A thermal spike model is proposed for the analysis of latent track formation in insulators. The model predicts that above a threshold electronic stopping power ${\mathit{S}}_{\mathit{e}\mathit{t}}$ ${\mathit{R}}_{\mathit{e}}^2$∼ln${\mathit{S}}_{\mathit{e}}$ for 1≤${\mathit{S}}_{\mathit{e}}$/${\mathit{S}}_{\mathit{e}\mathit{t}}$≤2.7 followed by ${\mathit{R}}_{\mathit{e}}^2$∼${\mathit{S}}_{\mathit{e}}$ for 2.7≤${\mathit{S}}_{\mathit{e}}$/${\mathit{S}}_{\mathit{e}\mathit{t}}$ (${\mathit{R}}_{\mathit{e}}$ being the effective track radius). A simple expression is derived for the evaluation of ${\mathit{S}}_{\mathit{e}\mathit{t}}$ from material parameters. A good agreement is found with literature data on latent tracks in magnetic insulators. The analysis showed that the width of the temperature distribution is a(0)=(4.5±0.25) nm and the energy deposited in the spike is 0.17${\mathit{S}}_{\mathit{e}}$.

InSb, GaSb, InP, InAs, and GaAs single crystals were irradiated with Pb ions in the range of 385–2170 MeV. The samples were studied by transmission and high-resolution electron microscopy and Rutherford backscattering in channeling geometry. The energetic ions induced isolated tracks in all crystals but GaAs. The thermal spike analysis revealed that the variation of the damage cross section with the ion energy is considerably weaker than in insulators. The widths of the thermal spike $a\left(0\right)\mathrm{}$ was estimated. The analysis was extended to recent ${\mathrm{C}}_{60}$ experiments on Ge and Si. A quantitative relation was found between $a\left(0\right)\mathrm{}$ and the gap energy $E_g:$ $a\left(0\right)\mathrm{}$ is reduced with increasing $E_g,$ and its lowest value is close to that found in insulators.

Amorphous tracks induced by monoatomic and cluster ion beams are compared in ${\mathrm{LiNbO}}_3$ and ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}.$ In agreement with the prediction of our model, at high energy deposition $R_e^2{/S}_e=\mathrm{const}$ ($R_e$ is the effective track radius, $S_e$ is the electronic stopping power) for monoatomic and cluster ion irradiations. This indicates that the considerably higher energy density in the experiments with cluster ion beams does not modify the track formation. The analysis shows that the width of the thermal spike does not depend on the ion velocity in the range 0.02–20 MeV/nucleon. On the other hand, a strong variation of the efficiency of the energy deposition into the thermal spike g is observed around 2 and 4 MeV/nucleon for ${\mathrm{LiNbO}}_3$ and ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12},$ respectively. The results cannot be explained by the variation of the δ-electron distribution with the specific ion energy E. The importance of the electron-lattice ion and ion-ion interactions are emphasized. The relative shift of the $g\left(E\right)\mathrm{}$ curves is related to the different fraction of heavy elements in the two insulators.

Experimental data on track formation in yttrium iron garnet (YIG) are analyzed using a thermal-spike model. Good agreement between predictions and the data is found. For irradiations with low and high ion velocities the efficiency of the energy deposition in the thermal spike is 35 and 19%, respectively, leading to a lower damage cross section A in the latter case. When A is plotted versus the energy deposited in the thermal spike, all track data follow a single curve. The variation of A due to the broadening of the δ-electron energy distribution with ion velocity is discussed.