Titanium and copper in Si: Barriers for diffusion and interactions with hydrogen

We present the results of a theoretical study of the diffusion barriers of titanium and copper in crystalline silicon, and of the interactions between titanium and hydrogen, and between copper and hydrogen. The calculations were performed using various molecular clusters and the Hartree-Fock method. The method of partial retention of diatomic differential overlap (PRDDO) predicts diffusion barriers of 3.29 eV for ${\mathrm{Ti}}^{+}$, 2.25 eV for ${\mathrm{Ti}}^0$, and 0.24 eV for ${\mathrm{Cu}}^{+}$. PRDDO also predicts that substitutional ${\mathrm{Ti}}^0$ is a deep trap for interstitial H, with a gain in energy of 1.84 eV relative to atomic H far outside the cluster. AB initio Hartree-Fock calculations show that a ${\mathrm{Ti}}^{+}$ ion at a tetrahedral interstitial site also forms a bond with interstitial H, with a dissociation energy of 2.31 eV. On the other hand, interstitial ${\mathrm{Cu}}^{+}$ does not form a bond with H. Several issues relevant to H passivation of interstitial 3d transition-metal impurities in Si are discussed.