Reductions in the thermal conductivity of irradiated silicon governed by displacement damage

We report on the measured thermal conductivity of silicon irradiated with an array of ions: ${\mathrm{C}}^{2+},$ ${\mathrm{N}}^{2+},$ ${\mathrm{Al}}^{2+},$ ${\mathrm{Si}}^{2+},$ ${\mathrm{P}}^{2+},$ and ${\mathrm{Ge}}^{2+}$. Results are analyzed in consideration of ion mass, radius, and induced displacement damage. Recrystallization of select samples via annealing demonstrates that structural disorder imparted by incident ions, rather than the ions themselves, drive the reduction in thermal conductivity. This, in turn, is dictated by the mass of the ion. A generalized model is provided to relate thermal conductivity to displacement damage. Knowledge of the displacements-per-atom profile can thus be used to predict thermal conductivity reduction for silicon devices in extreme environments.

Figure 1

SRIM simulations of the dpa profile (a) and ion concentration profile (b) for each ion implanted in a silicon target. The calculations assume a dose of $1\times {10}^{15}$ ${\mathrm{cm}}^{-2}$.

Figure 2

Measured thermal conductivity as a function of ion dose for all as-implanted samples (a) as well as ${\mathrm{Ge}}^{2+}$ as-implanted/annealed (b).

Figure 3

Total energy loss to recoil events as a function of ion radius (a) and mass (b). The dashed line in (a) shows the average energy loss for a given atomic period, and in (b) is a linear fit to the data, which serves as a guide to the eye.

Figure 4

Measured thermal conductivity of all ions as a function of integrated dpa. The dashed line models the data assuming a defect scattering coefficient proportional to the integrated dpa (shown in the inset). The gray region provides an upper and lower bound to the model accounting for a 95% confidence interval in the fitted relation between the scattering coefficient and the integrated dpa.