1. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Via unit cells. From left to right: (a) TSV cell as used in Ref. [8], showing the many features that can appear in a TXV array, (b) Cu– glass via cell used to investigate boundary conditions, and (c) Cu–glass cell for investigating the contribution of films Figure Legend:

2. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Heat flux vectors at a vertical cross section of a unit cell. The top and bottom faces of the cell have constant flux boundary conditions of the same magnitude. The midplane contains an isotherm, as evidenced by the parallel flux vectors there. Units are in W/m 2. Figure Legend:

3. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Unit cell for investigating convection boundary condition. The lateral dimensions and materials are held constant, while the top boundary condition and substrate thickness are varied. Due to symmetry, a quarter-cell is modeled in practice. Figure Legend:

4. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Dependence of k eff,z on substrate thickness and applied heat transfer coefficient Figure Legend:

5. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Via cell total thermal resistance, calculated from FEM. Related to k eff,z data presented in Fig. 4 by Eq. (7). Cells in the “thick substrate” regime have converged to a linear asymptote unique to each h. Three high h datasets are not plotted for clarity. Figure Legend:

6. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Microspreading resistance of thick TXV substrates. Each point is the intercept of the linear asymptote for datasets of the type in Fig. 5 (there were three not included for clarity). The curve is the correlation given by Eq. (10). Figure Legend:

7. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Unit cell for investigating the effect of material contact. Lateral dimensions, via, and substrate material are held constant. Film conductivity and substrate thickness are varied. After demonstrating the limiting case of thick films, film thickness and the varying upper boundary are held constant. Figure Legend:

8. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Evolution of k eff,z of a TXV array as an adhered film increases in thickness. Film conductivity is 40 W/m K, and substrate thickness is 200 μm. Figure Legend:

9. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 k eff,z versus contacting material thermal conductivity for different substrate/cell thicknesses Figure Legend:

10. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Microspreading resistance versus contacting material conductivity. Each point is obtained from FEM data in Fig. 9. The curve is the correlation given by Eq. (11). Figure Legend:

11. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Maximum cell spreading resistance as a function of nondimensional via diameter and conductivity Figure Legend:

12. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Value of the discount factor, f, for all 1200 axisymmetric cells. The points that fall farthest from the curve are those cells with the smallest via diameters. Circles correspond to the convection boundary condition, while diamonds correspond to film contact. Figure Legend:

13. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Modeling Thermal Microspreading Resistance in Via Arrays J. Electron. Packag. 2016;138(1):010909-010909-9. doi:10.1115/1.4032348 Detail view of data in Fig. 12, with ± 15% bounds on ζ plotted. Cells with (d/P*)< 0.18 are excluded. Figure Legend: