Impact of oxygen on gallium doped germanium

Germanium (Ge) has advantageous materials properties and is considered as a mainstream material for nanoelectronic applications. Understanding dopant–defect interactions is important to form well-defined doped regions for devices. Gallium (Ga) is a key p-type dopant in Ge. In the present density functional theory study, we concentrate on the structures and electronic structures of Ga doped Ge in the presence of Ge vacancies and oxygen. We provide information on the defect structures and charge transfer between the doped Ga atom and the nearest neighbor Ge atom. The calculations show that the presence of Ga on the Ge site facilitates the formation of nearest neighbor Ge vacancies at 0.75 eV. The formation of interstitial oxygen is endoergic with the formation of −2 charge in both bulk Ge and Ga substituted Ge although the substitution of Ga has slightly less impact on the oxygen interstitial formation. © 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0054643


I. INTRODUCTION
Germanium (Ge) is being considered by the community as it has better carrier mobilities, smaller bandgap, and lower dopant activation temperatures as compared to other technologically relevant group IV semiconductors [i.e., silicon (Si) or silicon germanium (Si 1−x Gex) alloys]. [1][2][3] Gallium (Ga) is technologically important in Ge as it is a ptype dopant. 1 Ga diffusion in Ge is consistent with the vacancy mechanism as it has a lower diffusion activation enthalpy than Ge self-diffusion. [4][5][6][7][8][9] Ge is, in many aspects, similar to Si; however, the solubility of oxygen in Czochralski-grown Ge is not as high as in Si. 10,11 At any rate, high oxygen concentrations can be introduced into Ge when there is oxygen gas or H 2 O vapor in the growth atmosphere. 1 In Ge, oxygen interstitials (O i ) are electrically inactive; therefore, oxygen is deemed not to be a problematic impurity. 1 At any rate, O i can interact with vacancies, which are the dominant defects in Ge to form vacancy-oxygen defects (known as A-centers) although these defects and their properties are not as well understood as in Si. [12][13][14][15][16][17][18][19] The interaction of isovalent atoms with oxygen and vacancies has been investigated in Ge using density functional theory (DFT). 17 In this study, it was shown that O i bind with nearest neighbor carbon or Si dopants. 17 Interestingly, in a recent study, Kipke et al. 20 determined that boron (B) diffusion in Ge is enhanced if the oxygen concentration is high, >10 19 cm −3 (the interesting fact that the heterodiffusion coefficient in a material is enhanced upon adding an increasing concentration of aliovalent dopants has also been observed in previous studies [21][22][23]. It is therefore anticipated that oxygen will also interact with other p-type dopants, such as Ga.
In this study, structures and electronic structures of Ga doped Ge in the presence of Ge vacancies and oxygen interstitials are discussed with the aid of DFT simulations. The current simulation technique provides information on the defect structures and charge transfer between the doped Ga atom and the nearest neighbor Ge atoms, assisting the interpretation of experimental data.

II. METHODOLOGY
All calculations were performed using a DFT code VASP (Vienna Ab Initio Simulation Package). 24 This code solves standard Kohn-Sham equations using plane wave basis sets and projected augmented wave (PAW) pseudopotentials. 25 In all calculations, a plane wave basis set with a cutoff of 500 eV and an 8 × 8 × 8 Monkhorst-Pack 26 k-point mesh were used. The exchange-correlation energy was modeled using the generalized gradient approximation (GGA) scheme as defined by Perdew-Burke-Ernzerhof (PBE). 27 All defect calculations were performed using a 2 × 2 × 2 supercell containing 64 atoms. The conjugate gradient algorithm 28 was used to perform full geometry optimization (both atom positions and lattice constants were relaxed simultaneously). In all relaxed configurations, forces on the atoms were less than 0.001 eV/Å. In order to describe the behavior of the localized Ge p states, we included the orbital dependent Coulomb potential (Hubbard U) and the exchange parameter J within the DFT+U calculations, as formulated by Dudarev et al. 29 We applied the values of U = 0 eV and J = 3.33 eV to the localized p states of Ge as reported in a previous study. 30

III. RESULTS AND DISCUSSION
A. Structure of germanium First, the crystal structure of cubic Ge (space group Fd3m, No: 227) 31 was relaxed under constant pressure to obtain equilibrium lattice constants to validate the quality of the basis sets and pseudopotentials. In order to obtain a good electronic structure, we used the Hubbard U parameter for p-states of Ge. Figure 1 shows the relaxed configuration of bulk Ge and its densities of state plots calculated using GGA and GGA+U methods. Table I reports the calculated lattice parameters and bandgaps together with experimental values. 31,32 There is good agreement between the calculated and experimental values of lattice parameters and bandgap values using the GGA+U approach. As there is a significant deviation between the calculated values using the GGA approach and experimental values, we opted to use the GGA+U method in the defect calculations.

B. Ga-substituted germanium
A single Ga atom was substitutionally doped on the Ge site. The relaxed structure shows that the Ga atom perfectly forms a tetragonal unit (GaGe 4 ) with almost identical bond lengths and angles to those calculated for the GeGe 4 unit in the Ge bulk [see Fig. 2 The substitution energy for a single Ga atom to replace a single Ge atom was calculated using the following equation: where E (Ga:Ge_bulk) is the total energy of a single Ga atom doped Ge bulk, E (Ge_bulk) is the total energy of bulk Ge, and E (Ge) and E (Ga) are the energies of Ge and Ga with respect to their bulk structures, respectively. The substitution energy is endothermic (1.72 eV), inferring the strong Ge-Ge bonds. The substitution energy of Ga in the presence of Ge vacancies and binding energy to form the FNN configuration from other two configurations are calculated (see Table II). Calculations reveal that the FNN configuration is energetically more stable than the SNN configuration (at 0.64 eV) and the TNN configuration (at 0.75 eV). The energy difference between the SNN and TNN configurations is 0.14 eV, indicating the stability of the SNN configuration over the TNN configuration. The substitution becomes easier (at 0.75 eV) in the presence of FNN Ge vacancies than in the absence of Ge vacancies. Once the position of vacancy is slightly shifted, the substitution energy increases. In the case of the TNN, the substitution energy is identical to the substitution energy calculated in the absence of Ge vacancies. This indicates that the substitution was not affected by the TNN Ge vacancy. Figure 4 shows the total DOS, atomic DOS plots, and banddecomposed charge density plots. The Fermi energy calculated for the FNN configuration is unaffected compared to that calculated for the Ga doped Ge bulk configuration [see Fig. 4(a)]. In the other two configurations, a slight reduction in the Fermi energy is noted. In all three cases, the final configurations exhibit metallic character. This is due to the electron charge density localized on the Ge atoms closer to Ga. The atomic DOS plots calculated for Ga show that both s and p states are strongly localized in the valence band.

D. Oxygen interstitial in the Ge bulk and its impact on the substitution of Ga
In this section, we discuss the incorporation of a single oxygen atom as an interstitial atom in the pristine Ge bulk and Ga-substituted Ge bulk. In the latter case, we considered two different configurations. In the first configuration (O i :Ga_NN), the oxygen atom interacts with nearest neighbor Ga [see Fig. 5(b)]. In the second configuration (O i :Ga_NNN), the doped Ga is present as the next nearest neighbor to the oxygen interstitial. The relaxed structures are shown in Fig. 5.
There is a strong bond nature between the interstitial oxygen and the adjacent Ge atoms [see Fig. 5(a)]. This is evidenced by the shorter bond lengths (1.79 Å) and significant charge transfer between the oxygen and Ge atoms [see Fig. 5(d)]. The interstitial oxygen is two-coordinated, forming a bent (or V-shape) structure with a Ge-O-Ge bond angle of 137. The incorporation energy of the oxygen atom into the bulk Ge was calculated using the following equation: where E O@Ge_bulk is the total energy of an oxygen atom incorporated into the bulk Ge, E Ge_bulk is the total energy of the bulk Ge, and E 1 2 O 2 is the total energy of half-molecule of oxygen. The incorporation energy is exothermic in all cases, meaning that oxygen is more stable inside the Ge bulk than its isolated molecular form (see Table III). The binding energy to form the O i :Ga_NN configuration from O i :Ga_NNN is −0.03 eV. Figure 6 shows the total and atomic DOS plots and banddecomposed charge density plots around the O atoms. The total DOS calculated for the oxygen interstitial in the Ge bulk shows that the oxygen incorporated configuration is a semi-conductor with a bandgap of 0.70 eV. However, Ga-doped configurations exhibit metallic character due to the electron density formed on the Ge atoms. Atomic DOS plots calculated for the incorporated oxygen atom show that its p-states are localized in the valence band, inferring the strong bonding between Ge and O. This is further confirmed by the band-decomposed charge density plots around the O atoms.

IV. CONCLUSIONS
In the present study, we employed advanced DFT modeling to predict the interaction of Ga with vacancies and O i . It was shown that the substitution of Ga promotes the formation of nearest neighbor Ge vacancies at 0.75 eV. Exoergic incorporation energies are calculated for the interstitial oxygen in the pristine Ge and Ga substituted Ge. Such favorable incorporation is further confirmed by the negative Bader charge of −2 on the incorporated oxygen. The oxygen interstitial formation has less impact on the Ga doping on Ge. The semiconducting nature of Ge vacancy or O i in the Ge bulk is converted into metallic upon Ga substitution.