the layer implanted with hydrogen at a temperature of 450°C in a vacuum with simultaneously transferring the silicon film with the thickness of approximately 540 nm. The obtained SOI wafer was subjected to multistep thermal oxidation in wet oxygen at T = 1000°C and in dry oxygen at Т = 850–950°C, with the result that silicon oxide layers were grown and removed to form SOI layers with a thickness of 4.7 and 2.2 nm. At the surface of SOI layers, there was a native oxide layer with a thickness of 1 and 1.4 nm, respectively. The subsequent annealing of the samples was performed in an N2 vapor flow in a furnace at temperatures of 800 to 1200°С for 15 min.

The properties of the resulting SOI structures were investigated by scanning electron microscopy (SEM) and spectral ellipsometry. In our experiments, SEM investigations of the surface morphology of the samples were conducted in a Raith Pioneer high-resolution electron-beam lithography system. An accelerating voltage of the electron beam was 10 kV. SEM images were taken using an electron beam both vertically incident (90°) and incident at a grazing angle of approximately 7° to the sample surface.

The spectral ellipsometry control of thickness and phase composition of the films in our experiments was carried out on an Ellips-1891 ellipsometer produced at the Rzhanov Institute of Semiconductor Physics [11]. The ellipsometer is created on the basis of a static measuring system, providing a high speed of measurements due to the absence of rotating elements and modulation of the signal. The measurement time at one wavelength is determined by sluggishness of the electron-enhancing tract. This allows attaining a high accuracy of measurements by accumulation of a large data set in a small time with subsequent averaging. As a light source, a xenon lamp with a power of 75 W and a monochromator was used. The measurements were made in the spectral range of 250–1000 nm. The light spot was a 1 × 3 mm ellipse. In the experiment, Ψ(λ) and Δ(λ) spectra were measured, and the parameters of the studied SiO2/Si/SiO2/Si structures were reconstructed from them. The optical spectra of the cut-off Si layer were simulated as a mixture of an amorphous (a-Si) and crystalline (c-Si) silicon phase with the use of the model of the effective medium. The adjustment process involved a search for the thickness of the cut-off silicon layer and the percentage ratio between the a-Si and c-Si phases under the condition of maximum coincidence of the experimental and model spectra. The accuracy of determination of the thickness was ±0.1 nm and that of the percentage of phases was ±1%.

RESULTS AND DISCUSSION

Figure 1 shows SEM images of the SOI surface with the initial silicon layer thickness of 4.7 nm after annealing at a temperature of 800°С at an electron beam angle of 90° (Fig. 1a) and 7° (Fig. 1b). It is seen from the figure that the sample surface is even and has no microirregularities or regions of rupture. The images of the surface of the same sample after annealing at a temperature of 1100°C are given in Figs. 1с and 1d. The electron microscopy study revealed that an increase in the annealing temperature lead to a change in the surface morphology. The film became nonuniform and ruptures appeared in it (Fig. 1с). The same changes are also seen at the grazing angle of electron beam incidence (Fig. 1d).

Fig. 1.
figure 1

SEM images of an SOI sample surface with an initial thickness of the silicon layer of 4.7 nm after annealing at temperatures of (a, b) 800 and (с, d) 1100°С at an electron beam angle of (a, c) 90° and (b, d) 7°.

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Figure 2 also illustrates SEM images of the surface of the SOI sample with the initial silicon layer thickness of 2.2 nm after annealing at temperatures of 800 and 1100°С at normal and grazing incidence of the electron beam. As is seen from Fig. 2a, after annealing at a temperature as low as 800°С, structural irregularities appear at the film surface, which can arise due to either ruptures in the film due to its thermal instability or a change in its stoichiometric composition. An increase in the annealing temperature to 1100°C leads to the situation in which the ruptures become more clearly seen (Figs. 2с and 2d). Openings between separate regions of the film, which became electrically independent, appear. Under irradiation with an electron beam, this leads to polarization of the dielectric and thus a worse contrast in the image (Fig. 2с) due to the possible instability of the beam. The film as a whole still did not break down into separate drops.

Fig. 2.
figure 2

SEM images of the SOI sample surface with the initial thickness of the silicon layer of 2.2 nm after annealing at temperatures of (a, b) 800 and (с, d) 1100°С at an electron beam angle of (a, c) 90° and (b, d) 7°.

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In addition to melting, the reason for origination of ruptures in the film can be deformations due to the difference between the thermal expansion coefficients of silicon and SiO2. Deformations in a Si thin film when its thickness is much smaller than the thickness of the SiO2 layer can be described with expression [12]

$$\varepsilon = \frac{\sigma }{E}(1 - \mu ),$$
(1)

where ε is deformation, σ is stress, Е = 163 GPa is the Young modulus for Si, and μ = 0.266 is the Poisson ratio for Si. The stresses that arise in the film due to the difference in the thermal expansion coefficients with the SiO2, can be evaluated as σ = (αSi − \({{\alpha }_{{{\text{Si}}{{{\text{O}}}_{2}}}}}\))ΔTE, where αSi = 2.33 × 10−6 °C−1 is the thermal expansion coefficient for silicon, \({{\alpha }_{{{\text{Si}}{{{\text{O}}}_{2}}}}}\) = 5.5 × 10−7 °C−1 is the thermal expansion coefficient for SiO2 [13]. After substituting numerical values into Eq. (1), we obtained the value of deformation at the annealing temperature of 1100°С of approximately 2 × 10−4. The obtained deformation value is insufficient for breakage of bonds in silicon to occur.

In order to elucidate the reasons for the observed structural changes in SOI films, we investigated the thickness and stoichiometric composition of the film as a function of the annealing temperature by the spectral ellipsometry technique. Figure 3 presents a change in the SOI film thickness, with the initial value of 4.7 nm, with an increasing annealing temperature. From the figure it is seen that a noticeable change in the film thickness occurs starting from temperatures of 900 to 1000°С. This process can be accounted for by silicon oxidation by residual oxygen coming from the outside in the nitrogen vapor atmosphere. However, the measurements reveal that the thickness of the upper SiO2 layer remains an almost unchanged value of 1.4 to 1.9 nm throughout the experiment. This indicates that the oxidation process occurs from the side of the buried SiO2 layer.

Fig. 3.
figure 3

The thickness of the SOI film, with the initial value of 4.7 nm, versus annealing temperature.

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Together with a decrease in the SOI layer thickness, a change in its phase composition was also observed (Fig. 4). Even the initial silicon film with a thickness of 4.7 nm has a nonuniform composition and its optical characteristics correspond to a mixture of crystalline (90%) and amorphous (10%) silicon phases. Starting from the annealing temperature of 800°С, the fraction of the amorphous phase in the silicon film begins to increase and, after annealing at a temperature of 1100°С, reaches 52%.

Fig. 4.
figure 4

The content of the amorphous phase in an SOI film with a thickness of 4.7 nm versus annealing temperature. In the inset to the figure, the Arrhenius dependence in shown.

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Similar dependences of the thickness and stoichiometric composition of the silicon-on-insulator layer on the temperature of subsequent annealing were obtained for a film with an initial thickness of 2.2 nm. These data are illustrated in Figs. 5 and 6, respectively. In this case, a decrease in the film thickness and growth of an amorphous phase in it also take place starting from the temperature of 800°C; however, these changes occur more rapidly than those in the films with a thickness of 4.7 nm. After annealing at a temperature of 1100°C, the fraction of the amorphous phase in the film was 100%, and the thickness was approximately 0.2 nm.

Fig. 5.
figure 5

The thickness of the SOI film, with an initial value of 2.2 nm, versus annealing temperature.

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Fig. 6.
figure 6

The content of the amorphous phase in the SOI film with a thickness of 2.2 nm versus annealing temperature. In the inset to the figure, the Arrhenius dependence in shown.

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During isochronal annealing, a change in the fraction of the amorphous phase in the films as a function of temperature, with no regard for the inverse process of recovery of the crystalline matrix, can be described by an equation for an nth order reaction [14]

$$\frac{{d{{N}_{a}}}}{{dt}} = - KN_{{ai}}^{n},$$
(2)

where N is the fraction of the amorphous phase in the film, K is the rate of the amorphization reaction, and n is the reaction order. Let us assume that the reaction rate constant k does not depend on the initial phase composition of the film. Then, it can be described by the Arrhenius equation

$$K = {{K}_{0}}\exp \left( { - \frac{{{{E}_{{\text{a}}}}}}{{kT}}} \right),$$
(3)

where K0 is the reaction rate at Т → ∞ and Еа is the activation energy of the process. The boundary conditions for our process can be written as

$${{N}_{a}}(t,T) = {{N}_{a}}(0,0) + {{N}_{c}}(0,0)-{{N}_{c}}(t,T),$$
(4)

where Na(t, T) is the fraction of the amorphous phase in the film after annealing at a temperature Т for time t; Na(0, 0) is the fraction of the amorphous phase in the initial film; Nc(0, 0) is the fraction of the crystalline phase in the initial film; and Nc(t, T) is the fraction of the crystalline phase in the film after annealing at a temperature Т for time t. The maximum fraction of the amorphous phase in the film is

$${{N}_{{a,\max }}} = {{N}_{a}}(0,0) + {{N}_{c}}(0,0).$$
(5)

Integrating Eq. (2) over time t for the first-order process yields the expression

$$\ln \left[ {\frac{{{{N}_{{a,\max }}} - {{N}_{a}}(0)}}{{{{N}_{{a,\max }}} - {{N}_{a}}(T)}}} \right] = Kt.$$
(6)

For isochronal annealing, when one and the same sample is used, Eq. (6) can be rearranged into an equation in the form

$$\ln \left[ {\frac{{{{N}_{{a,\max }}} - {{N}_{{a,i - 1}}}}}{{{{N}_{{a,\max }}} - {{N}_{{a,i}}}}}} \right] = Kt,$$
(7)

where Na,i is the fraction of the amorphous phase after annealing at a temperature of Тi, and Na,i − 1 is the fraction of the amorphous phase after previous annealing. After substituting expression (7) into Eq. (3) we obtain

$$\ln \left[ {\frac{{{{N}_{{a,\max }}} - {{N}_{{a,i - 1}}}}}{{{{N}_{{a,\max }}} - {{N}_{{a,i}}}}}} \right] = {{K}_{0}}\exp \left( { - \frac{{{{E}_{{\text{a}}}}}}{{kT}}} \right).$$
(8)

After taking the logarithm of Eq. (8), we obtain the dependence

$$\ln \left[ {\ln \left( {\frac{{{{N}_{{a,\max }}} - {{N}_{{a,i - 1}}}}}{{{{N}_{{a,\max }}} - {{N}_{{a,i}}}}}} \right)} \right] = \frac{{{{K}_{0}}}}{t} - \frac{{{{E}_{{\text{a}}}}}}{{kT}}.$$
(9)

Plotting the dependence \(\ln \left[ {\ln \left( {\frac{{{{N}_{{a,\max }}} - {{N}_{{a,i - 1}}}}}{{{{N}_{{a,\max }}} - {{N}_{{a,i}}}}}} \right)} \right]\) on 1/kT, we find the activation energy of the amorphization process of the first order. For silicon films with a thickness of 4.7 and 2.2 nm, these dependences are presented in insets to Figs. 5 and 6, respectively. For 4.7-nm-thick films, the activation energy of growth of the fraction of the amorphous phase was ~1.7 eV, while that for 2.2-nm-thick films was 0.57 eV.

The effects of change in the thickness and stoichiometric composition of the films observed here can be explained by two main processes. First, oxidation of the films by interaction with atoms of residual oxygen in the N2 atmosphere, which penetrate into the film during annealing. However, the results of measurements demonstrate that in the process of annealing the  thickness of the upper SiO2 remains nearly unchanged. This means that no thermal oxidation of the film takes place from the side of the surface. In fact, the oxidation process in single-crystalline silicon occurs through interaction of oxygen atoms diffusing from the outside with vacancies equilibrium at a given temperature in it. As a result of such interaction, interstitial atoms are generated into the single-crystalline silicon lattice. In a bulk single crystal or a thick film of single-crystalline silicon, these interstitial atoms diffuse deeply and recombine with silicon vacancies there. In the case of thin films, this process is restricted by the film volume and concentration of free silicon vacancies present in it. In a nanometer-thick film, the concentration of vacancies is determined by not only the temperature, but also the concentration of interstitial silicon atoms, which diffusion deep into the film is limited. Therefore, interaction between oxygen coming into the film and silicon atoms is hampered. This is the reason that silicon films with a thickness smaller than 10 nm remain almost unoxidized [15]. Hence, it is reasonable to suppose that oxidation of the film proceeds from the side of the buried SiO2 layer due to diffusion of oxygen atoms and interaction between them and weakened bonds in the transition layer in the vicinity of the Si/SiО2 interface. In addition, excess oxygen atoms can easily diffuse into the buried SiO2 layer through the silicon film, with their form being that of an О2 molecule unbound to the lattice [16]. The oxygen diffusion coefficient in silicon at a temperature of 1100°С is approximately 10−10 cm2/s [16]. For the annealing time of 15 min, this corresponds to a diffusion length of approximately 3 × 10−4 cm, which is 3 orders of magnitude larger than the thickness of the films that we used in the experiments.

Analysis of the activation dependences (insets to Figs. 4 and 6) shows that they differ for the films with thicknesses of 4.7 and 2.2 nm. The activation energy of amorphization of the films with a thickness of 4.7 nm is approximately 1.7 eV (inset to Fig. 4). The energy of Si–Si bond breakage in single-crystalline silicon is approximately 1.8 eV [17]. In nanometer-thick films, the average energy of the Si–Si bond can be lower due to the smaller average coordination number of the atoms. A decrease in the film thickness to 2.2 nm is accompanied by a decrease in the activation energy of formation of an amorphous phase. This effect can be due to a lower average binding energy between silicon atoms due to the growing contribution from poorly coordinated atoms at the surface. On the other hand, a decrease in the film thickness caused by film oxidation involves interaction between silicon atoms and oxygen atoms diffusing from SiO2. Oxygen diffuses from the SiO2 layer to the Si/SiO2 interface in the molecular form [18, 19]. In particular, it was demonstrated in [19, 20] that for silicon films thicker than 1.5 nm oxygen in an atomic form is located only in immediate vicinity of the Si/SiO2 interface. This means that, for silicon oxidation, expenditure of energy is necessary for dissociation of an O2 molecule, which is near 1.2 eV is silicon oxide [17], and for overcoming the energy barrier for interaction with a weakened Si–Si bond, whose energy is approximately 0.2–0.3 eV [21, 22]. The sum of these energies is ~1.5 eV and is close to the activation energy observed experimentally in Fig. 4. Generation of interstitial atoms into the Si film during oxidation can also result in a growth in the fraction of the amorphous phase.

One possible reason for a decrease in the activation energy of formation of an amorphous phase in films with a thickness of 2.2 nm compared to that in films with a thickness of 4.7 nm may be their initial structural nonuniformity (Fig. 2). Therefore, the oxidation process in these films can proceed both in the plane of the interface with the buried oxide layer and in the regions of film rupture. The amorphization mechanism for such films requires further investigation.

CONCLUSIONS

The thermal stability and structural changes in silicon-on-insulator films with thicknesses of 4.7 and 2.2 nm were investigated after annealing at temperatures of 800 to 1200°С. The research was carried out using scanning electron microscopy and spectral ellipsometry. It was demonstrated that the films remained continuous throughout the studied range of annealing temperatures. With an increasing annealing temperature, a decrease in the film thickness and a change in the film composition occurred. It has been found that with an increasing annealing temperature the fraction of the crystalline phase in the films decreased and the fraction of an amorphous phase increased. The activation energy of the process of film amorphization was different for the films with thicknesses of 4.7 and 2.2 nm; it was ~1.7  and 0.57 eV, respectively. The results were explained by diffusion of oxygen atoms into the silicon film and rearrangement of Si–Si bonds.