Catalytically mediated epitaxy of 3D semiconductors on van der Waals substrates

The formation of well-controlled interfaces between materials of different structure and bonding is a key requirement when developing new devices and functionalities. Of particular importance are epitaxial or low defect density interfaces between 2D materials and 3D semiconductors or metals, where interfacial structure influences electrical conductivity in field effect and optoelectronic devices, charge transfer for spintronics and catalysis and proximity-induced superconductivity. Epitaxy and hence well-defined interfacial structures have been demonstrated for several metals on van der Waals-bonded substrates. Semiconductor epitaxy on such substrates has been harder to control, for example during chemical vapor deposition of Si and Ge on graphene. Here, we demonstrate a catalytically-mediated heteroepitaxy approach to achieve epitaxial growth of 3D semiconductors such as Ge and Si on van der Waals-bonded materials such as graphene and hexagonal boron nitride. Epitaxy is “transferred” from the substrate to semiconductor nanocrystals via solid metal nanocrystals that readily align on the substrate and catalyze the formation of aligned nuclei of the semiconductor. In situ transmission electron microscopy allows us to elucidate the reaction pathway for this process and to show that solid metal nanocrystals can catalyze semiconductor growth at a significantly lower temperature than direct chemical vapor deposition or deposition mediated by liquid catalyst droplets. We discuss Ge and Si growth as a model system to explore the details of such heterointerfacing and its applicability to a broader range of materials.This work was supported by the EPSRC (EP/K016636/1 and EP/P005152/1) and ERC (Grant 279342: InSituNANO

Catalytically mediated epitaxy of 3D semiconductors on van der Waals substrates

The formation of well-controlled interfaces between materials of different structure and bonding is a key requirement when developing new devices and functionalities. Of particular importance are epitaxial or low defect density interfaces between two-dimensional materials and three-dimensional semiconductors or metals, where an interfacial structure influences electrical conductivity in field effect and optoelectronic devices, charge transfer for spintronics and catalysis, and proximity-induced superconductivity. Epitaxy and hence well-defined interfacial structure has been demonstrated for several metals on van der Waals-bonded substrates. Semiconductor epitaxy on such substrates has been harder to control, for example during chemical vapor deposition of Si and Ge on graphene. Here, we demonstrate a catalytically mediated heteroepitaxy approach to achieve epitaxial growth of three-dimensional semiconductors such as Ge and Si on van der Waals-bonded materials such as graphene and hexagonal boron nitride. Epitaxy is “transferred” from the substrate to semiconductor nanocrystals via solid metal nanocrystals that readily align on the substrate and catalyze the formation of aligned nuclei of the semiconductor. In situ transmission electron microscopy allows us to elucidate the reaction pathway for this process and to show that solid metal nanocrystals can catalyze semiconductor growth at a significantly lower temperature than direct chemical vapor deposition or deposition mediated by liquid catalyst droplets. We discuss Ge and Si growth as a model system to explore the details of such hetero-interfacing and its applicability to a broader range of materials.This work was supported by the EPSRC (EP/K016636/1 and EP/P005152/1) and ERC (Grant 279342: InSituNANO

An arithmetic regularity lemma, associated counting lemma, and applications

Szemeredi's regularity lemma can be viewed as a rough structure theorem for arbitrary dense graphs, decomposing such graphs into a structured piece (a partition into cells with edge densities), a small error (corresponding to irregular cells), and a uniform piece (the pseudorandom deviations from the edge densities). We establish an arithmetic regularity lemma that similarly decomposes bounded functions f : [N] -> C, into a (well-equidistributed, virtual) -step nilsequence, an error which is small in L^2 and a further error which is miniscule in the Gowers U^{s+1}-norm, where s is a positive integer. We then establish a complementary arithmetic counting lemma that counts arithmetic patterns in the nilsequence component of f. We provide a number of applications of these lemmas: a proof of Szemeredi's theorem on arithmetic progressions, a proof of a conjecture of Bergelson, Host and Kra, and a generalisation of certain results of Gowers and Wolf. Our result is dependent on the inverse conjecture for the Gowers U^{s+1} norm, recently established for general s by the authors and T. Ziegler