Source/Drain Materials for Ge nMOS Devices: Phosphorus Activation in Epitaxial Si, Ge, Ge_1−xSn_x and Si_yGe_1−x−ySn_x

The n-Ge, n-Ge_1−xSn_x, n-Si_yGe_1−x−ySn_x (either lattice-matched or tensile strained with respect to Ge), and the Si:P layers were epitaxially grown by chemical vapor deposition (CVD) on blanket Ge Virtual Substrates (VSs) using a 300 mm production compatible epi tool (ASM Intrepid XP^TM). The n-Ge, n-Ge_1−xSn_x, n-Si_yGe_1−x−ySn_x layers with x, y ≤ 0.08 were grown at 440 °C, 315 °C and 400 °C, respectively, using conventional gas precursors (GeH₄, SiH₄, SnCl₄, and PH₃ or AsH₃). Whereas, the Si:P layers were grown at 450 °C using Si₃H₈. The resistivity, the active carrier concentration and the Hall mobilities for as-grown layers were extracted using MHE measurements.¹⁷ A Hall scattering factor of 1 has been assumed in this study. The Sn percentage in Ge_1−xSn_x layers was measured by Rutherford Backscattering Spectroscopy (RBS). The Si and Sn percentage in Si_yGe_1−x−ySn_x and the total P and As concentrations in each layer were obtained from Secondary Ion Mass Spectrometry (SIMS) measurements. Contact resistivities were extracted from the MR-CTLM structures as shown in Fig. 2 (adapted from Ref. 14) using the fabrication scheme described in Fig. 3. For each material, the growth conditions providing the highest active carrier concentration, the lowest resistivity and a thickness of ∼50 nm were used for the MR-CTLM measurements.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

First principles simulations were carried out in a cubic 216 Ge atoms supercell using Vienna ab initio Simulation Package (VASP) combined with the projector augmented wave (PAW) method.^18–21 The electron exchange and correlation were described by two different methods i.e. standard generalized gradient approximation (GGA)/Perdew-Burke-Ernzerhof (PBE) functional and Heyd-Scuseria-Ernzerhof (HSE06) range-separated hybrid functional.^22–24 We will demonstrate that the choice of electron exchange and correlation functional is critical to understand the stability of the dopant-dopant and the dopant-vacancy clusters. A 350 eV kinetic energy cutoff and the Γ point sampling of the Brillouin zone were used for both methods. The atomic positions were relaxed until forces on each atom were below 1 × 10⁻³ eV Å⁻¹. Our previous work in Refs. 2 and 25 was limited to understanding the dopant-vacancy interactions. In this work, we extend our study not only to describe the sensitivity of different electron exchange and correlation functionals but also to understand the atomic interactions among substitutional P, Sn and the possibility of P- and Sn-clustering along with occurrence of dopant-vacancy clusters in Ge. In addition, the energetic cost to incorporate various dopant-dopant and dopant-vacancy clusters will be benchmarked, which have been missing so far.

The positron states and the annihilation characteristics for different defect complexes were modeled using local-density approximation.²⁶ We assume that the electron density is not affected by the presence of positron and use a so-called "conventional-scheme" within the zero-positron-density limit of the TCDFT.²⁶ The repulsive forces of the localized positrons on the ions were taken into account and the Doppler spectra were calculated using PAW all-electron wavefunctions and the state dependent scheme for annihilating electron-positron pairs.^27–29 The computed spectra were convoluted with the experimentally determined detector resolution before comparison with the experimental results.

The size and the chemical environment of dominating open-volume defects in pure Ge and Ge_1−xSn_x layers with different P-doping levels were studied using positron annihilation spectroscopy measurements. The conventional line shape parameters, the S and the W were used to describe the annihilation spectrum. The integration windows for the S and the W parameters were set at $0\lt | p| \lt 0.5$ a.u. and $1.5\lt | p| \lt 3.5$ a.u., respectively, where $| p|$ is the Doppler shift in terms of momentum and a.u. stands for the atomic units. The depth profiling was done with Doppler Broadening Spectroscopy (DOBS) using mono-energetic positrons (0.5–25 keV) obtained from a low-energy positron beam. The momentum density of annihilating electron-positron pairs was studied using coincidence Doppler Broadening Spectroscopy (CDOBS). The special feature of CDOBS measurements is the significantly reduced peak-to-background ratio especially at high momenta. This is important since, the annihilation spectrum at high momenta is dominated by positrons annihilating with core electrons. Thanks to the reduced background, slight changes in core electrons contribution around the annihilation site can be detected.³⁰ E.g. in case of mono-vacancy defects in Ge, any variation in the number of P atoms around the mono-vacancy, when the Ge atoms are replaced by P atoms, is reflected in a difference in the number of core electrons (i.e. the 3d shell of Ge is missing). The reduced probability of positrons annihilating with the core electrons indeed leads to changes in annihilation spectrum and this in-turn allows to determine the chemical environment around the dominating open-volume defect.

The systems were modeled using a supercell made of 216 Ge atoms, in which the positions of 2 P atoms were systematically varied to scan all possible atomic configurations, placing the P atoms at different radial distances from each other (ranging up to ∼8.5 Å). The total energies for the different configurations were then obtained by relaxing both the atomic coordinates and the lattice parameters. The obtained energy values were compared with the energy of the reference system for which the P–P pairs were set farthest apart from each other. Figure 7a reports the change in total energy with respect to this reference system for the most stable conformations containing 2 P atoms. Calculations were done using the standard GGA/PBE and the hybrid, HSE06 exchange-correlation functionals.^22–24

Zoom In Zoom Out Reset image size

At this stage, it is interesting to note that the P–P interaction as described in literature is based on a standard GGA/PBE functional.⁴⁰ It is well established that the classical GGA/PBE exchange-correlation functional describes Ge as a metallic system.^41,42 This pathological behavior can be corrected using different first-order techniques, namely by using either a GGA+U approach, as implemented in Ref. 42, or a hybrid exchange-correlation treatment with the HSE06 functional.^23,24 In this communication, we employ the HSE06 technique to study the dopant-dopant and the dopant-defect interactions in Ge and benchmark it against a standard GGA/PBE approach.

Based on the GGA/PBE calculations, one would conclude that the concomitant existence of 2 P atoms in their immediate vicinity maximizes the difference in total energy due to their Columbic repulsions (Fig. 7a). Following this driving force, the total energy of the system is reduced with the increase in distance between the P atoms. On the other hand, hybrid calculations based on HSE06 predict that the formation of a P–P dimer (i.e. 2 P atoms lying as first nearest neighbors) leads to the most stable configuration, which suggest that P clustering can lead to the deactivation of the dopants in Ge. So far, we have been considering only 2 P atoms in a 216 atoms Ge supercell, which corresponds to a doping concentration of 0.92%. It however must be noted that a doping concentration of 0.92% already exceeds the solid solubility of P in Ge (0.16%).⁴³ This implies that there is a high probability for the occurrence of P–P dimers for these P-doping levels, where the active carrier concentration starts to decrease/saturate in comparison to the total P concentration in the epitaxial Ge layers. To understand the local atomic arrangement adopted in the presence of even higher concentrations, we evaluated the formation of P clusters with more than 2 atoms. The inclusion of the 3rd P atom was started from the most stable relaxed geometry obtained for 2 P atoms in dimer configuration (i.e. first nearest neighbor configuration with the lowest energy as suggested by hybrid calculations). In such a situation, the system attains its minimum energy configuration when the 3rd P atom is placed far away from the existing P–P dimer. This result was obtained for both the GGA/PBE and HSE06 calculations (Fig. 7b).

Regardless of the concentration, and for any subsequent addition of P atoms, the GGA/PBE calculations predict that the lately added P atom should lie as far as possible from the existing P atoms. However, the description obtained by HSE06 calculations leads to a different insight. The minimum energy for the system with an even number of P atoms occurs, when the P atoms are present as 1nn, as shown in Fig. 7c for the case of 4 P atoms in the Ge lattice. In this configuration, the 4^th P atom was added at 3.3 and 7.3 Å from the centroid of 3 P atoms as 1nn. We also checked the scenario in which the initial configuration is chosen as being the most stable conformation in the case of 3 P atoms (i.e. P–P dimer + 1 P atom at 7.6 Å). In this situation, the most stable configuration occurs when the newly added P atom forms a dimer with the existing isolated P atom (i.e. P₂-P₂ dimers at 8.7 Å in Fig. 7c). The configuration P₃ + 1 P at 7.3 Å was chosen as isolated/ reference system in Fig. 7c.

The question which arises at this level is, the reason for which the electrostatic interaction between the P atoms arranged as 1nn would be underestimated using GGA. A part of the answer can be found in the tendency of GGA to promote an over delocalization of the wavefunction of the valence electrons. This is reflected in Fig. 8 by the signature of the partial density of states (PDOS) for 2 P atoms in 1nn configurations (i.e. P–P dimers). The band energies in the horizontal axis are shifted with respect to the Fermi energy (i.e. 0 eV represents the Fermi-level). As depicted in Fig. 8a, there is underestimation/ no opening of the bandgap, when GGA is used as exchange-correlational functional, which minimizes the energy difference between the bonding and anti-bonding orbitals in Ge. The consequence of this artefact (i.e. the bandgap underestimation), leads to an increase in occupancy of the valence electrons in the anti-bonding orbitals. The enhanced electronic population in the anti-bonding orbitals increases the energy of the system. On the other hand, the bandgap opening resulting from the improved treatment of the Hartree-Fock exchange the HSE06 exchange-correlation functional enhances the energy difference between the bonding and anti-bonding orbital states (Fig. 8b). Consequently, lesser anti-bonding states are available to promote the delocalization of the wavefunction of the valence electrons. The resulting decreased (increased) electronic population in the anti-bonding (bonding) orbitals stabilizes the system.

Zoom In Zoom Out Reset image size

In order to obtain a detailed description of the electronic population in bonding and anti-bonding orbitals, together with the nature of the bonds involved (i.e. single (σ) or double (π) bond) between Ge-Ge, Ge-P and P–P, a natural bond orbital (NBO) analysis was performed using the VASP compatible periodic NBO software developed by Dunnington et al.⁴⁴ in combination with correlation-consistent polarized triple zeta (cc-pVTZ) basis sets ⁴⁵. For a detailed explanation on the NBO analysis, the reader is referred to Ref. 44.

Table II lists the resulting average electronic population in various natural bond orbitals when 2 P atoms are arranged as 1nn in Ge using the GGA and HSE06 exchange-correlational functionals. Clearly, the HSE06 description leads to a electron occupancy that decreases in the Ge-P ${\sigma }^{* }$ anti-bonding orbitals or vice-versa, increases in the Ge-P σ bonding orbitals. The lowering in the electronic population of Ge-P ${\sigma }^{* }$ orbitals stabilizes the system more significantly with the HSE06 functional as compared to the GGA case. Furthermore, it is interesting to note that P atoms are only three-fold coordinated and form σ bond only with the nearest neighbor Ge atoms. The P atoms do not share the electrons between each other and exist as lone pairs (LP). However, the HSE06 functional increases the electronic population of the lone pairs by the reduction of electron delocalization in the anti-bonding states. As a result, the electronic signature of the LP appears within the bandgap in the HSE06 calculations (see sharp blue peak near the Fermi-level for P PDOS in Fig. 8b). The enhanced electrostatic interaction between the P atoms for the HSE06 functional is reflected by the variation in bond lengths. Figure 9 illustrates the changes in the bond lengths for P–P dimers and for the nearest neighbor Ge atoms after relaxation using the GGA and HSE06 exchange-correlation functionals. The distance between the 2 P atoms with HSE06 is set to 2.906 Å in comparison to 2.712 Å for the GGA simulations. This, in-turn, leads to a contraction of the Ge-P bonds (2.345 Å) for HSE06 in comparison (2.389 Å) to the GGA simulations. On the other hand, when 2 P atoms are placed at ∼8.5 Å apart from each other (i.e. in an "isolated" scenario), the P atoms remain four-fold coordinated to Ge. This results in an increase of the Ge-P bond lengths (∼2.430 Å) and in electronic population of the Ge-P ${\sigma }^{* }$ orbitals as the contribution of the exchange energy vanishes at long ranges.

Zoom In Zoom Out Reset image size

Table II.  The NBO analysis for P–P dimers in a Ge lattice using the standard GGA/PBE and the hybrid, HSE06 exchange-correlation functionals.

NBOs	Occupancy GGA	Occupancy HSE06
Ge-P σ	1.856	1.907
Ge-P ${\sigma }^{* }$	0.158	0.098
Ge-Ge σ	1.885	1.899
Ge-Ge ${\sigma }^{* }$	0.089	0.071
P LP(1)	1.664	1.759
P LP(2)	1.664	1.759

The random nature of the Ge_1−xSn_x alloy is evident from Fig. 10. It is found that the difference in total energy for the Sn–Sn configurations at different radial distances with respect to the most isolated case, i.e. with a Sn pair at 8.3 Å, lies below the thermal energy accessible at 300 K (i.e. k_bT = 25 meV). This holds true, when the Sn atoms occupy atomic positions separated by at-least 4 Å apart from each other. Furthermore, similar trends were obtained for the GGA/PBE and the HSE06 calculations. Note that the configuration is assumed to be stable whenever the difference in total energy between the chosen system and the reference one is below or equal to the thermal energy at 300 K.

Zoom In Zoom Out Reset image size

Albeit, all configurations are energetically favorable for Sn–Sn pairs positioned from 2nn onwards, it is found that the Sn–Sn pairs remain bound for certain separations. This effect is purely elastic in origin, and was also reported for the Si:C compounds by Rücker et al.⁴⁶ It turns out that there is a local minimum for the relaxed 3nn configuration, when the Sn–Sn couple is set at opposite sides of the hexagonal coordination ring of Ge. This is due to a non-overlap of the strain vectors as illustrated in the inset of Fig. 10. Along these axes, the configuration results in minimum bond-bending distortions. Whereas, the overlap of strain vectors at 1nn (and for the other nearest neighbor distances) leads to strong bond-bending distortions and results in an increase in the energy for this given conformation. It must however be noted that the minimum energy configuration found for the third nearest neighbor coordination of the Sn–Sn pair is not as distinct as for the case of the complementary C-C pair in Si. The 3nn C-C pair in Si is more strongly bound as reflected by an energy difference of −0.14 eV.⁴⁶

For higher Sn concentrations and irrespective of the computational approach used (i.e. GGA/PBE or HSE06), we obtained a similar trend as in the case of 2 Sn atoms in the Ge lattice. The atomic structure has the tendency to adopt a random distribution for their positions, as long as they lie at-least 2nn apart from the other Sn sites. Our findings that 2 Sn atoms can coexist as 2nn onwards, are in line with the random distribution of Ge_1−xSn_x alloys evidenced by Extended X-ray Absorption Fine Structure (EXAFS) results from Gencarelli et al.⁴⁷

So far, we considered atomic interactions of extrinsic species at substitutional sites within the body of the defect-free Ge lattice. The situation alters when a vacancy (i.e. a missing Ge atom) is added to the system. In this case, the energy of the different configurations (i.e. P_n-V and Sn_m-V) is the lowest when either the Sn or P atom is placed as a 1nn with respect to the position of the vacancy. Similarly, when both Sn and P atoms are present together in the Ge lattice with vacancies, the minimum energy configuration occurs when both Sn and P decorate the vacancies as first nearest neighbors. It must be noted that the P atoms around the E-centers (i.e. dopant-vacancy clusters) remain electrically in-active. They do not contribute to the electrical conduction in Ge or Ge_1−xSn_x layers.⁴⁸

Until now, the energetic landscape for all possible conformations of the interacting species e.g. interactions between P (or Sn) atoms and between a P (or Sn) atom and a vacancy were mapped in order to identify the minimum energy configurations. The energetic cost to constitute different defect structures are illustrated by calculating their formation enthalpies (${\rm{\Delta }}{H}_{f}$) according to Eq. 1, adapted from Ref. 49:

$$\begin{eqnarray}&&{\rm{\Delta }}{H}_{f}={E}^{{Defect}}-{E}^{{Ge}}-{n}_{D}{\mu }_{D}+{n}_{{Ge}}{\mu }_{{Ge}}\end{eqnarray} \tag{ 1 }$$

where E_Defect is the total energy of the supercell containing the defect. E^Ge is the total energy of the host Ge crystal without any defect. n_D (D = P, Sn ...) and n_Ge are the number of the dopant atoms added and the number of Ge atoms removed from the system, respectively. μ_D and μ_Ge are the chemical potentials of the dopant and Ge atoms with respect to the elemental solid.

Figure 11 shows the ΔH_f values for the minimum energy configurations of P_n clusters. The increasing ΔH_f values with the accumulation of more P atoms in P_n clusters clearly demonstrates that their evolution becomes energetically costly. On the contrary, the decreasing ΔH_f values of P_n-V clusters with increasing P concentration suggests that the P atoms are incorporated together with vacancy. However, if this hypothesis persists, the concentration of open-volume defects should either be negligible or at-least, less than the total P concentration at low P-doping levels and should increase eventually for higher P concentrations in experimentally grown Ge layers. We will demonstrate later using PAS measurements that the concentration of open-volume defects remains indeed constant in Ge for P-doping levels going from 2.9 × 10¹⁸ cm⁻³ to 3.6 × 10¹⁹ cm⁻³. For P concentrations above 3.6 × 10¹⁹ cm⁻³, not only the concentration of open-volume defects, but also the number of P atoms present as 1nn around them, increase with P-doping.

Zoom In Zoom Out Reset image size

Until now, we have discussed two possible scenarios which can cause dopant deactivation in P-doped Ge, namely the P clustering and the formation of P_n-V clusters. The first principles simulation results discussed in Fig. 11 predict the manifestation of P_n-V clusters as the most dominating mechanism to kick-in at high P concentrations causing severe dopant deactivation in Ge. Therefore, point-defect engineering strategies are required to hinder the formation of large P_n-V clusters. The idea of codoping of Ge:P with Sn was motivated by the possibility that the passivation of vacancies by Sn atoms could enhance the dopant activation in Ge. If Sn atoms trap free vacancies, less sites around the vacancies would be available for P atoms. As a result, the P atoms would remain four-fold coordinated which would result in a higher P-doping activation in Ge_1−xSn_x, as compared to Ge.^4,5 However, the HSE06 simulations do not support this idea. According to our simulation results, it is highly unlikely that the Sn_m-V clusters are formed because of their too high formation enthalpies in comparison to the P_n-V clusters. Figure 12 shows the calculated formation enthalpies using Eq. 1 for various Sn_m-V, Sn_mP_nV and P_n-V clusters. It is evident from the calculated ΔH_f values that the conformation of P_n-V clusters involve minimal energetic cost followed by the Sn_mP_nV and the Sn_m-V complexes for same number of alien atoms around the mono-vacancy. The rapid shift of the ΔH_f values for the Sn_mP_nV clusters toward the P_n-V complexes with increase in number of P atoms around the vacancy implies that the former are most likely to occur subsequent to the formation of P_n-V clusters. Moreover, the Sn_mP_nV complexes are expected to be P-rich with increasing P-doing in Ge_1−xSn_x alloys. It must be noted that any P atoms present in form of Sn_mP_nV complexes also remains deactivated in the Ge lattice. This simulation results are in line with the electrical results and give a qualitative explanation for the fact that experimentally extracted highest electron concentrations are very similar for Ge:P and Ge_1−xSn_x:P (Fig. 4). Meaning, there is hardly any impact of Sn-doping on boosting the dopant activation in P-doped Ge. This leads us to the question, what is the dominant defect type and its chemical environment in epitaxially grown Ge or Ge_1−xSn_x films? To answer these questions, we will now switch to the PAS analysis on Ge and Ge_1−xSn_x layers.

Zoom In Zoom Out Reset image size

The upper panel of Fig. 13 shows the normalized DOBS (W parameters as function of positron implantation energy, Fig. 13a) and the CDOBS (experimental momentum distributions in form of ratio plots scaled to defect-free Ge-reference, Fig. 13b) measurement results obtained on P-doped epitaxial Ge films. The different shaded regions in Fig. 13a indicate the energy intervals where measured W parameters correspond mainly to the positrons annihilating in the top Ge:P layer (0.5-5 keV), the Ge-VS (5-10 keV) and the silicon substrate (above 10 keV), respectively. The steep decay in W parameters throughout the Ge epi-layers indicate that the as-grown layers are full of open-volume defects. Furthermore, the decrease in W parameters with increasing P-doping as seen for P concentrations above 3.6 × 10¹⁹ cm⁻³, signifies an increased concentration of open-volume defects in the Ge films. Interestingly, no change in the W parameters has been observed for the P-doping ranging from 2.9 × 10¹⁸ to 3.6 × 10¹⁹ cm⁻³. This means that the concentration of dominant open-volume defect remains constant in this doping range. For higher P concentrations, the decrease in measured W parameters suggests that the dopant incorporation in Ge goes together with the incorporation of vacancies. This is line with our theoretical results presented in Fig. 11, suggesting the lower formation enthalpies for the larger P_n-V (n > 2) clusters at high P concentrations.

Zoom In Zoom Out Reset image size

The identification of the dominant defect-type and its chemical environment is determined from the CDOBS measurements. These measurements were done at a positron incident energy of 4.5 keV. At this energy nearly all positrons annihilate in the top Ge:P layer. The momentum distributions for the different Ge films as function of P-doping are shown in Fig. 13b. The measured intensities in the peak region (1 < p < 1.5 a.u.) confirm the presence of mono-vacancy defects. Typically, lower intensities are observed in the peak region for the larger open-volume defects.⁵⁰ The positron annihilation at high momenta (p > 1.5 a.u.) is mainly dominated by the positron annihilating with the 3d core electrons of Ge.³⁰ The decrease in intensity at high momenta with increasing P-doping signifies that the chemical environment around the mono-vacancy is changed. This decrease in intensity is due to the increased number of P atoms around the mono-vacancies. This reduces the annihilation probability of the positrons with core electrons at high momenta, since P atoms do not have 3d shell electrons. The calculated momentum distributions for P_n-V clusters in Ge as shown in Fig. 13c confirm the observed trend of decreasing intensity at high momenta. However, it must be noted that in Fig. 13c only single defect types (e.g. P₁-V or P₂-V) are modeled under periodic boundary conditions. On the other hand, the experimental spectra shown in Fig. 13b are superpositions of positrons annihilating in P_n-V clusters within the Ge films with different n-values. By comparing Figs. 13b and 13c, it can be concluded that the open-volume defects (i.e. mono-vacancies) which dominate the measured annihilation spectra for Ge layers are passivated by at-least 2 P atoms for P-doping ranging from 3.2 × 10¹⁹ to 6 × 10¹⁹ cm⁻³ and by at-least 3 P atoms in case of P-doping concentrations above 9 × 10¹⁹ cm⁻³.

The lower panel of Fig. 13 shows PAS results as obtained on the Ge_1−xSn_x:P layers. The DOBS measurement results in Fig. 13d show similar characteristics for the W parameters as function of P-doping in the Ge_1−xSn_x layers as observed in case of Ge:P layers (i.e. the concentration of open-volume defects increases with P-doping). Figure 13d includes a comparison of a Ge:P and a Ge_1−xSn_x layers which contains nearly the same electron carrier concentration (5.7 × 10¹⁹ cm⁻³ vs 4.7 × 10¹⁹ cm⁻³) and nearly the same total P concentration (1.4 × 10²⁰ cm⁻³ vs 1.5 × 10²⁰ cm⁻³). This allows to study the impact of Sn-doping on the positron trapping. In this case, the Ge sample was grown using Ge₂H₆ at a similar temperature (320 °C) as used to grow the Ge_1−xSn_x layers (315 °C). Apparently, the Ge_1−xSn_x layer exhibits higher W parameter. This increase in the W parameter is attributed to the reduced size of the dominating open-volume defects in the Ge_1−xSn_x layers due to presence of Sn atoms around them.

In our previous work (Ref. 25), we have demonstrated that the relaxation effects for the atoms present around the vacancy play an important role in positron trapping. Since the Sn atoms relax in the inward direction with respect to the vacancy, the size of the open-volume defect in case of Sn_m-V clusters becomes considerably smaller, which prevents the positron trapping. On the other hand, for the Sn_mP_n-V clusters where the alien atoms around the open-volume defect relax in both outward (P atoms) and the inward direction (Sn atoms), in this case the positron remains trapped within the open-volume if there are at-least 2 P atoms around the mono-vacancy.²⁵

The CDOBS measurements in Fig. 13e show momentum distributions for positrons annihilating in the Ge_1−xSn_x layers with different P concentrations. The incident positron energy for CDOBS measurements on Ge_1−xSn_x layers was the same as in the case of Ge:P layers (i.e. 4.5 keV). The intensities measured in the peak region (1 < p < 1.5 a.u.) once again confirm that both as-grown Ge:P and the Ge_1−xSn_x:P layers have the same type of dominant open-volume defects (i.e. mono-vacancies). The decreased intensity at high momenta with increasing P-doping clearly reflects the increase in number of P atoms around the mono-vacancy. The mono-vacancy sized defect complexes which dominate the measured annihilation spectrum are passivated by at-least 2 P atoms in case of a P concentration of 3.4 × 10¹⁹ cm⁻³ and by at-least 3 P atoms for P concentrations above 8.1 × 10¹⁹ cm⁻³. The result obtained on the pure Ge sample, which is included in Fig. 13e, clearly exhibits a lower intensity at high momenta as compared to the Ge_1−xSn_x layer with a similar P concentration, although the dominating defect cluster in both samples has at-least 3 P atoms present around the mono-vacancy. This higher intensity obtained for the Ge_1−xSn_x layer is attributed to the presence of Sn atoms around the vacancy along with the P atoms. The calculated momentum distribution for different Sn_mP_n-V clusters are shown in Fig. 13f. The presence of a Sn atom around a mono-vacancy, e.g. in case of Sn₁P₃-V complex leads to slight increase in intensity at high momenta as compared to P₃-V cluster. On the other hand, a significant increase in intensity is observed for Sn₁P₂-V and Sn₂P₂-V complexes with respect to a P₂-V cluster. The experimental spectra shown in Fig. 13e for the Ge_1−xSn_x layers with different P concentrations are superpositions of positrons annihilating in the P_n-V and the Sn_mP_n-V clusters. Therefore, we conclude that there is at-least 1 Sn atom around the mono-vacancy for the Ge_1−xSn_x sample with highest P concentration (i.e. 1.5 × 10²⁰ cm⁻³). Although the dominant defect in the Ge_1−xSn_x layer has at-least 3 P atoms around the vacancy, there are still Sn_mP_n-V clusters with at-least 1 Sn atom present around them which contributes toward the measured annihilation which ultimately results in an increased intensity at high momenta for the Ge_1−xSn_x layer with same P concentration as in the Ge:P layer.