Electronegativity and doping in Si1-xGex alloys

Silicon germanium alloys are technologically important in microelectronics but also they are an important paradigm and model system to study the intricacies of the defect processes on random alloys. The key in semiconductors is that dopants and defects can tune their electronic properties and although their impact is well established in elemental semiconductors such as silicon they are not well characterized in random semiconductor alloys such as silicon germanium. In particular the impact of electronegativity of the local environment on the electronic properties of the dopant atom needs to be clarified. Here we employ density functional theory in conjunction with special quasirandom structures model to show that the Bader charge of the dopant atoms is strongly dependent upon the nearest neighbor environment. This in turn implies that the dopants will behave differently is silicon-rich and germanium-rich regions of the silicon germanium alloy.

The evolution in dielectrics and the introduction of high dielectric constant (high-k) dielectrics has allowed the replacement of silicon (Si) with better materials such as germanium (Ge) and silicon germanium (Si 1−x Ge x ) [1][2][3][4][5][6][7][8][9][10] . Random alloys such as Si 1-x Ge x are different to elemental semiconductors as two atom species can occupy one lattice site. The consequence is that there is inhomogeneity of the local environments as there will be Si-rich and Ge-rich regions that will in turn influence the energetics of defect processes 3,6,11,12 . From a thermodynamic viewpoint, Saltas et al 11 . investigated self-diffusion in Si 1-x Ge x with respect to temperature and Ge concentration using the cBΩ thermodynamic model [13][14][15][16] . Saltas et al. 11 identified significant deviations from linearity of the activation energies with respect to compositions and attributed this non-linear behaviour to the bulk properties of Si and Ge.
From a density functional theory (DFT) perspective modelling random alloys can be computationally intensive (or even intractable depending on the issue under investigation) as it necessitates a high number of calculations and very large supercells (>10 3 atoms) 17 . As it has been previously discussed the special quasirandom structures (SQS) approach 17 can lead to manageable supercells while mimicking the statistics of random alloys [18][19][20][21][22][23] .
The present study aims to use SQS in synergy with DFT to study the effect of electronegativity on doping in Si 1-x Ge x alloys (x = 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875). The most significant n-type dopants (N, P, As and Sb) and p-type dopants (B, Al, Ga and In) are considered as they exhibit a range of electronegativities. From a fundamental viewpoint the association of composition, electronegativity and doping is important to understand and improve the electronic properties of alloy semiconductors.

Results and Discussion
Structure of Si 1-x Ge x alloys. The reasoning and efficacy of SQS to describe Si 1-x Ge x alloys and other related random alloys (for example Sn 1-x Ge x and Si 1-x-y Ge x Sn y ) has been discussed extensively in previous work and therefore here we will only briefly discuss this approach for completeness 24,25 . Typical DFT calculations of perfectly ordered structures require the formation of a supercell that is expanded throughout space by the use of periodic boundary conditions. For disordered random alloys the analogous approach is not practically feasible as it requires the construction of very large supercells (>10 3 atoms) 17 with the atoms being randomly positioned at the lattice sites. The advantage of the SQS method is that it efficiently mimics the statistics of random alloys with small supercells (for example 16-32 atoms in Si 1-x Ge x ) 25 and this allows the practical application of DFT in materials were many defect calculations are needed [18][19][20][21][22][23] . A key advantage of the SQS approach is that the atomistic nature is maintained and this leads to a distribution of distinct local environments that exist in real random alloys.  a role on the formation of n-type and p-type doped areas in Si 1-x Ge x . What is the impact of electronegativity of dopants and the local environment in Si 1-x Ge x alloys?
Here we considered full geometry optimizations (positions and cell) of n-type dopants (N, P, As and Sb) and p-type dopants (B, Al, Ga and In) in Si 1-x Ge x configurations (x = 0.125, 0250, 0.375, 0.500, 0.625, 0.750 and 0.875) to examine the local coordination of the dopants formed with the nearest neighbour atoms (Si and Ge). The simulation technique permitted us to determine the Bader charge 32,33 on each dopant and the nearest neighbour atoms attached to the dopants in the relaxed configurations. The Bader charge approximation enabled us to discuss the electronegativity trend of the dopants present in Si 1-x Ge x alloys. In the Bader charge analysis, electronic charges on individual atoms in the lattice are calculated based on the partitioning method as implemented by Bader 34 . Zero flux surfaces are used to divide atoms and partition the charge density 32,33 . A zero flux surface of the gradients of the electron density is expressed by the following equation as discussed by Yu et al 35 .
Where ρ → r ( ) is the electron density, and the n is the unit vector perpendicular to the dividing surface at any surface point → r . Partition of charges are based on the continuum probability density of trajectories → P r t [ ( , ) ] as defined by the following equation: is the probability flux at any point and time. www.nature.com/scientificreports www.nature.com/scientificreports/ First we discuss the correlation observed between the electronegativity (or ionization potential) of n-type dopants and their Bader charges. Figure 1 report the electronegativity values 36 of dopants, the electronegativity difference between dopants and Si (or Ge) and calculated Bader charges on the dopants. Electronegativities of N, Si and Ge are reported being 3.04, 1.90 and 2.01 respectively 36 . As nitrogen has higher electronegativity than that of Si or Ge, electronegativity difference (N-Si = 1.14 or N-Ge = 1.03) is positive. This reflects in the negative Bader charge on N (−3.15). Here we discuss the results for one of the seven configurations. Figure 2 reports the Bader charge on each dopants in seven different configurations and the sum of the Bader charges of the nearest neighbor atoms (Si or Ge). It is clear that in all seven configurations N gains ~3.00 electrons from Si and Ge to complete its outer shell. Total Bader charge of Si and Ge attached to N is ~+3.00 confirming that those three electrons are transferred from Si and Ge. Figure 3 shows the relaxed structures of all seven configurations, Bader charges and bond distances (N-Si and N-Ge). In all seven configurations, the Bader charge on the Si is ~+1.00. There are two different coordination environments observed. In the first five configurations (x = 0.125-0.625), N forms a trigonal planar structure with three nearest neighbor Si atoms. Each Si atom transfers ~1.00 electron to N to form a N 3stable electronic configuration. The N-Si bond distance in all configurations are ~1.85 Å showing the strong bonding formed between the N and the Si. In the sixth configuration (x = 0.750), a trigonal planar structure is formed two Si and one Ge atoms with N. In this case, each Si atom loses ~one electron and Ge atom loses 0.83 electrons. Slight reduction in the charge transfer by Ge is due to the lower electronegativity difference between N and Ge compared to that between N and Si 36 . This reflects in the longer bond distance of N-Ge than N-Si. In the last configuration (x = 0.875), N forms a distorted tetrahedral coordination with three Ge atoms and one Si atom. All three Ge atoms transfer ~0.70 electrons and one Si atom loses 1.00 electron leaving ~3.00 www.nature.com/scientificreports www.nature.com/scientificreports/ electrons on the N atom. Long N-Ge distances (~2.20 Å) confirms the weak bonding and reduction in the charge transfer. Figure 4 shows constant charge density plots associated with the dopants. Electronegativity values of P and As are 2.19 and 2.18 respectively and these values are slightly larger than the values of Si and Ge (refer to Fig. 2). Electronegativity difference between P (or As) and Si (or Ge) is still positive but smaller than that observed between N and Si (or Ge). However, both P and As gain ~3.00 electrons. Relaxed configurations of P together with the bond distances and Bader charges are reported in Figure S1 in the supplementary information. Corresponding charge density plots are shown in Figure S2. In all seven configurations, P forms a tetrahedral coordination. Bader charges on Si or Ge varies from +0.60 to +0.81. Bond distances are  www.nature.com/scientificreports www.nature.com/scientificreports/ longer compared to those observed in N•Si 1-x Ge x . This is due to the lower electronegativity and larger atomic radius of P than that of N. The Bader charges on the As in each configuration is negative and their magnitude vary from −1.89 to −3.10 (refer to Figs. 2 and S3). The negative charges on the As atoms are due to lose of electrons from Si and Ge as evidenced by the positive Bader charges (from +0.16 to +0.78). The formation of tetrahedral unit is observed in all cases with the longer bond distance as expected due to the larger atomic radius of As compared to that of N and P. Charge density plots are shown in Figure S4 in the supplementary information.
Electronegativity difference between Sb and Si (or Ge) is very small (refer to Fig. 1). This is reflected in the Bader charge on Sb. A very small amount of negative or positive charge is observed on the Sb atom in all cases (refer to Figs. 2 and S5). Total Bader charges on the nearest neighbor atoms are also small. Long Sb-Si or Sb-Ge bond distances are observed due to the large atomic radius of Sb and small electronegativity difference. Charge density plots are shown in Figure S6 in the supplementary information.
Charge transfer between dopants and Si (or Ge) can be explained in terms of ionization potentials. Figure 1  b shows the ionization potentials 37 of dopants and Si and Ge. The largest ionization potential is observed for N. Ionization potential difference between N and Si (or Ge) is observed. This implies that the formation of positive charge on N is highly unlikely or gaining of electrons to form negative charge is highly likely. Ionization potential decreases from N to Sb meaning that the formation of positive charge become slightly favourable or gaining of electrons become less favourable. Negative values noted for other dopants indicate that they are highly unlikely to gain electron from Si or Ge and highly likely to lose electrons to become positively charged. This is reflected in the positive Bader charge (+3.00) observed on Al, Ga and In. Figure 6 shows the Bader charge on each dopant and total Bader charge on the nearest neighbour atoms. In the case of B, in all seven configurations B atom is negatively charged and the nearest neighbour atoms are positively charged. Optimized structures, bond distances and Bader charges are shown in Fig. 7. Boron forms a tetrahedral coordination with Si and Ge in all configurations. Shorter B-Si distance compared to B-Ge is due to the smaller atomic radius of Si than that of Ge. In Fig. 8, we show the charge density plots of B. Aluminium forms a tetrahedral coordination with the nearest neighbour Si or Ge atoms. Bader charge on Al in each configuration is +3.00. The total charge on the nearest neighbour atoms are negative in all cases but not equal to −3.00. Figure 9 shows the relaxed structures, bond distances and Bader charges of Al and corresponding charge density plots are shown in Fig. 10. The tetrahedral coordination is observed for gallium in Si 1-x Ge x . The Bader charge is +3.00 on Ga. Total Bader charge on the nearest neighbour atoms is negative and the magnitude differs from −1.20 to −2.50 (refer to Figure S7). The remaining negative charges should have been spread out on the second nearest neighbor atoms. Figure S8 exhibits the charge density plots associated with Ga. Finally, the Summary. Electronic structure calculations were employed to study substitutional doping in a range of Si 1-x Ge x alloys. It is demonstrated that the Bader charge of the substitutional dopants is dependent upon their nearest neighbours and the composition of the alloy. It is found that n-type dopants (N, P, As and Sb) accept electrons from the nearest neighbour atoms (Si and Ge). In particular N, P and As gain almost 3 electrons to form stable X 3ion. Sb accepts only a small amount of electrons as its electronegativity is very closer to the values of Si and Ge. Among p-type dopants, boron accepts electrons while other dopants (Al, Ga and In) loses their outer most three electrons. This is due to the higher electrone gativity of B than that of Si and Ge. The present methodology can be employed to energy materials (fuel cell, battery materials) related systems were random alloys are important 38,39 . This is because in these structurally disordered materials the local environments are bound to influence the dopant diffusion and the electronic properties, which are in turn important for the applicability of the materials in fuel cell and battery materials 38,39 . Methods. All the calculations were spin polarized using the VASP DFT code that uses plane wave basis sets 40,41 . Exchange correlation was modeled using generalized gradient approximation (GGA) as parameterized by Perdew, Burke and Ernzerhof 42 . All the calculations were performed on 64-atomic site supercell consisting of two 32-atomic site SQS cells, a plane wave basis set, cut-off energy of 500 eV and a 4 × 4 × 4 Monkhorst-Pack 43