Impurity diffusion induced dynamic electron donors in semiconductors

Low-energy impurity diffusion in a host material is often regarded as an adiabatic process, characterized by its adiabatic potential energy barrier. Here we show that the diffusion process in semiconductors can involve nonadiabatic electron excitations, rending it to be a more complicated process. Impurity diffusion in a device at working temperature can pump one electron up from localized impurity state into the host conduction band and causes the impurity to be a dynamic donor since it temporarily loses its electron to the host. This nonadiabatic process, against a common belief, fundamentally change the diffusion behavior, including its barrier height and diffusion path. Although we mainly demonstrate this process with Au metal impurity in bulk Si through time-dependent density functional theory simulations, we believe this could be a rather common phenomenon as it is shown that the similar phenomena also exist in Zn, Cd impurities diffusion in bulk Si, and Ti diffusion in $\mathrm{Ti}{\mathrm{O}}_2$. We believe this study can open up a new direction of inquiry for such diffusion behavior in semiconductor.

Figure 1

(a) The diffusion path of interstitial Au atom along the ⟨111⟩ direction. The big blue balls represent Si atoms, and the small orange balls track the trajectory of the interstitial Au atom. The high symmetry sites such as the tetrahedral site (T-site) and the hexagonal site (H-site) are marked. (b) and (c) The diffusion trajectory of Au impurity in the BOMD and TDDFT simulations when the initial kinetic $E_k\left(t_0\right)=0.45\mathrm{eV}$. (d) and (e) The corresponding Au impurity movement distance and kinetic energy as a function of time. (f) and (g) Evolution of adiabatic state energy levels as functions of time in BOMD and rt-TDDFT simulations. Green (blue) lines represent the impurity level-1 (level-2) inside the Si band gap. Red solid circles indicate the occupations of the impurity electron with its size represents the amplitude of the occupation. (h) The PES along the diffusion path of Au and $\mathrm{A}{\mathrm{u}}^{+}$ based on NEB method. Here we set the minimum energy of the PES to zero.

Figure 2

(a) Au atom movement distance away from the initial position at the T-site as a function of time for different initial kinetic energy $E_k=0.31$, 0.35, 0.45, 0.55, and 0.65eV under temperature $T=550\mathrm{K}$ based on the rt-TDDFT simulations. Inset shows the kinetic energy of Au atom from the H-site to the T-site based on BOMD simulation. (b) Au atom movement trajectory along $\langle \overline{1}01\rangle$ ($x$ axis) and ⟨010⟩ ($y$ axis) direction.

Figure 3

(a) Evolution of eigenvalues at the supercell Γ-point as the interstitial Au impurity moves away from its initial T-site based on the DFT calculation. The diffusion path of Au atom, from the T-site through the H-site to the T-site along the ⟨111⟩ direction, and M and N are two points between the T- and H-sites along the path. Green (blue) lines represent the impurity level 1 (level-2) in the Si band gap. The insets are the wave functions of two impurity states for Au at the T- and H-sites, respectively. (b) The schematic diagram for two anticrossing levels around the H-site with a gap of Δ. (c) and (d) Comparison of the excited electrons between the rt-TDDTF simulations (blue bars) and classic LZT (red bars) for fixed initial kinetic energy to 0.45 eV but different temperature and fixed temperature to 550 K but different initial kinetic energies, respectively.