A New Solution to the Grain Boundary Grooving Problem in Polycrystalline Thin Films When Evaporation and Diffusion Meet in Power Electronic Devices.

This paper constituted an extension of two previous studies concerning the mathematical development of the grain boundary grooving in polycrystalline thin films in the cases of evaporation/condensation and diffusion taken separately. The thermal grooving processes are deeply controlled by the various mass transfer mechanisms of evaporation-condensation, surface diffusion, lattice diffusion, and grain boundary diffusion. This study proposed a new original analytical solution to the mathematical problem governing the grain groove profile in the case of simultaneous effects of evaporation-condensation and diffusion in polycrystalline thin films by resolving the corresponding fourth-order partial differential equation ∂y∂t=C∂2y∂x2-B∂4y∂x4 obtained from the approximation ∂y∂x2≪1. The comparison of the new solution to that of diffusion alone proved an important effect of the coupling of evaporation and diffusion on the geometric characteristics of the groove profile. A second analytical solution based on the series development was also proposed. It was proved that changes in the boundary conditions of the grain grooving profile largely affected the different geometric characteristics of the groove profile.

Thermal Fatigue Effect on the Grain Groove Profile in the Case of Diffusion in Thin Polycrystalline Films of Power Electronic Devices.

In a previous paper, we solved the partial differential equation of Mullins' problem in the case of the evaporation-condensation in electronic devices and gave an exact solution relative to the geometric profile of the grain boundary grooving when materials are submitted to thermal and mechanical solicitation and fatigue effect. In this new research, new modelling of the grain groove profile was proposed and new analytical expressions of the groove profile, the derivative and the groove depth were obtained in the case of diffusion in thin polycrystalline films by the resolution of the fourth differential equation formulated by Mullins that supposed y'2≪1. The obtained analytical solution gave more accurate information on the geometric characteristics of the groove that were necessary to study the depth and the width of the groove. These new findings will open a new way to study with more accuracy the problem of the evaporation-condensation combined to the diffusion phenomenon on the material surfaces with the help of the analytical solutions.

Effect of load sequence interaction on bond-wire lifetime due to power cycling.

Experimental investigations on the effects of load sequence on degradations of bond-wire contacts of Insulated Gate Bipolar Transistors power modules are reported in this paper. Both the junction temperature swing ([Formula: see text]) and the heating duration ([Formula: see text]) are investigated. First, power cycling tests with single conditions (in [Formula: see text] and [Formula: see text]), are performed in order to serve as test references. Then, combined power cycling tests with two-level stress conditions have been done sequentially. These tests are carried-out in the two sequences: low stress/high stress (LH) and high stress/low stress (HL) for both [Formula: see text] and [Formula: see text]. The tests conducted show that a sequencing in [Formula: see text] regardless of the direction "high-low" or "low-high" leads to an acceleration of degradations and so, to shorter lifetimes. This is more pronounced when the difference between the stress levels is large. With regard to the heating duration ([Formula: see text]), the effect seems insignificant. However, it is necessary to confirm the effect of this last parameter by additional tests.

New solution of the partial differential equation of the grain groove profile problem in the case of evaporation/condensation.

This paper constitutes a new contribution on the resolution of Mullins problem in the case of the evaporation-condensation and gives an exact and explicit solution of the second partial differential equation relative to the geometric profile of the grain boundary grooving. New analytical expressions of the solution, the groove profile, the derivative and the groove deep were obtained:[Formula: see text]It was proved that the found solution gave more accurate results relative to those obtained by Mullins that neglected the first derivative (|y'| ≪ 1) relative to 1. The results obtained by this new solution can be advantageously used to give more precise solution of the general problem when combining the two phenomena relative to the evaporation-condensation and the surface diffusion in thin polycrystalline films.