Anisotropic etching is a widely used process in semiconductor manufacturing, in particular, for micro- and nanoscale texturing of silicon surfaces for black silicon production. The typical process of plasma-assisted etching uses energetic ions to remove materials in the vertical direction, creating anisotropic etch profiles. Plasmaless anisotropic etching, considered here, is a less common process that does not use ions and plasma. The anisotropy is caused by the unequal etching rates of different crystal planes; the etching process, thus, proceeds in a preferred direction. In this paper, we have performed quantum chemistry modeling of gas-surface reactions involved in the etching of silicon surfaces by molecular fluorine. The results confirm that orientation-dependent etch rates are the reason for anisotropy. The modeling of F2 dissociative chemisorption on F-terminated silicon surfaces shows that Si–Si bond breaking is slow for the Si(111) surface, while it is fast for Si(100) and Si(110) surfaces. Both Si(100) and Si(110) surfaces incorporate a larger number of fluorine atoms resulting in Si–Si bonds having a larger amount of positive charge, which lowers the reaction barrier of F2 dissociative chemisorption, yielding a higher etch rate for Si(100) and Si(110) surfaces compared to Si(111) surfaces. Molecular dynamics modeling of the same reactions has shown that the chosen reactive bond order potential does not accurately reproduce the lower reaction barriers for F2 dissociative chemisorption on Si(100) and Si(100) surfaces. Thus, reparameterization is necessary to model the anisotropic etching process that occurs at lower temperatures.

Orientation-dependent etching of silicon has been used for texturing of silicon surfaces via dry and wet etching processes to produce black silicon.1,2 The etch rate in the (111) direction is much slower than in the (100) and (110) directions, and the resulting anisotropic etching process can be used to create nanostructures. Plasmaless atmospheric dry etching (ADE) commercialized by Nines Photovoltaics is a cost-effective method of nanoscale silicon surface texturing. A schematic of this process is shown in Fig. 1, illustrating the experimental etching results from Ref. 3 at 3.33% F2 in air and substrate temperatures of 200 and 300 °C. In the ADE process implemented by Nines Photovoltaics, a silicon wafer is transported on a heated conveyer through a reaction chamber containing the F2 gas. The substrate temperature, F2 concentration, and duration of exposure to F2 all control the etch process. Kafle et al.3–6 showed that at temperatures higher than 200 °C, nanoscale pits are formed on a partly oxidized Si(100) surface during plasmaless etching. Nucleation of the pits due to anisotropic etching begins at reactive sites where the oxide layer is absent. The slope of the pit walls is defined by the angle between the Si(111) surface and Si(100) surface; these planes intersect at an angle of about 55°, as shown in Figs. 1(b) and 1(d). The cone-shaped nanostructures shown in Fig. 1(b) gradually disappear with increasing temperature [see Fig. 1(c)] as the etching process becomes more isotropic. It is schematically shown in Fig. 1(d) how the anisotropic etching profile appears on the Si(100) surface due to the slow etching of Si(111). Our focus is limited to the analysis of anisotropic etching on a molecular level, using DFT (density functional theory) simulations of reaction pathways and investigating the suitability of a reactive bond order (REBO) molecular dynamics potential for simulating this anisotropic etching process. We did not study the effects of F2 concentration or process duration on etch anisotropy during ADE processing; nor have we examined the process of pit nucleation on the partly oxidized surface. It should be noted that a similar effect, where silicon is slowly etched in the (111) direction compared to the (100) direction by Cl2/Ar inductively coupled plasma, was observed by Du et al.7 

FIG. 1.

Schematic representation of ADE of F-terminated Si surfaces at different substrate temperatures: (a) the initial Si(100) surface structure; surface structure after etching by F2 molecules as observed by Kafle et al. (Ref. 3); (b) at 200 °C, which is anisotropic (orientation-dependent); and (c) surface structure after etching at 300 °C, which becomes more isotropic. (d) Schematic representation of etch profile formation during orientation-dependent etching of silicon by F2.

FIG. 1.

Schematic representation of ADE of F-terminated Si surfaces at different substrate temperatures: (a) the initial Si(100) surface structure; surface structure after etching by F2 molecules as observed by Kafle et al. (Ref. 3); (b) at 200 °C, which is anisotropic (orientation-dependent); and (c) surface structure after etching at 300 °C, which becomes more isotropic. (d) Schematic representation of etch profile formation during orientation-dependent etching of silicon by F2.

Close modal

To identify the reasons for anisotropy, we performed quantum chemistry modeling of F2 dissociative chemisorption on silicon surfaces. In our modeling, we assume that the etching of silicon by F2 proceeds on the F-terminated surfaces and that the rate of silicon etching is determined by the rate of F2 chemisorption. The calculated reaction rates of F2 dissociative chemisorption on Si(100) and Si(110) match the rate of silicon etching by F2 gas as measured by Mucha et al.8 (see Sec. II D). In addition, our calculations reproduce the experimental trend that F2 gas etches the Si(111) surface more slowly compared to other surface orientations as illustrated in Fig. 1(d). The charge density analysis (described in Sec. II C) showed that passivating F atoms attract electron density from the uppermost Si atoms and that the amount of positive charge on an individual Si atom increases with the number of bonded passivating F atoms. Si(100) and Si(110) surfaces are passivated by a larger amount of F atoms per surface Si atom compared to Si(111) (Sec. II A). F2 molecules approaching the surface become negatively charged and, as a result, are more strongly attracted to Si(100) and Si(110) surfaces than the Si(111) surface. The analysis shows that the etching limiting step is F2 dissociative chemisorption on silicon, and their activation barriers (Ea) for Si(100) and Si(110) are approximately equal, Ea [Si(100)] ≈ Ea [Si(110)], and are small compared to Ea [Si(111)] (Sec. IV).

Additionally, we performed the classical molecular dynamics simulation of etching. It was determined that the REBO potential that was typically used for this chemistry reasonably represents chemisorption on Si(111) but did not accurately represent the reaction path for F2 dissociative chemisorption on Si(100) and Si(110) surfaces, overestimating the required activation energy. As a result, the anisotropic orientation-dependent etching process that creates conelike nanostructures cannot be simulated using this potential without further reparameterization. The results can be found in Sec. III.

As is well known, bulk silicon crystallizes into a diamond cubic crystal structure in which each atom has four nearest neighbors forming the sp 3 hybridized tetrahedral structure. The structures of fluorinated Si(100), Si(110), and Si(111) surfaces and the top 6 silicon atoms, so-called Si6 chairs, on these surfaces are shown in Fig. 2. The reaction path of F2 dissociative chemisorption passes via the transition state (TS), where an F2 molecule adsorbed on the Si6 chair forms a reaction center with attacked Si–Si. In other words, only two atoms in the Si6 chair are partaking in the reaction, and the stoichiometry of the reaction centers is F2..Si2Fn. The reaction centers have different “n” depending on the surface orientation. Namely, there is an F2..Si2F2 reaction center on Si(100) and Si(110) surfaces and an F2..Si2F1 reaction center on the Si(111) surface as illustrated in Fig. 2. Note that the reaction centers shown in Fig. 3 are coupled with possible reaction channels A and B: one F atom of the F2 molecule bounces off the surface yielding a free F atom or both F atoms are adsorbed without the formation of free atoms. Both channels are illustrated in Fig. 3 for all Si6 chair configurations.

FIG. 2.

Fluorinated Si6 chair on 100 (a), 110 (b), and 111 (c) oriented silicon surfaces.

FIG. 2.

Fluorinated Si6 chair on 100 (a), 110 (b), and 111 (c) oriented silicon surfaces.

Close modal
FIG. 3.

Dissociative chemisorption of F2 molecules on fluorinated Si6 chairs on 100 (a), 110 (b), and 111 (c) oriented surfaces via F2..Si2Fn transition state and leading to single F atom abstraction or two F atoms adsorption.

FIG. 3.

Dissociative chemisorption of F2 molecules on fluorinated Si6 chairs on 100 (a), 110 (b), and 111 (c) oriented surfaces via F2..Si2Fn transition state and leading to single F atom abstraction or two F atoms adsorption.

Close modal

It should be noted that the Si(100) surface can undergo reconstruction to minimize the energy of the top layer.9 Therefore, in Sec. II C, we also consider F2 dissociative chemisorption on F-terminated Si(100) reconstructed surfaces as well. We showed that the reconstructed F-terminated Si(100) surface is more reactive (less stable) with F2 molecules than the unreconstructed Si(100) surface. Thus, we assumed that the etching of silicon in the (100) direction is not accompanied by reconstruction and proceeds on the unreconstructed Si(100) surface.

As mentioned in Sect. II A, the chemisorption of F2 proceeds via two competitive reaction channels known as chemisorption with single atom abstraction (channel A) and with two atom adsorption (channel B). Channel A requires four elementary steps to etch one silicon atom, while channel B requires only two, as shown in Fig. 4. The first step is the same for both reaction channels A and B. The divergence between channels A and B appears when the TS goes down to the reagent valley, resulting in two different products (see Sec. II C). The importance of channel A is that free F atoms are released, which should affect the etch profile. These highly reactive free F atoms can also etch the silicon surface, but rather than the anisotropic, orientation-dependent etch that is possible with molecular fluorine, atomic F etches Si(100), Si(110), and Si(111) with the same rate. Thus, chemisorption that proceeds via channel A causes the etch profile to become more isotropic.

FIG. 4.

Reaction mechanisms of Si2Fn silicon surface etching (SiF4 desorption) by F2 molecules via channels A and B. The first step is shared by both channels, which have the same TS.

FIG. 4.

Reaction mechanisms of Si2Fn silicon surface etching (SiF4 desorption) by F2 molecules via channels A and B. The first step is shared by both channels, which have the same TS.

Close modal

Thus, we performed quantum chemistry modeling and found TSs of the first step in F2 chemisorption on Si(100), Si(110), and Si(111) surfaces. Other steps and evolution toward products in channels A and B are not considered. However, the calculated reaction barriers of step 1 match the measured activation energies for silicon etching by molecular fluorine (see Sec. IV). This agreement confirms our assumption that step 1 is the rate-determining step of the etching process.

Quantum chemistry modeling was performed using broken symmetry orbitals calculated by the unrestricted u-B3LYP DFT functional in the gaussian 1610 software package. The Lanl2dz basis set and pseudopotential for Si atoms were used in our simulations. All structures were visualized by Chemcraft software.11 

An Si32F32 cluster was used to mimic the structure of fluorinated Si surfaces. The free bonds of external Si atoms were closed by fluorine atoms. The reaction center geometries of four transition states (TSs) corresponding to the reactions of F2 dissociative chemisorption on an Si(100) surface with and without surface reconstruction, on an Si(110) surface, and on an Si(111) surface are shown in Fig. 5. In all transition states considered here, the F–F bond is perpendicular to the Si–Si bond. On the reaction path after the transition state, an intermediate biradical structure is observed where singlet and triplet states are overlapping, as shown in Fig. 6. Natural population analysis was performed to calculate atomic charges. The charges on the Si2Fn reaction centers on the Si32F32 cluster before the reaction and in TS can be found in Fig. 7. (The Si6 chair of the Si32F32 cluster reacting with an F2 molecule is shown in the displayed structure, while other atoms were omitted to simplify the picture.) The charge distribution is quite complex; the total charge of the reaction center is not zero, but the total charge of the whole F2..Si32F32 molecular system is zero. As shown in Fig. 7, the charge on the Si atoms of the F2..Si2Fn reaction centers increases slightly as F2 molecules approach the Si–Si bond due to attraction of electron density by F2 molecules. However, the majority of positive charge on these Si atoms is due to electron displacement to F substitutes that form a part of the reaction center not due to electron displacement to F2 molecules. Thus, the reactivity of the surface is determined by the surface stoichiometry, which, in turn, determines the surface charges and the reaction barrier for F2 dissociation.

FIG. 5.

Geometries of transition states of F2 dissociative chemisorption on reconstructed 100 (a), unreconstructed 100 (b), 110 (c), and 111 (d) surfaces of the Si32F32 cluster.

FIG. 5.

Geometries of transition states of F2 dissociative chemisorption on reconstructed 100 (a), unreconstructed 100 (b), 110 (c), and 111 (d) surfaces of the Si32F32 cluster.

Close modal
FIG. 6.

Reaction pathway of F2 dissociative chemisorption on a 111-oriented surface of the Si32F32 cluster.

FIG. 6.

Reaction pathway of F2 dissociative chemisorption on a 111-oriented surface of the Si32F32 cluster.

Close modal
FIG. 7.

Charge distribution on the Si2Fn reaction centers on 100 (a), 110 (b), and 111 (c) surfaces of the Si32F32 cluster before the reaction with F2 (step 1) and in TSs. To simplify the picture, the atoms of the Si6 chair only are presented, while other atoms were omitted.

FIG. 7.

Charge distribution on the Si2Fn reaction centers on 100 (a), 110 (b), and 111 (c) surfaces of the Si32F32 cluster before the reaction with F2 (step 1) and in TSs. To simplify the picture, the atoms of the Si6 chair only are presented, while other atoms were omitted.

Close modal
Pre-exponential factors in the Arrhenius equations were calculated using the Eyring equation,12 
(1)
where kB and h are Boltzmann’s and Planck’s constants, Z v i b T S and Z v i b S i 32 F 32 are vibrational partition functions of the TS geometry and the isolated Si32F32 cluster, and Z t o t F 2 is the total partition function of the isolated F2 molecule. The partition functions in Eq. (1) were calculated using gaussian 16 software. The pre-exponential factor A in Eq. (1) is a function of temperature; therefore, it was fitted using the standard form in a temperature range from 298.15 to 1000 K,
(2)
The rate of the surface reaction can be described either as a reaction probability or in the standard Arrhenius form,
(3)
where m and CF2 are the mass and density of F2, Ea is the activation energy of the reaction, and ρs is the surface site density. Thus, the probability γ of F2 dissociative chemisorption can be calculated using the following equation:
(4)
where γ 0 ( T ) = 2 π m k B h Z v i b T S Z v i b S i 32 F 32 Z t o t F 2 ρ s T 0 depends on temperature because the partition functions are functions of temperature. Hereinafter, we assume that T0 = 298.15 K. γ 0 ( T T 0 ) n 2 is a function, where γ 0 and n2 parameters were chosen to fit calculated γ 0 ( T ) T T 0 values at a temperature range from 298.15 to 1000 K. The values of Ea, A, γ 0 , n1, and n2 can be found in Table I, where these parameters are substituted into the expression of rate constants and probabilities,
(5a)
(5b)
TABLE I.

Rate constants and probabilities of F2 dissociative chemisorption on (100), (110), and (111) surfaces of an Si32F32 cluster. The rate constants and probabilities are expressed in Arrhenius form according to Eqs. (5a) and (5b). E a exp is the experimental value of the activation energy. r-100 and u-100 indicate the (100) surface with reconstruction and without reconstruction, respectively.

SurfaceA′ (m3/s)n1γ0n2Ea (eV)Eaexp (eV)
r-100 8.82 × 10−21 2.20 0.0011 1.60 0.13 0.1616 
u-100 1.23 × 10−20 2.20 0.0016 1.70 0.31 0.398 
110 7.52 × 10−20 2.50 0.0096 1.96 0.35 — 
111 3.90 × 10−20 2.50 0.0050 1.96 0.57 0.6117 
SurfaceA′ (m3/s)n1γ0n2Ea (eV)Eaexp (eV)
r-100 8.82 × 10−21 2.20 0.0011 1.60 0.13 0.1616 
u-100 1.23 × 10−20 2.20 0.0016 1.70 0.31 0.398 
110 7.52 × 10−20 2.50 0.0096 1.96 0.35 — 
111 3.90 × 10−20 2.50 0.0050 1.96 0.57 0.6117 

The presence of the biradical structure in Fig. 6 is consistent with dissociative chemisorption via single atom abstraction as proposed by Tate et al.,13,14 in which only one atom of F2 forms an Si–F bond, while the other F atom desorbs into the gas phase [channel A in Fig. 4 and product A in Fig. 6]. Channel B in Fig. 4 and product B in Fig. 6 correspond to the reaction channel of dissociative chemisorption, where both atoms of the F2 molecule adsorb on the silicon surface resulting in two Si–F bonds. Note that molecular dynamic simulations by Carter et al.15 showed that both reaction channels yielding product A and product B are present, and they are the dominant reaction channels on a clean, unpassivated Si(100) surface. We expect that the reaction channel with single atom abstraction decreases the selectivity of orientation-dependent etching because one of the F atoms of the F2 molecule (which initially desorbs into the gas phase) is redeposited on the substrate and nonselectively etches Si(100), Si(110), and Si(111) surfaces.

As mentioned in the Introduction, Mucha et al.8 measured the rate of silicon etching by F2 gas. Unfortunately, they did not mention the orientation of the silicon surface exposed to the reactants. Nevertheless, we can compare our etch rate (R) calculated using Eq. (6) (Sec. II A) with the measured R by Mucha et al.,
(6)
(7)
where M(Si) is the molar mass of silicon, p(Si) is the density of bulk silicon, NA is Avogadro’s number, ps is the surface site density, and A and Ea are the pre-exponential factor and activation energy of F2 dissociative chemisorption on an Si32F32 cluster (Sec. II A).

The results are presented in Fig. 8, which shows that our calculations give good agreement with experimental data if we assume that the exposed surface in the experiment is the Si(100) facet or the Si(110) facet. [We arbitrarily chose the density of n(F2) to be equivalent to 1 Torr partial pressure in order to present the result in convenient units, monolayers per second.] Note that the effect of atomic F released by the single atom abstraction mechanism is not considered in our calculation of the etch rate in Eq. (7) and Fig. 8.

FIG. 8.

Calculated etch rate of unreconstructed Si(100), Si(110), and Si(111) surfaces by 1 Torr F2 in monolayers per second (ML/s), compared to the measured etch rate by Mucha et al. (Ref. 8) in solid red.

FIG. 8.

Calculated etch rate of unreconstructed Si(100), Si(110), and Si(111) surfaces by 1 Torr F2 in monolayers per second (ML/s), compared to the measured etch rate by Mucha et al. (Ref. 8) in solid red.

Close modal

Pullman et al.16 experimentally studied dissociative chemisorption of F2 on an Si(100)(2 × 1) surface saturated with a single monolayer of fluorine by exposing the fluorine-saturated surface to supersonic F2 beams of variable energy. They found that no reaction occurs below 0.16 eV of incident energy. Note that this experiment aimed to study the reaction of F2 dissociative chemisorption without subsequent etching. Therefore, we assume that the studied reaction proceeded on initially relaxed Si(100) with surface reconstruction. Indeed, our calculated reaction barrier for F2 dissociative chemisorption on the reconstructed Si(100) surface (0.13 eV) is close to the measured threshold value of F2 incident energy (0.16 eV). In other words, the measured threshold value of F2 incident energy is determined by the barrier of F2 dissociative chemisorption on the reconstructed surfaces.

The reaction of molecular fluorine with an Si(111) surface was studied by Tatsumi and Hiroi17 in an ultrahigh vacuum reactor. They found that the effective activation energy for the surface reactions of molecular fluorine leading to Si(111) surface etching at temperatures below 580 °C was 0.61 eV. According to our calculations, the reaction barrier for F2 dissociative chemisorption on Si(111) is 0.57 eV.

We also performed classical molecular dynamics (MD) simulations to deepen our understanding of crystallographic orientation-dependent etching of Si by F2. In these simulations, Si–F interactions are described using a reactive empirical bond order (REBO) potential. These types of force fields are commonly used to simulate covalently bonded materials (such as Si) as well as their reactions with a variety of gaseous species. We use the REBO potential parameterized by Humbird and Graves.18 

In order to utilize the MD code in an efficient manner, we simulate the etching process by a series of “impact simulations.” These simulations consist of a semi-infinite Si slab with a vacuum space above the slab in the z direction. The Si slab consists of Si atoms in a diamond cubic lattice. Periodic boundary conditions are imposed in x and y directions to make the slab semi-infinite. The bottom two layers are fixed to prevent drift of the slab due to incoming F2 impacts. During an “impact simulation,” an F2 molecule is placed in a random position in the vacuum space above the Si slab. The height of the molecule is chosen such that it is just outside the interaction distance of the Si slab. The velocity components of F2 are randomly sampled from the Maxwell–Boltzmann distribution at 300 K. We only consider molecules with a negative z component of velocity, so the molecule will impact the Si slab. Next, a microcanonical ensemble (constant number of atoms, constant volume, and constant total energy) MD simulation is run lasting approximately 2 ps. After the trajectory is complete, species that have been etched or sputtered are deleted from simulation. In addition, species that are weakly bound to the surface are also deleted. After this, a Berendsen thermostat19 is applied to the simulation cell to remove excess energy introduced by the incoming species and to maintain the temperature of the Si slab. More information on the thermostat procedure and product deletion routines can be found in previous studies.20,21 This procedure is repeated until the desired fluence of F2 is reached. We consider Si slabs with different crystal facets facing the vacuum space to study the different etching behavior of the facets. The surface area for the Si slab with the (100) surface exposed (both unreconstructed and reconstructed) is about 472.5 Å2. For the slab with the (110) surface exposed, the surface area is about 626.4 Å2. The surface area for the Si slab with the (111) surface exposed is roughly 613.8 Å2. The depth of each cell is large enough such that no F2 molecules will interact with the fixed layer. The lattice constant in all cells corresponds to diamond cubic Si at 300 K. Even though we consider temperatures higher than 300 K, the lattice constant remains the same in our simulations. In reality, the crystal will expand as the temperature is raised. However, because the thermal expansion of Si is very small (the lattice constant increases by about 0.5% from 298.5 to 1513.2 K22), we ignore this expansion in our simulations.

Our classical MD simulations did not show silicon etching at temperatures below 900 K. (F2 bounced off of the silicon surfaces every time.) In order to explain the absence of etching, we performed intrinsic reaction coordinate (IRC) DFT calculations of F2 dissociative chemisorption on Si32 clusters for all TSs shown in Fig. 3. IRC calculations follow the steepest descent path from the TS to the reagent and product valleys. The same reaction pathways were recalculated using the REBO classical MD potential. As shown in Figs. 9(a)9(c), very high barriers appear on the (100) and (110) reaction paths recalculated by the classical MD potential, which do not appear on the DFT-calculated reaction paths. The (111) reaction path, on the other hand, is quite accurately reproduced by the REBO potential.

FIG. 9.

Reaction path of F2 dissociative chemisorption on reconstructed (100) (a), (110) (b), and (111) (c) surfaces of the Si32 cluster calculated by DFT and recalculated with the REBO classical MD potential. Inverse reaction rates on reconstructed 100 (dash-dotted line), unreconstructed 110 (dashed line), and 111 (solid line) surfaces were calculated by DFT (d).

FIG. 9.

Reaction path of F2 dissociative chemisorption on reconstructed (100) (a), (110) (b), and (111) (c) surfaces of the Si32 cluster calculated by DFT and recalculated with the REBO classical MD potential. Inverse reaction rates on reconstructed 100 (dash-dotted line), unreconstructed 110 (dashed line), and 111 (solid line) surfaces were calculated by DFT (d).

Close modal

The lack of etching observed in molecular dynamics simulations at temperatures below 900 K can be explained by high reaction barriers. The reactions are very slow below 900 K and, as a result, cannot be simulated by classical MD in a reasonable amount of time. In the case of Si(100) and Si(110) surface etching, the barriers are overestimated and additional fitting of the potential would be required for Si + F2 chemistry in order to correct this. Without reparameterization, the MD potential would be unable to simulate the anisotropic etching described earlier in the paper. The reaction barrier for F2 dissociative chemisorption on Si(111) calculated by the REBO potential is very close to the DFT value (0.61 vs. 0.57 eV). However, the inverse reaction rate (timescale of the reaction) is still higher than 1 ns at temperatures below 900 K [see Fig. 6(d)]. The etching probabilities calculated by classical MD and the probabilities of F2 dissociative chemisorption calculated by transition state theory (TST) can be found in Fig. 10.

FIG. 10.

Probabilities of F2 dissociative chemisorption on an Si32F32 cluster calculated by TST under the DFT approach and probabilities of silicon slab etching calculated by classical MD for (100), (110), and (111) silicon surfaces.

FIG. 10.

Probabilities of F2 dissociative chemisorption on an Si32F32 cluster calculated by TST under the DFT approach and probabilities of silicon slab etching calculated by classical MD for (100), (110), and (111) silicon surfaces.

Close modal

As our DFT calculations show, the dissociative chemisorption of F2 on Si(111) proceeds over a significantly higher barrier than the dissociative chemisorption on Si(100) and Si(110) surfaces. This results in a lower reaction probability [Fig. 10] and, hence, a lower etch rate for the Si(111) surface. We also demonstrate that etching of the (100) surface with reconstruction is faster than etching on the (100) surface without reconstruction. We assume that the removal of surface layers by fluorine proceeds without reconstruction. Thus, it is equally probable that the F2 molecule dissociates on unreconstructed (100) and (110) surfaces, so etching in the (100) and (110) directions proceeds at the same rate. The low etch rate of the Si(111) surface, by comparison, explains the orientation-dependent etching that was used by Kafle et al.3–6 for texturing silicon surfaces during black silicon production.

We attribute the high etch rate of Si(100) and Si(110) to the fact that these surfaces are passivated by a larger number of F atoms per surface Si atom compared to Si(111) surfaces. The electron density is displaced from Si atoms to more electronegative passivating F atoms, resulting in a partial positive charge on Si atoms [Fig. 11]. (This effect is known as the inductive effect in organic chemistry). The amount of positive charge on a surface increases with “n,” and as a result, Si(100) and Si(110) surfaces accumulate larger amounts of positive charge relative to the Si(111) surface. Thus, the reaction barrier for dissociative chemisorption of molecular fluorine is smaller for Si(100) and Si(110) surfaces compared to Si(111) surfaces [Fig. 11(b)]. An F2 molecule approaching the silicon surface becomes negatively charged, attracting electron density from surface Si atoms. As a result, F2δ− is more strongly attracted to Si(100) and Si(110) surfaces than to the Si(111). This leads to observed fast etching in (100) and (110) directions and slow etching in the (111) direction.

FIG. 11.

Electron displacement (red arrow) leading to δ1 + δ2 charges on the Si2Fn reaction centers caused by electronegative F substitutes on F-terminated Si(100), Si(110), and Si(111) surfaces (a). The calculated δ1 + δ2 charge on Si–Si dimer of the Si2Fn reaction center on Si(100), Si(110), and Si(111) surfaces and the barriers (Ea) of F2 dissociative chemisorption on these dimers (b).

FIG. 11.

Electron displacement (red arrow) leading to δ1 + δ2 charges on the Si2Fn reaction centers caused by electronegative F substitutes on F-terminated Si(100), Si(110), and Si(111) surfaces (a). The calculated δ1 + δ2 charge on Si–Si dimer of the Si2Fn reaction center on Si(100), Si(110), and Si(111) surfaces and the barriers (Ea) of F2 dissociative chemisorption on these dimers (b).

Close modal

Our simulations show that the activation barriers of F2 dissociative chemisorption are 0.31 eV on Si(100), 0.35 eV on Si(110), and 0.57 eV on Si(111). Finally, we collect calculated parameters for rate constants and probabilities of F2 dissociative chemisorption on silicon surfaces in Table I.

Orientation-dependent etching of silicon via molecular F2 has been studied using quantum chemistry methods. Activation barriers, reaction rates, and probabilities for F2 dissociative chemisorption on (100), (110), and (111) surfaces were calculated. It was shown that the reaction barrier of F2 dissociative chemisorption is a function of the surface stoichiometry, which, in turn, determines the amount of positive charge on surface Si atoms. As a result, the etching of Si(111) is significantly slower than (100) and (110) surfaces. Our simulation results are consistent with previously published experimental data and explain the mechanism of orientation-dependent etching of Si by F2 gas.

Additionally, we describe two reaction channels of F2 dissociative chemisorption. We expect that the desorption of F atoms during F2 dissociation is significant during the etching process. This is consistent with dissociative chemisorption via single atom abstraction, which was proposed previously. We expect that the reaction channel via single atom abstraction causes nonorientation-dependent etching with the isotropic profile.

We also used molecular dynamics simulations to investigate the suitability of a REBO potential for modeling silicon etching via molecular F2. While the REBO potential reasonably described F2 dissociative chemisorption on Si(111), it predicts unrealistically high reaction barriers for dissociative chemisorption on Si(110) and Si(100). This results in very slow etching rates and an inability to reproduce the anisotropic etching mechanism studied in this work. In the future, molecular dynamics modeling of this process will require reparametrized potentials that accurately describe orientation-dependent reaction barriers.

The research described in this paper was conducted under the Laboratory Directed Research and Development (LDRD) Program at Princeton Plasma Physics Laboratory, a national laboratory operated by Princeton University for the U.S. Department of Energy under Prime Contract No. DE-AC02-09CH11466. The United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.

In addition, this research used computing resources on the Princeton University Adroit Cluster and Stellar Cluster. The authors gratefully acknowledge discussions about the classical MD code with David Humbird (DWH Process Consulting).

The authors have no conflicts to disclose.

Omesh Dhar Dwivedi: Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Yuri Barsukov: Conceptualization (equal); Investigation (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Sierra Jubin: Investigation (equal); Writing – original draft (equal); Writing – review & editing (equal). Joseph R. Vella: Investigation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Igor Kaganovich: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article and from the corresponding author upon reasonable request.

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