A first principles study of H₂S adsorption and decomposition on a Ge(100) surface

Abstract

We employed density functional theory (DFT) calculations to examine the adsorption configurations and possible reaction paths for H₂S on a Ge(100) surface. There are four reaction paths proposed for the decomposition of adsorbed H₂S on a Ge(100) surface and the corresponding structural conformations are studied extensively. The present study shows two new possible products and a detailed reaction mechanism for H₂S adsorption on a Ge(100) surface and the results are compared with our previous study of H₂S adsorption on a Si(100) surface (J. Phy. Chem. C, 115, 2011, 19203). The density of states (DOS) and electron density difference (EDD) analyses are used to illustrate the interaction between S-containing species and surface Ge atoms.

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1. Introduction

Over the past few decades, high mobility semiconductors have been investigated as a replacement for the Si channel due to their potential applications in high-performance metal-oxide-semiconductor (MOS) devices.^1–3 Recently, Germanium (Ge) has attracted much attention because it gives bulk electron and hole motilities at room temperature which are higher than the conventional silicon based materials.^4,5 However, major drawbacks of the application of Ge in these devices are the poor quality of its thermal oxide compared to SiO₂ and the Ge-based MOS devices has high interface state density (D_it) which would result in low carrier mobility in the channel. These limitations can be overcome by the passivation of Ge surface prior to the deposition of the gate dielectric which is a key issue for semiconductor surfaces.^6,7

Also, the practical use of this semiconductor in the devices requires the passivation to prevent oxidation and maintain the surface order during device processing. Sulfur (S) has been shown to be one of the best passivants of semiconductor surfaces.⁴ Anderson et al., reported that the sulfur passivation of the germanium surface via both solution and vacuum deposition techniques.⁸ A sulfur adlayer is deposited on a semiconductor surface through immersion in a solution of (NH₄)₂S⁸ or on its exposure to elemental sulfur or H₂S.⁹ On the other hand, Houssa et al. proposed two approaches for the passivation of Ge surface to promote metal-oxide-semiconductor field-effect transistor (MOSFET).¹⁰ One of two approaches is the exposure of the Ge surface to H₂S, resulting in the formation of S–Ge bonds. Indeed, the Ge energy band gap is free of surface states after H₂S exposure, resulting in the electrical passivation of the surface, which is a crucial requirement for the potential use of Ge in the MOSFET.

Similar to Si(100) and C(100) surfaces, the reconstructed Ge(100)-2 × 1 surfaces consist of dimers connected by a strong σ-bond and a weak π-bond.¹¹ The diamond surface has symmetric dimers with a bond length of approximately 1.4 Å, whereas the Si and Ge surfaces both have larger asymmetric, or tilted, dimers with a bond length of 2.3–2.5 Å.^12–14 Distortion of the dimer bonds induces a charge transfer from the down (electrophilic) to the upper (nucleophilic) surface atom.¹⁵ Such zwitterionic characteristics allow the surface to undergo a nucleophilic/electrophilic reaction, often with direct analogies to the molecular systems. The adsorption of sulfur on Ge(100) surface has been studied both experimentally and theoretically.^16–18

Previously, the S-passivation on Ge(100) surface has been investigated using low-energy electron diffraction (LEED),^8,19 high-resolution electron-energy loss spectroscopy (EELS),²⁰ ultraviolet photoelectron spectra (UPS),²¹ X-ray photoelectron spectra (XPS),²² temperature programmed desorption (TPD),²³ Near edge X-ray absorption fine structure (NEXAFS)²⁴ and multiple internal reflection-Fourier transform infrared spectrometer (MIR-IR).²⁵ Kuhr and Ranke²¹ showed in their UPS study that, H₂S adsorbs dissociatively at 300 K on a Ge surface; then decomposes completely to form sulfur at 550 K. To understand the sulfidation of the Ge(100) surfaces and its possible passivating reactions, we choose H₂S as a passivant to be adsorbed on the Ge(100) surface. In this study, we report ab initio theoretical investigations to provide a complete description of the adsorption effects and thermal decompositions of H₂S on Ge(100) surface. We thereby elucidates possible mechanisms of thermal decomposition on Ge(100) that was more conformed to real surface.

2. Computational details

DFT calculations are performed using the Vienna ab initio simulation package (VASP).^26–28 The Vanderbilt ultra-soft pseudopotential is used to describe the election–ion interactions²⁹ and the electron–electron exchange and correlation contributions by the generalized gradient approximation (GGA) with energy truncated at 300 eV. The Brillouin zone is sampled with Monkhorst-Pack grid, and the calculations were performed with (4 × 2 × 1) Monkhorst-Pack mesh k-points. We optimized the structures based on the conjugate gradient-minimization scheme taking into consideration of spin polarization. The validities of all the optimized structures and determined transition states (TSs) are checked through normal-mode frequency analysis. For a real minimum structure, all frequency must be positive; TS must have one imaginary frequency corresponding to the reaction coordinate. The clean surfaces are then modeled in the form of a slab. The c(4 × 2) unit cell consisted of nine atomic layers separated by a 20 Å vacuum to prevent interactions between the surface adsorbates and the preceding slab. The optimized geometry of the model Ge(100) surface considered in this study is depicted in Fig. 1.

Fig. 1 The optimized structure of Ge(100)-c(4 × 2) surface: (a) front view, (b) side view and (c) top view.

In the structural optimizations, the positions of the last three Ge layers along with the H-passivated layer on the bottom are fixed upon adsorption of H₂S and the remaining substrate atoms are allowed to relax with the adsorbates. To economize computing time, only the upper two atomic layers of the surface and adsorbate are relaxed in the vibrational frequency calculations. The adsorption energies are obtained by

E_ads = E_Total − (E_Gas + E_Surface)

in which E_Total, E_Gas and E_Surface are the respective calculated electronic energies of the adsorbed species on the surface, a gaseous molecule, and a clean surface. A negative value for E_ads indicates an exothermic adsorption. The relative energies (E_rel) are defined as

E_rel = E_{(LM or FS)} − E_H2Sad

in which E_H2Sad and E_{(LM or FS)} are the calculated adsorption energies of H₂S and local minima or final products, respectively. The nudged-elastic-band (NEB) method is applied to locate the transition state structures positioned to interpolate a series of system images between the initial and final states on the potential-energy surface.^30,31 A spring force between adjacent images is used to maintain constant spacing between the images, and a true force is applied to impel the images into the minimum energy path (MEP), mimicking an elastic band. Each image is optimized using the NEB algorithm based on a constrained algorithm of molecular dynamics. The highest point on the MEP corresponds to a transitional structure on the proposed reaction path and its energy, relative to that of the initial state, became the activation barrier of the reaction.

The electron density difference (Q_diff) is calculated in a similar manner to the calculation of adsorption energy

Q_diff = Q_A/Surf − (Q_Surf + Q_A)

where Q_diff is the difference at each grid point in the total electron density matrix between that of the adsorbate-bonded surface (Q_A/Surf) and that of the sum of the surface (Q_Surf) and the single adsorbate molecule (Q_A). According to this definition, positive and negative values correspond to increasing and decreasing electron densities, respectively.

3. Results and discussion

3.1. Adsorption of H₂S, HS and S on a Ge(100) surface

To ensure the reliability of the computational method, we have calculated the lattice parameters for bulk germanium using various pseudopotentials and the values are given in Table S1 of ESI.† As can be seen from those values PAW-PBE and the ultrasoft pseudopotential with the generalized gradient approximation (US-GGA) gives the least discrepancy between the calculated and experimental lattice parameters among the tested pseudopotentials. In order to compare with our previous study of H₂S adsorption on a Si(100) surface,³² we considered US-GGA method for further calculations. Also, we have performed the benchmark calculations for the H₂S adsorption on the clean Ge(100) surfaces with different functionals and different cutoff energy values and the calculated values are given in Table S2.† It has been observed that the trends of the calculated values with different cutoff energies and functionals are almost similar and hence we have chosen the US with 300 eV cutoff energy values for our further study. Table S3† presents the comparison of calculated bond lengths and bond angles of clean Ge(100) surface with other studies³³ and it has been found that the calculated bond lengths are in agreement with the previous experimental reports.^34–36

Previously, we found that the H₂S has three stable adsorption conformations on the Si(100) surfaces with orientation of the S–H bond;³² similarly here we considered the same conformation of H₂S adsorbed on Ge(100) surfaces (denoted as H₂S_ad, H₂S_ad-1, and H₂S_ad-2) and the optimized structures are shown in Fig. 2. The calculated adsorption energies and structural parameters for different conformations of H₂S are summarized in Table 1. Among these three conformations, H₂S_ad is found to be the most stable with adsorption energy −0.49 eV and the other two conformations H₂S_ad-1 and H₂S_ad-2 adsorbed on the surface with adsorption energies −0.40 and −0.30 eV, respectively. From Table 1, it has been observed that the bond length of the Ge–Ge dimer is increased (∼0.04 Å) and the tilting angle of Ge dimer is decreased to 16° from 20° after the adsorption of H₂S on the Ge surface, indicating the decreased zwitterionic and π-bond characters of the Ge dimer upon the adsorption of H₂S. The calculated S–Ge bond length value for the most stable conformation (H₂S_ad) is 2.61 Å, and the two remaining S–H bond lengths are 1.35 and 1.38 Å. The structural parameters of other two conformations, H₂S_ad-1 and H₂S_ad-2, are similar to those of H₂S_ad. Fig. 3 shows the DOS of surface Ge down atom and H₂S molecule before and after adsorption on Ge(100) surface, respectively. It is noticed from this figure that the H₂S molecule possesses C_2v symmetry with four valence states labelled as 4a₁, 2b₂, 5a₁, and 2b₁ according to their orbital symmetries. These results are similar to that of our previous study.³² The partial DOS (see Fig. S1 of ESI†) indicates that states 4a₁ and 2b₁ are contributed mainly from 3s and 3p_z of S atom and 2b₂ and 5a₁ states arise from the hybridization of orbitals 3p_x and 3p_y of the S atom. All S 3p atomic orbitals (2b₂, 5a₁, and 2b₁ states), especially 3p_x and 3p_y of adsorbed H₂S have good overlaps with d orbitals of the buckled-down Ge which is bonded to the H₂S molecule.

Fig. 2 The optimized structures of different conformations of H₂S adsorbed on Ge(100) surface: (a) H₂S_ad, (b) H₂S_ad-1, and (c) H₂S_ad-2.

Table 1 The calculated structural parameters and adsorption energies (E_ads) for hydrogen sulphide (H₂S) adsorption on Ge(100) surface

System	d(S–H) (Å)	d(S–Ge) (Å)	d(Ge–Ge) (Å)	∠HSH (deg)	Ge–Ge tilting angle (deg)	Eads (eV)	Eads^a (eV)
a The calculated adsorption energy for H2S adsorption on Si(100) surface taken from previous study.^32
H2Sad	1.35/1.38	2.61	2.58	92.4	16	−0.49	−0.74
H2Sad-1	1.35/1.37	2.64	2.58	91.9	17	−0.40	−0.70
H2Sad-2	1.33/1.39	2.63	2.57	92.5	16	−0.30	−0.65

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Fig. 3 The DOS of a H₂S molecule before (dashed line) and after (black solid line) adsorption on Ge(100) and DOS of Ge down atom (bond black line) bonded with H₂S.

3.2. Reaction mechanism of H₂S on Ge(100)

We consider the reaction pathway for adsorption of H₂S on Ge(100) surface analogous to our previous study of the adsorption of H₂S on Si(100).³² The calculated structural parameters and relative energies of intermediates and final products are listed in Table 2. The reaction energies, reaction barriers, and calculated imaginary frequencies of transition state structures are summarized in Table 3. The corresponding structures of intermediates and final products are shown in Fig. 4 and the top views of their corresponding transition state structures are shown in Fig. S2 of ESI.† The potential energy diagram (PES) for the adsorption and dissociation of H₂S on the Ge(100) surface are shown in Fig. 5. According to the calculation, the possible reaction paths are summarized in the following scheme:

Table 2 The calculated structural parameters and relative energies for dissociatively adsorbed H₂S on Ge(100) surface

Local minima and final products	d(Ge–Ge)^a (Å)	d(Ge–Ge)^b (Å)	d(S–Ge) (Å)	d(H–Ge) (Å)	Erel^d (eV)
a Bond length of a Ge(1)–Ge(2) dimer which is bonded either with HS or S.b Bond length of a Ge(3)–Ge(4) or Ge(5)–Ge(6) which is bonded with dissociative H.c Taken from ref. 18.d Relative energy for H2S on Si(100) surface are given in parenthesis.
LM1I	2.55	2.58	2.28	1.57	−0.89 (−0.95)
LM1II	2.51 (2.46^c)	2.51 (2.46^c)	2.28 (2.18^c)	1.55 (1.56^c)	−1.03 (−1.43)
LM1III	2.60	2.53	2.29	1.54	−0.96 (−1.31)
LM2I	2.52	2.58	2.10	1.55	−0.67 (−1.05)
LM2II	2.52	2.54	2.11	1.55	−0.67 (−1.33)
LM3I	2.56	2.59	2.11	1.55	−0.16 (−1.13)
LM3II	2.62	2.48	2.12	1.54	−1.03 (−1.45)
LM3III	2.54	2.58	2.11	1.56	−1.19 (−1.45)
LM3IV	3.88	2.57	2.24/2.33	1.55	−0.88 (−1.46)
LM3V	3.45	2.55	2.21/2.34	1.55	−1.12 (−1.59)
FSI	2.74	2.73	2.36	1.56	−0.81 (−1.38)
FSII	2.52	2.47	2.17 (2.16^c)	1.54 (1.56^c)	−1.27 (−2.63)
FSIII	2.51	2.53	2.33	1.55	−1.34 (−2.12)
FSIV	3.56	—	2.25/2.28	1.55	−1.21 (−1.99)

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Table 3 The calculated reaction barriers (^‡E, eV), reaction energies (ΔE, eV), and imaginary frequencies (IMF, cm⁻¹) for the transition states of decomposition of H₂S on Ge(100) surface

Reaction path	^‡E	ΔE	IMF
H2Sad → TS1I → LM1I	0.53	−0.89	227i
H2Sad → TS1II → LM1II	0.49	−1.03	661i
H2Sad → TS1III → LM1III	0.10	−0.96	300i
LM1I → TS2I-a → LM2I	0.90	0.22	492i
LM1II → TS2I-b → LM2I	0.88	0.36	419i
LM1III → TS2II-a → LM2II	1.89	0.29	1029i
LM1II → TS2II-b → LM2II	1.07	0.36	421i
LM2I → TS3I → LM3I	1.26	0.51	552i
LM2II → TS3II → LM3II	1.71	−0.36	405i
LM2II → TS3III → LM3III	1.24	−0.52	274i
LM2I → TS3IV → LM3IV	0.47	−0.32	128i
LM2II → TS3V → LM3V	0.30	−0.46	197i
LM3I → TS4I → FSI	0.48	−0.65	145i
LM3II → TS4II → FSII	1.20	−0.10	119i
LM3III → TS4III → FSIII	0.58	−0.01	162i
LM3IV → TS4IV → FSIV	1.13	−0.22	919i
LM3V → TS4V → FSIV	1.43	−0.09	347i

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Fig. 4 Top view of all the local minima's and the final products of the reactions for the adsorption of H₂S on Ge(100) surface.

Fig. 5 Potential-energy diagram for adsorption and decomposition of H₂S on Ge(100) surface. All potential energies of intermediates, transition structures, and final products are referred to the H₂S molecule adsorbed on the surface.

The possible reaction pathways described in the above scheme includes first dehydrogenation, second dehydrogenation and sulfur bridged adsorption. The H₂S_ad species can undergo a first dehydrogenation through three paths. The first path is through TS1_I, with a 0.53 eV barrier, to produce LM1_I intermediate; i.e., one H atom of H₂S dissociated and migrated to the Ge atom of an adjacent dimer along [001] direction. It has been observed that the first dehydrogenation has higher energy barrier due to the H atom being adsorbed on the Ge(3) atom. The second path creates the intermediate LM1_II via TS1_II with a barrier of 0.49 eV; i.e., the dissociated H and HS separately adsorb on each of a dimer's Ge atom. The third path yields intermediate LM1_III via TS1_III with the smallest barrier 0.10 eV; the resulting H and HS adsorb on Ge atoms of adjacent dimers along direction [010]. Fig. 6a and b show the EDD contour plots which contain the dimeric S–Ge(1) bond with S–H_a and S–Ge(1) bond with S–H_b bond, respectively. It can be seen from Fig. 6a that the electron density increases between the S and Ge(1) atoms which is bonded to H₂S, indicating a strengthening of S–Ge bond. In the meanwhile, the increased electron density is observed between the H and Ge(5) atoms of a neighboring Ge dimer along [010] direction (Fig. 6a) which interacts with each other through a hydrogen bond. This interaction results in the lower energy barrier (0.10 eV) in the first dehydrogenation for H₂S_ad to form LM1_III. As summarized in Table 3, the reaction energies of the first dehydrogenations for the three paths are −0.89, −1.03, and −0.96 eV, respectively. LM1_II and LM1_III are comparably stable because the first dissociated H preferably adsorbs on the electron rich atoms like Ge(2) and Ge(5) atoms. The S–Ge bond length in LM1_I, LM1_II, and LM1_III are shortened by ∼0.3 Å, compared to that of in the H₂S_ad. In H₂S_ad, H₂S adsorbed on a Ge atom via a dative bond; whereas in LM1_I∼III, it is adsorbed on a Ge atom via a covalent bond.

Fig. 6 EDD contours of H₂S_ad on a plane containing (a) a S–Ge(1) bond and a dimeric S–H_a bond along [010] and (b) a S–Ge(1) bond and a dimeric S–H_b bond along [001]. The red and blue colors represent the increasing and decreasing electron densities, respectively.

Further, the local minima's LM1_I, and LM1_II can undergo dehydrogenation and form LM2_I via the transition states, TS2_I-a and TS2_I-b with energy barriers of 0.90 and 0.88 eV, respectively. LM2_II can be produced from the dehydrogenation of LM1_III and LM1_II via transition states, TS2_II-a, and TS2_II-b with barriers of 1.89 and 1.07 eV, respectively. From Table 2, it has been observed that the structural parameters of LM2_I and LM2_II are almost similar. The S–Ge bond of LM2 species is much shorter than that of LM1, indicating a stronger S–Ge bond in species LM2. The energy barriers of the second dehydrogenation, LM1 → LM2, are higher than that of first dehydrogenation H₂S_ad → LM1. In the reaction mechanism, there are two types of intermediates between the LM2 and the final products; one is formed through the migration of H atom from LM2_I/LM2_II (LM3_I, LM3_II and LM3_III) and another one is formed through the bridging of two Ge dimer atoms via S adatom (LM3_IV and LM3_V). In the first type, the transition states TS3_I, TS3_II, and TS3_III are having the energy barriers of 1.26, 1.71, and 1.24 eV, respectively between the LM2_I–II and LM3_I–III. Also, the S adatom remains bonded with Ge atom and has a dangling bond in LM3_I–III. The final products, FS_I∼III are formed from LM3_I–III via TS4_I–III with respective energy barriers of 0.48, 1.20, and 0.58 eV. LM3_I–III can further transform with small barriers to the final products, FS_I–III. In FS_I–III, the S adatom bridges either two neighboring dimers along [001] direction or two Ge atoms of a dimer or two neighboring dimers along [010] direction, respectively. In LM3_IV and LM3_V, the S adatom bridges two Ge atoms of a dimer (Fig. 4i and j) and their formation barriers by corresponding transition states, TS3_IV and TS3_V are 0.47 eV and 0.30 eV, respectively. Further, LM3_IV and LM3_V isomerized to form the final product FS_IV (Fig. 4n), with high barriers (1.13 and 1.43 eV), respectively. From Table 2, it has been noticed that the dimeric Ge–Ge bond length remains nearly at 2.56 ± 0.06 Å in all the intermediates and final products, except LM3_IV, LM3_V, FS_I and FS_IV. In the FS_I, the Ge(1)–Ge(2) bond length increases to 2.74 Å because the Ge–S–Ge has ring stress. Also, the Ge(1)–Ge(2) bond is cleaved in LM3_IV, LM3_V and FS_IV, so the bond length increases to 3.5–3.8 Å.

There are four reaction paths for the dissociation of H₂S on Ge(100) surface are proposed and they are; H₂S_ad → LM1_I/LM1_II → LM2_I → LM3_I → FS_I, H₂S_ad → LM1_II/LM1_III → LM2_II → LM3_II → FS_II, H₂S_ad → LM1_II/LM1_III → LM2_II → LM3_III → FS_III, and H₂S_ad → LM1_II → LM2_I/LM2_II → LM3_IV/LM3_V → FS_IV. However from the calculated results of the rate-determining steps (RDS) for the final products (FS_I, FS_II, FS_III and FS_IV) are LM2_I → LM3_I, LM2_II → LM3_II, LM2_II → LM3_III and LM3_V → FS_IV, respectively. Their barriers at the rate-determining step are 1.26, 1.71, 1.24 and 1.43 eV, respectively. Among the four, the third RDS has the lowest energy barrier. According to these calculations, FS_III is thermodynamically more stable than the others and hence it can be the major product. The more ring strains in FS_I and FS_IV due to their inter- or intra-dimer lead to break the dimer bonds, so they are unstable products among the others.²³ From the above, it has been noticed that the final product FS_III is favorable in terms of both kinetic and thermodynamic points.

From Table 1, it has been found that the calculated adsorption energy values for three possible adsorption conformations of H₂S on Ge(100) surface are smaller than that of Si(100) surface. When H₂S adsorbs on surface, the 3p orbitals (2b₂, 5a₁, and 2b₁) of S atom have more significant overlap with p orbitals of buckled-down Si atom³² than the d orbitals of buckled-down Ge atom. The strong overlap between the p-orbitals of S and Si atoms result in the large adsorption energies for the adsorption of H₂S_ad on Si(100) surface.³² From Table 2, it is noticed that the relative energies for all the intermediates and final products of adsorption of H₂S on Si(100) surface are more negative than those on Ge(100) surface, which indicates that those are more stable on the Si surface. Based on the present and previous studies,³² we summarized the total reaction energies for final products, energy barriers for RDS and RDS pathways from H₂S adsorbed on Ge or Si surface and are shown in Table 4. As can be seen from this table, FS_II and FS_III are thermodynamically favourable products for the H₂S adsorption on Ge(100) and Si(100), respectively. Their RDSs are from LM2 to LM3 via second dehydrogenation process. In the kinetic point of view, FS_I and FS_IV are the favorable products for Si surface and FS_I and FS_III are the major products for Ge surface. From the above results, it is noted that the final product FS_III is thermodynamically and kinetically favorable product for the H₂S adsorption on Ge surface. From the above results it has been observed that the S-passivation products on Si(100) surface are more stable than Ge(100) surface.

Table 4 The calculated total reaction energies (ΔE in eV) for the final products, energy barrier (^‡E in eV) for RDSs and their corresponding pathways for the adsorption of H₂S on Ge and Si surface

Final products	ΔE		^‡E		RDS
	Ge	Si	Ge	Si	Ge	Si
FSI	−0.81	−1.38	1.26	1.19	LM2I → LM3I	LM2I → LM3I
FSII	−1.27	−2.63	1.71	1.63	LM2II → LM3II	LM2II → LM3II
FSIII	−1.34	−2.12	1.24	1.54	LM2II → LM3III	LM2II → LM3III
FSIV	−1.21	−1.99	1.43	1.22	LM3V → FSIV	LM3V → FSIV

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3.3. Density of states (DOS)

The electronic structure is intimately related to their fundamental physical and chemical properties. To further understand the adsorption modes of H₂S on Ge(100), we analyzed DOS of most possible reaction pathway i.e., H₂S_ad → LM1_II → LM2_II → LM3_III → FS_III, which includes five different S conformations such as H₂S, HS, S adatom and bridged S atoms. The plotted DOS for H₂S_ad, LM1_II, LM2_II, LM3_III and FS_III are shown in Fig. 7 and it compares the different S conformations adsorbed on Ge(100) surface. In the Fig. 7, the sharp band appears between −10 to −15 eV relative to the Fermi level is attributed from the 3 s orbital of S atoms, which is adsorbed on the surface with different configurations. Initially, when the H₂S species absorbs on the Ge(100) surface, this band located at −15.86 eV region (Fig. 7a) and the first and second dehydrogenation shifts this band towards the Fermi level (from −15.86 to −13.5/−11.8 eV, see Fig. 7b and c). This upward shift can be explained that the interaction of H₂S on the surface via dative bond, whereas after the first dehydrogenation, LM1_II species interact with surface via single bond. Also, the peak at −8.2 eV region (Fig. 7a) is due to the p_x orbital of S atom shifts close to the Fermi level after the first dehydrogenation and finally it overlaps with the p_y and p_z orbitals after the second dehydrogenation, which is due to the interaction of S atom with the surface by either dative or covalent bond. In LM2_II and LM3_III, S atom adsorbed in a similar way and hence, the PDOS for adsorbed S atom resembles same (at −11.89 and −12.67 eV respectively in Fig. 7c and d). Finally, the FS_III possesses bridged S conformation on Ge(100) surface, so its 3s orbital band shifted downward and close to the HS conformation. Also, the broad band in the region of 0 to −5 eV, shows the bonding interaction of p orbitals of S and Ge surface atoms. These above results demonstrate that DOS spectra can comprehensively explain the interaction of adsorbed S atom and surface Ge atom.

Fig. 7 The total DOS of S adatom in (a) H₂S_ad, (b) LM1_II, (c) LM2_II, (d) LM3_III, and (e) FS_III structures.

3.4. Vibrational frequency analysis for H₂S adsorption on Ge(100)

In order to guide a future surface vibrational spectroscopic study, the vibrational frequencies for adsorbed species on Ge(100) surface are analyzed. The calculated vibrational frequencies for the adsorbed species such as, H₂S, LM, and FS species are summarized in Table 5. The bands observed at 2577 and 2159 cm⁻¹ for H₂S species are due to asymmetric and symmetric S–H stretching modes. The strong interaction between H_b and Ge(5) atoms (see Fig. 6) leads to weaken the S–H_b bond resulted in redshift of wave number for S–H stretching mode (2159 cm⁻¹). The H–Ge stretching bands are observed in the range of 1900–2024 cm⁻¹. The calculated S–H and H–Ge stretching modes of LM1_II are in agreement with the previous EELS experimental values of 2532 cm⁻¹ and 1967 cm⁻¹.³⁷ For S–Ge stretching bands, LM1_I∼III belong to the first dissociated group which display similar S–Ge stretching vibration on the surface. There is about 80 cm⁻¹ difference between the H₂S_ad and LM1_I–III for S–Ge stretching mode, which is due to the change in interaction type, i.e. from dative bond to covalent bond between sulfur atom and Ge surface. The other dissociated intermediates (LM2_I–II and LM3_I–III) exhibits blue shift in the IR spectrum, which is due to the increase in the bond order of S–Ge after the second dehydrogenation. The S–Ge stretching bands for LM3_IV–V and FS_I–IV are observed at about 300–420 cm⁻¹ which is red shifted due to the interaction of bridged sulfur atom with the Ge atom via covalent bond. As shown in Table 5, the calculated S–Ge vibration frequencies of FS_I are red shifted (about 50 to 130 cm⁻¹) compared to other final products, which indicates that the bond of dimeric Ge become longer because of the ring stress from the Ge–S–Ge bonds.

Table 5 The calculated vibrational frequencies of the initial state (H₂S_ad), local minima's (LM), and final products (FS) for the decomposition of H₂S on Ge(100) surfaces

System	νH–S (cm^−1)	νH–Ge (cm^−1)	νS–Ge (cm^−1)
H2Sad	2577/2159		265
LM1I	2600	1926	342
LM1II	2544	1967	331
LM1III	2389	2024	348
LM2I		1962/1915	456
LM2II		1979/1968	461
LM3I		1970/1921	463
LM3II		2000/1968	448
LM3III		1948/1927	450
LM3IV		1913/1908	351/310
LM3V		1934/1916	364/295
FSI		1914/1903	291/282
FSII		1998/1994	421/267
FSIII		1991/1983	344/276
FSIV		1951/1923	396/333

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4. Conclusions

We have performed the detailed investigation of the adsorption and dissociation of H₂S on Ge(100) surface using density functional theory calculations. Our results show that among the three different conformation, H₂S_ad is found to be adsorbed stably on the surface. Possible reaction paths are proposed for dehydrogenation between adsorbed H₂S and S adatoms. In the first step, adsorbed H₂S partially dissociates and produced HS and H and in the second step, HS further dissociates into S adatom. Further, the EDD contour indicate that the increased electron density between the H atom and Ge(5) atom of a neighboring Ge dimer along [010] which leads to the lower energy barrier (0.10 eV) in the first dehydrogenation for H₂S_ad to LM1_III. The results show that the four final products have more stable conformations via LM1, LM2, and LM3 intermediates. We found that FS_I and FS_III are kinetically favored products whereas FS_II and FS_III are thermodynamically favored products for the H₂S adsorption on the Ge surface. In addition, the interactions between S and Ge atoms are identified by DOS spectra. The calculated results of IR spectra are in good agreement with the available experimental EELS data.

Acknowledgements

We thank Ministry of Science and Technology (MOST 101-2113-M-011-004-MY3), Taiwan for supporting this research financially. We are also grateful to National Center of High-Performance Computing, Institute of Nuclear Energy Research, and Atomic Energy Council in Taiwan for their support.

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Footnote

† Electronic supplementary information (ESI) available: ESI Table S1 lists the lattice parameters of Ge obtained with various pseudopotentials. Table S2 displays dimer bond length (d_D) and dimer tilting angle (θ) for a clean Ge(100) surface, compared with results from other calculations and experimental data. Fig. S1 illustrates the partial DOS of H₂S adsorbed on the Ge(100) surface. Fig. S2 shows a top view of all transition structures on the reaction paths of adsorbed H₂S. See DOI: 10.1039/c4ra08887e

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