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4
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84927265778
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There are too many experimental studies of the Si(100) surface to be considered in detail here. References to work which will not be considered explicitly below can be found in J.E. Griffith and G.P. Kochanski, Crit. Rev. Solid State Mat. Sci. 16, 255 (1990); R.I.G. Uhrberg and G.V. Hansson, ibid. 17, 133 (1991).
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5
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0027038172
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It is also not possible to give a comprehensive list of references to theoretical work dealing with the reconstruction of the Si(100) surface. We will restrict ourselves to a consideration of recent first principles studies and only refer to a small number of other theoretical works. More extensive references can be found in J.P. Lafemina
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It is also not possible to give a comprehensive list of references to theoretical work dealing with the reconstruction of the Si(100) surface. We will restrict ourselves to a consideration of recent first principles studies and only refer to a small number of other theoretical works. More extensive references can be found in J.P. Lafemina, Surf. Sci. Rep. 16, 133 (1992).
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(1992)
Surf. Sci. Rep.
, vol.16
, pp. 133
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24
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84927265775
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Analogous studies have been made of the Ge surface.
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54
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1842816907
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In this scheme, only special k points in the interior of the Brillouin zone are used. This scheme has the disadvantage that each sampling density is obtained by using a unique set of k points. That is, none of the kpoints used in one grid can be kept when upgrading to a finer grid.
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(1976)
Phys. Rev. B
, vol.13
, pp. 5188
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Monkhorst, H.J.1
Pack, J.D.2
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55
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84927265773
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Although the sampling densities are equal, the four points chosen for the c(4 ×2) surface are not the same as for the other reconstructions. The reason for not using identical sampling points for the two unit cells from the start is that we want to begin with special symmetry points that are mapped onto themselves by the symmetry operations of time reversal and lattice translation. For these points, one can make use of the symmetry so that only half the number of expansion coefficients for the wave functions are needed, thus gaining a factor 4 in computation speed and making this scheme as efficient as the Monkhorst Pack scheme (Ref. 50). These are the only points that will be treated self consistently and must therefore be calculated first. For the p(2 ×2) reconstruction these points are Γ, J, K, and J′ and for the c(4 ×2) reconstruction, Γ, J, and the point midway between J′ and K. After we have completed our convergence tests and want to compare absolute energies, we shall take care to use identical samplings.
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59
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84927265772
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P.J.H. Denteneer, Ph.D. thesis, Eindhoven Technical University, 1987;
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62
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84927265771
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One should always compare energies calculated with exactly the same k points. As noted earlier, the four k points calculated self consistently are not the same for the p(2 ×2) and c(4 ×2) unit cells. To calculate the appropriate eigenvalue sums, we regroup the points so that the 4 k point energy for the c(4 ×2) reconstruction was calculated using the same sampling points as for the other reconstructions.
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65
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84927265770
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Where the effect of the geometry optimization has been calculated explicitly with a higher cutoff energy, the corresponding correction could be made to the energy difference shown in Fig. refres. Because we have not calculated it for cutoffs higher than 16 Ry for all the reconstructions, we choose to include the correction as part of the error.
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69
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84927265769
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G. Brocks and P.J. Kelly, (unpublished).
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73
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84927265768
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This relationship is largely empirical. In general, the total energy is not given by a sum of single particle eigenvalues. The usual approach is to relate total energy differences to differences between sums of single particle eigenvalues using a force theorem or frozen potential type approximation; see Ref. onlineciteForce. We are not aware of any attempts to apply such ideas within the framework of plane wave pseudopotential calculations.
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74
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84927265767
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This splitting must occur in all calculations which make use of a slab representation (Refs. 9 11,13 15,17,19,20). The simplest way to remove this blemish is to take the average of the split pairs, which is presumably the solution adopted by most of the above authors. A more difficult problem is that of identifying resonant states. We are not aware of any simple way of doing this unambiguously for a finite slab. This problem is, at least formally, best treated with Greens function methods. See Ref. onlineciteKruger and references therein.
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