Effect of pad geometry on current density and temperature distributions in solder bump joints

Three-dimensional thermo-electrical finite element analyses were conducted to simulate the current density and temperature distributions in solder bump joints with different pad geometries.The effects of pad thickness,diameter and shape on current density and temperate distributions were investigated respectively.It was found that pads with larger thickness or/and diameter could reduce current density and temperature in solder bump significantly.Pad shapes affected the current density and temperature distributions in solder bumps.The relatively low current density and temperature didn＇t occur in the bump joint with traditional rounded pad but occurred in bump joints with octagonal and nonagonal pads respectively.Therefore,optimized pad geometry may be designed to alleviate the current crowding effect and reduce the bump temperature,and therefore delay electromigration failure and increase the mean-time-to-failure.

Particle Density in Zero Temperature Symmetry Restoring Phase Transitions in Four-Fermion Interaction Models

By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μc in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μc but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.

A Model-Independent Discussion of Quark Number Density and Quark Condensate at Zero Temperature and Finite Quark Chemical Potential

Generally speaking, the quark propagator is dependent on the quark chemical potential in the dense quantum chromodynamics （QCD）. By means of the generating functional method, we prove that the quark propagator actually depends on p4 ＋ iμ from the first principle of QCD. The relation between quark number density and quark condensate is discussed by analyzing their singularities. It is concluded that the quark number density has some singularities at certain # when T = 0, and the variations of the quark number density as well as the quark condensate are located at the same point. In other words, at a certain # the quark number density turns to nonzero, while the quark condensate begins to decrease from its vacuum value.

Thermodynamic properties of ZnSe under pressure and with variation in temperature

The thermodynamic properties of Zn Se are obtained by using quasi-harmonic Debye model embedded in Gibbscode for pressure range 0–10 GPa and for temperature range 0–1000 K. Helmholtz free energy, internal energy, entropy,Debye temperature, and specific heat are calculated. The thermal expansion coefficient along with Gruneisen parameter are also calculated at room temperature for the pressure range. It is found that internal energy is pressure dependent at low temperature, whereas entropy and Helmholtz free energy are pressure sensitive at high temperature. At ambient conditions,the obtained results are found to be in close agreement to available theoretical and experimental data.

Porosity Evaluation and the Power Spectral Densities Analyses of Carbon-Nickel Composite Films Annealed at Different Temperatures

The densification and the fractal dimensions of carbon-nickel films annealed at different temperatures 300, 500, 800, and 1000℃ with emphasis on porosity evaluation are investigated. For this purpose, the refractive index of films is determined from transmittance spectra. Three different regimes are identified, T 〈 500℃, 500℃ 〈 T 〈 800℃ and T 〉 800℃. The Rutherford baekscattering spectra show that with increasing the annealing temperature, the concentration of nickel atoms into films decreases. It is shown that the effect of annealing temperatures for increasing films densification at T 〈 500℃ and T 〉 800℃ is greater than the effect of nickel concentrations. It is observed that the effect of decreasing nickel atoms into films at 500℃ 〈 T 〈 800℃ strongly causes improving porosity and decreasing densification. The fractal dimensions of carbon-nickel films annealed from 300 to 500℃ are increased, while from 500 to 1000℃ these characteristics are decreased. It can be seen that at 800℃, films have maximum values of porosity and roughness.

Influence of the position relationship between gas–liquid interface and laser focus on plasma evolution characteristics in jet LIBS technology

In order to understand the characteristics of breakdown process,plasma evolution and spectral emission in liquid jets laser-induced breakdown spectroscopy methods under the influence of the position variation between laser focus and gas–liquid interface,this work takes the plasma generated by laser-induced liquid jets as the object of study and discusses the changes in the spatial and temporal evolution characteristics and spectral radiation of the plasma when the position parameters between the laser focal point and the gas–liquid interface are different.The initial breakdown position is always between the front interface and the focus when the laser focus moves along the vertical direction of the interface,forming a phenomenon like’interface effect’.The relationship between laser pulse energy and breakdown probability exhibits a law similar to a‘hysteresis curve’in the study of breakdown threshold.In this work,plasma with smaller size,rounder shape,stronger radiation,higher temperature,and higher density can be produced when the focus position is in the liquid column 0.2 mm away from the front interface.Simultaneously,the spectral signal intensity and signal-to-back ratio of the characteristic peaks of target elements in water reach maximum values,and the spectral signal becomes more stable(relative standard deviation value reaches 2%).The Ca element’s ion radiation at 393.366 nm and atomic radiation at 422.673 nm are studied using narrow-band filtering imaging and time-space resolution spectroscopy.The findings demonstrate that the laws of ion and atomic radiation are not perfectly consistent in space and time.

Growth of small diameter multi-walled carbon nanotubes by arc discharge process

Multi-walled carbon nanotubes （MWCNTs） are grown by arc discharge method in a controlled methane environment. The arc discharge is produced between two graphite electrodes at the ambient pressures of 100 tort, 300 torr, and 500 torr. Arc plasma parameters such as temperature and density are estimated to investigate the influences of the ambient pressure and the contributions of the ambient pressure to the growth and the structure of the nanotubes. The plasma temperature and density are observed to increase with the increase in the methane ambient pressure. The samples of MWCNT synthesized at different ambient pressures are analyzed using transmission electron microscopy, scanning electron microscopy, Raman spectroscopy, Fourier transform infrared spectroscopy, and X-ray diffraction. An increase in the growth of MWCNT and a decrease in the inner tube diameter are observed with the increase in the methane ambient pressure.

Atmospheric pressure plasma jet utilizing Ar and Ar/H_2O mixtures and its applications to bacteria inactivation

An atmospheric pressure plasma jet generated with Ar with H2O vapor is characterized and applied to inactivation of Bacillus subtilis spores. The emission spectra obtained from Ar/H2O plasma shows a higher intensity of OH radicals com- pared to pure argon at a specified H2O concentration. The gas temperature is estimated by comparing the simulated spectra of the OH band with experimental spectra. The excitation electron temperature is determined from the Boltzmann＇s plots and Stark broadening of the hydrogen Balmer H/3 line is applied to measure the electron density. The gas temperature, ex- citation electron temperature, and electron density of the plasma jet decrease with the increase of water vapor concentration at a fixed input voltage. The bacteria inactivation rate increases with the increase of OH generation reaching a maximum reduction at 2.6% （v/v） water vapor. Our results also show that the OH radicals generated by the Ar/H2O plasma jet only makes a limited contribution to spore inactivation and the shape change of the spores before and after plasma irradiation is discussed.

Spectroscopic Studies of the Laser Produced Lead Plasma

Spectroscopic emission of lead plasma, generated by the fundamental （1064 nm） and second harmonics （532 nm） of a Q-switched pulsed Nd： YAG laser, is studied. The spectral lines of neutral atoms and singly ionized lead ions were shown predominantly. The profiles of neutral lead lines observed were used to extract the excitation temperature using Boltzmann plots, whereas electron number density was determined from the profile of Stark broadened line. The variations of excitation temperature and electron number density as a function of laser energy were studied.

Langmuir Probe Measurements of an Expanding Argon Plasma

In this work,we studied the effects of the discharge current,gas flow rate and vessel pressure on the electron temperature and density of Ar plasma by Langmuir probe measurement.The argon plasma was created by a one-cathode arc source.The experimental results show that with increasing discharge current and gas flow rate,the electron temperature and density increase.It is found that when the discharge current is 70 A,90 A and HO A at an argon flow rate of2000 seem,the electron densities at about 0.186 m distance from the nozzle are 13.00×10^18 m^-3,14.04×10^18 m^-3 and 15.62×10^18 m^-3,and the electron temperatures are 0.38 eV,0.58 eV and0.71 eV,respectively.The positive I-V characteristic is explained.

Time-Resolved Emission Spectroscopic Study of Laser-Induced Steel Plasmas

Laser-induced steel plasma is generated by focusing a Q-switched Nd：YAG visible laser（532 nm wavelength） with an irradiance of 1 x 109 W/cm2 on a steel sample in air at atmospheric pressure.An Echelle spectrograph coupled with a gateable intensified charge-coupled detector is used to record the plasma emissions.Using time-resolved spectroscopic measurements of the plasma emissions,the temperature and electron number density of the steel plasma are determined for many times of the detector delay.The validity of the assumption by the spectroscopic methods that the laser-induced plasma（LIP） is optically thin and is also in local thermodynamic equilibrium（LTE） has been evaluated for many delay times.From the temporal evolution of the intensity ratio of two Fe I lines and matching it with its theoretical value,the delay times where the plasma is optically thin and is also in LTE are found to be 800 ns,900 ns and 1000 ns.

Micro-pinch formation and extreme ultraviolet emission of laser-induced discharge plasma

Extreme ultraviolet(EUV)source produced by laser-induced discharge plasma(LDP)is a potential technical means in inspection and metrology.A pulsed Nd:YAG laser is focused on a tin plate to produce an initial plasma thereby triggering a discharge between high-voltage electrodes in a vacuum system.The process of micro-pinch formation during the current rising is recorded by a time-resolved intensified charge couple device camera.The evolution of electron temperature and density of LDP are obtained by optical emission spectrometry.An extreme ultraviolet spectrometer is built up to investigate the EUV spectrum of Sn LDP at 13.5 nm.The laser and discharge parameters such as laser energy,voltage,gap distance,and anode shape can influence the EUV emission.

Color-flavor dependence of the Nambu-Jona-Lasinio model and QCD phase diagram

We study the dynamical chiral symmetry breaking/restoration for various numbers of light quarks flavors N_(f) and colors N_(c) using the Nambu-Jona-Lasinio(NJL) model of quarks in the Schwinger-Dyson equation framework,dressed with a color-flavor dependence of effective coupling.For fixed N_(f)=2 and varying N_(c),we observe that the dynamical chiral symmetry is broken when N_(c) exceeds its critical value N_(c)^(c)≈2.2.For a fixed N_(c)=3 and varying N_(f),we observe that the dynamical chiral symmetry is restored when Nf reaches its critical value N_r^(c)≈8.Strong interplay is observed between N_(c) and N_(f),i.e.,larger values of N_(c) tend to strengthen the dynamical generated quark mass and quark-antiquark condensate,while higher values of N_(f) suppress both parameters.We further sketch the quantum chromodynamics(QCD) phase diagram at a finite temperature T and quark chemical potential μ for various N_(c) and N_(f).At finite T and μ,we observe that the critical number of colors N_(c)^(c) is enhanced,whereas the critical number of flavors N_(f)^(c) is suppressed as T and μ increase.Consequently,the critical temperature T_(c),μ_(c),and co-ordinates of the critical endpoint(T_(c)^(E),μ_(c)^(E)) in the QCD phase diagram are enhanced as N_(c) increases and suppressed when N_(f) increases.Our findings agree with the lattice QCD and Schwinger-Dyson equations predictions.

Characteristics of laser induced discharge tin plasma and its extreme ultraviolet radiation

In this paper,a CO_(2) laser induced discharge plasma extreme ultraviolet(EUV)source experimental device was established.The optical emission spectroscopy was used to diagnose the characteristics of the plasma,and the evolution of electron temperature and electron density with time was obtained.The influence of discharge voltage on plasma parameters was analyzed and discussed.The EUV radiation characteristics of the plasma were investigated by self-made grazing incidence EUV spectrometer.The EUV radiation intensity and conversion efficiency were discussed.

Hugoniot equation of state of olivine and its geodynamic implications

Large olivine samples were hot-pressed synthesized for shock wave experiments. The shock wave experiments were carried out at pressure range between 11 and 42 GPa. Shock data on olivine sample yielded a linear relationship between shock wave velocity D and particle velocity u described by D=3.56(?0.13)+2.57(?0.12)u. The shock temperature is determined by an energy relationship which is approximately 790°C at pressure 28 GPa. Due to low temperature and short experimental duration, we suggest that no phase change occurred in our sample below 30 GPa and olivine persisted well beyond its equilibrium boundary in metastable phase. The densities of metastable olivine are in agreement with the results of static compression. At the depth shallower than 410 km, the densities of metastable olivine are higher than those of the PREM model, facilitating cold slab to sink into the mantle transition zone. However, in entire mantle transition zone, the shock densities are lower than those of the PREM model, hampering cold slab to flow across the "660 km" phase boundary.