Heat transfer through soldered and bonded joints of multilayer semiconductor devices studied by laser photothermal beam-deflection method

Laser Thermal Wave Diagnostics of the Thermal Resistance of Soldered and Bonded Joints in Semiconductor Structures

“…This situation can be illustrated by the example of the simplest structure shown in Figure 2 . Using the concept of incident and reflected thermal waves and following the approach developed in [ 57 , 58 ], the alternative temperature components for three regions can be presented in the form of plane waves where x is the coordinate shown in Figure 2 , t is the time, l is the thickness of the second layer, q n were obtained from the heat equations for each layer and q n = (−1 + i ) ( ω /2 κ n ) 1/2 , ω is the cyclic frequency of thermal waves, κ n is the thermal diffusivity of the n th layer, a is the amplitude of the incident thermal wave, and r , b , c , τ are coefficients to be determined from boundary conditions.…”

“…In [ 57 , 58 ], the coefficients at the exponents r , c , d , and τ as functions of the wave amplitude a were found in the analytical form by solving the heat equations for the structure shown in Figure 2 with common boundary conditions representing the continuity of temperature and heat flux at interfaces. In these publications, it was shown that in the case of a thin intermediate layer, the thermal problem for the structure in Figure 2 can be reduced to the problem of two regions between which there is the real TR r th and the reactive thermal conductance of the capacitive type z th where K 2 and ρ 2 C 2 are the thermal conductivity and the volumetric heat capacity of the intermediate layer, respectively, and i is the imaginary unit.…”

“…Usually, their values are determined from the comparison of the obtained experimental data and the corresponding theoretical results. At present, such theoretical 3D models have been developed both for the cases where the intermediate layers are located parallel to the sample surface [ 59 , 60 ] and perpendicular to it [ 58 , 61 ]. Numerical algorithms taking into account the temperature discontinuity induced by the contact TR are also being developed for calculating heat fluxes in multilayer structures [ 56 ].…”

Studies of the thermal conductivity and thermal resistance of solder layers with lead-free pastes by the photodeflection method

“…The heatremoving properties of such devices depend primarily on the interface (solder layer between a photovoltaic converter and a heat-removing base (HB)) quality. We have already studied the heat-removing properties of lead-containing solder joints [5][6][7]. It was found that the compositional uniformity of the solder layer is disturbed in the soldering process, and thermal resistances form at its boundaries, altering the heat-removing properties of the structure as a whole [7].…”

“…Figure 1 shows the cut surface of one of the structures with AIM solder paste imaged with an optical microscope and by the PD method. The model of formation of a PD signal from multilayer objects, which was developed in our earlier study [6], was used for quantitative analysis. This model factors in both the parameters of layers and inhomogeneous boundary conditions between layers.…”