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56349145442
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In contrast to an NVT ensemble our system does not exchange heat with a thermal bath, instead the total energy is conserved, which enables us to investigate the energy transfer during these exothermic reactions. Introducing a thermostat would, in effect, introduce instantaneous cooling of the reaction, whereas for a semiconductor surface we expect heat transfer away from the adsorption site should occur primarily via phonon excitation and on a relatively long time scale.
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In contrast to an NVT ensemble our system does not exchange heat with a thermal bath, instead the total energy is conserved, which enables us to investigate the energy transfer during these exothermic reactions. Introducing a thermostat would, in effect, introduce instantaneous cooling of the reaction, whereas for a semiconductor surface we expect heat transfer away from the adsorption site should occur primarily via phonon excitation and on a relatively long time scale.
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56349084873
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For example, looking at the complete dissociation, a 0.75 ML O adatom coverage, corresponding to 3 O atoms in a (2×2) unit cell, is by 0.07 eV per O atom less stable than a coverage of 0.19 ML O adatoms, corresponding to 3 O atoms in a (4×4) unit cell.
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For example, looking at the complete dissociation, a 0.75 ML O adatom coverage, corresponding to 3 O atoms in a (2×2) unit cell, is by 0.07 eV per O atom less stable than a coverage of 0.19 ML O adatoms, corresponding to 3 O atoms in a (4×4) unit cell.
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56349137428
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On performing convergence tests with a higher k -point density (3×3×1 and 4×4×1), we reproduced the same trend in stability and obtained heats of adsorption for the lBB, DB, and Siu sites of 5.24, 5.04, and 4.15 eV, respectively.
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On performing convergence tests with a higher k -point density (3×3×1 and 4×4×1), we reproduced the same trend in stability and obtained heats of adsorption for the lBB, DB, and Siu sites of 5.24, 5.04, and 4.15 eV, respectively.
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56349108793
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The physical origin that a complete dissociation is the most stable reaction product can be viewed in terms of balancing the energy costs for splitting the O-O and Si-Si bonds with the energy gains for forming the Si-O bonds. Our calculations show that to split off a single gas phase O atom from the O3 costs 1.44 eV, whereas to split the remaining O2 costs a further 5.68 eV. Thus, a complete dissocation of ozone would cost 7.12 eV. On the other hand, the adsorption of a single O atom or three single O atoms, enables the formation of two or six Si-O bonds, respectively. Since the energy of Si-O bonds, however, varies dependent on structure, and since Si-Si bond are also broken, DFT calculations are crucial in understanding and determining the actual stability of each structure.
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The physical origin that a complete dissociation is the most stable reaction product can be viewed in terms of balancing the energy costs for splitting the O-O and Si-Si bonds with the energy gains for forming the Si-O bonds. Our calculations show that to split off a single gas phase O atom from the O3 costs 1.44 eV, whereas to split the remaining O2 costs a further 5.68 eV. Thus, a complete dissocation of ozone would cost 7.12 eV. On the other hand, the adsorption of a single O atom or three single O atoms, enables the formation of two or six Si-O bonds, respectively. Since the energy of Si-O bonds, however, varies dependent on structure, and since Si-Si bond are also broken, DFT calculations are crucial in understanding and determining the actual stability of each structure.
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56349087178
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In this adsorption site, the O atom bridges two Si atoms from neighboring dimers along the dimer row.
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In this adsorption site, the O atom bridges two Si atoms from neighboring dimers along the dimer row.
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32
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56349115146
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Depending on its recoil, we found trajectories where the gas phase O2, instead of desorbing, reacted with the Sid of the opposite row and dissociated in a way described by
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Depending on its recoil, we found trajectories where the gas phase O2, instead of desorbing, reacted with the Sid of the opposite row and dissociated in a way described by Ciacchi (Ref.).
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Ciacchi1
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56349170507
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Except for (a), where we used a (2×2) cell, we enlarged our surface cell in (b), (c), and (d) to a unit cell of (4×2) size, which includes two rows with two dimers each. Accordingly, we have adapted the k -point sampling for the (4×2) supercell to a Monkhorst-Pack grid of 1×2×1 dimensions. For visualization purposes we show figure (a) also as a (4×2) surface cell, by including periodic image atoms. The larger cells were necessitated by trajectories involving multiple adsorbed atoms spread across the simulation cell.
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Except for (a), where we used a (2×2) cell, we enlarged our surface cell in (b), (c), and (d) to a unit cell of (4×2) size, which includes two rows with two dimers each. Accordingly, we have adapted the k -point sampling for the (4×2) supercell to a Monkhorst-Pack grid of 1×2×1 dimensions. For visualization purposes we show figure (a) also as a (4×2) surface cell, by including periodic image atoms. The larger cells were necessitated by trajectories involving multiple adsorbed atoms spread across the simulation cell.
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To study how the highly exothermic complete dissociation affects the surface oxidation, longer time scales, surface temperature, and a larger unit cell would have to be considered, which is beyond the scope of this work.
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To study how the highly exothermic complete dissociation affects the surface oxidation, longer time scales, surface temperature, and a larger unit cell would have to be considered, which is beyond the scope of this work.
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56349091649
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The activation barriers for O diffusion from Siu to DB and lBB sites have been calculated by
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The activation barriers for O diffusion from Siu to DB and lBB sites have been calculated by Hemeryck (Ref.) to be 0.11 and 0.38 eV, respectively. Due to the large heat of adsorption released during the dissociation, the O adatom on the Siu diffuses easily into the more stable DB or lBB sites.
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Hemeryck1
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56349171931
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Ozone molecules with velocities ranging from 400-800 m/s gave the same qualitative reaction outcome.
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Ozone molecules with velocities ranging from 400-800 m/s gave the same qualitative reaction outcome.
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34249083772
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10.1016/j.susc.2007.03.038
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