Epitaxial metal nanocrystal-semiconductor quantum dot hybrid structures for plasmonics

Many mathematical objects are closely related to each other. While studying certain aspects of a mathematical object, one tries to find a way to "view" the object in a way that is most suitable for a specific problem. Or, in other words, one tries to find the best way to model the problem. Many related fields of mathematics have evolved from one another this way. In practice, it is very useful to be able to transform a problem into other terminology: it gives a lot more available knowledge and that can be helpful to solve a problem. This thesis deals with various closely related fields in discrete mathematics, starting from linear error-correcting codes and their weight enumerator. We can generalize the weight enumerator in two ways, to the extended and generalized weight enumerators. The set of generalized weight enumerators is equivalent to the extended weight enumerator. Summarizing and extending known theory, we define the two-variable zeta polynomial of a code and its generalized zeta polynomial. These polynomials are equivalent to the extended and generalized weight enumerator of a code. We can determine the extended and generalized weight enumerator using projective systems. This calculation is explicitly done for codes coming from finite projective and affine spaces: these are the simplex code and the first order Reed-Muller code. As a result we do not only get the weight enumerator of these codes, but it also gives us information on their geometric structure. This is useful information in determining the dimension of geometric designs. To every linear code we can associate a matroid that is representable over a finite field. A famous and well-studied polynomial associated tomatroids is the Tutte polynomial, or rank generating function. It is equivalent to the extended weight enumerator. This leads to a short proof of the MacWilliams relations for the extended weight enumerator. For every matroid, its flats form a geometric lattice. On the other hand, every geometric lattice induces a simple matroid. The Tutte polynomial of a matroid determines the coboundary polynomial of the associated geometric lattice. In the case of simple matroids, this becomes a two-way equivalence. Another polynomial associated to a geometric lattice (or, more general, to a poset) is the Möbius polynomial. It is not determined by the coboundary polynomial, neither the other way around. However, we can give conditions under which the Möbius polynomial of a simple matroid together with the Möbius polynomial of its dual matroid defines the coboundary polynomial. The proof of these relations involves the two-variable zeta polynomial, that can be generalized from codes to matroids. Both matroids and geometric lattices can be truncated to get an object of lower rank. The truncated matroid of a representable matroid is again representable. Truncation formulas exist for the coboundary and Möbius polynomial of a geometric lattice and the spectrum polynomial of a matroid, generalizing the known truncation formula of the Tutte polynomial of a matroid. Several examples and counterexamples are given for all the theory. To conclude, we give an overview of all polynomial relations

Coupling of single InGaAs quantum dots to the plasmon resonance of a metal nanocrystal

The authors report the coupling of single InGaAs quantum dots (QDs) to the surface plasmon resonance of a metal nanocrystal. Clear enhancement of the photoluminescence (PL) in the spectral region of the surface plasmon resonance is observed which splits up into distinct emission lines from single QDs in micro-PL. The hybrid metal-semiconductor structure is grown by molecular beam epitaxy on GaAs (100) utilizing the concept of self-organized anisotropic strain engineering for realizing ordered arrays with nanometer-scale precise positioning of the metal nanocrystals with respect to the QD

Long wavelength (> 1.55 mu m) room temperature emission and anomalous structural properties of InAs/GaAs quantum dots obtained by conversion of In nanocrystals

We demonstrate that molecular beam epitaxy-grown InAs quantum dots (QDs) on (100) GaAs obtained by conversion of In nanocrystals enable long wavelength emission in the InAs/GaAs material system. At room temperature they exhibit a broad photoluminescence band that extends well beyond 1.55 mu m. We correlate this finding with cross-sectional scanning tunneling microscopy measurements. They reveal that the QDs are composed of pure InAs which is in agreement with their long-wavelength emission. Additionally, the measurements reveal that the QDs have an anomalously undulated top surface which is very different to that observed for Stranski-Krastanow grown QDs

Epitaxial metal nanocrystal-semiconductor quantum dot hybrid structures for plasmonics

Many mathematical objects are closely related to each other. While studying certain aspects of a mathematical object, one tries to find a way to "view" the object in a way that is most suitable for a specific problem. Or, in other words, one tries to find the best way to model the problem. Many related fields of mathematics have evolved from one another this way. In practice, it is very useful to be able to transform a problem into other terminology: it gives a lot more available knowledge and that can be helpful to solve a problem. This thesis deals with various closely related fields in discrete mathematics, starting from linear error-correcting codes and their weight enumerator. We can generalize the weight enumerator in two ways, to the extended and generalized weight enumerators. The set of generalized weight enumerators is equivalent to the extended weight enumerator. Summarizing and extending known theory, we define the two-variable zeta polynomial of a code and its generalized zeta polynomial. These polynomials are equivalent to the extended and generalized weight enumerator of a code. We can determine the extended and generalized weight enumerator using projective systems. This calculation is explicitly done for codes coming from finite projective and affine spaces: these are the simplex code and the first order Reed-Muller code. As a result we do not only get the weight enumerator of these codes, but it also gives us information on their geometric structure. This is useful information in determining the dimension of geometric designs. To every linear code we can associate a matroid that is representable over a finite field. A famous and well-studied polynomial associated tomatroids is the Tutte polynomial, or rank generating function. It is equivalent to the extended weight enumerator. This leads to a short proof of the MacWilliams relations for the extended weight enumerator. For every matroid, its flats form a geometric lattice. On the other hand, every geometric lattice induces a simple matroid. The Tutte polynomial of a matroid determines the coboundary polynomial of the associated geometric lattice. In the case of simple matroids, this becomes a two-way equivalence. Another polynomial associated to a geometric lattice (or, more general, to a poset) is the Möbius polynomial. It is not determined by the coboundary polynomial, neither the other way around. However, we can give conditions under which the Möbius polynomial of a simple matroid together with the Möbius polynomial of its dual matroid defines the coboundary polynomial. The proof of these relations involves the two-variable zeta polynomial, that can be generalized from codes to matroids. Both matroids and geometric lattices can be truncated to get an object of lower rank. The truncated matroid of a representable matroid is again representable. Truncation formulas exist for the coboundary and Möbius polynomial of a geometric lattice and the spectrum polynomial of a matroid, generalizing the known truncation formula of the Tutte polynomial of a matroid. Several examples and counterexamples are given for all the theory. To conclude, we give an overview of all polynomial relations

In islands and their conversion to InAs quantum dots on GaAs (100): structural and optical properties

We report growth of crystalline In islands on GaAs (100) by molecular beam epitaxy at low temperatures. The islands have a pyramidlike shape with well defined facets and epitaxial relation with the substrate. They are of nanoscale dimensions with high density. Above a certain substrate temperature, associated with the melting point of In, noncrystalline round shaped islands form with larger size and lower density. Upon conversion of the In islands into InAs islands under As flux, the final shape does not depend on the original crystalline state but on the annealing temperature of the InAs islands. Clear photoluminescence is observed from InAs quantum dots after conversion of the crystalline In islands

Long wavelength (> 1.55 mu m) room temperature emission and anomalous structural properties of InAs/GaAs quantum dots obtained by conversion of In nanocrystals

We demonstrate that molecular beam epitaxy-grown InAs quantum dots (QDs) on (100) GaAs obtained by conversion of In nanocrystals enable long wavelength emission in the InAs/GaAs material system. At room temperature they exhibit a broad photoluminescence band that extends well beyond 1.55 mu m. We correlate this finding with cross-sectional scanning tunneling microscopy measurements. They reveal that the QDs are composed of pure InAs which is in agreement with their long-wavelength emission. Additionally, the measurements reveal that the QDs have an anomalously undulated top surface which is very different to that observed for Stranski-Krastanow grown QDs

Thermal and plasma enhanced atomic layer deposition of Al2O3on GaAs substrates

A good dielectric layer on the GaAs substrate is one of the critical issues to be solved for introducing GaAs as a candidate to replace Si in semiconductor processing. In literature, promising results have been shown for Al2O 3on GaAs substrates. Therefore, atomic layer deposition (ALD) of Al2O3has been studied on GaAs substrates. We have been investigating the influence of the ALD process (thermal vs plasma-enhanced ALD) as well as the influence of the starting surface (no clean vs partial removal of the native oxide). Ellipsometry and total X-ray reflection fluorescence were applied to study the growth of the ALD layers. Angle-resolved X-ray photoelectron spectroscopy was used to determine the composition of the interlayer. Both processes were shown to be roughly independent of the starting surface with a minor dependence for the thermal ALD. Thermally deposited ALD layers exhibited better electrical characteristics based on capacitance measurements. This could be linked to the thinner interlayer observed for thermally deposited Al2 O3. However, the Fermi level was not unpinned in all cases, suggesting that more work needs to be done for passivating the interface between GaAs and the high- k layer. © 2009 The Electrochemical Society