Absolute frequency measurements of the D2D_2 line and fine-structure interval in 39^{39}K

We report a value for the $D_2$-line frequency of $^{39}$K with 0.25 ppb uncertainty. The frequency is measured using an evacuated ring-cavity resonator whose length is calibrated against a reference laser. The $D_2$ line presents a problem in identifying the line center because the closely-spaced energy levels of the excited state are not resolved. We use computer modelling of the measured spectrum to extract the line center and obtain a value of 391 015 578.040(75) MHz. In conjunction with our previous measurement of the $D_1$ line, we determine the fine-structure interval in the $4P$ state to be 1 729 997.132(90) MHz. The results represent significant improvement over previous values.Comment: 4 pages, 3 figure

Re‐emitted positron spectroscopy of cobalt and nickel silicide films

The techniques of re‐emitted positron spectroscopy (RPS) have been employed in the first systematic investigation of the positronic properties of the various stoichiometric phases (M2Si, MSi, and MSi2) of Co and Ni silicide films grown in situ on Si substrates. The positron work function is found to be negative for all of the different phases; thus implanted positrons may be re‐emitted. The energy of the re‐emitted positrons is found to have a surprisingly large variation for the different phases. This feature should provide the image contrast necessary to observe each phase on a microscopic scale using the positron re‐emission microscope (PRM). The positron deformation potential, E+d≡V(∂Σ/∂V), was determined for CoSi2 films; it can be used to estimate the size of the positron diffusion constant, which is found to be comparable to that of other metals. Thus the short positron diffusion length (of order 150 Å) determined from depth‐profiling measurements of CoSi2 films must be a result of positron trapping in either the film or at the interface with the Si substrate. RPS results considered as a function of film thickness support the conclusion that defects in the film (misfit dislocations and/or vacancies) represent the major source of positron trapping.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87603/2/264_1.pd

Depth-profiling plasma-induced densification of porous low-k thin films using positronium annihilation lifetime spectroscopy

Positronium annihilation lifetime spectroscopy (PALS) has been used to depth profile the densification induced in a porous low-dielectric constant (k) thin film by typical device integration processing, including exposure to plasmas and oxygen ashing. Such “integration damage” has previously been observed as an undesirable increase in k accompanied by shrinkage in the porous film thickness. PALS confirms that the structural damage is confined to a surface layer of collapsed pores with the underlying pores being undamaged. The dense layer thickness determined by PALS increases with plasma exposure time. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70582/2/APPLAB-81-8-1447-1.pd

Positron tunneling microscopy

A new technique for analyzing thin film growth processes, called positron tunneling microscopy (PTM), is proposed as an extension of the recently developed positron reemission microscope. The unique feature of a PTM is that image contrast is provided by the exponential reemission probability for positrons tunneling through thin-film overlayers that present an energy barrier to reemission. Results of positron tunneling experiments show that PTM should have monolayer thickness resolution to processes that locally affect either the tunneling barrier's width, such as islanding and subsurface roughness, or the barrier's energy, such as lattice strain in pseudomorphic growth and compositional mixing in interdiffusion alloying. In the case of these latter effects where there may be no topological contrasts at all, experimental results are discussed in greater detail. Comparisons of PTM with existing electron microscopies are presented where appropriate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28554/1/0000356.pd

Revealing hidden pore structure in nanoporous thin films using positronium annihilation lifetime spectroscopy

The highly inhomogeneous pore morphology of a plasma-enhanced-chemical-vapor-deposited ultralow-kk dielectric film (k = 2.2)(k=2.2) has been revealed using depth-profiled positronium annihilation lifetime spectroscopy (PALS) combined with progressive etch back of the film surface. The film is found to have a dense surface layer, an intermediate layer of 1.8 nm1.8nm diameter mesopores, and a deep region of ∼ 3 nm∼3nm diameter mesopores. After successively etching of the sealing layer and the isolated 1.8 nm1.8nm pore region, PALS reveals that the underlying large pores are highly interconnected. This inhomogeneous pore structure is proposed to account for observed difficulties in film integration.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87843/2/121904_1.pd

The critical window for the classical Ramsey-Tur\'an problem

The first application of Szemer\'edi's powerful regularity method was the following celebrated Ramsey-Tur\'an result proved by Szemer\'edi in 1972: any K_4-free graph on N vertices with independence number o(N) has at most (1/8 + o(1)) N^2 edges. Four years later, Bollob\'as and Erd\H{o}s gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K_4-free graph on N vertices with independence number o(N) and (1/8 - o(1)) N^2 edges. Starting with Bollob\'as and Erd\H{o}s in 1976, several problems have been asked on estimating the minimum possible independence number in the critical window, when the number of edges is about N^2 / 8. These problems have received considerable attention and remained one of the main open problems in this area. In this paper, we give nearly best-possible bounds, solving the various open problems concerning this critical window.Comment: 34 page

Probing diffusion barrier integrity on porous silica low-k thin films using positron annihilation lifetime spectroscopy

The technique of positron annihilation lifetime spectroscopy (PALS) has been used to investigate the continuity and thermal stability of thin barrier layers designed to prevent Cu atom diffusion into porous silica, low-dielectric constant (k) films. Nanoglass™ K2.2-A10C (A10C), a porous organosilicate film, is determined to have interconnected pores with an average tubular-pore diameter of (6.9 ± 0.4) nm. Cu deposited directly on the A10C films is observed to diffuse into the porous structure. The minimum necessary barrier thickness for stable continuity of Ta and TaN layers deposited on A10C is determined by detecting the signal of positronium (Ps) escaping into vacuum. It is found that the 25 nm thick layers do not form continuous barriers. This is confirmed by the presence of holes observed in such films using a transmission electron microscope. Although 35 nm and 45 nm Ta and TaN layers perform effectively at room temperature as Ps barriers, only the Ta-capped samples are able to withstand heat treatments up to 500 °C500 °C without breakdown or penetration into the porous film. TaN interdiffusion into the silica pores is indicated by the reduction of the Ps lifetime after high annealing temperatures. The validity of using Ps diffusion to test barrier layers designed to inhibit Cu diffusion is discussed. The procedures to standardize the testing of barrier layer integrity and thermal stability using PALS are proposed. Extension to probing barrier layers in realistic vias and trenches should be straightforward. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71187/2/JAPIAU-89-9-5138-1.pd

An overview of the Michigan Positron Microscope Program

An overview of the Michigan Positron Microscope Program is presented with particular emphasis on the second generation microscope that is presently near completion. The design and intended applications of this microscope will be summarized.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87602/2/391_1.pd

Bounds for graph regularity and removal lemmas

We show, for any positive integer k, that there exists a graph in which any equitable partition of its vertices into k parts has at least ck^2/\log^* k pairs of parts which are not \epsilon-regular, where c,\epsilon>0 are absolute constants. This bound is tight up to the constant c and addresses a question of Gowers on the number of irregular pairs in Szemer\'edi's regularity lemma. In order to gain some control over irregular pairs, another regularity lemma, known as the strong regularity lemma, was developed by Alon, Fischer, Krivelevich, and Szegedy. For this lemma, we prove a lower bound of wowzer-type, which is one level higher in the Ackermann hierarchy than the tower function, on the number of parts in the strong regularity lemma, essentially matching the upper bound. On the other hand, for the induced graph removal lemma, the standard application of the strong regularity lemma, we find a different proof which yields a tower-type bound. We also discuss bounds on several related regularity lemmas, including the weak regularity lemma of Frieze and Kannan and the recently established regular approximation theorem. In particular, we show that a weak partition with approximation parameter \epsilon may require as many as 2^{\Omega(\epsilon^{-2})} parts. This is tight up to the implied constant and solves a problem studied by Lov\'asz and Szegedy.Comment: 62 page

Chosen-ciphertext security from subset sum

We construct a public-key encryption (PKE) scheme whose security is polynomial-time equivalent to the hardness of the Subset Sum problem. Our scheme achieves the standard notion of indistinguishability against chosen-ciphertext attacks (IND-CCA) and can be used to encrypt messages of arbitrary polynomial length, improving upon a previous construction by Lyubashevsky, Palacio, and Segev (TCC 2010) which achieved only the weaker notion of semantic security (IND-CPA) and whose concrete security decreases with the length of the message being encrypted. At the core of our construction is a trapdoor technique which originates in the work of Micciancio and Peikert (Eurocrypt 2012