the thermal management of printed circuit boards is of increasing importance as the power density of components and circuits continues to rise. the situation is complicated by the use of boards with multiple sheets of copper embedded in the electrically insulating boards to provide electromagnetic shielding and to allow more three-dimensional connectivity of the circuitry by the use of vias.

on account of the much higher thermal conductivity κ of copper, the thermal properties are expected to be drastically altered by the embedded layers, possibly introducing overall anisotropy as well as thermal resistance at the interfaces.

we have made detailed measurements¹ of the conductivity for heat flowing in a direction, either parallel (κ_p) or perpendicular (κ_n) to the plane of the board. the measurements show negligible thermal resistance at the interfaces between copper and glass-epoxy. we find that the conductivity within each copper layer (κ_cu = 385 ± 15 wm^–1k^–1) is very similar to that of bulk cu, while the conductivity within the glass-epoxy (κ_ge = 0.59 wm^–1k^–1) is approximately 700 times smaller than κ_cu.

this leads to large anisotropy (_p/_n) in the board-averaged conductivity which is found to increase with the number of continuous layers of copper. it was expected that the board-averaged in-plane conductivity κ_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 or embedded, was found to be far more important than that of topical circuitry.

the board averaged conductivities can be calculated to within 10% of the measured values by use of the following expressions:

_p[wm^–1k^–1] = 0.8 + 350(z_cu/z) and

_n [wm^–1k^–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 board of total thickness z. z_cu and z must have the same units.

table 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. z is the full sample thickness (cm) and z_cu is the total thickness (µm) of continuous copper layers. topical circuitry refers to the circuitry visible on either or both surfaces.

κ_n is the board-averaged thermal conductivity (wm^–1k^–1) for heat flowing in a direction perpendicular to the board, and κ_p is the board-averaged conductivity (wm^–1k^–1) measured with heat flowing in the plane of the board. (the blanks in the table occur because the κ_n and κ_p measurements were performed separately and required very differently cut samples). the dominance of the conductivity by the continuous layers of copper and the negligible effect of topical circuitry are apparent.

1. k. azar and j e graebner, experimental determination of thermal conductivity of printed wiring boards, to appear in the journal of electronic packaging, 1995

j.e. graebner
at&t bell laboratories,
murray hill, n.j.