Theoretical Investigation of Ge(100) Nitridation by Nitric Oxide

Article pubs.acs.org/JPCC

Theoretical Investigation of Ge(100) Nitridation by Nitric Oxide: Monomeric or Dimeric Dissociation? Jing Hui He,† Wei Mao,† Jing Kun Gao,‡ and Guo Qin Xu*,† †

Department of Chemistry, National University of Singapore, 3 Science Drive 3, Singapore 117543 and Department of Civil and Environmental Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, Pennsylvania 15213, United States

‡

ABSTRACT: Oxynitridation of Ge surfaces by nitric oxide (NO) is an important method to synthesize the gate dielectric for Ge-based microelectronics. Understanding the atomic processes of NO oxynitridation on Ge(100) is highly desirable to improve the N incorporation efficiency. Adsorption and dissociation of NO on Ge(100) were investigated on periodic models using DFT calculations. The nondissociative precursors can transform into various dissociative products, resulting in lowering the system energy as well as increasing the coordination numbers of N and O atoms. The transition state search shows that both monomeric and dimeric dissociative pathways are possible. The interdimer route for monomeric dissociation is unfavorable at low temperatures due to the relatively large barriers. In contrast, the intradimer dissociation is preferable due to the existence of an intermediate state, in which the N−O bond is significantly weakened. When a high concentration of NO molecules is adsorbed on Ge(100), three dimeric adsorption structures with two O atoms attached on surfaces are thermodynamically and kinetically favorable to form but difficult to dissociate even at room temperature. Their further release of N2 at elevated temperatures would deteriorate the nitrogen incorporation ratio. Our results are useful for optimizing the oxynitridation of Ge(100) by nitric oxide. grammed desorption (TPD).15 The dosed NO molecules were found to desorb after an onset dosage, resulting in a peak around 220 K. Besides this large molecular desorption peak, a small desorption feature of N2 was also found at 180−190 K, indicating that the minority of NO molecules undergoes dimeric dissociation. In view of increasing the N incorporating ratio, the release of N2 during the adsorption process should be suppressed. Electron-stimulated desorption (ESD) of NO and N2O dosed on Ge(100) leads to the release of N2 and N2O, further suggesting the possible dimerization of NO on Ge(100) during adsorption.16,17 Nevertheless, the existence of NO dimers is yet to be verified by more evidence, as this dimeric mechanism simply ignored the contribution from monomeric adsorption and dissociation of isolated NO molecules. Meanwhile, this dimeric mechanism is different from the case of NO on Si(100), where molecules dissociate monomerically at 20 K18 and completely dissociate above 150 K.19 Given the structural similarities between Ge(100) and Si(100), the discrepancies in the mechanism and reactivity of NO are noticeable. Since neither of the other experimental surface tools, X-ray photoelectron spectroscopy (XPS) nor highresolution electron energy loss spectroscopy (HREELS), provided convincing evidence on dimeric adsorption,15

1. INTRODUCTION As the development of Si-based transistors and integrated circuits has been increasingly difficult through the conventional scaling technique, germanium has received renewed attention due to its intrinsically higher carrier mobility than that of Si.1,2 However, the native oxide of Ge, GeO2, is of high water solubility, high density of defects, and low thermal stability, not suitable to serve as the gate dielectric. Therefore, finding a good gate dielectric material becomes a key step in the fabrication of Ge-based circuits. Germanium oxynitride (GeOxNy) is a promising candidate3 because it is able to improve the stability of the Ge substrate against thermal and wet treatment,4,5 to suppress the diffusion of Ge into the high-κ metal-oxide layer,6 and to reduce the leakage current.3 The most straightforward method to grow germanium oxynitride is to anneal Ge substrates in plasma or wet atmosphere of nitric oxide.7−13 This method does not induce unwanted foreign elements, thus the synthesized germanium oxynitride is of high purity. However, compared to other nitridation gases, the nitridation efficiency, evaluated by the N incorporation ratio of nitric oxide, is still low.14 To improve the nitridation efficiency, it is necessary to understand the atomic mechanism how NO molecules adsorb, dissociate, and incorporate N atoms into Ge surfaces. Particularly, the focus is on the reactions of NO on Ge(100) due to its technological importance in microelectronics. The adsorption and desorption of nitric oxide on Ge(100) was investigated experimentally using temperature-pro© 2013 American Chemical Society

Received: June 6, 2013 Revised: July 19, 2013 Published: July 23, 2013 17111

dx.doi.org/10.1021/jp405602q | J. Phys. Chem. C 2013, 117, 17111−17118

The Journal of Physical Chemistry C

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theoretical calculation would be an alternative method to predict the reaction products and related reaction mechanisms. In this study, we investigated the atomic processes in the initial stages of NO adsorption and dissociation on the Ge(100) surface using DFT calculations. Various monomeric and dimeric precusors/products were searched, and the reaction pathways among them were predicted by searching the transition states.

2. THEORETICAL METHODS All calculations were performed using software CASTEP in Materials Studio (version 5.5) of Accelrys.20 Spin-unrestricted DFT and norm-conserving pseudopotentials were employed. The generalized gradient approximation (GGA) with Perdew− Burke−Ernzerhof (PBE) parametrizations21 were used to estimate the exchange-correlation effect. The kinetic energy cutoff was 330 eV. A 2 × 4 × 1 Monkhorst−Pack grid was applied for Brillouin zone sampling.22 The force convergence criteria of geometric optimization was 0.02 eV/Å. A thermal smearing of 0.025 eV was used to accelerate the SCF convergence. The Ge(100) surface was simulated by periodic slabs of c(4 × 2) reconstruction with six layers of Ge atoms separated by a vacuum layer of 15 Å in thickness. Each layer consists of eight Ge atoms or four Ge dimers. Two bottom Ge layers without hydrogen saturation were frozen during geometric optimization. The lattice constant of Ge was set at 5.712 Å according to the relaxation of bulk crystal. The Broyden−Fletcher−Goldfarb−Shanno (BFGS) method was used in geometric optimization, and a linear synchronous transit/quadratic synchronous transit (LST/QST) method was employed to find transition states. The found transition states were further confirmed by the existence of one imaginary frequency (Gamma point) connecting the regents and products. To completely search nondissociative precursors of NO on Ge(100), we considered 30 initial adsorption structures in Figure 1a−d. The initial adsorbing sites include dimer atoms (1, 2), troughes between dimers (3, 4) or between dimer rows (5, 6, 7), and the bridge of dimers (8) in Figure 1a. NO stands on each position with two possible orientations: N-attached vertically on the surface (NT1−NT8) or O-attached (OT1− OT8, Figure 1b). NO may also be bound parallel to dimer atom pairs or back-bonds with N (NPI−NPVI) or O (OPI− OPIV) at the upper positions (Figure 1c and d). During dissociation, the N−O bonds cleave, and the N atoms may bind 1/2/3/4 Ge atoms, whereas O may connect one or two Ge atoms, respectively. Twelve dissociative products (not shown here) were found, and their geometric structures were discussed. In dimeric adsorption, two NO molecules dimerize first to form the cis-ONNO chain. The cis-ONNO chain bridges a pair of Ge atoms (OO1−OO4) through two O atoms or through two N atoms (NN1 and NN2) in Figure 1f.

Figure 1. Schematic diagram of possible adsorbing sites and orientations of NO on Ge(100)-c(4 × 2). (a) Vertical configurations of NO on Ge(100) with N-attachment or O-attachment and (b) their possible adsorbing sites from 1 to 8. (c) Parallel configurations of NO on Ge(100) with N or O at an upper position and (d) their bidentate binding sites marked by the arcs 1 to 6. (e) Dimeric adsorption of ONNO chains with NN or OO attachment and (e) their bidentate binding sites marked by the arcs 1 to 4.

Figure 2. Top and side views of NO monomeric precursors on the Ge(100)-c(4 × 2) surface. (a) N12−O3: N inserts into a dimer. (b) N17−O. (c) N1−O3. (d) N1−O2. (e) N12−O2. (f) N−O4. The products are named by: “N” + “the labels of N binding Ge atom” + “O”+ “ -” + “the labels of O binding Ge atoms” throughout the paper. “-” indicates a nondissociative product with a N−O bond. The numbers 1−4 label four dimer atoms, and 5−10 label six sublayer atoms. Blue balls: N atoms. Red balls: O atoms. Cyan balls: Ge atoms. Sublayers are not shown for clarity through this paper. The structural parameters are listed in Table 1.

3. RESULTS AND DISCUSSION 3.1. Monomeric Adsorption. 3.1.1. Precursors. As the starting point of dissociations, nondissociative precursors of NO were worthy to be investigated. After geometric optimizations, six stable nondissociative structures were found and shown in Figure 2. Their energies and structural parameters were listed as well in Table 1. In these structures, the N−O bond lengths increase from 1.10 Å in the free state to 1.33−1.44 Å, indicating significant weakening of N−O. The

adsorption energies vary from −0.08 to 1.01 eV, lower than that of NO on Si(100) (1.67−1.97 eV) by ∼1 eV.23 The lower 17112



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O and N−O4 have low barriers of 0.10 and 0.12 eV, respectively. Because of the negative binding energies, they prefer to desorb from Ge(100) even at low temperatures. 3.1.2. Dissociative Products. On the basis of the nondissociative precursor, we first consider the possible products from single NO molecules, namely, the monomeric products. The monomeric dissociative products could be divided into three groups: N-2-fold, N-3-fold, and N-4-fold, according to the coordination number of N in Figure 3. When the N atom of

Table 1. Energies and Bond Lengths of Monomeric Precursors bond lengths (Å) configurations N12−O3 N17−O N1−O3 N1−O2 N12−O2 N−O4 free NO

system energies (eV) −0.64 0.08 −0.67 −1.01 −1.00 0.05

N−O

N−Ge

O−Ge

1.44 1.33 1.41 1.42 1.44 1.38 1.10

1.89 (1)a, 1.87 (2) 1.84 (1), 1.88(7) 1.96 (1) 1.97 (1) 1.83(1), 1.91(2)

1.74 (3) 1.76 (2) 1.74 (2) 1.70(2) 1.72 (4)

a

Numbers in parentheses indicate the bound Ge atom labeled in Figure 2a.

reactivity of Ge could be attributable to the orbital size mismatches of 4s and 4p from Ge with 2s and 2p from N/O, leading to less effective orbital overlapping. NO can insert into a dimer bond or a back-bond with its N end, forming N12−O3 or N17−O. Although the corresponding N−O and N−Ge lengths are nearly the same in these two structures, they differ significantly in the binding energies. N12−O3 is more stable than the free system by 0.64 eV, whereas N17−O is slightly less stable than the interaction-free system by 0.08 eV. The higher binding energy of N12−O3 than that of N17−O mainly results from the formation of an extra O−Ge bond, which connects the O atom with a neighboring dimer. The formation of the O−Ge bond further weakens the N−O bond to 1.44 Å in N12−O3. However, the analogous structure of N12−O3 on Si(100) only appears as a transition state in the process of interdimer dissociation.23 In addition, the configuration of NO vertically inserting into a dimer with the N end, reported on Si(100), was not found on Ge(100). In Figures 2c and d, NO bridges two dimer atoms in parallel configurations, respectively. The intradimer product N1−O2 has the highest binding energy among the six nondissociative products (1.01 eV), larger than that of the interdimer binding N1−O3 (0.67 eV). Since the corresponding N−O, N−Ge, and O−Ge bond lengths are nearly the same in these two models, the difference in energies probably arises from the substrate. In N1−O2, NO binds to one dimer and eliminates two dangling bonds, leaving the neighboring dimer intact. In contrast, in N1−O3, NO interacts with two dimers, releasing two unreacted Ge dimer atoms, which are of higher energies than an unreacted dimer. Figure 2e shows another intradimer adduct, in which NO is tilted and twisted on the dimer, no longer parallel to the dimer. Although in this structure the coordination number of N becomes three and the N−Ge and O−Ge bond lengths are shorter than that in N1−O2, the energy is the same as N1−O3. This structure is an important intermediate in the dissociative processes, which we will discuss later. Finally, Figure 2f is the only O-attached nondissociative adsorption configuration. The O-end of NO is unable to insert into any dimer bond or backbond due to the limited valence number of O. Although the adsorption energy is close to zero, N−O4 cannot be simply considered as the physisorption state as the N−O bond is significantly elongated. The N-end may be activated and can accept another NO molecule. We also searched the formation barriers for these nondissociative products. N12−O3, N1−O3, and N1−O2 can be directly formed without any barriers. On the other hand, N17−

Figure 3. Structures of monomeric dissociative products. Blue balls: N atoms. Red balls: O atoms. Cyan balls: Ge atoms. The structural parameters are listed in Table 2.

NO inserts into a dimer, the O atom can insert into back-bonds (N12O48, N12O28) or dimer bonds (N12O34). Once the N atom inserts into a back-bond, the O atom can break into a dimer (N17O12, N17O34). Among these five models, the most stable one is N12O28, in which N and O insert into a dimer and its adjacent back-bond. Compared to N12O48 with N and O inserting into a dimer and an isolated back-bond, respectively, N12O28 is more stable by 0.15 eV. This promotive effect of an inserted N between a dimer to the accommodation of O at the adjacent back-bond was previously reported for NO on Si(100).24 One plausible explanation is that the inserted N expands the dimer atom outward, lowering the stress to be generated by the insertion of oxygen. For other models in which the 2-fold N and O atoms are isolated from each other, their binding energies are around 2.6−2.9 eV. The structures with N inserting into a dimer (N12O34, N12O48) 17113



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Table 2. Energy and Bond Lengths of Dissociative NO Adsorption Products bond length (Å) configurations

a

system energy (eV)

N12O34 N12O48 N12O28 N17O12 N17O34

−2.89 −2.85 −3.01 −2.65 −2.70

N127O2 N127O28 N157O37 N157O2 N157O28 N157O12

−1.61 −2.54 −3.35 −1.71 −2.20 −3.29

N1257O12

−3.50

N−Ge N-2-fold 1.74(1), 1.73(1), 1.74(1), 1.69(3), 1.60(1), N-3-fold 1.75(1), 1.80(1), 1.83(1), 1.82(1), 1.79(1), 1.83(1), N-4-fold 1.96(1),

O−Ge

1.72(2)a 1.75(2) 1.69(2) 1.78(8) 1.68(2) 1.91(2), 1.81(2), 1.88(5), 1.86(5), 1.92(5), 1.88(5),

1.69(3), 1.62(4), 1.60(2), 1.62(1), 1.71(4), 1.88(7) 1.94(7) 1.88(7) 1.90(7) 1.97(7), 1.88(7),

1.55(2) 1.63(2), 1.66(3), 1.55(2) 1.62(2), 1.65(1),

2.01(2), 2.05(5), 2.06(7)

1.59(4) 1.66(8) 1.68(8) 1.67(2) 1.78(8)

1.68(8) 1.67(7) 1.66(8) 1.62(2)

1.67(1), 1.64(2)

Numbers in parentheses indicate the bound Ge atoms labeled in Figure 2a.

Table 3. Estimated Attempting Frequencies (v) of NO Dissociative Processes at Different Temperatures estimated attempting frequencies (Hz)a temperature (K) 20 180 300 a

Ea = 0.2 eV −38

2 × 10 1 × 107 2 × 109

Ea = 0.4 eV

Ea = 0.6 eV

−89

−139

8 × 10 3 × 101 1 × 106

3 × 10 8 × 10−5 4 × 102

Ea = 0.8 eV −189

1 × 10 2 × 10−10 2 × 10−1

Ea = 1.0 eV 1 × 10−240 1 × 10−16 8 × 10−5

v = v0e−Ea/kBT, v0 = 5 THz.

20/180/300 K are estimated in Table 3. These three temperatures correspond to the reported conditions at which NO on Si(100) starts to dissociate,18 NO nondissociatively desorbs from Ge(100),15 and room temperature, respectively. One can find that at 20 K the rates of all the dissociative processes with barriers larger than 0.2 eV are negligible. At 180 K, reactions with barriers of around 0.2 eV are facile to occur with an attempting frequency much greater than 1 Hz, and reactions with barriers around 0.4 eV may have visible rates. The reactions with barriers equal to or larger than 0.6 eV are still inactive at this temperature. Once a reaction barrier is around or larger than 1 eV, the reaction cannot “occur” even at room temperature. Although these are rough estimations, nevertheless, they should be valid for our qualitative discussion. 3.2.1. Interdimer Dissociations. The possible dissociation involving two dimers was investigated. We found several dissociative channels starting from the nondissociative products: N1−O3, N17−O, and N12−O3 in Figure 4. First, N17−O and N1−O3 may dissociate onto two dimers, producing the interdimer products: N17O12, N17O34, and N157O34. However, these channels have large energy barriers (0.71−1.02 eV) as well. Since the desorption of N17−O is almost barrierless and exothermic (binding energy: −0.08 eV), it is highly likely that NO in N17−O desorbs from the Ge surfaces before dissociation. Apart from direct monomeric dissociation, N1−O3 may first transit to another nondissociative precursor N12−O3. Then, N12−O3 can further dissociate to N12O48, N12O34, and N12O28. Although these dissociative products are highly exothermic (>2.2 eV), their reaction barriers are too high (>1 eV) to be surmounted even at room temperature. These barriers are much higher than that of similar interdimer dissociation of NO on Si(100), where a barrier of 0.17 eV was reported.23 This is attributable to the

are slightly more favorable than those with N inserting into a back-bond (N17O12, N17O34). When the N atom is coordinated by three Ge atoms, the system can be further stabilized. As shown in Figure 3, the N atom can incorporate into the Ge surface and be surrounded by one dimer atom and two sublayer atoms (N157O37, N157O2, N157O28, and N157O12) or one dimer and one sublayer atom (N127O2 and N127O28). The promotive effect of incorporated N to the insertion of O appears again in these structures. As listed in Table 2, the models with adjacent N−Ge and O− Ge bonds (N157O37 and N157O12) are of higher binding energies than N157O28. Among all monomeric dissociative structures, the N--fold model N1257O12 has the highest binding energy. In this model, N incorporates into the subsurface, being surrounded by a tetrahedron composed of two dimer atoms (1, 2) and two sublayer atom (5, 7). Four N−Ge bonds are nearly equal in length (1.96−2.06 Å), larger than that of N-2/3-fold models. The top dimer atom (1) is pushed outward, producing a protrusion with the oxygen atom. The formation of 4-fold coordinated nitrogen is abnormal because nitrogen is usually 3fold coordinated in neutral molecules. Thus, its existence needs further experimental verification. 3.2. Pathways of Monomeric Dissociations. We intend to search the favorable pathways using estimated reaction rates by calculating the energy barriers of each process between those products. The reaction rates, evaluated by attempting frequencies of these processes, can be estimated using the Arrhenius equation: v = v0e−Ea/kBT, where v0, Ea, ka, and T refer to the prefactor, energy barrier, Boltzmann constant, and temperature. If the prefactor is assumed to be 5 THz as a typical phonon frequency of bulk Ge,25 the attempting frequencies for the barriers of 0.2, 0.4, 0.6, 0.8, and 1.0 eV at 17114



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O) atom on the top of the dimer atom can transfer to the neighboring back-bond, leaving the O (or N) atom to bridge the dimer and forming N17O12 (or N12O28). The direct transformation of N1−O2 to N17O12 and N17O28 has barriers as high as 1 eV, unlikely to occur at room temperature. Alternatively, N1−O2 may first transit to the intermediate N12−O2 by overcoming a small barrier of 0.39 eV. A similar structure was reported for NO on Si(100).23,26 Such a twisted configuration results in the lower energies of transition states from N12−O2 to N12O28 (0.41 eV) and to N17O12 (0.18 eV). Since N1−O2 and N12−O2 are almost energetically degenerate and have similar N−O bond lengths, it is surprising at a first glance that N12−O2 has a remarkably higher reactivity than N1−O2. In fact, NO molecules in N1−O2 and N12−O2 have different connectivities; therefore, the close bond lengths mean comparable bonding strength. To compare the bonding states of N−O in these two products, we plot their spatial distributions of spin density in Figure 6. As N and O have higher electron affinities than that of Ge, any bonding between Ge and NO would transfer electrons from Ge atoms to antibonding orbitals of the molecule. In N1−O2, the highest occupied molecular orbital which is filled by the unpaired electron is mainly from the molecule. The inset of Figure 6a shows that the single electron remains in the π* orbital of NO, like in the free state. In contrast, N12−O2 disperses the spin into the bulk in Figure 6b, indicating the π* of NO has been occupied due to the electron transfer from Ge to NO. This suggests a larger amount of charge transfer in N12−O2 than in N1−O2. Indeed, the Hirshfeld charge analysis shows that N and O carry charges of −0.09 and −0.16 in N1−O2 but −0.14 and −0.19 in N12−O2, respectively. The more electron transfer to the NO antibonding orbital weakens the N−O bonding. The Mulliken bond analysis also shows that NO has a lower bond order (0.18) in N12−O2 compared to N1−O2 (0.38), in good agreement with the spin density results. In short, N12−O2 has weaker N−O bonding, thus it is easier to dissociate than N1−O2. Once the N−O bond in N12−O2 was cleaved, the N and O species can diffuse independently to further stabilize the system. The N atom gradually increases its coordinate number from two in N17O12, to three in N157O12, and finally to four in N1257O12. These conversions all have barriers lower than 0.4, readily occurring at moderately low temperatures. On the other hand, N12O28 can be converted to N127O28 and N157O28 with the increase of the N coordination number. Since N127O28 and N157O28 are less stable than N12O28, the inverse process of N157O28 → N127O28 → N12O28 is more favorable with much lower barriers (0.38 and 0.13 eV). The third dissociative product of N12−O2 is N127O2, in which N turns to be 3-fold coordinated while O is retained as the adatom on the top of the dimer atom. N127O2 can be further converted to the more stable structure of N157O2. The O adatoms in N127O2 and N157O2 can be inserted into backbonds (N127O28 or N157O28) or dimer bonds (N157O12) with similar barriers around 0.6 eV, which means the reaction may be pinned at 180 K. The conversion of the O adatom to the back-bond inserted O was also investigated in the case of O2 adsorption on Ge(100), where a comparable barrier was reported employing a cluster model.27 However, in Figure 4, all products were connected with barriers close to or less than 0.4 eV, which means the monomeric dissociation at low temperature (e.g., 180 K) is possible.

Figure 4. Reaction pathways of NO interdimer dissociations. The system energies in parentheses are relative to the interaction-free system. The arrows indicate the possible reaction ways, and the numbers on the arrows are the reaction barriers. The energies are in units of eV.

large distance between two dimers as well as the less effective orbital overlapping on Ge(100), rendering the barrier higher. In short, the monomeric dissociations in interdimer routes are unlikely to occur due to the high reaction barriers. 3.2.2. Intradimer Dissociations. We moved on to search the intradimer dissociative processes, starting from the nondissociative precursor, N1−O2. The detailed dissociative routes from N1−O2 are summarized in Figure 5. N1−O2 is a stable intradimer adduct with a binding energy of 1.01 eV. The N (or

Figure 5. NO intradimer dissociation from N1−O2. The system energies in parentheses are relative to the interaction-free system, in units of eV. The arrows indicate the possible reaction ways, and the numbers on the arrows are the reaction barriers in units of eV. The structure in the square brackets is a stereoisomer of N12−O2 with the same energy. NO tilts to an opposite direction as in N12−O2. 17115



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Figure 6. Spin densities of structures (a) N1−O2 and (b) N12−O2. The insets show their top views, respectively. The isovalue to plot the isosurfaces is 0.005/Å3. Blue balls: N atoms. Red balls: O atoms. Cyan balls: Ge atoms.

Figure 7. Dimeric adsorption and dissociation of NO on Ge(100). The system energies in parentheses are relative to the interaction-free system including two free NO molecules and the substrate. The arrows indicate the possible reaction ways, and the numbers on the arrows are the reaction barriers. The energies are in units of eV.

3.3. Dimeric Adsorption. If the dosing concentration of NO increases, NO molecules may first dimerize and then react with the Ge(100) surface. The dimerization is accessible for gaseous or weakly bound NO molecules on the Ge(100) substrate such as N−O4 and N17−O, which are of diffusion barriers as low as 0.10 eV. Figure 7 shows the optimized structures of dimeric products. Dimeric ONNO chains may bind to Ge dimers in intradimer (OO1), interdimer (OO2), or crossdimer configurations (OO4). These three reactions are kinetically and thermodynamically favorable with formation energies around −11 eV as well as no formation barriers. The

barrierlessness of these reactions is not surprising because of a concerted [4 + 2] cycloaddition mechanism.28 After adsorption, the N−N distances reduce from 2.15 Å to 1.35−1.59 Å (Table 4), indicating the formation of covalent N−N bonds. Compared to the monomeric dissociations, the binding energies per NO molecule of dimeric products are around 5.5 eV, larger than that of the most stable monomeric dissociative product N1257O37 (3.50 eV). The larger binding energies of OO configurations originate from the formation of two Ge−O bonds and one N−N bond. The only exception is OO3, in which the ONNO chain fails to connect two upper 17116



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4. CONCLUSIONS In conclusion, we have elucidated the atomic processes of NO dissociation on the Ge(100) surface using DFT calculations. Six nondissociative precursors were found with binding energies varying from slightly negative to 1 eV. They can transform into various monomeric dissociative products, resulting in the increase of system binding energies as well as the coordination number of N and O atoms. The transition state search shows that both monomeric and dimeric dissociative pathways exist. The interdimer routes for monomeric dissociations are unfavorable at low temperatures due to energy barriers >1 eV. In contrast, the intradimer dissociation route is preferable due to the existence of an intermediate state N12−O3, which has weak N−O bonding and is easy to dissociate. When high concentrations of NO molecules are adsorbed on Ge(100), NO may dimerize first and bind on Ge(100) in the form of ONNO chains. Three adsorption structures with two O atoms attached on surfaces are thermodynamically and kinetically favorable to form but difficult to dissociate even at room temperature. Under electron stimulation or thermal activation, these dimeric products dissociate and release N2, deteriorating the N incorporation rate in the oxynitridation process. Thus, the dosing concentration of NO should be kept at a low level to avoid the dimeric dissociation. Our study provided a detailed understanding of the atomic processes of NO dissociation on Ge(100). The results would be useful for optimizing the oxynitridation of Ge(100) by nitric oxide.

Table 4. Bond Lengths in Dimeric NO Adsorption Productsa bond lengths (Å) configurations

N−N

interaction-free system NN1 NN2 OO1 OO1−N2 OO2 OO2−N2 OO3 OO4 OO4−N2

2.15 2.19 2.01 1.4 1.19 1.36 1.19 1.59 1.12

N−O 1.10, 1.29, 1.21, 1.42,

1.10 1.05 1.21 1.42

N-G 1.941 1.99, 2.02

1.68, 1.67, 1.68, 1.53,

1.38, 1.39 1.40, 1.40 1.39, 1.39

O−Ge

1.69 1.64 1.68 1.53

1.71 1.71, 1.70 1.40, 1.41

a

Blank entries mean that there is no substantial bonding between those two atoms.

dimer atoms possibly due to a large distance between them. Two NO molecules react with the surface independently, forming a double N−O4 configuration. The OO3 configuration has a higher binding energy per NO molecules, possibly due to the adsorbate−adsorbate interaction. The further releases of N2 from OO1, OO2, and OO4 are highly important in the view of N incorporation ratio in oxynitridation processes. Comparing OO1 with OO1−N2, OO2 with OO2−N2, or OO4 with OO4−N2, the system energies surprisingly do not change significantly. This is because the cleavage of two N−O bonds cancels out the energy gain from the formation of one N−N triple bond. Nevertheless, OO1−N2−B (−13.40 eV) indicates that after desorption of N2 the dative O atoms could incorporate into the Ge surface to further lower the system energies. The transition state search suggests the release of N2 in a concerted way (OO1 → OO1−N2, OO2 → OO2−N2, OO4 → OO4−N2) is unlikely even at room temperature because the barriers are around 2 eV. Alternatively, desorption of N2 via a N2O intermediate state is slightly preferable. In this way, the ONNO chains first break one of their N−O bonds, forming N2O adducts on the surface. Then the desorption of N2 from N2O adducts is much easier with barriers less than 0.56 eV. Nevertheless, the first steps (OO1 → OO1−N2O, OO2 → OO2−N2O, OO4 → OO4−N2O) still have barriers larger than 1 eV. Because of the higher exothermicity of OO1, OO2, and OO4 configurations than any monomeric products, it is also thermodynamically unfavorable to cleave the ONNO chain into two isolated NO monomeric products. Therefore, the ONNO dimers could be trapped on Ge surfaces upon formation at room temperature. Electron stimulation may activate the OO-configurations and help to release N2 and N2O at 180 K as reported.16,17 At higher temperatures in the normal oxynitridation process, N2 will also be released from those OOconfigurations. To enhance the incorporation efficiency of N atoms during nitridation of Ge, the low dosing concentration of NO is necessary to avoid the formation of dimeric products. In contrast to four OO configurations, NN1 and NN2 states both have much smaller binding energies (2.12 and 1.82 eV). The N−N bond lengths (2.19 and 2.01 Å in Table 4) approach that of the gaseous dimeric state, indicating that two NO molecules still interact weakly, unlike in OO1, OO2, and OO4 configurations. Thus we proposed that NN configurations cannot form any energetically competitive chain structure, and the system will react following the monomeric ways.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.H. He thanks Prof. Cheng Han Song for useful discussions. We are grateful to the financial support from the Ministry of Education, Singapore (Grant No. R-143-000-462-112). The calculations were performed on NUS HPC clusters.

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REFERENCES

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Theoretical Investigation of Ge(100) Nitridation by Nitric Oxide

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