Creep behavior of eutectic Sn-Cu lead-free solder alloy

Tensile creep behavior of precipitation-strengthened, tin-based eutectic Sn-0.7Cu alloy was investigated at three temperatures ranging from 303–393 K. The steady-state creep rates cover six orders of magnitude (10⁻³−10⁻⁸ s⁻¹) under the stress range of σ/E=10⁻⁴−10⁻³. The initial microstructure reveals that the intermetallic compound Cu₆Sn₅ is finely dispersed in the matrix of β-Sn. By incorporating a threshold stress, σ _th, into the analysis, the creep data of eutectic Sn-Cu at all temperatures can be fitted by a single straight line with a slope of 7 after normalizing the steady-state creep rate and the effective stress, indicating that the creep rates are controlled by the dislocation-pipe diffusion in the tin matrix. So the steady-state creep rate, , can be expressed as exp , where Q_c is the activation energy for creep, G is the temperature-dependent shear modulus, b is the Burgers vector, R is the universal gas constant, T is the temperature, σ is the applied stress, A is a material-dependent constant, and , in which σ _OB is the Orowan bowing stress, and k_R is the relaxation factor. An erratum to this article is available at .     

Planar defects and double-domain epitaxy in epitaxial YSi<Subscript>2−x</Subscript> and ErSi<Subscript>2−x</Subscript> thin films on Si substrates

Interfacial reactions of Y and Er thin films on both (111)Si and (001)Si have been studied by transmission electron microscopy (TEM). Epitaxial rare-earth (RE) silicide films were grown on (111)Si. Planar defects, identified to be stacking faults on planes with 1/6 displacement vectors, were formed as a result of the coalescence of epitaxial silicide islands. Double-domain epitaxy was found to form in RE silicides on (001)Si samples resulting from a large lattice mismatch along one direction and symmetry conditions at the silicide/(001)Si interfaces. The orientation relationships are [0001]RESi_2−x// Si, RESi_2−x//(001)Si and [0001]RESi_2−x/ Si, RESi_2−x//(001)Si. The density of staking faults in (111) samples and the domain size in (001) samples were found to decrease and increase with annealing temperature, respectively.     

Linear systems in a saturated mode and convergence as gain becomes large of asymptotically stable equilibrium points of neural nets

We study solutions of the linear system in a saturated mode

Effects of substrate orientation and surface reconstruction on patterned substrate OMVPE of GaAs

Organometallic vapor phase epitaxial growth of GaAs on 320 nm high mesas was used to study the dependence of lateral growth upon the substrate misorientation from (100) and the mesa wall orientation on the substrate. GaAs (100) substrates were misoriented by 3° toward eight major crystallographic directions, consisting of the four nearest [111] and [110] directions. The mesa sidewalls were oriented either parallel to the 〈011〉 and 〈01 〉 directions or rotated by 45° to be parallel to the 〈001〉 and 〈010〉 directions. GaAs films were grown with TMGa and TBA at T=575°C. The lateral growth rates were up to 25 times higher than the vertical growth rate of 1.3 μm/hour. Optical microscopy and atomic force microscopy (AFM) showed that under the given growth conditions lateral growth off mesa sidewalls is most rapid in the 〈011〉 and/or 〈0 〉 directions and less in the perpendicular 〈01 〉 and 〈0 1〉 directions (lateral growth anisotropy). By raising the temperature to 625°C lateral growth in the 〈01 〉 -〈0 1〉 directions increased while it remained almost constant in the 〈011〉 -〈0 〉 directions. Published results show that the partial pressure of As also affects lateral growth. Differences in the lateral growth rates in the 〈011〉 and its opposite 〈0 〉 directions result from substrate misorientation but not from the orientation of the mesa walls on the substrate. Anisotropic lateral growth rates in different crystallographic directions appear to be caused by both, (1) 1-dimensional Ga diffusion defined by surface reconstruction, and (2) a relatively low energy barrier to atoms flowing over high-to-low terrace steps. A lateral growth model is proposed that describes anisotropic lateral growth at mesa sidewalls in terms of growth conditions and substrate misorientations. The model also explains the difference in the preferential lateral growth directions between MBE and OMVPE.     

Estimation of Energy Aliasing Error for Nonbandlimited Signals

In this paper, we investigate the problem of approximating a given (not necessarily bandlimited) signal, x(t), by a (bandlimited) interpolation or sampling series of the form:

Extruded Bismuth-Telluride-Based <Emphasis Type="Italic">n</Emphasis>-Type Alloys for Waste Heat Thermoelectric Recovery Applications

Thermoelectric (TE) generator modules for a number of waste heat recovery applications are required to operate between room temperature and 500 K, a temperature range for which the composition of bismuth-telluride-based alloys needs to be adjusted to optimize performance. In particular n-type alloys do not perform as well as p-type and require a more systematic study. We have produced, by mechanical alloying followed by hot extrusion, alloys, within the range with fixed carrier concentration () to optimize their TE performance in the temperature range 300 K to 420 K. The optimum composition has been identified to be and which is very close to the composition that also maximizes the ratio of the electron mobility to the lattice component of the thermal conductivity. The optimized alloy performance can be further increased by adjusting the carrier concentration.     

Creep behavior of eutectic Sn-Cu lead-free solder alloy

Due to a typographical error incorporated during the editing process, the following is a correction of that error. Tensile creep behavior of precipitation-strengthened tin-based eutectic Sn-0.7Cu alloy was investigated at three temperatures ranging from 303 to 393 K. The steady-state creep rates cover six orders of magnitude (10⁻³ s⁻¹ to 10⁻⁸ s⁻¹) under the stress range of σ/E=10⁻⁴ to 10⁻³. The initial microstructure reveals that intermetallic compound Cu₆Sn₅ is finely dispersed in the matrix of β-Sn. By incorporating a threshold stress, σ_th, into the analysis, the creep data of eutectic Sn-Cu at all temperatures can be fitted by a single straight line with a slope of 7 after normalizing the steady-state creep rate and the effective stress, indicating that the creep rates are controlled by the dislocation pipe diffusion in tin matrix. So the steady-state creep rate, , can be expressed as , where Q_C is the active energy for creep, G is the temperature-dependent shear modulus, b is the Burgers vector, R is the universal gas constant, T is the temperature, σ is the applied stress, A is a material-dependent constant, and σ_th=σ_OB√1−k _R ² , in which σ_oB is the Orowan bowing stress and k_R is the relaxation factor. J. Electron. Mater. 31(5)(2002), pp.442–448. The online version of the original article can be found at     

Pre-avalanche Ultraviolet Photoconduction Properties of Transitional-Metal-Doped ZnO Nanowires

The ultraviolet (UV) photoelectric characteristics of transitional metal (Cu) doped ZnO nanowires produced by the self-catalytic vapor–liquid–solid (VLS) method were investigated by performing a series of photoconduction and time-resolved measurements. The photocurrent voltage characteristics obtained on the nanowires configured as two-terminal metal–semiconductor–metal photodetectors exhibited a nonmonotonic behavior attributed to the interplay of several limiting mechanisms: Schottky contacts and trapping/detrapping effects that take place at low and intermediate (pre-avalanche) bias regimes, respectively. In the intermediate biases, the photocurrent was power-law dependent, i.e., changed with voltage as and for excitation wavelengths of 365 nm, 302 nm, and 254 nm, respectively. The dependence of the exponent on the wavelength of the light is analyzed and explained based on the detailed consideration of the contribution of different deep-defect Cu levels formed within the band gap of ZnO. The study will be important to those working in the area of ZnO-based nanophotodetectors, optical switches, and sensors.     

Growth of oriented diamond film on single crystalline 6H-SiC substrates

The bias-enhanced nucleation (BEN) technique in hot-filament chemical vapor deposition (HF-CVD) has been applied to single crystalline 6H-SiC substrates for the deposition of oriented diamond. The results of scanning electron microscopy (SEM) showed that on (000 ) face not only oriented diamond with relationship (111) Dia.//(000 )6H-SiC and 〈110〉Dia.//(11 0)6H-SiC, but also high nucleation density (>10⁹ cm⁻²) have been achieved. In the case of deposition on (0001) face of 6H-SiC under the same experimental conditions, although the nucleation density of diamond was enhanced, however, oriented diamond was not found. Diamond nucleation density is higher on (0001) face than that on (000 ) face. The differences in diamond oriented nucleation and nucleation density on these two faces are attributed to the difference of their specific free surface energy. The experimental results have shown that the 6H-SiC substrate surfaces are etched by the accelerated H-ions during BEN process, and many micro-triangular crystals with the faces of the kind {01 4} are formed on the substrate surface. Diamonds nucleate on the top of the micro-triangular crystals. Micro-Raman spectrum shows a strong feature of diamond crystals at 1334 cm⁻¹.     

On the distance to the instability border of hurwitz polynomials with coefficients that depend affinely onm parameters and a particular convexity property ofH n

Let

A kinetic study of structured surface relief patterning of GaP (\bar 1\bar 1\bar 1)

Orientation dependent etching of photolithographically patterned GaP was investigated using solutions of HCl:CH₃COOH:H₂O₂. The pattern was prepared using standard ultraviolet lithography and was a two-dimensional grid with an 18 μm repeat, consisting of 15 μm squares separated by 3 μm spaces. The mask sides were aligned along the and directions. Under appropriate etching conditions, high quality arrays of pyramids were prepared. These pyramids were defined by , and facets. It was shown that the etching process depended on the degree of solution aging after initial mixing. For a freshly prepared solution, the etching rate showed an inverse dependence on time. For short etching times (below 5 min), an intermediate etching profile was followed, while for long times (greater than 5 min) etching was kinetically controlled. We demonstrated that controlled etching at extremely low rates (0.1–0.5 μm/min) is feasible with this new approach.     

Finite-Memory Systems

Let K be a field, k and n positive integers and let matrices with coefficients in K. For any function

Effect of off-orientation of seed crystal on silicon carbide (SiC) single-crystal growth on the (11 $$\bar 2$$ 0) surface0) surface

The effect of off-orientation growth has been investigated in terms of stacking fault formation during physical vapor transport (PVT) growth of silicon carbide (SiC) single crystals on the (11 0) seed crystal surface. Occurrence of stacking fault formation is largely dependent on the direction of off-orientation, and basal plane stacking fault density is significantly reduced by growing the crystals on a (11 0) seed crystal off-oriented toward 〈0001〉. The density of the basal plane stacking faults rapidly decreases from 100–150 cm⁻¹ to ∼10 cm⁻¹ as the degree of off-orientation is increased from 0 to 10 deg. The results are interpreted in the framework of microscopic facet formation during PVT growth, and the introduction of off-orientation of seed crystal is assumed to prevent (01 0) and (10 0) microfacet formation on the (11 0) growing surface through modification of the surface growth kinetics and to suppress the stacking fault formation. An erratum to this article is available at .     

Predicting and Understanding Order of Heteroepitaxial Quantum Dots

Heteroepitaxial self-assembled quantum dots (SAQDs) will allow breakthroughs in electronics and optoelectronics. SAQDs are a result of Stranski–Krastanow growth, whereby a growing planar film becomes unstable after an initial wetting layer is formed. Common systems are and For applications, SAQD arrays need to be ordered. The roles of crystal anisotropy, random initial conditions and thermal fluctuations in influencing SAQD order during early stages of SAQD formation are studied through a simple stochastic model of surface diffusion. Surface diffusion is analyzed through a linear and perturbatively non-linear analysis. The role of crystal anisotropy in enhancing SAQD order is elucidated. It is also found that SAQD order is enhanced when the deposited film is allowed to evolve at heights near the critical wetting surface height that marks the onset of non-planar film growth.     

The shape of self-assembled InAs islands grown by molecular beam epitaxy

We have determined the shape of InAs quantum dots using reflection high energy electron diffraction. Our results indicate that self-assembled InAs islands possess a pyramidal shape with {136} bounding facets. This shape is characterized by C_2v symmetry and a parallelogram base, which is elongated along the direction. Cross-sectional transmission electron microscopy images taken along the [110] and directions as well as atomic force microscopy images strongly support the {136} shape. Furthermore, polarization-resolved photoluminescence spectra show strong in-plane anisotropy, with emission predominantly polarized along the direction, consistent with the proposed quantum dot shape.     

Effect of substrate orientation on phase separation in epitaxial GaInAsSb

The effect of substrate misorientation on phase separation in Ga_1−xIn_xAs_ySb_1−y nominally lattice matched to GaSb is reported. The layers were grown at 575°C by organometallic vapor phase epitaxy on vicinal (001) GaSb substrates, miscut or (101). Ga_1−xIn_xAs_ySb_1−y (x ~ 0.1, ~ 0.09) layers, which have 300-K photoluminescence (PL) peak emission at ~2.1 μm, grow stepbunched and exhibit minimal phase separation. The full width at half maximum of 4-K PL spectra is slightly smaller at 7 meV for layers grown on substrates miscut toward compared to 9 meV for layers grown on substrates miscut toward and (101). Ga_1−xIn_xAs_ySb_1−y layers with higher alloy composition (0.16≤x≤0.19, 0.14≤y≤0.17), which have 300-K PL peak emission at ~2.4 μm, have significant phase separation. These layers are characterized by increased lattice constant variations and epitaxial tilt, broad PL spectra with significant band tailing, and strong contrast modulation in transmission electron microscopy. The degree of decomposition depends on substrate miscut direction: Ga_1−xIn_xAs_ySb_1−y layers grown on (001) substrates are more homogeneous than those grown on (001) and (001)2°→(101) substrates. The results are attributed to the smaller adatom diffusion length on substrates miscut toward .     

Coarsening of three-dimensional droplets by two-dimensional diffusion: Part II. Theory

Theoretical modeling of coarsening among a finite cluster of precipitates is implemented, using the multipole expansion method. This method requires the diffusion field to behave quasi-statically. Two approximate solutions were developed, one to monopolar order, and other to the dipolar order. The conventional Gibbs-Thomson equilibrium relationship was used as the boundary condition at the precipitate-matrix interface. Part I of this paper considers a liquid-liquid system in a mixed-dimensional geometrical configuration, wherein three-dimensional precipitates interact via a diffusion field constrained in two dimensions. This kind of geometric configuration is often encountered in island evolution dynamics and phase segregation in thin films. The initial experimental configuration of droplets provides the initial condition for the simulation. Both monopole and dipole approximations closely follow the experimentally observed scaling laws, characteristic for the mixed-dimensional coarsening (N^−4/3 and ⁴, varied linearly with time, where N is the number of droplets in the experimental field of view, and is the average droplet radius). Good agreement is observed for time evolution of radii of some individual precipitates. Certain deviations appearing among the two approximate solutions and the experimental data are discussed.     

CdZnTe graded buffer layers for HgCdTe/Si integration

To investigate the potential benefits of compositional grading for dislocation control in CdTe/Si growth, Cd_1−xZn_xTe buffer layers with x graded smoothly from 1 to 0 have been deposited on Si (211) surfaces. Growth has been characterized using reflection high-energy electron diffraction (RHEED), x-ray diffraction (XRD), and etch pit density measurements. XRD showed an increase in rocking curve full-width at half-maximum (FWHM) and global lattice tilt with decreasing x values. Tilt was also observed to increase as buffer growth temperature was increased. Final surface dislocation densities did not decrease below 7×10⁶ cm⁻². EPD surface dislocation measurements showed reduced dislocation densities and dislocation clustering along the and lines for CdTe cap layers grown on partially graded Cd_1−xZn_xTe buffer layers with slow compositional grading rates. Samples grown with faster grading rates showed higher final EPD values, with dislocations clustering along the and lines.     

Structural Analysis of CdTe Hetero-epitaxy on (211) Si

X-ray diffraction full-width at half-maximum (XRD FWHM), reflection high-energy electron diffraction (RHEED), and atomic force microscopy (AFM) indicate a mosaic structure for molecular-beam epitaxy (MBE) (211)B CdTe/Si. AFM measurements indicate long, thin, small-angle-disoriented grains for CdTe/Si epilayers. These disoriented grains are ~1 μm in the [] direction and are ~40 nm in the [] direction. The RHEED pattern in the [] direction depicts nearly ideal single-crystal periodicity. The RHEED pattern in the [] direction is indicative of small-angle-disoriented crystalline grains. Scanning electron microscopy (SEM), AFM, and XRD measurements all indicate an approximate factor of 10 increase in the Everson etch pit density (EPD) over standard Nomarski microscopy Everson EPD determination.