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Hydrogen molecules and platelets in germanium
ARTICLE IN PRESS
Physica B 376–377 (2006) 105–108 www.elsevier.com/locate/physb
Hydrogen molecules and platelets in germanium B. Hourahinea,, R. Jonesb, P.R. Briddonc a
SUPA, Department of Physics, University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow G4 0NG, UK b School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK c School of Natural Sciences, University of Newcastle upon Tyne, Herschel Building, Newcastle upon Tyne NE1 7RU, UK
Abstract There has been substantial interest in the behaviour of hydrogen in silicon over the last decade, often focused on the behaviour of the interstitial hydrogen molecule and f1 1 1g oriented platelets. Less is known about analogous hydrogen-related defects in germanium, but planar defects are known, and the molecule has possibly been observed recently by Raman scattering. We present preliminary results of first-principles calculations on both the H2 molecule and a range of platelet geometries in germanium. For comparison the molecule in GaAs and Si is also simulated. Energetics and vibrational modes of the defects are presented. Our calculations show the observed weak mode at 3834 cm1 in Ge is indeed consistent with the interstitial hydrogen molecule. r 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Bb; 63.20.Pw; 78.30.j; 61.72.Tt Keywords: Hydrogen; Germanium; Theory; Platelet; Molecule
1. Introduction In proton-implanted and hydrogen plasma treated silicon and germanium, large (typically hundreds of nanometers across) structures are observed [1] near the surface. These disk shaped platelets are oriented to lie in f1 0 0g and f1 1 1g planes. The f1 1 1g platelets in silicon have been the subject of a large number of studies, while their germanium analogues remain poorly understood. Infrared and Raman spectra of silicon containing platelets show at least four distinct bands in the region 2000–2200 cm1 [2]. The relative intensities of the bands depend on the thermal history of the sample used, and are consistent with three distinct types of structure with saturated silicon dangling bonds, one of the structures also having local inversional symmetry. It has been shown that conversion between two distinct types of platelet occur at around 100 C [3], with the appearance of H2 molecules inside of the resulting structure.
Corresponding author. Tel.: +44 141 548 2325; fax: +44 141 552 2891.
E-mail address: [email protected] (B. Hourahine). 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.028
There have been a number of theoretical attempts to predict the structure of platelets. Van de Walle et al. [4,5] examined pairs of H0bc in two adjacent Si–Si bonds arrayed in the same ð1 1 1Þ plane. They found a small lowering in energy with respect to isolated H0bc , and similarly found that two H placed to break a Si–Si bond also was more stable. Both configurations were higher in energy than molecular hydrogen in the lattice though. Dea´k et al. [6] considered five models for platelets: (1) Groups of hydrogen molecules at adjacent T di sites. (2) Groups of H0bc in adjacent bonds along the same ð1 1 1Þ plane. (3) Pairs of hydrogen atoms breaking a Si–Si bond, so forming two Si–H bonds (2Si–H). (4) Pairs of hydrogen atoms saturating the dangling bonds formed by removing a double layer of silicon ½V2 H2 n . (5) Groups of H2 defects aligned in the same direction. They found that the third model, i.e., pairs of hydrogen atoms breaking a Si–Si bond, and forcing apart two ð1 1 1Þ planes, was the most likely to be the defect responsible for
ARTICLE IN PRESS B. Hourahine et al. / Physica B 376–377 (2006) 105–108
106
Table 1 Measured and calculated vibrational modes (cm1 ) of H2 in several host materials Si
H2 HD D2
Ge
Expt. [22–26]
½1 0 0
½1 1 0
½1 1 1
Expt. [12,13]
½1 0 0
½1 1 0
½1 1 1
3627 3191.1 2645
3522.4 3057.1 2491.7
3542.3 3075.3 2505.7
3544.1 3078.1, 3078.6 2507.5
3834
3731.0 3237.2 2639.2
3702.9 3213.5 2619.3
3702.1 3213.4, 3213.4 2618.8
GaAs–T As
GaAs–T Ga
H2 HD D2
2782
Expt. [27]
½1 0 0
½1 1 0
½1 1 1
Expt. [21]
½1 0 0
½1 1 0
½1 1 1
3934.1 3446.5 2842.6
3813.0 3308.3 2697.6
3806.0 3303.0 2692.6
3797.9 3303.4, 3289.5 2687.1
4043 3602 2920
3838.8 3331.9 2715.9
3834.7 3328.4 2712.9
3817.6 3311.7, 3316.5 2700.9
For HD in Si, the 3191:1 cm1 mode originates from a J ¼ 1 ! J ¼ 1 transition [22]. Since the calculations use statically aligned molecules, the h1 1 1i alignment has two inequivalent H atoms, the values for both the HD and DH configurations are then given. In GaAs, the calculated energy difference DE between H2 at Ga and As surrounded T sites is found to be 0:2 eV (experimentally this has been determined to be DE ¼ 60 meV, see Ref. [21]).
platelets, and calculated that an interplanar separation of 5.92 A˚ between the silicon atoms forced apart by the hydrogen was the most stable. Zhang et al. [7] also considered variations of the H2 structure studied by Dea´k et al. They suggested that a double-layer f1 1 1g platelet formed of alternating H2 units was 0.15 eV lower in energy than interstitial H2 molecules, however, a lower energy geometry with a half-stacking fault, ð2Si2HÞSF=2 , was also simulated. Martsinovich et al. [8] showed that such topological defects may be important for small platelets. Kim and Chang [9] developed a model for the conversion of the double-layer H2 units into the third structure modelled by Dea´k et al. with production of a hydrogen molecule per repeat unit. Relatively few studies exist for platelets in Ge (for example see Refs. [10,11]). Hiller et al. [12] observe the formation of molecule containing platelets after hydrogenation. Modes at 1980 and 4155 cm1 were assigned to Ge–H and H2 vibrations in the resulting structure. Additionally an assignment for the isolated H2 molecule in Ge was made to a mode at 3925 cm1 (see Table 1 and Ref. [13]).
120 Ry plane-wave fitting to the charge density, with a 23 or 6 6 2 Monkhorst–Pack [17] k-point sampling scheme for the molecules or platelets. Hartwigsen–Goedecker– Hutter [18] pseudopotentials were used for the semiconductor hosts while a bare proton was used for the hydrogen potential. All atoms were allowed to relax by a conjugate gradient method (in the case of the platelets the energy was also minimised with respect to the lattice vectors). The second derivatives of the energy were found for the H atoms and immediate neighbours, in the case of the platelet geometries, the cells were repeated to a 3 3 1 geometry before calculation of the derivatives. Quasi-harmonic vibrational modes were then calculated from the dynamical matrix (further details are given in Ref. [14]). The error in the calculated modes of the molecules, between the 216 atom host values presented here and for a 512 atom cell, was estimated to be 3 cm1 by comparing against minimal contracted basis calculations for 64, 216 and 512 cells.
2. Calculations
3.1. Interstitial molecules
The observed modes were compared against firstprinciples density functional results [14,15], in conjunction with cubic cells of between 64 and 512 atoms for the molecule and 12 atom trigonal cells for the platelets. The wavefunctions of the host material were represented with a real-space contracted Cartesian–Gaussian basis centred on each atom, using two independent contracted groups of four separate exponents (with different contraction coefficients for s and p) and an additional uncontracted d set. The hydrogen used an uncontracted set of 4 s and p functions. The Hartree and Perdew–Wang [16] exchangecorrelation energies were calculated using a converged
The resulting modes for interstitial H2 in Si, GaAs and Ge are shown in Table 1, for statically aligned molecules along ½1 0 0, ½1 1 0 and ½1 1 1 directions. The energy differences between these orientations are negligible (5 meV in all host materials shown), and the molecule is then expected to be a free rotor, in agreement with previous results (see for example Refs. [19,20]). From these statically aligned calculations, an estimate can be made for the vibrational mode of the J ¼ 0 molecule by taking a weighted average of the static configurations. This leads to modes of 3713, 3222, and 2627 cm1 for interstitial H2 , HD, and D2 in Ge. The H2 mode falls 120 cm1
3. Results
ARTICLE IN PRESS B. Hourahine et al. / Physica B 376–377 (2006) 105–108
lower than the observed value, this is also typical of the error in calculated H2 modes for Si and GaAs. However, the calculated values for the molecule at the As surrounded T site in GaAs are in somewhat poorer agreement with experiment, 200 cm1 in the case of H2 . Notice that GaAs is a compound semiconductor and because of this there are two possible interstitial sites for H2 : one with Ga closest neighbours (T Ga ), the other one with As atoms nearby (T As ). For H2 in Si, Ge, and at the T Ga site in GaAs, the calculations systematically underestimate the observed frequencies by about 120 cm1 . Following this trend, one would expect the mode for H2 at the T As site in GaAs to lie around 3950 cm1 rather than the observed 4043 cm1 [21]. This discrepancy could hint that either the behaviour of H2 when surrounded by anions differs from the other three cases, or that the Raman mode at 4043 cm1 may instead possibly be due to H2 trapped in some kind of void or platelet.
107
Table 3 Vibrational modes of several platelet structures, cm1 H
D
H
D
(2Ge–H)
1966 1886
1400 1343
ð2Ge2HÞSF=2
1990 1961
1417 1396
ðH2 Þ
1837 1695
1308 1206
ðH2 ÞSF=2
1920 1740
1367 1238
(2Ge–H + H2 )
4111 1984 1882
2909 1420 1341
(2Ge–H + 2H2 )
4146 2025 1956
2933 1441 1393
The average position of the vibrational bands are shown.
50 cm1 . This then suggests that the width of the band observed at 1980 and 4155 cm1 may in part be due to a range of concentrations of hydrogen molecules in different platelets.
3.2. Platelets 4. Conclusions The energies of several platelet geometries are shown in Table 2 for a chemical potential of half the energy of an interstitial H2 molecule in Ge (however, platelet containing material is unlikely to be in thermodynamic equilibrium). For the geometries which do not contain H2 molecules, the double-layer H2 structure of Zhang et al. ðH2 ÞD is found to be the lowest in energy, however, a structure where two adjacent ð1 1 1Þ layers of Ge–Ge bonds are broken and passivated is also found to be competitive energetically (4Ge–H). Structures containing molecules are found to be lower in energy (as would be expected by the larger open space inside a platelet when compared to the interstitial site in Ge) and further decrease with additional H2 (2Ge–H + 2H2 ). The presence of half-stacking faults is found to have a relatively small effect on the energy of the platelets. The vibrational modes of a few structures are shown in Table 3. The molecule containing platelets posses modes at around 4120 cm1 , with the frequency increasing as a second molecule is added. There are two bands of Ge–H related modes in these structures, and again increasing the number of hydrogen molecules pushes these upwards by
Table 2 Energy of several platelet geometries in germanium E f (eV) DC (A˚) (2Ge–H) H2
0.4 0.6 1.0 ðH2 ÞD (2Ge–H + H2 ) 1.2 (2Ge–H + 2H2 ) 2.0
2.38 0.90 2.44 2.42 2.67
E f (eV) Dc (A˚) ð2Ge2HÞSF=2 ðH2 ÞSF=2 (4Ge–H) (2Ge–H + H2 ÞSF=2
0.5 0.6 0.9 1.2
1.14 0.84 4.43 2.21
The hydrogen chemical potential is chosen to be half of the energy of H2 at a T site in Ge. Formation energies compared to the molecule, and dilation along the c direction are shown. SF/2 denotes the presence of a halfstacking fault in the structure.
The results of LDA DFT calculations are presented for molecules and selected platelet structures in germanium. Recently observed vibrational modes at 1980 and 4155 cm1 are shown to be consistent with molecule filled platelets, while the modes at 3826 and 3834 cm1 are consistent with interstitial H2 . Acknowledgements The authors thank M. Hiller and E.V. Lavrov for helpful discussion. B.H. acknowledges the Royal Society of Edinburgh BP Research Fellowship for funding. References [1] N.M. Johnson, F.A. Ponce, R.A. Street, R.J. Nemanich, Phys. Rev. B 35 (1987) 4166. [2] J.N. Heyman, J.W. Ager, E.E. Haller, N.M. Johnson, J. Walker, C.M. Doland, Phys. Rev. B 45 (1992) 13363. [3] E.V. Lavrov, J. Weber, Phys. Rev. Lett. 87 (2001) 185502. [4] C.G. Van de Walle, Y. Bar-Yam, S.T. Pantelides, Phys. Rev. Lett. 60 (1988) 2761. [5] C.G. Van de Walle, P.J.H. Denteneer, Y. Bar-Yam, S.T. Pantelides, Phys. Rev. B 39 (1989) 10791. [6] P. Dea´k, C.R. Ortiz, L.C. Snyder, J.W. Corbett, Physica B 170 (1991) 223. [7] S.B. Zhang, W.B. Jackson, Phys. Rev. B 43 (1991) 12142. [8] N. Martsinovich, M.I. Heggie, C.P. Ewels, J. Phys.: Condens. Matter 15 (2003) S2815. [9] Y.S. Kim, K.J. Chang, Phys. Rev. Lett. 86 (2001) 1773. [10] S. Muto, S. Takeda, M. Hirata, Mater. Sci. Forum 196–201 (1995) 1171. [11] T. Akatsu, K.K. Bourdelle, C. Richtarch, B. Faure, F. Letertre, Appl. Phys. Lett. 86 (2005) 181910. [12] M. Hiller, E.V. Lavrov, J. Weber, Phys. Rev. B 71 (2005) 045208. [13] M. Hiller, E.V. Lavrov, J. Weber, Raman spectroscopy of hydrogen molecules in germanium, this conference. [14] R. Jones, P.R. Briddon, The ab initio cluster method and the dynamics of defects in semiconductors, in: Semiconductors and
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[15] [16] [17] [18] [19] [20] [21]
B. Hourahine et al. / Physica B 376–377 (2006) 105–108 Semimetals, vol. 51A, Academic Press, San Diego, 1998, pp. 287–349 (Chapter 6). J. Coutinho, R. Jones, P.R. Briddon, S. O¨berg, Phys. Rev. B 62 (2000) 10824. J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244. H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. C. Hartwigsen, S. Goedecker, J. Hutter, Phys. Rev. B 58 (1998) 3641. W.B. Fowler, P. Walters, M. Stavola, Phys. Rev. B 66 (2002) 075216. B. Hourahine, R. Jones, Phys. Rev. B 67 (2003) 121205. E.V. Lavrov, J. Weber, Physica B 340–342 (2003) 329.
[22] E.E. Chen, M. Stavola, W. Beall Fowler, P. Walters, Phys. Rev. Lett. 88 (2002) 105507. [23] R.E. Pritchard, M.J. Ashwin, J.H. Tucker, R.C. Newman, E.C. Lightowlers, M.J. Binns, S.A. McQuaid, R. Falster, Phys. Rev. B 56 (1997) 13118. [24] R.E. Pritchard, M.J. Ashwin, J.H. Tucker, R.C. Newman, Phys. Rev. B 57 (1998) 15048. [25] A.W.R. Leitch, V. Alex, J. Weber, Phys. Rev. Lett. 81 (1998) 421. [26] E.V. Lavrov, J. Weber, Phys. Rev. Lett. 89 (2002) 215501. [27] J. Vetterho¨ffer, J. Wagner, J. Weber, Phys. Rev. Lett. 77 (1996) 5409.
Physica B 376–377 (2006) 105–108 www.elsevier.com/locate/physb
Hydrogen molecules and platelets in germanium B. Hourahinea,, R. Jonesb, P.R. Briddonc a
SUPA, Department of Physics, University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow G4 0NG, UK b School of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK c School of Natural Sciences, University of Newcastle upon Tyne, Herschel Building, Newcastle upon Tyne NE1 7RU, UK
Abstract There has been substantial interest in the behaviour of hydrogen in silicon over the last decade, often focused on the behaviour of the interstitial hydrogen molecule and f1 1 1g oriented platelets. Less is known about analogous hydrogen-related defects in germanium, but planar defects are known, and the molecule has possibly been observed recently by Raman scattering. We present preliminary results of first-principles calculations on both the H2 molecule and a range of platelet geometries in germanium. For comparison the molecule in GaAs and Si is also simulated. Energetics and vibrational modes of the defects are presented. Our calculations show the observed weak mode at 3834 cm1 in Ge is indeed consistent with the interstitial hydrogen molecule. r 2005 Elsevier B.V. All rights reserved. PACS: 61.72.Bb; 63.20.Pw; 78.30.j; 61.72.Tt Keywords: Hydrogen; Germanium; Theory; Platelet; Molecule
1. Introduction In proton-implanted and hydrogen plasma treated silicon and germanium, large (typically hundreds of nanometers across) structures are observed [1] near the surface. These disk shaped platelets are oriented to lie in f1 0 0g and f1 1 1g planes. The f1 1 1g platelets in silicon have been the subject of a large number of studies, while their germanium analogues remain poorly understood. Infrared and Raman spectra of silicon containing platelets show at least four distinct bands in the region 2000–2200 cm1 [2]. The relative intensities of the bands depend on the thermal history of the sample used, and are consistent with three distinct types of structure with saturated silicon dangling bonds, one of the structures also having local inversional symmetry. It has been shown that conversion between two distinct types of platelet occur at around 100 C [3], with the appearance of H2 molecules inside of the resulting structure.
Corresponding author. Tel.: +44 141 548 2325; fax: +44 141 552 2891.
E-mail address: [email protected] (B. Hourahine). 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.12.028
There have been a number of theoretical attempts to predict the structure of platelets. Van de Walle et al. [4,5] examined pairs of H0bc in two adjacent Si–Si bonds arrayed in the same ð1 1 1Þ plane. They found a small lowering in energy with respect to isolated H0bc , and similarly found that two H placed to break a Si–Si bond also was more stable. Both configurations were higher in energy than molecular hydrogen in the lattice though. Dea´k et al. [6] considered five models for platelets: (1) Groups of hydrogen molecules at adjacent T di sites. (2) Groups of H0bc in adjacent bonds along the same ð1 1 1Þ plane. (3) Pairs of hydrogen atoms breaking a Si–Si bond, so forming two Si–H bonds (2Si–H). (4) Pairs of hydrogen atoms saturating the dangling bonds formed by removing a double layer of silicon ½V2 H2 n . (5) Groups of H2 defects aligned in the same direction. They found that the third model, i.e., pairs of hydrogen atoms breaking a Si–Si bond, and forcing apart two ð1 1 1Þ planes, was the most likely to be the defect responsible for
ARTICLE IN PRESS B. Hourahine et al. / Physica B 376–377 (2006) 105–108
106
Table 1 Measured and calculated vibrational modes (cm1 ) of H2 in several host materials Si
H2 HD D2
Ge
Expt. [22–26]
½1 0 0
½1 1 0
½1 1 1
Expt. [12,13]
½1 0 0
½1 1 0
½1 1 1
3627 3191.1 2645
3522.4 3057.1 2491.7
3542.3 3075.3 2505.7
3544.1 3078.1, 3078.6 2507.5
3834
3731.0 3237.2 2639.2
3702.9 3213.5 2619.3
3702.1 3213.4, 3213.4 2618.8
GaAs–T As
GaAs–T Ga
H2 HD D2
2782
Expt. [27]
½1 0 0
½1 1 0
½1 1 1
Expt. [21]
½1 0 0
½1 1 0
½1 1 1
3934.1 3446.5 2842.6
3813.0 3308.3 2697.6
3806.0 3303.0 2692.6
3797.9 3303.4, 3289.5 2687.1
4043 3602 2920
3838.8 3331.9 2715.9
3834.7 3328.4 2712.9
3817.6 3311.7, 3316.5 2700.9
For HD in Si, the 3191:1 cm1 mode originates from a J ¼ 1 ! J ¼ 1 transition [22]. Since the calculations use statically aligned molecules, the h1 1 1i alignment has two inequivalent H atoms, the values for both the HD and DH configurations are then given. In GaAs, the calculated energy difference DE between H2 at Ga and As surrounded T sites is found to be 0:2 eV (experimentally this has been determined to be DE ¼ 60 meV, see Ref. [21]).
platelets, and calculated that an interplanar separation of 5.92 A˚ between the silicon atoms forced apart by the hydrogen was the most stable. Zhang et al. [7] also considered variations of the H2 structure studied by Dea´k et al. They suggested that a double-layer f1 1 1g platelet formed of alternating H2 units was 0.15 eV lower in energy than interstitial H2 molecules, however, a lower energy geometry with a half-stacking fault, ð2Si2HÞSF=2 , was also simulated. Martsinovich et al. [8] showed that such topological defects may be important for small platelets. Kim and Chang [9] developed a model for the conversion of the double-layer H2 units into the third structure modelled by Dea´k et al. with production of a hydrogen molecule per repeat unit. Relatively few studies exist for platelets in Ge (for example see Refs. [10,11]). Hiller et al. [12] observe the formation of molecule containing platelets after hydrogenation. Modes at 1980 and 4155 cm1 were assigned to Ge–H and H2 vibrations in the resulting structure. Additionally an assignment for the isolated H2 molecule in Ge was made to a mode at 3925 cm1 (see Table 1 and Ref. [13]).
120 Ry plane-wave fitting to the charge density, with a 23 or 6 6 2 Monkhorst–Pack [17] k-point sampling scheme for the molecules or platelets. Hartwigsen–Goedecker– Hutter [18] pseudopotentials were used for the semiconductor hosts while a bare proton was used for the hydrogen potential. All atoms were allowed to relax by a conjugate gradient method (in the case of the platelets the energy was also minimised with respect to the lattice vectors). The second derivatives of the energy were found for the H atoms and immediate neighbours, in the case of the platelet geometries, the cells were repeated to a 3 3 1 geometry before calculation of the derivatives. Quasi-harmonic vibrational modes were then calculated from the dynamical matrix (further details are given in Ref. [14]). The error in the calculated modes of the molecules, between the 216 atom host values presented here and for a 512 atom cell, was estimated to be 3 cm1 by comparing against minimal contracted basis calculations for 64, 216 and 512 cells.
2. Calculations
3.1. Interstitial molecules
The observed modes were compared against firstprinciples density functional results [14,15], in conjunction with cubic cells of between 64 and 512 atoms for the molecule and 12 atom trigonal cells for the platelets. The wavefunctions of the host material were represented with a real-space contracted Cartesian–Gaussian basis centred on each atom, using two independent contracted groups of four separate exponents (with different contraction coefficients for s and p) and an additional uncontracted d set. The hydrogen used an uncontracted set of 4 s and p functions. The Hartree and Perdew–Wang [16] exchangecorrelation energies were calculated using a converged
The resulting modes for interstitial H2 in Si, GaAs and Ge are shown in Table 1, for statically aligned molecules along ½1 0 0, ½1 1 0 and ½1 1 1 directions. The energy differences between these orientations are negligible (5 meV in all host materials shown), and the molecule is then expected to be a free rotor, in agreement with previous results (see for example Refs. [19,20]). From these statically aligned calculations, an estimate can be made for the vibrational mode of the J ¼ 0 molecule by taking a weighted average of the static configurations. This leads to modes of 3713, 3222, and 2627 cm1 for interstitial H2 , HD, and D2 in Ge. The H2 mode falls 120 cm1
3. Results
ARTICLE IN PRESS B. Hourahine et al. / Physica B 376–377 (2006) 105–108
lower than the observed value, this is also typical of the error in calculated H2 modes for Si and GaAs. However, the calculated values for the molecule at the As surrounded T site in GaAs are in somewhat poorer agreement with experiment, 200 cm1 in the case of H2 . Notice that GaAs is a compound semiconductor and because of this there are two possible interstitial sites for H2 : one with Ga closest neighbours (T Ga ), the other one with As atoms nearby (T As ). For H2 in Si, Ge, and at the T Ga site in GaAs, the calculations systematically underestimate the observed frequencies by about 120 cm1 . Following this trend, one would expect the mode for H2 at the T As site in GaAs to lie around 3950 cm1 rather than the observed 4043 cm1 [21]. This discrepancy could hint that either the behaviour of H2 when surrounded by anions differs from the other three cases, or that the Raman mode at 4043 cm1 may instead possibly be due to H2 trapped in some kind of void or platelet.
107
Table 3 Vibrational modes of several platelet structures, cm1 H
D
H
D
(2Ge–H)
1966 1886
1400 1343
ð2Ge2HÞSF=2
1990 1961
1417 1396
ðH2 Þ
1837 1695
1308 1206
ðH2 ÞSF=2
1920 1740
1367 1238
(2Ge–H + H2 )
4111 1984 1882
2909 1420 1341
(2Ge–H + 2H2 )
4146 2025 1956
2933 1441 1393
The average position of the vibrational bands are shown.
50 cm1 . This then suggests that the width of the band observed at 1980 and 4155 cm1 may in part be due to a range of concentrations of hydrogen molecules in different platelets.
3.2. Platelets 4. Conclusions The energies of several platelet geometries are shown in Table 2 for a chemical potential of half the energy of an interstitial H2 molecule in Ge (however, platelet containing material is unlikely to be in thermodynamic equilibrium). For the geometries which do not contain H2 molecules, the double-layer H2 structure of Zhang et al. ðH2 ÞD is found to be the lowest in energy, however, a structure where two adjacent ð1 1 1Þ layers of Ge–Ge bonds are broken and passivated is also found to be competitive energetically (4Ge–H). Structures containing molecules are found to be lower in energy (as would be expected by the larger open space inside a platelet when compared to the interstitial site in Ge) and further decrease with additional H2 (2Ge–H + 2H2 ). The presence of half-stacking faults is found to have a relatively small effect on the energy of the platelets. The vibrational modes of a few structures are shown in Table 3. The molecule containing platelets posses modes at around 4120 cm1 , with the frequency increasing as a second molecule is added. There are two bands of Ge–H related modes in these structures, and again increasing the number of hydrogen molecules pushes these upwards by
Table 2 Energy of several platelet geometries in germanium E f (eV) DC (A˚) (2Ge–H) H2
0.4 0.6 1.0 ðH2 ÞD (2Ge–H + H2 ) 1.2 (2Ge–H + 2H2 ) 2.0
2.38 0.90 2.44 2.42 2.67
E f (eV) Dc (A˚) ð2Ge2HÞSF=2 ðH2 ÞSF=2 (4Ge–H) (2Ge–H + H2 ÞSF=2
0.5 0.6 0.9 1.2
1.14 0.84 4.43 2.21
The hydrogen chemical potential is chosen to be half of the energy of H2 at a T site in Ge. Formation energies compared to the molecule, and dilation along the c direction are shown. SF/2 denotes the presence of a halfstacking fault in the structure.
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