Location and Electronic Nature of Phosphorus in the Si Nanocrystal − SiO2 System

Up to now, no consensus exists about the electronic nature of phosphorus (P) as donor for SiO2-embedded silicon nanocrystals (SiNCs). Here, we report on hybrid density functional theory (h-DFT) calculations of P in the SiNC/SiO2 system matching our experimental findings. Relevant P configurations within SiNCs, at SiNC surfaces, within the sub-oxide interface shell and in the SiO2 matrix were evaluated. Atom probe tomography (APT) and its statistical evaluation provide detailed spatial P distributions. For the first time, we obtain ionisation states of P atoms in the SiNC/SiO2 system at room temperature using X-ray absorption near edge structure (XANES) spectroscopy, eliminating structural artefacts due to sputtering as occurring in XPS. K energies of P in SiO2 and SiNC/SiO2 superlattices (SLs) were calibrated with non-degenerate P-doped Si wafers. results confirm measured core level energies, connecting and explaining XANES spectra with h-DFT electronic structures. While P can diffuse into SiNCs and predominantly resides on interstitial sites, its ionization probability is extremely low, rendering P unsuitable for introducing electrons into SiNCs embedded in SiO2. Increased sample conductivity and photoluminescence (PL) quenching previously assigned to ionized P donors originate from deep defect levels due to P.

B) concentrations around 0.25 atom-% (1 25 10 20 . × cm −3 ). With P concentrations in the 0.5 to 8 atom-% range, clustering with dopant inactivation, defect formation and massive out-diffusion occur already in bulk type Si layers for structure sizes of 30 ≤ nm in ultra-large scale integration (ULSI) 16,17 . Local P density fluctuations in SiNCs prevent to provide exactly one active dopant per SiNC 18 . The vast majority of SiNCs are undoped and very few SiNCs have multiple dopants. Latter leads to significant random deterioration of their electronic properties by exchange coupling 19 . Massive P densities in SiNC systems lead to P localized in SiO 2 , in SiO x surrounding SiNCs and P gettered by dangling bonds (DBs) at NC interfaces, all being critical for the electronic structure. So far, unpaired electrons bound to P were investigated by electron paramagnetic resonance (EPR) at very low temperatures 9,10 . Thermal broadening of EPR resonances prevented measurements at room temperature (T = 300 K). XANES is not restricted to low temperatures and yields information on the electronic state of all P at T = 300 K. Excited P K shell electrons in XANES have tremendously increased mean free paths as compared to X-ray photoelectron spectroscopy (XPS) due to their high kinetic energy E kin 20 . We boosted sampling depths further by using XANES in fluorescence yield mode, allowing for non-destructive probing depths three orders of magnitude above XPS values. Due to the low E kin of P L-III shell electrons, XPS is extremely surface sensitive. Probing samples below their original surface by XPS requires sputtering off top material, introducing artefacts as function of chemical species like sputter yield and atom re-coordination and re-ordering.
We report on h-DFT calculations of P at central lattice and interstitial sites in completely OH-terminated SiNCs, of saturated P at the surface of such NCs, in SiO 0.9 as sub-oxide shell around SiNCs and in SiO 2 , delivering insights into the specific electronic structure due to P. The spatial distribution of P atoms in SiNC/SiO 2 systems is derived from APT data and their statistical processing to yield the P distribution profile from the SiO 2 matrix to the interior of the SiNCs. We discuss P data from h-DFT and XANES together with P spatial statistics from APT and obtain a detailed picture of the electronic behaviour of prospective P donors depending on their positions and bond geometries in SiNC/SiO 2 systems. The 1s core level energies from h-DFT are used to assign XANES signals to respective P configurations in h-DFT approximants.

Results
Hybrid DFT calculations. Figure 1 shows optimized approximants of a SiO 2 reference (α-quartz), of SiO 2 with P on a central Si site (SiO 2 :P), of a SiO 0.9 reference and of P-doped SiO 0.9 (SiO 0.9 :P). Fig. 1 further shows optimized approximants of a fully OH-terminated SiNC of 15 Å size as NC reference (OH-SiNC), and this NC with saturated (penta-valent) P substituting a corner Si atom (OH-SiNC > P(OH) 3 ), an OH group on such corner Si atom (OH-SiNC-P(OH) 4 ) and a H atom at the OH group substituted by P(OH) 4 (OH-SiNC-O-P(OH) 4 ). Fig. 1 also shows optimized approximants of fully OH-terminated 15 Å SiNCs with P on a central Si lattice site (OH-SiNC-P[Si]) and on a central interstitial cite (OH-SiNC-P[is]). Interstitial P coordinates relative to its 1-nn Si atoms were used from experiment 21 . Convergence of structural optimization of the approximant was accepted for residual forces on interstitial P and its 1-nn Si atom (and all other atoms) of 309 μeV/Å (11.3 μHa/Å) which is ca. 1.3% of the convergence threshold of maximum residual forces, see to Methods section at end of article. The atomic displacement associated with this minute residual force was 0.0032 Å (0.32 pm) which is ca. 94% of the convergence threshold of residual displacements of 0.003403 pm -a rather large value for such residual force. This variance is an indication of a somewhat flat energy landscape. Thereby, it is rather difficult to calculate an exact diffusion path of interstitial P. This may explain why dopant atoms on Si lattice sites were considered in ab-initio thermodynamic diffusion simulations [22][23][24][25] , but dopant atoms on interstitial positions were not included. Further details on DFT calculations can be found in the Methods section at the end of the article.
Electronic Structure of P in SiO 2 . The SiO 2 HOMO-LUMO gap is 7.83 eV which is 89% of the experimental value of ca. 8.8 eV 26 . We consider P on tetragonal Si sites in SiO 2 and SiO. P is surrounded by SiO 2 at least to its 5 th next neighbour (5-nn) atom. Oxidation enthalpies 27 4 ), leaving P with a DB in analogy to P donors in bulk Si. The DB of P is strongly associated with α-HOMO and β-LUMO, describing one state with its two spin configurations α and β (Fig. 2a). We compare the energies of frontier MOs with HOMO and LUMO energies of the OH-SiNC reference (Fig. 2, green lines). The β-LUMO energy of SiO 2 :P is 0.01 eV above the LUMO of the OH-SiNC approximant while the α-HOMO of SiO 2 :P is 0.41 eV below the HOMO of the OH-SiNC approximant. The barrier height for electron (hole) transport is given by the conduction (valence) band offset between Si and SiO 2 of 3.2 eV (4.5 eV) 26 . These values show that P in SiO 2 reduces the transport barrier for electrons (holes) by 97% (85%), causing an extreme increase in electron conductivity and a considerably increased hole conductivity. These defect levels are an important electronic aspect of P in SiO 2 : It causes a massive increase in SiO 2 conductivity while not working as a donor. Several works build their evidence of SiNC doping on conductivities increasing with P concentrations of 0. 5  Electronic Structure of P in SiO. Approximants for SiO 0.9 and SiO 0.9 :P are based on α-quartz. Every second O bridge Si-O-Si is substituted by a bond Si-Si. As with SiO 2 :P, we have a DB on P occupied with one electron in the SiO 0.9 :P approximant at a central Si lattice site, again resulting in two different spin orientations per MO (α β , ). Frontier MOs are similar to SiO 2 :P, describing the DB of P with one electron occupying the α-HOMO. The α-HOMOβ-LUMO gap of 1.96 eV is 0.76 eV below E gap = 2.72 eV of the OH-SiNC reference. The HOMO in SiO 0.9 :P is located 1.05 eV above the HOMO of the OH-SiNC reference. Hence, P presents a deep recombination center in SiO x shells ( Fig. 2b) which cover SiNCs with a thickness of 1 to 1.5 mono layers (MLs) 28 . This finding is supported by PL quenching reported for high P concentrations mentioned above 3,29 .
The LUMO of SiO 0.9 :P facilitates electron transport by diminishing the electron barrier. As for the SiO 2 :P approximant, electron (hole) barriers are decreased down to 32% (removed completely). For SiO 0.9 and SiO 0.9 :P approximants, a helical arrangement of Si atoms along the 001 vector (Fig. 1c,d) dominates MOs from E − E vac = 0.2 to − 8.5 eV. The inner bonds of these Si backbones can resist electron transfer to O to some extent, diminishing the splitting of their bonding and anti-bonding MOs. Experiments yield E gap (SiO) ≈ 2.48 eV 30 , our calculations overestimate this value by 54%. This may be due to the very balanced local stoichiometry of the SiO 0.9 reference and SiO 0.9 :P approximants as well as their high space group symmetry which allows for mentioned Si helices. Local Si segregation suggests that SiO is not uniform 13 which can lower the band gap. The P concentration can be calculated as for the SiO 2 :P approximant, yielding 0.56 atom-% for SiO 0.9 :P.
Electronic Structure: Saturated P at SiNC interfaces. Tetravalent P atoms substantially gain binding energy when gettering their DBs at NC interfaces and maximize binding energies of Si atoms providing DBs. It is thus energetically unfavourable for P at the NC interface to have a DB. This finding is supported by a maximum P density at SiNC interfaces derived from APT below.
We show the DOS of the OH-SiNC reference approximant along with the DOS of all three approximants containing bond-saturated P at the interface (Fig. 3). Fully gettered P at NC interfaces does not introduce defect levels within the HOMO-LUMO gap of the SiNC. The DOS of OH groups has an energy gap of 8.0 eV, corresponding to 91% of the experimental band gap of SiO 2 26 . The DOS of the SiNC approximants expose a small shift of HOMO and LUMO to higher binding energies, correlating with an increasing number of O atoms 31,39 . Electronic Structure of P within SiNCs. We consider P on a central Si lattice site OH-SiNC-P[Si] and on a central interstitial site OH-SiNC-P[is]. P on a Si lattice site generates a HOMO 0.51 eV below the LUMO energy (Fig. 4a). While this HOMO presumably becomes a donor state for vanishing quantum confinement, its ionization energy E ion = 0.51 eV is too big to ionize SiNCs with a reasonable probability at T = 300 K; ≈ × − . Interstitial P introduces two gap states, a HOMO 0.57 eV above the HOMO of the 1.5 nm SiNC and a LUMO 0.46 eV below the LUMO of the SiNC (Fig. 4b). Both states due to P cannot donate electrons but provide efficient carrier recombination with a transition energy of 1.72 eV. As this transition is optically active at a wavelength of ca. 720 nm, it must be considered for PL spectra of P-doped SiNC/SiO 2 species. Both cases of P in OH-SiNC introduce recombination levels into SiNCs.
Atom Probe Tomography. We show the APT scan of a SiNC SL in SiO 2 where SiNCs are enclosed by iso-surfaces with atomic concentrations of Si N 0 7 Si ≥ . , i.e. 70 ≥ atom-% Si (Fig. 5a). With the molar ratio of Si O 1 2 / = / in SiO 2 , we derive the molar SiO 2 partition P SiO 2 of SiNCs via Ignoring the P partition of ca. 1 atom-%, we get P 21 SiO 2 ≤ mol-% SiO 2 and P P 1 7 9 Si SiO 2 = − ≥ mol-% Si for volumes enclosed by iso-surfaces. We note that the real P SiO 2 value is lower due to APT projection artefacts. Detailed statistical analyses of APT data 32 revealed that about 15% of the P atoms are found within SiNCs, whereas about 30% are trapped at the interface and about 55% reside in the surrounding SiO 2 matrix. This relatively low P concentration in SiNCs can be explained by self-purification [22][23][24][25] , by solubilities of P in Si and SiO 2 and by the high relative SiO 2 volume of 85% in our samples. Zooming into the APT scan shows P atoms within SiNCs (Fig. 5b). A notable P concentration within SiNCs appears to disprove self-purification. However, interstitial P 21 should have a much higher probability to exist in SiNCs as compared to P built into SiNC lattice sites. It does not require bond breakage and can exploit the fast diffusivity and high saturation density of P. An inclusion of such P configurations into ab-initio thermodynamic diffusion simulations would complement existing self-purification models which only consider foreign atoms at SiNC lattice sites. Tomogram data from APT used for a cluster analysis 32 comprised numerous SiNCs in SiO 2 :P. The resulting proxigram shows the radial concentration of Si, O and P (Fig. 5c). We found a strong accumulation of P atoms in the SiNC/ SiO 2 interface shell with SiO x≈1 and also an increased P concentration within SiNCs. XANES spectroscopy. We measure P K spectra to determine the P oxidation stage by its K shell electron binding energy (Fig. 6), using a non-degenerate P-doped Si wafer (donor density = 0 2 to 1 10 19 . × cm −3 or 0.004 to 0.02 atom-%) for calibration. We assign XANES results to P environments using 1s core levels calculated by h-DFT with all-electron MO-BSs. P 1s core level energies from h-DFT correspond to 97.864% of P K XANES energies, see table 1. We calibrated h-DFT values by a factor of 1.02183 as supported by h-DFT P 1s core level energies of P 2 O 5 (P +5 ) and P 2 O 3 (P +3 ) approximants calculated with the same h-DFT route (Fig. 7).

Discussion
Origin of PL quenching of SiNCs containing P. Diffusion of P through Si proceeds at high rates during SiNC segregation anneal with T 1100 ≈ °C. Experimental data shown above and DFT calculations [22][23][24][25] indicate that P appears to be within SiNCs on interstitial sites with a probability of nearly 100%. Auger recombination was assumed to cause PL quenching in SiNC/SiO 2 material systems with high P concentrations 3 . Our findings do not support this assumption. With extremely low P ionization probabilities, the difference in free carrier densities of doped and intrinsic SiNCs is virtually nil. The Auger  35,36 . P located within SiNCs or within SiO x shells around SiNCs are deep defect centers which appear to provide the most efficient and fastest path for non-radiative carrier recombination. This process explains PL quenching already at reasonably high P densities 29 still below values reported elsewhere 3,4 . Co-doping with B was shown in experiment to increase PL intensities while transition energies decreased below those of undoped SiNCs 3 . Localized states of B and P at or within SiNCs provide strong radiative transitions as donor electrons directly relax into acceptor states. PL energies decreasing with co-doping 37 (table 1). A hint of a signal shoulder might exist for all SiNC samples at the XANES peak for P 0 at 2144.8 eV. An indication of a signal occurs for the smallest SiNC size of 2 nm, suggesting a slightly increased doping probability for ultrasmall SiNCs also observed by EPR 10 , though the ultrasmall SiNC size notably increases the signal background for XANES and presumably EPR. Our results show that P does not provide electrons to SiNCs embedded in SiO 2 with reasonable probabilities.

Conclusion
We carried out DFT calculations for the SiNC/SiO 2 system to monitor the electronic nature of P. On a lattice site within OH-terminated SiNCs, P introduces a deep donor level with E ion = 0.51 eV; ionisation for small SiNCs is virtually nil, but is likely to increase for SiNCs with diminishing quantum confinement. However, formation energies of P on Si lattice sites [22][23][24] suggest that P in SiNCs occurs almost exclusively on interstitial sites which is indirectly corroborated by experiments showing an extremely small density of P atoms with unpaired electrons even for 10 nm SiNCs 9,10 . On a central interstitial site within SiNCs, P cannot donate an electron (E ion > 2 eV), but forms two deep defect levels with a recombination transition at 1.72 eV. At SiNC interfaces, fully saturated P have no impact on frontier molecular orbitals, leaving HOMO and LUMO energies virtually unchanged. In SiO shells around SiNCs, P is again unable to donate an electron, but induces a deep defect level which triggers massive recombination. This defect causes PL quenching -as opposed to Auger recombination -and increases SiO shell conductivities which were both interpreted as evidence for successful SiNC doping in the literature 3,8 . Although P atoms in SiO 2 are deep defects which cannot donate electrons, they tremendously improve inter-NC conductivities in particular for electrons by diminishing electron (hole) barriers by 97% (85%) of the conduction (valence) band offset between bulk phases of Si and SiO 2 . Massively increased conductivities were assumed to prove successful SiNC doping 6,8 . APT analyses revealed an enrichment of P at SiNC interfaces, which appears to be due to DB saturation and support h-DFT analyses of fully O-saturated P at SiNC interfaces. SiNCs were found to contain significant amounts of P. While this appears to contradict self-purification theory, interstitial P with considerably more favourable thermodynamics and its high diffusivity and saturation density has not been considered in self-purification modeling. Core level (K shell) electron energies of P in SiO 2 and SiNC/SiO 2 samples were measured by XANES at room temperature. In contrast to bulk Si, P atoms in SiNC/SiO 2 samples could not donate electrons into 2 to 5 nm size NCs in SLs or in annealed bulk SiO x films with reasonable probabilities, confirming our h-DFT results. We conclude that conventional doping of SiNCs with P does not provide majority charge carriers to SiNCs embedded in SiO 2 . Alternative approaches for majority carrier introduction into embedded SiNCs and ultrasmall Si nanovolumes such as embedding material effects 39 have to be explored to advance SiNC-based nanoelectroncis and ULSI.  51 10 4 . × − Ha/Å), respectively. Electronic structures were computed with the same route; B3LYP/6-31G(d) // B3LYP/6-31G(d). Additional information is available on accuracy tests and tests of functional group termination as approximation of the dielectric 31,39,47 . During all calculations, no MO symmetry constraints were applied and tight convergence criteria were set for the self-consistent field routine.

Methods
Alternative approaches to the B3LYP h-DF with similar accuracy are the Heyd-Scuseria-Ernzerhof h-DF (HSE06) 48  Characterisation. We examined the position of P within the SiNC/SiO 2 system by APT using a Cameca LEAP 4000X HR instrument with a reflectron-type time-of-flight mass spectrometer and a pulsed UV laser (355 nm, 10 ps pulse length, 70 pJ pulse energy, 100 kHz repetition rate). During the analyses (chamber pressure 1 10 11 × − mbar), specimens were cooled to temperatures of around 76 K. The mass resolution of the system was m m 800 ∆ / ≈ , around 36% of all atoms are detected. Specimen tips have been prepared by the cut-and-lift-out technique using an ALTURA 875 dual-beam Focused Ion Beam instrument 32 . The P K-edge absorption in XANES was measured at the SUL-X beamline at the Angströmquelle Karlsruhe (ANKA). Monochromatic X-rays were obtained using a Si(111) double crystal monochromator with an energy resolution of about 0.2 eV at 2150 eV with fixed exit. Scans were carried out using a shallow incident angle to maximize the SL or thin layer volume of samples for excitation. Absorption was measured by monitoring the P Kα fluorescence emission using a seven element Si(Li) fluorescence detector (SGX Sensortech). The signal is normalized to the incident photon flux measured simultaneously by a custom made ionization chamber (ADC, US) filled with N 2 at a pressure of 50 mbar. Energies  were calibrated to 2152 eV at the white line maximum of the P K-edge XANES spectrum of NaH 2 PO 2 ⋅ 2 H 2 O. The energy step size across the XANES region was 0.2 eV. XANES peaks of our samples show a full width half maximum of ca. 2 eV. P K XANES spectra have been pre-and post-edge background corrected and normalized to the edge jump with the ATHENA program of the IFEFIT package 52 .

E (eV)
q(e a ) samples/  Table 1. Core level energies of P (1s from h-DFT, K shell from XANES). Bold numbers present XANES values, underlined numbers indicate approximants with same or similar configuration to samples indicated by arrow. Further shown are P atomic charges, P configuration (DFT approximant, XANES sample), number of P 1−nn O atoms, P valence state and remarks. a Values are Mulliken charges for DFT approximants and derived analytically for P in Si wafer (see text). b P valence state is zero (0), tri (III), tetra (IV), penta (V) or unknown (??) Figure 7. P 2 O 3 and P 2 O 5 approximants for XANES calibration. Approximants of P 4 O 6 (a) and P 4 O 10 (b) cages constituting P 2 O 3 (P +3 ) and P 2 O 5 (P +5 ), respectively 27 .