Dissolution of donor-vacancy clusters in heavily doped n-type germanium

We have investigated two types of Ge layers doped either in situ or ex situ using ion implantation followed by FLA. The in situ doped, about 500 nm-thick Ge layers were grown epitaxially on (100) Si substrates by low-energy plasma-enhanced chemical vapor deposition (LEPECVD). Further details about the LEPECVD and the deposition of highly doped Ge epilayers can be found elsewhere [26, 27]. Basically, the single-crystalline Ge epilayers were grown at 773 K at a rate of ∼1 nm s⁻¹ using GeH₄ as the precursor. N-type doping of Ge was realized by adding PH₃ molecules into the reactor chamber with a PH₃/GeH₄ ratio of 1.7%. In the as-grown layer, the maximum effective carrier concentration estimated from Hall effect is found to be around 3.5 × 10¹⁹ cm⁻³, while the P distribution obtained by SIMS reveals that the concentration of P incorporated into Ge is in the range of 1 × 10²⁰ cm⁻³. For ex situ doping, about 400 nm-thick intrinsic-Ge layer was grown on Si substrate by molecular beam epitaxy (MBE). P was implanted with three different fluences (1 × 10¹⁵ cm⁻², 0.4 × 10¹⁵ cm⁻², 4 × 10¹⁵ cm⁻²) and energies (60 keV, 100 keV, 180 keV) respectively in order to ensure the formation of about 300 nm-thick Ge doped layer with a P concentration of around 1.8 × 10²⁰ cm⁻³. This implantation with three different fluences and energies allows to obtain a box-like distribution of P in Ge. After depositing the crystalline Ge layer, millisecond-FLA was performed. Ge samples were FLA either from the front-side (f-FLA) or rear-side (r-FLA) for 20 ms at a maximum temperature of about 1050 ± 50 K in the continuous flow of nitrogen [28]. Such temperature is achieved during the flash with the energy density of 100 J cm⁻². The increase of the flash energy density above 105 J cm⁻² causes the melting of Ge layer, which should be avoided due to strong dopants segregation when Ge recrystallizes from liquid phase. In our FLA system (FLA100), an eight-inch wafer can be homogeneously annealed during a single flash with a maximum temperature easily exceeding the melting point of either Ge or Si. The maximum achieved temperature during the FLA process is self-limited by the melting temperature of the material to be annealed. The FLA for the current experiments was performed with the bank of twelve 26 cm-long Xe lamps with an emission spectrum covering the spectral range from UV to near infrared. During r-FLA, the flash-light is absorbed by the Si substrate and the heat wave propagates from Si to the Ge layer. In such a case, the Ge/Si interface is hotter than the Ge surface. In contrast, during (f-FLA), the main part of the flash spectrum is absorbed within the first 100 nm of the Ge layer. Therefore, during f-FLA, the Ge surface is the hottest. Those two different annealing procedures generate a temperature gradient across the Ge layer, either from the surface to the Ge/Si interface or in the opposite direction. The thermal stability of dopants were investigated using conventional rapid thermal annealing system. Samples were annealed for 100 s in continuous flow of N₂. The annealing temperature was in the range of 250 °C–610 °C.

The type and distribution of defects in P-doped Ge were investigated by positron annihilation lifetime spectroscopy (PALS). The positron lifetime experiments were performed at the mono-energetic positron spectroscopy beamline, which is a beamline of the radiation source electron Linac for beams with high brilliance and low emittance (ELBE) at Helmholtz–Zentrum Dresden–Rossendorf (Germany) [29–31]. A digital lifetime CrBr₃ scintillator detector operated by a homemade software utilizing a SPDevices ADQ14DC-2X with 14 bit vertical resolution and 2 GS s⁻¹ horizontal resolution was used. This detector is optimized for room-temperature measurements and possesses a time resolution down to about 0.205 ns. The resolution function required for spectrum analysis is composed of two Gaussian functions with distinct intensities depending on the positron implantation energy, E_p, and appropriate relative shifts. All spectra contain at least 5 × 10⁶ counts. The lifetime spectra were analyzed as a sum of time-dependent exponential decays (according to the equation: N(t) = Σ_i I_i /τ_i ·exp(−t/τ_i )) convoluted with the spectrometer timing resolution [32] using the non-linearly least-squared-based package PALSfit fitting software [33]. The indices i corresponds to different discrete lifetime components in the spectra with individual lifetimes τ_i and intensities I_i . Regarding the accuracy of PALS, a spectrum with a single lifetime component or a spectrum with multiple components but sufficiently separated from each other can be fitted giving the accuracy down to 1 ps. In general, the possibility of obtaining a reliable multi-component fit is restricted due to the limited time resolution of the spectrometer and the statistics of the measurements. More technical details can be found in reference [34].

2.2.1. Electrical and structural properties

Figure 1 shows the SIMS profile of the P distribution and the depth profiles of electrically active carriers measured by ECV. The atomic concentration of P is in the range of 1 × 10²⁰ cm⁻³ and does not alter upon r-FLA or f-FLA. Obviously, the FLA process at about 1050 K for 20 ms is too short to cause significant P diffusion.

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However, the comparison between the carrier concentration before and after annealing shows that the energy deposited by 20 ms-FLA is sufficient to increase the amount of electrically active P atoms from 3.5 × 10¹⁹ cm⁻³ to about 8.0 × 10¹⁹ cm⁻³ after r-FLA and to about 6.2 × 10¹⁹ cm⁻³ after f-FLA. In the as-grown sample, the carrier concentration is evenly distributed over the layer thickness. A significant enhancement of the activation efficiency of P in Ge was obtained after annealing with the FLA energy densities in the order of 90 J cm⁻² or higher. The annealing of the sample with energy densities lower than 60 J cm⁻² did not improve the carrier concentration. On the other hand, the annealing with the energy densities in the range of 60–90 J cm⁻² slightly increases the carrier concentration. After r-FLA, the highest carrier concentration is detected about 100 nm above the Ge/Si interface and decreases slightly towards the surface. The profile of the carrier distribution follows the heat-wave propagation in the annealed sample from the Ge/Si interface towards the surface. In order to clarify the influence of the temperature gradient on the carrier distributions in P-doped Ge, the ECV measurements were also performed on samples annealed from the front side. After f-FLA the highest carrier concentration is close to the sample surface and decreases with depth as expected.

After r-FLA, the highest carrier concentration was found to be in a depth of about 100 nm above the Ge/Si interface, i.e. above the Ge layer region containing the highest concentration of structural defects (e.g. threading dislocations). The interface quality and the threading dislocation density in the as-grown and the annealed samples were investigated by cross-sectional TEM analysis. Figure 2 shows representative bright-field TEM images obtained from the as-grown sample (figure 2(a)) as well as from the samples annealed from the rear side (figure 2(b)).

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We found a relatively high density of different structural defects at the Ge–Si interface as expected. These defects are created due to the lattice mismatch between Ge and Si. The treading dislocations and other large structural defects are effective trapping centers for donors [35]. Therefore, near the Ge/Si interface the effective carrier concentration is lower than in the center of the film. During r-FLA, the heat wave penetrates the Ge layer from the Si substrate, which means that the thermal load in the vicinity of the Ge/Si interface region is the highest. In such a case, the highest carrier concentration was found to be about 100 nm above the interface region (above 8 × 10¹⁹ cm⁻³), since the highest thermal load is therein (see figure 1). Assuming that P_x V clusters, where x ⩽ 4, are mainly responsible for the deactivation of P in Ge [36, 37], the dissociation of these clusters must take place during the millisecond-range annealing. The dissociation of P_x V clusters is most pronounced at the depths where the thermal load is the highest. However, near the Ge/Si interface the density of dopant-vacancy clusters is higher than in other regions. Therefore, the carrier concentration just at the Ge/Si interface is a bit lower than in the center of the film.

We have also investigated the thermal stability of heavily doped n-type Ge using post-grown annealing. The P-doped Ge samples presented in figure 3 are samples fabricated either by LEPCVD (black squares) or ion implantation (red circles) while the As-doped Ge (green triangles) are data taken from reference [7]. Before thermal stability test the P-doped samples were annealed from rear-side by FLA for 20 ms at 100 J cm⁻². The deactivation of P was performed for 100 s in the temperature range of 250 °C–610 °C. According to reference [7] the As doped samples were annealed for 10 min. The deactivation of As doped Ge starts already at 250 °C. The effective carrier concentration reduces from 1 × 10²⁰ cm⁻³ to 9 × 10¹⁹ cm⁻³. The increase of the annealing temperature up to 350 °C reduces the electron concentration down to 4.5 × 10¹⁹ cm⁻³ and after annealing at 550 °C the electron concentration decreases to 1.7 × 10¹⁹ cm⁻³, which is the solid solubility of As in Ge. Both P doped samples behave slightly different compared to As doped Ge. First, the effective carrier concentration slightly increases after annealing at 300 °C and next it starts to decrease. The significant change of the effective carrier concentration was visible after annealing at the temperature higher than 550 °C, which is much more than for As doped samples. After annealing at 610 °C the effective carrier concentration in the in situ doped and in ion implanted samples decreases to about 4 × 10¹⁹ cm⁻³ and 8.5 × 10¹⁹ cm⁻³, respectively. Much higher thermal stability of P-doped Ge can be due to higher activation enthalpy for diffusion of P than for As (2.85 eV for P vs 2.71 eV for As) [13]. The activation enthalpy for Sb diffusion in Ge is even lower (2.55 eV) suggesting the lowest thermal stability. In Ge technology most of annealing steps, besides dopant activation, do not excess 500 °C. This means that P-implanted Ge can be effectively used as n-type channel material for Ge-based nanoelectronics and optoelectronics.

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To investigate the role of the vacancy-containing clusters in more detail, PALS measurements were performed.

Using DB-PAS in heavily P-doped Ge with a P concentration in the range of 10²⁰ cm⁻³ and an electron concentration of about 2.7 × 10¹⁹ cm⁻³, Kujala et al and Vohra et al have shown that the main defect centers which deactivate electrically active P atoms are four donors bonded with a monovacancy (P₄V) or with a divacancy (P₄V₂) [36, 37]. These authors analyzed Ge crystals and epilayers with a doping level and a carrier concentration very close to those in the present work. Our as-grown samples contain a nearly constant concentration of the P₄V clusters within the Ge layer, which is further supported by PALS measurements. The experimentally obtained positron annihilation lifetime in the as-grown sample and in the samples after FLA (1050 K for 20 ms) consists of two components τ₁ and τ₂. The τ₁ component characterizes the annihilation lifetime of positrons within the layer, while the τ₂ component corresponds to positrons annihilated at the surface state defects and vacancy clusters.

Figure 4(a) shows the experimentally obtained depth/energy distribution of τ₁. The best fit of experimental data was achieved by fixing τ₂ at 500 ps, which is the annihilation time of positrons at the surface state. The large visibility of the surface states for low positron implantation energies, E_p < 6 keV, is likely due to positron back diffusion to the surface. The monotonic decrease of the relative intensity I₂ (I₂ = 100% − I₁) associated with τ₂ confirms that in addition. The positron annihilation lifetime in intrinsic bulk Ge is τ = 227.9 ps, while the shortest τ₁ experimentally determined for heavily P-doped Ge are in the range of 263–288 ps (at depth range of 120–300 nm) for implanted layer and about 277–298 ps for in situ doped after FLA. This observation indicates the presence of open volume defects such as divacancies, vacancy clusters and donor atoms bonded with vacancies since all these defects lead to an increase of τ [38–40]. In the following discussion, we use the hypothesis that the lifetime component τ₁ is related to P_x V and PV₂ defects as well as divacancies.

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Ab initio calculations yield a positron lifetime of around 275 ps and 329 ps for P₄V and PV₂, respectively. However, the relaxation of atoms around vacancies has not been taken into account, which causes underestimation of the calculated annihilation lifetime for donor-defect clusters of around 15 ps [36, 42, 43]. The calculated positron lifetime for neutral V and V₂ are found to be 260 and 320 ps [36], respectively, whereas the lifetime for large vacancy clusters in Ge is significantly higher, in the range of 400–800 ps, (see table 1) [44]. The calculated positron lifetime for mono- and divacancies decorated with P atoms is summarized in table 2. Theoretical calculations of positron lifetimes for the delocalized states (bulk lifetime) and the localized trapped states at defects were obtained by the atomic superposition approach using two-component DFT ab initio calculations [41]. For the electron–positron correlation, the generalized gradient approximation scheme is used [42]. The calculated positron lifetime for vacancy clusters in undoped Ge are summarized in table 1. In comparison to the neutral vacancies, inward relaxation of atoms around the vacancy is expected for charged defects, i.e. V²⁻ or V₂ ², which leads to a smaller open-volume and shorter positron lifetimes [37].

Hence, the calculated lifetime values are overestimated. Slotte et al have shown that above 200 K neutral monovacancies in Ge become mobile tending to form stable divacancies at room temperature [40]. Therefore, the annihilation of positrons in isolated monovacancies at room temperature in heavily n-type doped Ge can be excluded. In general, the positron annihilation lifetime increases with increasing size of the open volume defect as well as with increasing number of donors bonded with vacancies, but τ slightly decreases with increasing ionization state of the defect center [45]. Importantly, all defects are in their most negative charge state when the electron concentration increases above a certain level, which significantly increases the cross-section for positron annihilation [37]. In all samples, the τ₁ in the surface region (first 20 nm) is much longer than that measured in the middle of samples due to the influence of surface state defects. The measured τ₁ at the medium depth for in situ doped as-grown sample was found to be in the order of 302 ps. This is shorter than the annihilation lifetime in V₂, which indicates the positrons annihilation mainly in P₄V centers [40] but still a certain fractions is attracted by V₂. At larger thicknesses positron lifetime approaches the calculated values but the overall signal superimposes with the increasing number of positrons annihilating in the substrate due to a broader depth distribution (at E_p = 10 keV a small fraction of positrons can reach depth of even 800 nm), hence lowering artificially the lifetime value. Obtained τ₁ agrees well with theoretically calculated value for P₄V after considering the overestimation of the annihilation time due to neglecting the matrix relaxation, which is about 15 ps for monovacancies decorated with donors. After FLA for 20 ms, made independently from the rear-side or from the front-side, the τ₁ decreases down to 294 ps at depth of ∼120 nm (277 ps at 300 nm). The reduction of τ₁ by 8 ps is due to reduction of the number of P atoms bonded with monovacancy by two.

The shortest positron annihilation life time τ₁ = 286 ps (263 ps) at depth of ∼120 nm (∼300 nm) was measured for P-implanted sample and annealed from the rear-side. Here, we did not analyze samples implanted and annealed from the front-side because the front-side FLA of implanted Ge cause the formation of a polycrystalline layer, which stands for 1/3 of implanted thickness [28]. The τ₁ measured in P-implanted and annealed Ge is shorter from the in situ doped as-grown sample by 16 ps. Such reduction of positron annihilation lifetime suggests that the main annihilation center in P-implanted and annealed sample must be monovacancy bonded with one P atom.

In principle, before annealing, we have two different cases: (i) heavily doped epitaxial layer mainly with P₄V centers which concentration depends on the doping level and growth temperature and (ii) heavily doped amorphous Ge layer with P concentration in the order of 1.8 × 10²⁰ cm⁻³. In in situ doped epitaxial layer the post-grown millisecond range non-equilibrium thermal annealing dissolves the P_x V clusters into isolated P atoms and monovacancies. Since the carrier concentration after FLA increases by a factor of about three, the concentration of vacancy centers bonded with P must be reduced much below 10¹⁹ cm⁻³. The monovacancies in Ge are not stable at room temperature. Due to very short annealing time, only a part of them liberated from P₄V clusters can be trapped directly by existing larger open volume defects. From not constrained fits (not shown) we obtain lifetimes in the range of 500–800 ps with intensity below 15%, corresponding to mixture of surface states and larger vacancy clusters. During sample cooling (just after the FLA), the rest of the released monovacancies tends to form either divacancies [46] or can be again bonded with P atoms forming P_x V with x < 4. Due to ion implantation, on the other hand, the implanted layer becomes amorphous and during the FLA process it regrow epitaxially via explosive solid-phase recrystallization [30]. This changes significantly the final defect microstructure. The concentration of vacancies in an epitaxial layer strongly depends on the growth condition. As the growth temperature increases, the concentration of defects decreases but simultaneously the high-temperature growth ignites the dopant diffusion and segregation. Therefore, the growth conditions of doped epitaxial layers are compromises between the layer quality and doping level. During r-FLA of the sample with implanted P the temperature is close to the melting point of Ge. Therefore, the concentration of vacancies in the implanted layer recrystallized via explosive solid phase epitaxy is expected to be much lower compared to in situ heavily-doped epitaxial layers grown by CVD or MBE methods. Simultaneously, during explosive solid phase epitaxy dopants like P are incorporated into the substitutional position of Ge and diffusion of P is suppressed. Here, for the P concentration 1.8 × 10²⁰ cm⁻³ the electron concentration estimated from Hall effect is in the order of 1.2 × 10²⁰ cm⁻³. The P-implanted Ge is also more stable during second annealing step (see figure 3). After annealing at 610 °C the effective carrier concentration is reduced by 30% only. While the carrier concertation in in situ P-doped or in ion implanted As-doped Ge is reduced by 55% and 85%, respectively. The higher stability of the ion implanted and FLA samples is the most probably due to lower concentration of vacancies in the ultra-doped Ge-layer.

Figure 4(b) shows the relative intensities I₁ as a function of the annihilation depth/positron energy obtained from the as-grown, annealed and from implanted samples. After ion implantation and annealing, I₁ that is related to the concentration of positrons annihilated with lifetime τ₁ is close to 100%. It indicates that positrons in the implanted and annealed sample annihilates mostly in one type of defects centers, mainly in monovacancy bonded with one P atom. The remaining positrons traps consist of surface states and vacancy clusters. The I₁ in epitaxial layer is in the order of ∼90%. This suggests coexistence of different positron trapping centers with much longer annihilation lifetime e.g. structural defects (vacancy clusters) like threading dislocations visible in figure 2. It is worth mentioning that electrically active single P atoms incorporated into the Ge lattice are positively charged (donors), which is why they cannot trap positrons. After annealing I₁ clearly increases reflecting overall decrease of open volume defects related to larger vacancy complexes, especially in the closer to surface sample region.

For the sake of better understanding of the behavior of phosphorus-vacancy clusters as well as vacancy clusters during FLA, their thermal stability was calculated using the so-called mass action analysis [47, 48]. The following relevant clusters were considered: P_n V (n = 1–4), PV₂, and V_n (n = 2–4). DFT data for the binding energy of the clusters were taken from the works of Chroneos et al [21] and Sueoka and Vanhellemont [48]. Other important input parameters for the calculations were the total P concentration of 1 × 10²⁰ cm⁻³ (see figure 1) and the total vacancy concentration of about 2 × 10¹⁹ cm⁻³. The latter value was estimated from the finding of Kujala et al and Vohra et al [36, 37] which implies that the P₄V cluster is the dominating phosphorus-containing defect center in the as-grown P-doped Ge layers. This defect was assumed to contain the most part of vacancies. Figure 5 shows the calculated concentrations of the different clusters, the monovacancy and the electrically active P monomer, as a function of temperature. The results clearly confirm the assumption regarding the total vacancy concentration, since P₄V is the most stable cluster that starts dissolving above a temperature of 750 K. At the deposition temperature of the heavily P-doped Ge layer (773 K), the concentration of P₄V clusters and P monomers is 1.7 × 10¹⁹ and 2.6 × 10¹⁹ cm⁻³, respectively. At about 1050 K, the concentration of P₄V decreases to about 2.9 × 10¹⁸ cm⁻³ and that of P monomers increases up to 8.3 × 10¹⁹ cm⁻³. The concentration of the other clusters is below 2.5 × 10¹⁸ cm⁻³. Simultaneously with the dissociation of P₄V, the amount of monovacancies and V₄ increases significantly. The results of the mass action analysis are sufficient to interpret the experimental data based on the thermal equilibrium between the monomers (P and V) and the clusters. In the experiments, the electrical activation increases from about 3.5 × 10¹⁹ at 773 K to values between 6.0 × 10¹⁹ and 8.2 × 10¹⁹ cm⁻³ at 1050 K, while the calculation yields 2.9 × 10¹⁹ and 8.3 × 10¹⁹ cm⁻³ at the respective temperatures. The small differences might be due to neglecting some of the clusters (e.g. V₈) in the calculation. In addition, the estimated value of the total vacancy concentration might not be completely correct. On the other hand, in the above comparison of the data from figure 5 with the experimental results, it is assumed that the state created in the sample at 1050 K is 'frozen' and can be analyzed ex situ by ECV and PALS at room temperature.

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This is certainly not completely correct, although the cooling of the sample proceeds relatively fast after FLA. This process only slightly changes the sample state, in particular the concentration of electrically active P monomers. It should be further noticed that in the mass action analysis not only thermal equilibrium but a homogeneous distribution of phosphorus and vacancies is also assumed. Both conditions are not completely fulfilled in the experiment. Nevertheless, the hypothesis used to explain the PALS results of figure 4 is reasonably consistent with the data depicted in figure 5.

Ultimately, the results of this work on P activation by FLA in in situ doped epitaxial Ge layers are compared to those about diffusion-doping of Ge. Experimental results from SIMS and scanning spreading resistance techniques on the diffusion of n-type dopants in Ge revealed a donor (D) deactivation via the formation of neutral D₂V complexes [18, 19]. The formation of this defect complex occurs during dopant diffusion at elevated temperatures up to 1025 K. Certainly, upon cooling from the temperature at which the diffusion is activated even more stable defect clusters may form via the interaction of mobile DV pairs with D₂V complexes. However, since the cooling time is usually much shorter than the diffusion time, the formation of such defect clusters is effectively suppressed such that the distribution of the respective P-correlated defects formed during diffusion remains essentially unchanged. Considering these results, a FLA annealing at 1050 K is not expected to dissolve P₂V complexes, which also supports the temperature dependence of the P₂V concentration deduced from the mass action analysis and shown in figure 4. Accordingly, the remaining deactivation of P in the epitaxial Ge layer after FLA (see figure 1) is due to neutral P₂V complexes that first dissociate at even higher temperatures. P activation by FLA of in situ doped epitaxial Ge layers should therefore be caused by the dissolution of other complexes such as P₄V as discussed above.