Skip to main content
SpringerLink
Log in

New Method for Determining and Predicting Test Interconnect Pin Current Carrying Capacity

  • Published:
Journal of Electronic Testing Aims and scope Submit manuscript

Abstract

With new advances in the semiconductor technology, current carrying requirements for electronic packages and interconnects (sockets) are on the rise. Although there are a lot of documented methods for determining current carrying capacity (CCC) of electrical wires, there is no specific industry standard for determining current carrying capacity of socket pins and their contact interface with package balls and pads. This paper presents a new current carrying capacity measurement method, developed specifically to address the challenges of test socket pins and their contact interface with solder balls and pads. In addition, a method for predicting CCC in future test socket pins is presented and correlated to measured data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

Notes

  1. Measuring both, the ambient air temperature and air velocity inside the pin block is optional as described later in Section 5.3.

  2. Mikić’s [34] original definition of hardness specifies mean pressure based hardness value (Meyers hardness) and not Vickers hardness. Dieter [14] has pointed out that Vickers hardness can be used as substitutes for Meyer hardness due to small enough difference. Vickers hardness has been used in all calculations in this paper where hardness is called for.

  3. The equation for thermal contact conductance between two surfaces in plastic deformation has been published twice, the first time by Cooper et al. [12] in 1969, and then revised by Mikić in 1974 [34]. Cooper’s original 1969 equation was defined as follows:

    $$ {h}_s=1.45\ \frac{k_m\cdot {m}_e}{\sigma_e}{\left(\frac{P}{H_v}\right)}^{0.985} $$
    (18)

    Both equations have been tested in simulations and it was found that although their results vary by about 20%, their final impact on CCC is negligible. In the end, Mikić’s 1974 equation was used in this paper, because it was an improved revision of the earlier 1969 equation which Mikić himself coauthored and was aware of.

  4. Bowden and Tabor [7] arrived at the same equation for contact conductance ([7] p. 397) as Contius, but in a different form. We have compared their results for the copper cross-cylinders point to point contact case ([7] p. 397, fig. 2) to Contius’ equation and their results match those of Contius.

  5. Contius did not specify the force-area equation for line to line contact and did not provide the details of the geometry of the cylinders he used in his measurements. Using some details that Contius provided and additional theory that was developed in subsequent years, it was possible to derive this equation. Equation 26 is a rearranged and simplified form of the line to line contact area published by Barquins [4] and Chaudhury et al. [9], with the adhesive force term removed. A detailed derivation of this equation will be published in a future publication.

Abbreviations

a, b, c :

Quadratic polynomial coefficients

I pin _ measured :

Measured current flowing through the pin, A.

I pin _ derated :

Measured current flowing through the pin derated for tool test temperature and factor of safety, A

T pin _ at _ room :

Measured pin temperature at room temperature, °C

T pin _ at _ test :

Measured pin temperature at test tool temperature, °C

T test :

Tester ambient temperature during test, °C

T room :

Room ambient temperature, °C

F 20 % _ drop :

Pin force at 20% drop from the nominal pin force, kg

σ :

Equivalent Von Misses flow stress, Pa

ε p :

Equivalent plastic strain

\( {\varepsilon}_p^{\ast } \) :

Strain rate, \( {\varepsilon}_p^{\ast }=\dot{\varepsilon}/{\dot{\varepsilon}}_0 \)

\( \dot{\varepsilon} \) :

Equivalent plastic strain rate, sec−1

\( \dot{\varepsilon_0} \) :

Constant reference strain rate, sec−1. \( \dot{\varepsilon_0}=0.001\ {\sec}^{-1} \)

A JC :

Johnson-Cook (J-C) constant representing quasi-static yield stress, MPa

B JC :

J-C constant representing strain hardening effect, MPa

C JC :

Johnson-Cook constant representing strain rate effect

n JC :

Johnson-Cook constant representing strain hardening effect

m JC :

Johnson-Cook constant representing thermal softening effect

T H :

Homologous temperature ratio defined as \( {T}_H=\frac{\left(T-{T}_r\right)}{\left({T}_m-{T}_r\right)} \)

T m :

Melting temperature of the material, K

Tr :

Reference temperature (room temperature), K. Tr = 293 K

E1, E2 :

Young’s modulus of each of the materials in contact, Pa

ν1, ν2 :

Poisson’s ratio of each of the materials in contact

σ1, σ2 :

Surface roughness of materials in contact, m

h s :

Thermal contact conductance of materials in contact, \( \frac{W}{m^2\cdot K} \)

k m :

Mean harmonic thermal conductivity of materials in contact, \( \frac{W}{m\cdot K} \)

k1, k2 :

Thermal conductivity of each of the materials in contact, \( \frac{W}{m\cdot K} \)

m1, m2 :

Slope of asperities of each of the materials in contact

m e :

Effective slope of asperities

σ e :

Effective surface roughness, m

P :

Pressure squeezing the two materials in contact together, Pa

H v :

Vickers hardness of the softer material, Pa

k1, k2 :

Thermal conductivity of each of the materials in contact, \( \frac{W}{m\cdot K} \)

g :

Temperature jump distance, m

α :

Thermal accommodation coefficient

γ :

Ratio of specific heats for the gas,\( \frac{C_p}{C_v} \)

k g :

Thermal conductivity of gas,\( \frac{W}{m\cdot K} \)

μ :

Dynamic Viscosity, \( \frac{kg}{m\cdot \mathit{\sec}} \)

C v :

Specific heat at constant volume,\( \frac{J}{kg\cdot K} \)

λ :

Mean free path, m

δ :

Mean physical gas gap between materials in contact, m

P :

Pressure squeezing the two materials in contact together, Pa

H v :

Vickers hardness of the softer material, Pa

h g :

Thermal contact conductance of the air gap, \( \frac{W}{m^2\cdot K} \)

δ :

Mean physical gas gap, m

g :

Temperature jump distance, m

h s :

Thermal contact conductance of the two materials in contact, \( \frac{W}{m^2\cdot K} \)

h g :

Thermal contact conductance of the air gap, \( \frac{W}{m^2\cdot K} \)

A p2p :

Contact area for point to point contact, mm2

A l2l :

Contact area for line to line contact, mm2

k :

Constant relating contact area to force,\( \frac{mm^2}{kgf} \)

F :

Force pushing the two materials together, kgf

w :

Half width \( \left(\frac{width}{2}\right) \) of the contact line, mm

l :

Length of the contact line, mm2

F length :

Force applied between the two bodies in contact per unit length, \( \frac{kgf}{mm} \)

R :

Contact resistance between the two bodies, Ω

E c :

Composite Young’s modulus of the two materials in contact, Pa

ν :

Composite Poisson’s ratio of the two materials in contact

G :

Composite shear modulus of the two materials in contact, Pa

G1, G2 :

Shear modulus of materials in contact, Pa

ρ1, ρ2 :

Resistivity of materials in contact, Ω ⋅ m

Pf1, Pf2 :

Plating factor of the material in contact, used to account for the plating on the base metal. For non-plated metal Pf1 = Pf2 = 1.

η :

Empirical coefficient of order unity for clean interfaces

H :

Hardness of the softer material, Pa

ρ cont :

Resistivity of the contaminant film between the two surfaces in contact, Ω ⋅ m

d cont :

Thickness of the contaminant film between the two surfaces in contact, m

Ψ :

Plasticity index. If Ψ < 1, then the deformation is predominantly elastic. If Ψ ≥ 1, then the deformation is predominantly plastic.

C :

Constant that relates contact resistance to force with units as a function of n, Ω ⋅ kgn

n :

Constant that relates contact resistance to force. Unitless.

C a :

Electrical contact conductance per unit area between two bodies in contact,\( \frac{S}{m^2} \)

A :

Contact area between two bodies in contact, m2

g 1 :

Force of gravity,\( {g}_1=9.80665\ \frac{m}{{\mathit{\sec}}^2} \)

β :

Coefficient of thermal expansion (CTE),\( \frac{1}{K} \)

ν g :

Kinematic Viscosity,\( \frac{m^2}{\mathit{\sec}} \)

l pin :

Compressed pin length, m

d pin :

Pin barrel diameter, m

u g :

Velocity of fluid,\( \frac{m}{\mathit{\sec}} \)

h natural :

Natural convection coefficient, \( \frac{W}{m^2\cdot K} \)

h forced :

Forced convection coefficient, \( \frac{W}{m^2\cdot K} \)

Nu :

Nusselt Number

Pr :

Prandtl Number, \( \mathit{\Pr}=\frac{C_v\cdot \mu }{k_g} \)

Ra :

Rayleigh Number, Ra = Gr ⋅ Pr

Gr :

Grashof Number, \( Gr=\frac{g_1\cdot \beta \cdot \left({T}_{pin\_ at\_ room}-{T}_{room}\right)\cdot {l_{pin}}^3}{\nu_g} \)

Re :

Reynolds Number, \( \mathit{\operatorname{Re}}=\frac{\rho \cdot {u}_g\cdot {d}_{pin}}{\mu } \)

R Baycura :

Contact resistance between the two bodies, μΩ

F Baycura :

Force pushing the two materials together, N

C Baycura :

Constant that relates contact resistance to force with units as a function of nshe, \( \mu \varOmega \cdot {N}^{\frac{1}{2+{n}_{she}}} \)

n she :

Strength hardening exponent of the material in contact. Unitless.

References

  1. Antonetti VW (1992) Statistical variability of thermal interface conductance. In: NSF/DITAC Workshop, Melbourne, Australia, pp 37–45

    Google Scholar 

  2. Antonetti VW, Whittle TD, Simons RE (1993) An approximate thermal contact conductance correlation. J Electron Packag 115(1):131–134

    Article  Google Scholar 

  3. Bahrami M, Culham JR, Yananovich MM, Schneider GE (2006) Review of thermal joint resistance models for nonconforming rough surfaces. Appl Mech Rev 59(1):1–12

    Article  Google Scholar 

  4. Barquins M (1988) Adherence and rolling kinetics of a rigid cylinder in contact with a natural rubber surface. J Adhes 26(1):1–12

    Article  Google Scholar 

  5. Baycura OM (1969) Contact resistance determination by a point-slope method. IEEE Transactions on Industry and General Applications 2:208–211

    Article  Google Scholar 

  6. Billo EJ (2007) Excel for scientists and engineers: numerical methods. Wiley, pp 291–296

  7. Bowden FP, Tabor D (1939) The area of contact between stationary and moving surfaces. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences 169(938):391–413

    Google Scholar 

  8. Chan YC, Yang D (2010) Failure mechanisms of solder interconnects under current stressing in advanced electronic packages. Prog Mater Sci 55(5):428–475. Section 3

    Article  Google Scholar 

  9. Chaudhury MK, Weaver T, Hui CY, Kramer EJ (1996) Adhesive contact of cylindrical lens and a flat sheet. J Appl Phys 80(1):30–37. eq. 8

    Article  Google Scholar 

  10. Churchill SW, Chu HHS (1975) Correlating equations for laminar and turbulent free convection from a vertical plate. Int J Heat Mass Transfer 18:1323

    Article  Google Scholar 

  11. Contius E (2018) Der Einfluß der Größe des Druckes und der Fläche auf den Kontaktwiderstand. PhD diss., Technische Hochschule Dresden, 1929. In English, “The influence of total pressure and area on contact resistance.” Translated from German to English by Georgios Dogiamis and edited by Eli Gurevich

  12. Cooper MG, Mikić BB, Yovanovich MM (1969) Thermal contact conductance. Int J Heat Mass Transf 12(3):279–300

    Article  Google Scholar 

  13. Davis JR (2001) ASM specialty handbook: copper and copper alloys. ASM International, pp 471–472

  14. Dieter GE Jr (1961) Mechanical metallurgy. McGraw-Hill, New York, pp 282–295. Ch. 11

    Google Scholar 

  15. Earley M, Sargent J (2010) National Electrical Code (NEC) Handbook. NFPA-70. 2011 Edition. National Fire Protection Association. Sections 210.19(A)(1), 215.2(A)(1). pp 70–52, 70–59

  16. Fei Q, Tong A, Na C (2008) Strain rate effect and Johnson-Cook models of lead-free solder alloys. In: Electronic packaging technology & high density packaging, 2008. ICEPT-HDP 2008. International conference on. IEEE, pp 1–7

  17. Gurevich E Method of linear interpolation between multiple curves and its application to calculating electrical contact resistance. Unpublished as of June 2018

  18. Hertz H, Jones DE, Schott GA (1896) On the contact of rigid elastic solids and on hardness. Miscellaneous papers. Macmillan and Company, pp 163–183

  19. Hilpert R (1933) Wärmeabgabe von geheizten Drähten und Rohren im Luftstrom. Forschung auf dem Gebiet des Ingenieurwesens A 4(5):215–224

    Google Scholar 

  20. Holm R (1981) Electric contacts: theory and application, 4th edn. Springer-Verlag Berlin Heidelberg GmbH, p 43 eq. 8.07, 8.08

  21. Incropera FP, DeWitt DP, Bergman TL, Lavine AS (2007. Eq. 6.48) Fundamentals of heat and mass transfer, 6th edn. Wiley, p 371

  22. Incropera FP, DeWitt DP, Bergman TL, Lavine AS (2007. Table A-4) Fundamentals of heat and mass transfer, 6th edn. Wiley, Hoboken, p 941

  23. Incropera FP, DeWitt DP, Bergman TL, Lavine AS (2007. Table 7.2) Fundamentals of heat and mass transfer, 6th edn. Wiley, Hoboken, p 426

  24. Intel Quality System Handbook (2014) https://www.intel.com/content/www/us/en/quality/quality-system-handbook.html. Last accessed on April 18, 2018

  25. ISO 7730 2005 Specification. Ergonomics of the thermal environment — Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria. pp. 22–23, fig. A.2, table A.5

  26. Johnson KL (1985. Appendix 3) Contact mechanics. Cambridge University Press, pp 427–428

  27. Kennard EH (1938) Kinetic theory of gases, with an introduction to statistical mechanics. McGraw-Hill, New York, pp 311–327

    Google Scholar 

  28. Kuan CL, Huang J, Cheah BE, Kong J (2015) Method to improve ball grid array Imax distribution for small form factor package design. In: 2015 6th asia symposium on quality electronic design (ASQED). IEEE, pp 68–71

  29. Lambert MA, Fletcher LS (1997) Thermal contact conductance of spherical rough metals. J Heat Transf 119(4):684–690

    Article  Google Scholar 

  30. Little CW, Kouwenhoven WB (1953) The spreading and interface resistances of electric contacts. Transactions of the American Institute of Electrical Engineers, Part II: Applications and Industry 72(5):314–323

    Google Scholar 

  31. Madhusudana CV (2014) Thermal contact conductance, 2nd edn. Springer, New York, pp 31–32

    Book  Google Scholar 

  32. Madhusudana CV (2014) Thermal contact conductance, 2nd edn. Springer, New York, pp 42–43, 66–67

    Book  Google Scholar 

  33. McAdams WH (1954. Fig. 10-7) Heat transmission, 3rd edn. McGraw Hill, p 259

  34. Mikić BB (1974) Thermal contact conductance; theoretical considerations. Int J Heat Mass Transf 17(2):205–214

    Article  Google Scholar 

  35. Montgomery RB (1947) Viscosity and thermal conductivity of air and diffusivity of water vapor in air. J Meteorol 4(6):193–196

    Article  Google Scholar 

  36. Ooi MP-L, Kassim ZA, Demidenko SN (2007) Shortening burn-in test: application of HVST and Weibull statistical analysis. IEEE Trans Instrum Meas 56(3):990–999

    Article  Google Scholar 

  37. Seshan K (2018. Ch. 2) Limits and hurdles to continued CMOS scaling. In: Handbook of thin film deposition. William Andrew Publishing, pp 19–41

  38. Slade PG (ed) (2013) Electrical contacts: principles and applications, 2nd edn. CRC Press, pp 5–28

  39. Tanner LH, Fahoum M (1976) A study of the surface parameters of ground and lapped metal surfaces, using specular and diffuse reflection of laser light. Wear 36(3):299–316

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Todd Coons, Georgios Dogiamis, and Tannaz Harirchian for their contributions to this project.

Funding

This research was funded by Intel Corporation. No funding was received from external sources

Author information

Authors and Affiliations

  1. Intel Corporation, Chandler, AZ, USA

    Eli Gurevich & Pranit Deshmukh

Authors
  1. Eli Gurevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pranit Deshmukh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eli Gurevich.

Ethics declarations

Conflict of Interest

The authors do not have any conflict of interest to declare.

Additional information

Responsible Editor: H. Manhaeve

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gurevich, E., Deshmukh, P. New Method for Determining and Predicting Test Interconnect Pin Current Carrying Capacity. J Electron Test 36, 445–460 (2020). https://doi.org/10.1007/s10836-020-05896-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10836-020-05896-z

Keywords

Search

Navigation