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We show that under general conditions there is at least one natural inflationary direction for the Kähler moduli of type-IIB flux compactifications. This requires a Calabi-Yau which has h 2,1 > h 1,1 > 2 and for which the structure of the scalar potential is as in the recently found exponentially large volume compactifications. We also need -although these conditions may be relaxed -at least one Kähler modulus whose only non-vanishing tripleintersection is with itself and which appears by itself in the non-perturbative superpotential. Slow-roll inflation then occurs without a fine tuning of parameters, evading the η problem of F-term inflation. In order to obtain COBE-normalised density perturbations, the stabilised volume of the Calabi-Yau must be O(10 5 − 10 7 ) in string units, and the inflationary scale M inf l ∼ 10 13 GeV. We find a robust model independent prediction for the spectral index of 1 − 2 Ne = 0.960 → 0.967, depending on the number of efoldings.

Powder and double-crystal x-ray diffraction were used to study the structural propenies of highly strained (GaAs)N/(GaP)M short-period superlattices grown on GaAs (001) substrates. In spite of the large lattice mismatch (f = 3.6%) between GaAs and GaP and the competition for incorporation between As and F: high-quality short-period superlattices of GaAslGaP have been grown by a development of conventional moiecular beam epitaxy named atomic layer molecular beam epitaxy. The in-plane lattice parameter (ail) of the different superlattices was measured and studied as a function of the GaP content. We found that, for a given total superlattice thickness of 4000 A, the ctitical lattice mismatch is f. Y 0.5% (corresponding to an average GaP content of 13.6% in the superlattice). This means that for an average misfit or lattice mismatch above f, the superlattice staris to relax This experimental result is compared with predictions of critical thickness theories based on energy criteria. A clear relation of the degree of relaxation with peak width of the superlattice zeroth-order diffraction peak is found. High-resolution transmission electron microscopy has been performed to analyse the type of dislocations that relax the mismatched layers. 1. AppL Phys. 62 3898 Anderson T G, Chen 2 G, Kulakovskii V D, Uddin A and Wtin J T 19&7 Appl. Phys. Lerr. 51 752 Morris D, Roth A P, Masut RA, Lacelle C and Brebner J L 1988 J. Appl. Phys. 64 4135 Reithmaier J P, C e m H and Mch R 19895. Appl. Weng S L 1989 J. Appl. Phys. 66 2217 Phys. 54 48 A1 72

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