Oxidation kinetics of thin copper films and wetting behaviour of copper and Organic Solderability Preservatives (OSP) with lead-free solder

The oxide formation on thin copper films deposited on Si wafer was studied by XPS, SEM and Sequential Electrochemical Reduction Analysis SERA. The surfaces were oxidized in air with a reflow oven as used in electronic assembly at temperatures of 100 °C, 155 °C, 200 °C, 230 °C and 260 °C. The SERA analyses detected only the formation of Cu₂O but the XPS analysis done for the calibration of the SERA equipment proved also the presence of a CuO layer smaller than 2 nm above the Cu₂O oxide. The oxide growth follows a power-law dependence on time within this temperature range and an activation energy of 33.1 kJ/mol was obtained. The wettability of these surfaces was also determined by measuring the contact angle between solder and copper substrate after the soldering process. A correlation between oxide thickness and wetting angle was established. It was found that the wetting is acceptable only when the oxide thickness is smaller than 16 nm. An activation energy of 27 kJ/mol was acquired for the spreading of lead free solder on oxidized copper surfaces.From wetting tests on copper surfaces protected by Organic Solderability Preservatives (OSP), it was possible to calculate the activation energy for the thermal decomposition of these protective layers.     

Discrete optimization in public rail transport

Many problems arising in traffic planning can be modelled and solved using discrete optimization. We will focus on recent developments which were applied to large scale real world instances. Most railroad companies apply a hierarchically structured planning process. Starting with the definition of the underlying network used for transport one has to decide which infrastructural improvements are necessary. Usually, the rail system is periodically scheduled. A fundamental base of the schedule are the lines connecting several stations with a fixed frequency. Possible objectives for the construction of the line plan may be the minimization of the total cost or the maximization of the passengers’s comfort satisfying certain regulations. After the lines of the system are fixed, the train schedule can be determined. A criterion for the quality of a schedule is the total transit time of the passengers including the waiting time which should be minimized satisfying some operational constraints. For each trip of the schedule a train consisting of a locomotive and some carriages is needed for service. The assignment of rolling stock to schedule trips has to satisfy operational requirements. A comprehensible objective is to minimize the total cost. After all strategic and tactical planning the schedule has to be realized. Several external influences, for example delayed trains, force the dispatcher to recompute parts of the schedule on-line. A Web page with examples quoted in this survey can be found at http://www.math.tu-bs.de/mo/ismp.html.     

Real-time path integral approach to nonequilibrium many-body quantum systems

A real-time path-integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system coupled to a phonon background until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the evolution of the system in the interaction picture which is amenable to an efficient path integral (worldline) Monte Carlo approach. Results obtained for a model of inelastic tunneling spectroscopy reveal the applicability of the approach to a wide range of physically important regimes, including high (classical) and low (quantum) temperatures, and weak (perturbative) and strong electron-phonon couplings.     

Error bounds on complex floating-point multiplication

Given floating-point arithmetic with -digit base- significands in which all arithmetic operations are performed as if calculated to infinite precision and rounded to a nearest representable value, we prove that the product of complex values and can be computed with maximum absolute error . In particular, this provides relative error bounds of and for IEEE 754 single and double precision arithmetic respectively, provided that overflow, underflow, and denormals do not occur.

We also provide the numerical worst cases for IEEE 754 single and double precision arithmetic.

     

Recursion relations for the extended Krylov subspace method

The evaluation of matrix functions of the form f(A)v, where A is a large sparse or structured symmetric matrix, f is a nonlinear function, and v is a vector, is frequently subdivided into two steps: first an orthonormal basis of an extended Krylov subspace of fairly small dimension is determined, and then a projection onto this subspace is evaluated by a method designed for small problems. This paper derives short recursion relations for orthonormal bases of extended Krylov subspaces of the type K^m,mi+1(A)=span{A^-m+1v,…,A^-1v,v,Av,…,A^miv}, m=1,2,3,…, with i a positive integer, and describes applications to the evaluation of matrix functions and the computation of rational Gauss quadrature rules.     

On the choice of solution subspace for nonstationary iterated Tikhonov regularization

Tikhonov regularization is a popular method for the solution of linear discrete ill-posed problems with error-contaminated data. Nonstationary iterated Tikhonov regularization is known to be able to determine approximate solutions of higher quality than standard Tikhonov regularization. We investigate the choice of solution subspace in iterative methods for nonstationary iterated Tikhonov regularization of large-scale problems. Generalized Krylov subspaces are compared with Krylov subspaces that are generated by Golub–Kahan bidiagonalization and the Arnoldi process. Numerical examples illustrate the effectiveness of the methods.     

Recurrence relations for orthogonal rational functions

It is well known that members of families of polynomials, that are orthogonal with respect to an inner product determined by a nonnegative measure on the real axis, satisfy a three-term recursion relation. Analogous recursion formulas are available for orthogonal Laurent polynomials with a pole at the origin. This paper investigates recursion relations for orthogonal rational functions with arbitrary prescribed real or complex conjugate poles. The number of terms in the recursion relation is shown to be related to the structure of the orthogonal rational functions.     

1-Ethoxycarbonyl-3-ferrocenyl-propan-1,3-dion und Ferrocen-1,1'bis(2,4-dioxobutansäureethylester) als Liganden für Übergangsmetallionen. Kristallstruktur von Bis(1-ethoxycarbonyl-3-ferrocenyl-propan-1,3dionato)kupfer(II)

1-Ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and Ferrocene-1,1′bis(2,4-dioxobutanoic acid ethylester) as Ligands for Transition Metal Ions. Crystal Structure of Bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3dionato)copper(II) The ligands 1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dion and ferrocene-1,1′-bis(2,4-dioxo-butanoic acid ethylester) have been prepared by reaction of acetylferrocene or 1,1′-diacetylferrocene and diethyl oxalate. They yield neutral chelates with Cu^II, Ni^II, Zn^II, Co^II, and Mn^II. The acid dissociation constants of the ligands and the stability constants of their metal complexes including Fe^II complexes are reported. The structure of bis(1-ethoxycarbonyl-3-ferrocenyl-propane-1,3-dionato)copper(II) was determined by X-ray structure analysis. A cis arrangement with a nearly square planar coordination sphere at the Cu atom is found.