Mass transport equations unifying descriptions of isothermal diffusion, thermomigration, segregation, and position-dependent diffusivity

Tan, T. Y.

doi:10.1063/1.122551

Cited by 31 publications

(12 citation statements)

References 9 publications

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“…Because AuIn 2 is specifically much denser than In-49Sn solder, it seems unreasonable that the heavier AuIn 2 is able to float upward in liquid In-49Sn solder. An explanation is proposed based on the thermomigration theory: 15,16 the upper dome of the solder ball is irradiated with infrared heat during reflow, which gives rise to a temperature gradient between the top and bottom of the solder ball. Because of this temperature gradient, the liquid In49Sn solder migrates downward, and the AuIn 2 cubes are squeezed upward instead to settle on the upper side of the solder ball.…”

Section: Resultsmentioning

confidence: 99%

Intermetallic compounds formed during the reflow of In-49Sn solder ball-grid array packages

Chuang

Chang

Tsao

et al. 2003

Journal of Elec Materi

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The intermetallic compounds formed at the interfaces between In-49Sn solder balls and Au/Ni/Cu pads during the reflow of In-49Sn solder, ball-grid array (BGA) packages are investigated. Various temperature profiles with peak temperatures ranging from 140°C to 220°C and melting times ranging from 45 sec to 170 sec are plotted for the reflow processes. At peak temperatures below 170°C, a continuous double layer of intermetallics can be observed, showing a composition of Au(In,Ni) 2 /Au(In,Ni). Through selective etching of the In-49Sn solders, the intermetallic layer is made up of irregular coarse grains. In contrast, a number of cubic-shaped AuIn 2 intermetallic compounds appear at the interfaces and migrate toward the upper domes of In-49Sn solder balls after reflow at peak temperatures above 200°C for longer melting times. The upward floating of the AuIn 2 cubes can be explained by a thermomigration effect caused by the temperature gradient present in the liquid solder ball. The intermetallic compounds formed under various reflow conditions in this study exhibit different types of morphology, yet the ball shear strengths of the solder joints in the In-49Sn BGA packages remain unaffected.

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Section: Resultsmentioning

confidence: 99%

Intermetallic compounds formed during the reflow of In-49Sn solder ball-grid array packages

Chuang

Chang

Tsao

et al. 2003

Journal of Elec Materi

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“…Equation (4) is a phenomenological model that describes the segregation of

{Na}^{+}

arising from the inhomogeneity of the migration Gibbs free energy introduced at the insulator/semiconductor interface. [ 24 ] It is assumed that,

{boldJ}_{normalS} \to 0

C_{{SiN}_{normalx}}

and

C_{Si}

reach their equilibrium concentrations and that the kinetics of interface transfer, described by h is uncorrelated to the relative concentrations at both sides of the interface. While more elaborated segregation kinetics models can be introduced, [ 25,26 ] the low number of free parameters of Equation (4) facilitates the validation with experimental results and achieves a satisfactory fit to the experiments mentioned later.…”

Section: Model Descriptionmentioning

confidence: 99%

A Poisson–Nernst–Planck Model of Ion Transport and Interface Segregation in Metal–Insulator–Semiconductor Structures and Solar Cells

Martínez-Lorán

Gastrow

Clenney

et al. 2021

Physica Status Solidi (b)

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The presence of trace alkali ions, especially sodium (Na þ ), in semiconductor devices has long been identified as a cause of device instability due to ion-drift-induced voltage screening under operating temperatures and applied potentials. [1][2][3][4][5] In the last decade, it has been established that sodium contamination in silicon photovoltaic (PV) modules leads to a catastrophic power loss known as potential-induced degradation (PID), [6][7][8][9] which can lead to failure within a timescale of a few hours to several days under accelerated testing. [10][11][12][13][14][15] A critical component of PID is the transport of Na ions across the dielectric-Si interface, ultimately leading to shunting of the p-n junction. In contrast, the possibility of harnessing ion transport in dielectrics has attracted increasing interest for applications in neuromorphic computing. [16][17][18] Establishing rigorous models for these ion transport phenomena is a necessary step toward comprehensive control of mobile ions in established and novel semiconductor device architectures.Historically, electrostatic models of mobile charges in metal-insulatorsemiconductor (MIS) structures have had some success in reproducing phenomenological effects. [4,[19][20][21] Among these models, Snow et al. [19] proposed an analytical approximation to ion transport in MIS structures, which adequately describes electrostatic measurements of the image

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“…Tan [10,11] derived Eqs. 10 and 11 to express the diffusion flux and the concentration change, respectively.…”

Section: Segregation Gettering Modelmentioning

confidence: 99%

Analysis of the Segregation Phenomena of Copper in P/P+ Epitaxial Silicon Wefers

2006

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We investigated the segregation gettering of copper in P/P + epitaxial wafers and determined the segregation coefficient of copper in the P + layer at room temperature by evaluating the copper concentration using SIMS. The segregation coefficient of copper at the P + layer with a boron concentration less than 10 18 atoms/cm 3 was confirmed to be three-orders-of-magnitude lower than that expected by the theoretical model proposed. In this paper we discuss two possible explanations for these results. 1) The segregation coefficient of copper, that is, the dependence of the equilibrium concentration of copper on the boron concentration is overestimated in the theoretical model proposed. 2) Certain barriers work to prevent copper from diffusing and segregating near the surface of the wafers.

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Mass transport equations unifying descriptions of isothermal diffusion, thermomigration, segregation, and position-dependent diffusivity

Abstract: Articles you may be interested inDiffusion transport coefficients for granular binary mixtures at low density: Thermal diffusion segregation Phys. Fluids 25, 043302 (2013); 10.1063/1.4800775 Segregation and enhanced diffusion of nitrogen in silicon induced by low energy ion bombardment

Cited by 31 publications

References 9 publications

Intermetallic compounds formed during the reflow of In-49Sn solder ball-grid array packages

Intermetallic compounds formed during the reflow of In-49Sn solder ball-grid array packages

A Poisson–Nernst–Planck Model of Ion Transport and Interface Segregation in Metal–Insulator–Semiconductor Structures and Solar Cells

Analysis of the Segregation Phenomena of Copper in P/P+ Epitaxial Silicon Wefers

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