First-principles study of Fe and FeAl defects in SiGe alloys

First-principles, spin-polarized local-density-functional calculations are used to model interstitial iron $\left({\text{Fe}}_i\right)$ and its complexes with substitutional aluminum in dilute ${\text{Si}}_x{\text{Ge}}_{1-x}$ alloys $\left(x<8\%\right)$. We considered both the effect of direct bonding between ${\text{Fe}}_i$ or ${\text{Fe}}_i\text{Al}$ with Ge atoms in the $x\to 0$ limit and the evolution of the defect properties with the alloy composition. It is found that ${\text{Fe}}_i$ prefers Si-rich regions, but when placed near a Ge atom, its $\left(0/+\right)$ level is shifted toward the conduction band. However, the ionization energy of ${\text{Fe}}^{\left(+/+2\right)}{\text{-Al}}^{-}$ is only slightly changed by the presence of neighboring Ge atoms in the proximity. It is also found that indirect alloying effects shift the donor levels of ${\text{Fe}}_i$ and FeAl at a fast rate toward the valence band. The acceptor levels, however, remain approximately at the same distance from $E_v$.

Figure 1

(Color online) (a) Schematic of the positions of the calculated impurity-induced levels with respect to the bands of the host crystal. Levels are not to scale. (b) Representations of the wave function of the lower-lying doublet components ($e_{\alpha }$ and $e_{\beta }$) and $a_1$ one-electron states for the ${\text{Fe}}_{T1}\text{Al}$ defect. The $e$ states, shown in the left-hand side, are projected on the (111) plane, whereas the $a_1$ state, shown in the right-hand side, is projected on the $\left(11\overline{2}\right)$ plane. Si and Al atoms are represented by white and gray circles, respectively, and Fe, in the center of the tetrahedron, is hidden.

Figure 2

${\text{Fe}}_i\text{Al}$ configurations proposed by Zhao et al. (Ref. 17) and considered in this paper. The Al and Si atoms are represented by gray and white spheres, respectively. Black points represent different possible positions of the ${\text{Fe}}_i$ atom. $Tm$ designates the $m\text{th}$ neighbor interstitial $T$ site.

Figure 3

Proposed configuration-coordinate diagram for the ${\text{Fe}}_i\text{Al}$ defect in $p$-type Si. Experimental values from Ref. 24 are shown in square brackets. All the energies are given in electron volts.

Figure 4

Structures of ${\text{Fe}}_{T1}\text{Al}$ (left) and ${\text{Fe}}_{T2}\text{Al}$ (right) complexes in Si and SiGe. Si, Al, and Fe atoms are represented by white, gray, and black spheres, respectively. Si atoms labeled with letters were replaced by Ge atoms, forming ${\text{Fe}}_{T1}{\text{Al-Ge}}_{\alpha }$ and ${\text{Fe}}_{T2}{\text{Al-Ge}}_{\beta }$ complexes, with $\alpha =a$, $b$, $c$, or $d$, and $\beta =A$, $B$, or $C$.

Figure 5

(Color online) Donor levels of ${\text{Fe}}_i$ and ${\text{Fe}}_i\text{Al}$ complexes calculated using ${\text{C}}_i$ as marker, as a function of the Ge concentration $\left(x\right)$, along with the experimental level for ${\text{Fe}}_i$ (Ref. 27).

Figure 6

(Color online) Acceptor levels of ${\text{Fe}}_i\text{Al}$ complexes calculated using ${\text{Al}}_s$ as marker, as a function of the Ge concentration $\left(x\right)$. The calculated and experimental acceptor levels of ${\text{C}}_i$ are also shown for comparison. The experimental values are taken from Ref. 66.