Ab-Initio Calculation of the Optical Properties of Silicon Quantum Wires
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63 Mat. Roe.Soc. Symp. Proc. Vol. 452 0 1997 Materials Research Society
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E2
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Figure 1: (a) Imaginary part of the dielectric function C2for the 5x4 Si quantum wire, after a gaussian broadening of 0.02 eV. z polarization (solid line); average between x and y polarizations (dotdashed line). (b) The same for the 3x4 Si quantum wire
wire the cross section is delimited by zig-zag chains of 7 and 4 Si atoms,the edges being respectively t1.52 A and 5.76 Along. This structure is referred as 7x4. The smaller wire has a 3x4 structure of cross section 3.84 x 5.76 A2 . The intermediate ones has a 5x4 structure (7.68 x 5.76 A2 ). In the fully passivated wire all the dangling bonds are saturated by H atoms. We use crystalline-like Si-Si distance and a Si-Il distance of 1.64 A [7]. By varying the size of the vacuum region we move from isolated, non interacting wire to structures, where strong wire-wire interaction is present. The structures describing the partial passivated QW are obtained by removing the H atoms, those describing O-Si interaction are obtained substituting some of the H atoms with a 0-I1 complex, where the Si-O distance is 1.64 A, and the 0-H distance is 1.00 A [8]. The calculation of the optical properties is performed through the evaluation of the dipole matrix elements within LMTO-ASA [6]. This allows to evaluate directly the imaginary part of the dielectric function 2 : C24
w)= .r.e22
1 < kcý,kzIPaI.,k, > 12 6[E(k,) - E,(k•)
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hw]
(1)
It is possible to have informations about the PL processes looking at the features of c2 , containing the various inter-band transitions, weighted by the momentum optical matrix element. The real part, ci(w), is obtained by a Kramers-Kronig transformation of c2(w) in which a tail of the same form used in Ref. 9 is used for energies greater than 12.0 eV. RESULTS AND DISCUSSION Quantum confinement. The 62 functions of the fully H-passivated 5x4 and 3x4 QW are shownl in panels (a) and (b) of Fig. 1 16]. From the figure it is evident that the blue shift of the gap increases when the dimensions of the QW are reduced. The LDA gap of the 5x4 Si wire is 2.58 eV, while that of the 3x4 is 3.27 eV. Taking into account the self-energy correction to our DFT values of the gap (about 0.8 eV for QW of the dimensions considered in this study)
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Figure 2: Real part. of tihe dlielc~tric function e• for thle 5x4 (solid line) and 3x4 (dotdashed line) Si quantuml wirces.
our results are not so far from the corresponding experimaental results for absorption in PS: Zhang and B~ayliss [2] found optical band gaps of 2.3, 2.6 and 3 eV for fresh PS samples, whose wire diameters have been estimated to be 22, 19 and 13 A respectively. Furtherly, both Fig. 1(a) and 1(b) show well defined structures in the low energy side of the main peak of E2. These features, not present in bulk Si, are mainly related to the p~olar'
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