The thermal management of printed circuit boards is of increasing importanceas the power density of components and circuits continues to rise. Thesituation is complicated by the use of boards with multiple sheets of copperembedded in the electrically insulating boards to provide electromagneticshielding and to allow more three-dimensional connectivity of the circuitry bythe use of vias. On account of the much higher thermal conductivity of copper, the thermalproperties are expected to be drastically altered by the embedded layers,possibly introducing overall anisotropy as well as thermal resistance at theinterfaces.

We have made detailed measurements^{1} of the conductivity for heatflowing in a direction, either parallel (_{P}) or perpendicular (_{N}) to the plane ofthe board. The measurements show negligible thermal resistance at theinterfaces between copper and glass-epoxy. We find that the conductivity withineach copper layer (_{Cu}= 385 ± 15 Wm^{–1}K^{–1}) is very similar tothat of bulk Cu, while the conductivity within the glass-epoxy (_{ge} = 0.59 Wm^{–1}K^{–1})is approximately 700 times smaller than_{Cu}. This leadsto large anisotropy (_{P}/_{N}) in theboard-averaged conductivity which is found to increase with the number ofcontinuous layers of copper. It was expected that the board-averaged in-planeconductivity _{P}might be sensitive to the average fractional coverage by the topical circuitry. However, the effect of continuous layers of copper, either on the surface orembedded, was found to be far more important than that of topical circuitry. The board averaged conductivities can be calculated to within 10% of themeasured values by use of the following expressions:

_{P}[Wm^{–1}K^{–1}]= 0.8 + 350(Z_{Cu}/Z) and

_{N} [Wm^{–1}K^{–1}]= [1.69(1 – Z_{Cu}/Z)) + 0.0026(Z_{Cu}/Z)]^{–1},where Z_{Cu} is the total thickness of continuous Cu layers in a boardof total thickness Z. Z_{Cu} and Z must have the same units.

table cellspacing=”0″ 1

Sample |
N |
N_{c} |
Z |
Z_{Cu} |
Topical circuitry |
K_{N} |
K_{P} |

PC1 | 4 | 2 | 0.166 | 2 x 66 | none | 0.64 | |

PC2 | 6 | 4 | 0.168 | 4 x 66 | none | 0.71 | – |

PC5 | 2 | 0 | 0.156 | 0 | none | – | 0.81 |

PC6 | 8 | 2 | 0.147 | 2 x 34 | none | – | 15.9 |

PC7 | 8 | 2 | 0.143 | 2 x 34 | many vias | – | 14.6 |

PC8 | 8 | 2 | 0.146 | 2 x 34 | surface mounts | – | 14.5 |

PC11 | 1 | 1 | 0.150 | 1 x 32 | none | – | 9.0 |

PC12 | 6 | 1 | 0.149 | 1 x 34 | little | – | 8.1 |

Parameters describing printed-wiring-board samples. N is the nominal(maximum) number of layers of copper, including two surface layers. N_{c}is the number of continuous layers of copper actually presented in the sample. Zis the full sample thickness (cm) and Z_{Cu} is the total thickness (µm)of continuous copper layers. Topical circuitry refers to the circuitry visibleon either or both surfaces. _{N}is the board-averaged thermal conductivity (Wm^{–1}K^{–1})for heat flowing in a direction perpendicular to the board, and_{P} is theboard-averaged conductivity (Wm^{–1}K^{–1})measured with heat flowing in the plane of the board. (The blanks in the table cellspacing=”0″occur because the _{N}and _{P}measurements were performed separately and required very differently cutsamples). The dominance of the conductivity by the continuous layers of copperand the negligible effect of topical circuitry are apparent