Examining the characteristics of the volatile reaction products that drive the etching process is a critical component of studying and modeling etching mechanisms. The properties of these reaction products, particularly their stoichiometry, can vary significantly with increasing temperature, leading to considerable changes in the etching mechanisms. In such scenarios, fundamental characteristics of etching−such as reaction kinetics and the transition from isotropic to anisotropic etching−may undergo profound alterations. Therefore, analyzing the effects of temperature variations is essential to derive meaningful insights, especially regarding etching kinetics and anisotropy.

In the case of silicon etching by fluorine, determining the precise stoichiometry of the Si_xF_y etching products under various experimental conditions−including the gas or plasma state, concentration or flux of reactive species, temperature, and ion bombardment−is crucial. The aim of this study is to explain the formation conditions of various reaction products reported in previous research through a thermodynamic evaluation with respect to temperature and to validate these findings experimentally.

It is widely accepted that the major reaction product of silicon etching by fluorine at low temperatures is SiF₄. This result has been experimentally confirmed by numerous authors [1–8] under various operating conditions, including XeF₂, F, and SF₆ plasma. However, other minor reaction products have been identified by mass spectrometry, including Si₂F₆ [7–9], Si₃F₈ [7,9], and SiF₂ under certain plasma etching conditions [1].

Despite many difficulties in interpreting mass spectrometry results, it is now accepted that SiF₄ and Si₂F₆ are the main reaction products of silicon etching in gases. In plasma, identifying reaction products by mass spectrometry is even more challenging due to inelastic collisions within the plasma volume. Moreover, ion bombardment can alter the distribution of reaction products.

To avoid dissociation and recombination reactions in the plasma volume, Petit and Pelletier [1] analyzed the reaction products transmitted through a silicon grid subjected to ion bombardment of about a hundred eV in a SF₆ plasma, using mass spectrometry. After separating the contributions of SiF_x and COF_x species to peaks 47 and 66 (where x = 1 or 2), they verified that when the fluorine coverage on the silicon surface becomes less than the critical coverage (θ < θ_c), SiF₂ emerges as an important reaction product. While SiF₄ remains the major reaction product, SiF₂ can contribute up to 15 % of the reaction products [1]. Measurements by Winters and Plumb [7] and conclusions by Sebel et al. [10] on the significant production of SiF₂ in the presence of ion bombardment support this finding.

Beyond the identification of reaction products, some experimental observations about their distribution at room temperature (RT) are particularly interesting. For instance, Houle [8] found that during the etching of silicon by XeF₂, more SiF₄ desorbed from n-doped silicon than from p-doped silicon and, correspondingly, more Si₂F₆ desorbed from p-doped silicon than from n-doped silicon. Similarly, Yarmoff and McFeely [11] observed that during the etching of silicon by XeF₂, n⁺-doped samples exhibited a slightly thinner SiF_x layer (or coverage θ) than lightly doped samples, while p⁺-doped samples showed a much thicker SiF_x layer (greater coverage θ). Another interesting result [9] is that the percentage of desorbed Si₂F₆ is higher during the etching of silicon by atomic fluorine (F) than by XeF₂.

Several studies have demonstrated that the concentration of SiF_x adsorbed on the surface during etching is significantly altered as the substrate temperature increases. In these studies [9,11,12], at T = 300 K, the adsorbed SiF_x phase (layer) consists of a mixture of adsorbed species: SiF₃, SiF₂, and SiF. As the temperature rises, the amount of SiF₃ species in the layer decreases, while the amounts of SiF and SiF₂ increase. Beyond a temperature of approximately 600 K, the layer primarily consists of SiF [6,13].

Characterizing desorbed species during etching, Winters and Plumb [7] and Winters and Coburn [9] also revealed a change in etching reaction products as a function of substrate temperature. They showed, for the first time using mass spectrometry, that as the temperature increases, the contributions of Si₂F₆ and subsequently SiF₄ to the reaction products decrease, while the desorption of SiF₂ increases starting at 600 K. Above 600 K, SiF₂ becomes the main reaction product. In summary, SiF₄ is the dominant reaction product at temperatures T < 600 K, while SiF₂ becomes the dominant reaction product at temperatures T > 600 K.

Engstrom et al. [6], who obtained identical results, experimentally verified that the thermal desorption of SiF₂ was complete at 800 K and that the adsorption energy (corresponding to the desorption activation energy) of SiF₂ was 59 kcal/mol (2.56 eV).

The operational conditions for the etching depth according to temperature in SF₆ plasma were set as follows. Plasma generation was achieved using a radio-frequency (RF) power fixed at 500 W, with an SF₆ pressure maintained at 23 mTorr. The RF self-bias voltage was kept constant at −30 V, corresponding to an RF power range of 5 to 16 W. The temperature of the substrate was varied across a range from 30 to 500 °C. The etching process was carried out for a fixed duration of 2 min. In addition, the operational conditions to assess the influence of doping and temperature on silicon etching were as follows. The 2.45 GHz microwave power for plasma generation was fixed at 1,000 W, with the SF₆ pressure maintained at 3 mTorr. The RF self-bias voltage was set to −30 V, corresponding to an RF power of 10 W. The temperature range explored was from −83.7 to 30.0 °C. The etching process was conducted for a duration of 3 min.

3.1. Thermodynamic studies

Silicon/fluorine system

All previous studies have highlighted the apparent complexity of the various conditions under which silicon etching by fluorine-based gases and plasmas has been investigated. However, none of the cited studies report results related to a thermodynamic analysis of the silicon/fluorine system. Indeed, understanding the final state of a given system can provide valuable insights, particularly regarding the final reaction products or potential intermediate products on the path to equilibrium.

The present thermodynamic study focused on low-pressure conditions (a total pressure of 1 mTorr) and plotted the volumetric fraction of volatile reaction products, as recorded in the Thermodata database, as a function of temperature. The results are presented in Fig. 1. As shown in Fig. 1, up to 1,000 K, the stable final state of the system is SiF₄. Beyond 1,000 K, SiF₃ and subsequently SiF₂ emerge as the main stable products alongside SiF₄. This clearly demonstrates that in nearly all experimentally explored operating conditions, SiF₄ is indeed the final reaction product. Evidently, reaction products such as SiF₂ or Si₂F₆ are merely intermediate products that appear due to favorable reaction kinetics. A first observation regarding Fig. 1 concerns the absence of Si₂F₆ and Si₃F₈ among the potential reaction products. This omission is due to a lack of data, which explains their absence in the calculations [14]. However, some estimates suggest that the presence of Si₂F₆ [7–9] and Si₃F₈ [7,9] as intermediate products is likely and that they would compete with SiF₃ in the thermodynamic study. In terms of the results, Si₂F₆ would substitute for two SiF₃ molecules.

Figure 1. Volume fraction of volatile reaction products in the silicon/fluorine system as a function of temperature. The total pressure is fixed at 1 mTorr.

Stability of SF₆

A consequence of the change in the stoichiometry of reaction products during silicon etching in fluorine-based plasmas is the likely increase in the etching kinetics. Specifically, if the flux of F absorbed on silicon is assumed to remain constant and independent of the substrate temperature, the number of silicon atoms desorbed in the form of SiF_x reaction products varies inversely with x. In other words, the silicon etching rate should double when transitioning from SiF₄ to SiF₂.

A condition to verify this, for instance in SF₆ plasma, is that the flux of F provided by the plasma remains unchanged. It is therefore useful to first verify the stability of SF₆ within the temperature range accessible experimentally. The results [14] are presented in Figs. 2 and 3, which show the evolution of the volumetric fraction of volatile reaction products, as recorded in the Thermodata database, as a function of temperature. The calculations were performed for total pressures of 1 mTorr (Fig. 2) and 10 mTorr (Fig. 3). As expected, Figs. 2 and 3 show similar trends, but with shifts toward higher temperatures as the pressure increases. At 1 mTorr, SF₆ begins to decompose into F and SF₄ at around 900 K, whereas this decomposition starts at approximately 975 K at 10 mTorr. Beyond 1,200 K, SF₂ is also observed among the decomposition products. These results demonstrate that SF₆ is highly stable up to around 900 K and that its thermal dissociation will not contribute significantly to the dissociation occurring in the plasma.

Figure 2. Volume fraction of SF₆ decomposition products as a function of temperature. The total pressure is fixed at 1 mTorr.

Figure 3. Volume fraction of SF₆ decomposition products as a function of temperature. The total pressure is fixed at 10 mTorr.

3.2. Discussion on etching mechanisms

Reaction kinetics

The thermodynamic study of the Si/F system has shown that the stable final state is SiF₄ up to 1,000 K. In other words, Si₂F₆ and SiF₂ can only be considered intermediate reaction products on the path to the system’s stable final state. To arrive at distinct intermediate products, it is necessary to follow different reaction pathways. Therefore, to provide a comprehensive explanation for all the observed experimental results, it is essential to identify the common denominator governing the surface mechanisms that lead to the various reaction products. In proposing an explanation, it is important to note that, at a constant fluorine adsorption flux (v), the surface coverage (θ) decreases as the desorption flux increases, such as under the influence of ion bombardment. In the case of silicon etching activated solely by thermal means, the coverage rate can generally be expressed as follows:

Equation (1) demonstrates that, at a constant adsorption v, the θ rate varies depending on the reaction kinetics of etching, defined by the reaction time (τ). Thus, the shorter the τ is, or the faster the reaction rate is, the lower the θ will be. σ0 is the adsorption site density in the monolayer. A similar reasoning can apply to etching induced by ion bombardment: the more intense the ion bombardment is, the faster the induced desorption of reaction products and the lower the θ will be. In other words, the common denominator across all the experimental results related to silicon etching is the θ rate. If the θ is high, the adsorbed phase will contain SiF₃ and SiF₂ species in significant densities. If these species are in close proximity to each other, they can react (via a Langmuir-Hinshelwood reaction mechanism) to form SiF₄, Si₂F₆, and Si₃F₈ through the following reactions:

Naturally, as Si₂F₆ (or Si₃F₈) is inherently an unstable intermediate product, SiF₄ emerges as the predominant reaction product. When the θ decreases, the possibility of two SiF₃ groups being in close proximity is eliminated, resulting in SiF₄ becoming the sole reaction product at RT. With a further reduction in coverage, such as through thermal activation or ion bombardment, it becomes impossible for two SiF₂ groups to be adjacent. In this scenario, the only spontaneous reaction pathway involves the thermally activated desorption of SiF₂, which occurs from approximately 600 K. Similarly, in plasma environments, a decrease in coverage leads to a notable increase in the ion-induced desorption of SiF₂ [1].

In conclusion, at RT and high coverage levels, SiF₄ and Si₂F₆ are the dominant reaction products. At lower coverage levels, SiF₄ remains the primary reaction product. Under conditions of ion bombardment or elevated temperatures−where coverage levels are significantly lower−SiF₂ also emerges as an important reaction product. This framework provides a comprehensive explanation for the previous experimental observations. For instance, the faster reaction kinetics observed with n⁺-doped silicon compared to p⁺-doped silicon (i.e., a shorter τ for n⁺-doped silicon) result in lower fluorine coverage on n⁺-doped silicon than on p⁺-doped silicon. Accordingly, it is consistent to observe higher levels of Si₂F₆ (and lower levels of SiF₄) desorbed from p⁺-doped silicon relative to n⁺-doped silicon. Another notable finding is the higher percentage of Si₂F₆ desorbed during silicon etching by F compared to XeF₂. This result can be interpreted by positing [6] that the reaction kinetics are faster with XeF₂ than with F, as previously reported [9]. Under this assumption, the fluorine coverage rate on silicon is higher [as delineated in Eq. (1)] when etching with F, which explains the increased percentage of Si₂F₆. Furthermore, this difference in reaction kinetics implies that equilibrium (and thus the steady state) is achieved much more rapidly with XeF₂ (and F₂) than with F [6].

Consequences on the transition from isotropic to anisotropic etching

The consequences of these results and the hypotheses proposed to explain the transition from isotropic to anisotropic etching are relatively straightforward. At RT, when the surface is at the critical coverage (θ_c), a well-ordered layer of -SiF₂-SiF-SiF₂-SiF- is formed due to the repulsive interactions between neighboring fluorine adatoms. Under these conditions, the formation of SiF₄, and even more so Si₂F₆, is not possible. If the temperature of the silicon surface is increased, two modifications can occur. (i) Direct desorption of SiF₂ (as the temperature approaches 600 K): in this case, the transition disappears entirely. (ii) Creation of surface disorder: when kT becomes comparable to the energy of repulsive interactions between neighboring fluorine adatoms, the silicon surface transitions from a highly ordered state to a disordered one. Under these conditions, the isotropic-to-anisotropic etching transition, which is abrupt at RT, becomes increasingly gradual with rising temperature.

While it is feasible to estimate the desorption kinetics of SiF₂ based on its adsorption energy (2.56 eV), the lack of knowledge regarding the repulsive interaction energy between neighboring fluorine adatoms prevents an evaluation of the corresponding order-disorder transition temperature. While studying the isotropic-to-anisotropic etching transition as a function of temperature appears challenging, the evolution of the etching rate with temperature should be easier to observe in SF₆ plasma. At RT, where the predominant reaction product is SiF₄, the transition to SiF₂ as the primary reaction product at higher temperatures should result in a doubling of the etching rate (the transition occurs between 500 and 700 K). Beyond 700 K (400 °C), it is possible that the desorption of SiF could be observed, leading to another doubling of the etching rate.

Figure 4 shows that the etching rate, initially constant near RT, gradually increases thereafter. The increase in the etching rate is less than a factor of 1.5 at 800 K, whereas, based on experimental observations of reaction product evolution from the literature, an increase of at least a factor of two was expected (due to the transition from SiF₄ to SiF₂). However, the thermodynamic study of the Si/F system (Fig. 1) indicates that SiF₄ remains stable up to nearly 1,000 K, with SiF₃ only appearing at around 900 K and SiF₂ emerging at approximately 1,050 K. Consequently, a doubling of the etching rate is expected only beyond 1,000 K, which is above the temperature range of up to 800 K explored in this study.

Figure 4. Etching rate as a function of temperature. The etching duration is 2 min.

The experiments to assess the influence of doping on silicon etching were conducted and the results are shown in Fig. 5. Trends consistent with those reported in the literature are observed, specifically a clear difference in lateral etching rates between n⁺ and p⁺ layers. On the one hand, there is only a slight difference in lateral etching rates between heavily n⁺-doped silicon and lightly n-doped silicon [Fig. 5(a)]. On the other hand, a significant difference is observed between heavily p⁺-doped silicon and lightly p-doped silicon [Fig. 5(b)]. The qualitative results obtained on the n⁺/n and p⁺/p substrates are consistent with the expected outcomes, namely a higher reaction rate with n⁺-doped silicon compared to p⁺-doped silicon. Assuming a constant fluorine coverage rate (etching model hypothesis) on the bottom and sidewalls of the etch profile, a difference in lateral etching rate must necessarily appear when transitioning from an n⁺ layer to a p⁺ layer depending on the electronic structure of the surface. Conversely, the vertical etching rate (V_v) of silicon should be independent of both temperature and doping due to strong spontaneous etching in the temperature range explored in this study. To verify this, it is useful to plot the evolution of the vertical etching rate of silicon in an SF₆ plasma as a function of temperature and for all doping levels (Fig. 6). Within the limits of experimental error, it is confirmed that the vertical etching rate, under constant plasma operating conditions, is indeed independent of both temperature and doping. To analyze the experimental measurements of etching rates as a function of temperature, the ratio V_l/V_v of lateral etching rate (V_l) to vertical etching rates as a function of 1/T should be plotted. The results are presented in Fig. 7. It is observed that, within the explored temperature range, the ratio V_l/V_v remains approximately constant with respect to temperature, within the measurement uncertainties (± 5 %). However, it is confirmed once again that silicon doping has a significant impact on the V_l/V_v value.

Figure 5. (a) Scanning electron microscope images of the etched profiles of n+/n layers and (b) p+/p layers. The substrate temperature is −83.7 °C.

Figure 6. Evolution of the vertical etching rate of silicon in SF₆ plasma as a function of the inverse of temperature and for different doping levels.

Figure 7. Ratio V_l/V_v of the lateral etching rate to the vertical etching rate of silicon in SF₆ plasma as a function of the inverse of temperature and for different doping levels.

Silicon etching by fluorine is primarily driven by the formation of volatile reaction products, which is strongly influenced by temperature and fluorine coverage. These factors play a critical role in determining key etching characteristics, such as reaction kinetics and the transition between isotropic and anisotropic etching. At lower temperatures, etching follows the Langmuir-Hinshelwood mechanism, where bimolecular reactions occur between adsorbed species in close proximity. As the temperature rises, thermal desorption becomes the dominant mechanism, leading to the formation of products such as SiF₂ and SiF. Fluorine coverage further shapes the reaction pathways. Under low coverage, SiF₄ is the primary product, formed through bimolecular reactions of adsorbed SiF₂ species. In contrast, higher fluorine coverage encourages the formation of more complex intermediates, such as Si₂F₆ and Si₃F₈, through bimolecular or trimolecular reactions involving SiF₃ and SiF₂ species. Thermodynamic analysis provides valuable insight into the stability and distribution of these reaction products, which reflect the equilibrium state of the siliconfluorine system. The combination of temperature and fluorine coverage thus determines the stoichiometry and complexity of the reaction products formed during etching.

Special thanks to Dr. Jacques Pelletier and Prof. Ana Lacoste for data analysis and technical assistance.

The authors declare no conflicts of interest.