edfas.org ELECTRONIC DEVICE FAILURE ANALYSIS | VOLUME 26 NO. 2 24 are part of the same physical phenomenon and the flow of electric current and heat are coupled phenomena. Below are the coupling domains equations: (Eq 14) where Π = S · T From equation 1 it can be seen that the efficiency of the thermoelectric (TE) device depends on properties of materials through the dimensionless figure of merit ZT which is the Wiedemann-Franz law defined as:[5,11] ZT= S2 (σ ·T)/λ (Eq 15) S is the Seebeck coefficient, σ the electrical conductivity, λ the thermal conductivity. The theory states that there is no fundamental maximum limitation of the ZT. Moreover, several plausible extrapolations based on the use of optimum values for known materials indicate that ZT of 2-4 are possible. A ZT value of 3 is required for commercial devices. The product referred to as a power factor is: PF = S2σ (Eq 16) The maximum efficiency, η of the TE device for power generation is defined as the output of electrical power, P, divided by the thermal power, Q, is expressed as:[10] η= Pe/Qc = (TH - TC)/TH · (√(1 + ZTM) - 1)/(√(1 + ZTM )+ (TC/(TM)) (Eq 17) where TM is the average temperature, TH the hot side, and TC the cold side. In electronic cooling applications, a thermoelectric cooler (TEC) serves as device for transporting heat away from a surface that has a temperature higher the ambient temperature. The purpose of a TEC is to maintain the junction temperature of an electronic device below a safe temperature. As a result of the increasing miniaturization of electronic circuity and microprocessor, heat fluxes have also increased and are expected to exceed 100 W/cm2 for many commercial applications.[11] MATERIALS AND METHODS GEOMETRY DESCRIPTION AND MATERIALS The high pin count of BGA (typically in the range of > 250 connections) makes it one of the most popular packages of choice in the electronic packaging industry. BGAs also offer additional advantages such as small footprint, self-alignment, elimination of the need for lead inspection/straightening, and convenience of using standard processes and equipment for surface mounting.[4] The 3D geometric model chosen (48 balls) consists of different layers of materials shown in Fig. 2. Given the symmetric geometric and loads, we will consider only the ¼ of the entire geometry. The symmetry planes are (XZ) and (YZ). Table 1 shows the material properties used in the assembly. The parameters of the SnAgCu material in the Anand model are obtained from the experimental results. These parameters are presented in Table 2. To allow viscoplastic phenomena to occur and prevent temperature gradients in the test assembly due to thermal inertia of each material of the BGA component and the Fig. 1 Schematic of a BGA thermal resistance network.
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