TABLE 33.1 Thermal Conductivities of Typical Packaging Materials at Room Temperature aterials Thermal Conductivity(w/m K) Epoxy( dielectric) Ablefilm 550 dielectric Nylon 913444 0.33 poxy(conductive) 0.35 Thermal greases/past Borosilicate glass 80⑦0 older(Pb-In older 80-20 Au-Sn Silicon Aluminum Gold 886285 Copper Silver Diamond where q is the heat flow, k is the thermal conductivity of the medium, A is the cross-sectional area for heat flow, and dT/dx the temperature gradi The temperature difference resulting from the conduction of heat is thus related to the thermal conductivity of the material, the cross-sectional area, and the path length, Ax,or (T-T,cond =q(Ax/kA)[K] (33.2) The form of this equation suggests that, by analogy to electrical current flow in a conductor, it is possible to define a conduction thermal resistance as [ Kraus, 1958 Roond=(T1-T2)/q= Ax/kA [K/W] (33.3) Using the thermal conductivities tabulated in Table 33 1, conduction resistance values for packaging materials with typical dimensions can be found by use of Eq 33.3 or by inspection of Fig. 33.2. Values are seen to range from 2K/W for a 100 mm2 by 1 mm thick layer of epoxy encapsulant to 0.0006 K/W for a 100 mm? by 25 micron (1 mil) thick layer of copper. Similarly, the values of the conduction resistance for typical"soft "bonding materials are found to lie in the range of 0. 1 k/w for solder and 1-3K/w for epoxies and thermal pastes, for Ax/A ratios of 0.25 to 1 m-I e 2000 by CRC Press LLC
© 2000 by CRC Press LLC where q is the heat flow, k is the thermal conductivity of the medium, A is the cross-sectional area for heat flow, and dT/dx the temperature gradient. The temperature difference resulting from the conduction of heat is thus related to the thermal conductivity of the material, the cross-sectional area, and the path length, Dx, or (T1 – T2)cond = q(Dx/kA) [K] (33.2) The form of this equation suggests that, by analogy to electrical current flow in a conductor, it is possible to define a conduction thermal resistance as [Kraus, 1958] Rcond = (T1 – T2)/q = Dx/kA [K/W] (33.3) Using the thermal conductivities tabulated in Table 33.1, conduction resistance values for packaging materials with typical dimensions can be found by use of Eq. 33.3 or by inspection of Fig. 33.2. Values are seen to range from 2K/W for a 100 mm2 by 1 mm thick layer of epoxy encapsulant to 0.0006 K/W for a 100 mm2 by 25 micron (1 mil) thick layer of copper. Similarly, the values of the conduction resistance for typical “soft” bonding materials are found to lie in the range of 0.1 K/W for solder and 1–3K/W for epoxies and thermal pastes, for Dx/A ratios of 0.25 to 1 m–1. TABLE 33.1 Thermal Conductivities of Typical Packaging Materials at Room Temperature Materials Thermal Conductivity (W/m K) Air 0.024 Mylar 0.19 Silicone rubber 0.19 Solder mask 0.21 Epoxy (dielectric) 0.23 Ablefilm 550 dielectric 0.24 Nylon 0.24 Polytetrafluorethylene 0.24 RTV 0.31 Polyimide 0.33 Epoxy (conductive) 0.35 Water 0.59 Mica 0.71 Ablefilm 550 K 0.78 Thermal greases/pastes 1.10 Borosilicate glass 1.67 Glass epoxy 1.70 Stainless steel 15 Kovar 16.60 Solder (Pb-In) 22 Alumina 25 Solder 80-20 Au-Sn 52 Silicon 118 Molybdenum 138 Aluminum 156 Beryllia 242 Gold 298 Copper 395 Silver 419 Diamond 2000
Rend= OXA ABC/GJS Thermal Conductivity (W/m-K FIGURE 33.2 Conductive thermal resistances for packaging materials Thermal transport from a surface to a fluid in motion is called convective heat transfer and can be related the heat transfer coefficient, h, the surface-to-fluid temperature difference, and the"wetted"area, in the forn q= hA(Turf- Tluid)[wI (33.4) The differences among convection to a fast-moving fluid, a slowly flowing fluid, and a stagnant fluid, as well as variations in the convective heat transfer rate among various fluids, are reflected in the value of h. Some theoretical and many empirical correlations are available for determining this convective heat transfer coefficient (e.g, Kraus and Bar-Cohen, 1983). Using Eq (33. 4), it is possible to define the convective thermal resistance, as Ron =(hA)- K/WI (33.5) Values of this convective resistance, for a variety of coolants and heat transfer mechanisms, are shown in Fig. 33.3 for a typical heat source area of 10 cm and a velocity range of 2-8 m/s. These resistances are seen to vary from 100 K/W for natural convection in air to 33 K/w for forced convection in air, to 1 K/w in fluorocarbon liquid in forced convection to less than 0.5 K/ for boiling in fluorocarbon liquid Unlike conduction and convection, radiative heat transfer between two surfaces or between a surface and its surroundings is not linearly dependent on the temperature difference and is expressed instead as q=oAF(T1-T4)IWI (336) e 2000 by CRC Press LLC
© 2000 by CRC Press LLC Thermal transport from a surface to a fluid in motion is called convective heat transfer and can be related to the heat transfer coefficient, h, the surface-to-fluid temperature difference, and the “wetted” area, in the form q = hA(Tsurf – Tfluid) [W] (33.4) The differences among convection to a fast-moving fluid, a slowly flowing fluid, and a stagnant fluid, as well as variations in the convective heat transfer rate among various fluids, are reflected in the value of h. Some theoretical and many empirical correlations are available for determining this convective heat transfer coefficient (e.g., Kraus and Bar-Cohen, 1983). Using Eq. (33.4), it is possible to define the convective thermal resistance, as Rconv = (hA)–1 [K/W] (33.5) Values of this convective resistance, for a variety of coolants and heat transfer mechanisms, are shown in Fig. 33.3 for a typical heat source area of 10 cm2 and a velocity range of 2–8 m/s. These resistances are seen to vary from 100 K/W for natural convection in air to 33 K/W for forced convection in air, to 1 K/W in fluorocarbon liquid in forced convection to less than 0.5 K/W for boiling in fluorocarbon liquids. Unlike conduction and convection, radiative heat transfer between two surfaces or between a surface and its surroundings is not linearly dependent on the temperature difference and is expressed instead as q = sAF(T 1 4 – T 2 4) [W] (33.6) FIGURE 33.2 Conductive thermal resistances for packaging materials. 10 1 10-1 10-2 10-2 10-1 102 1 10 10-3 Thermal Conductivity (W/m. K) ABC/GJS Rcond (K/W) Epoxy Alumina Silicon Copper Rcond = ÆX/A ÆX/A = 1.0 m-1 ÆX/A = .75 m-1 ÆX/A = .5 m-1 ÆX/A = .25 m-1