Number series of atoms, interatomic bonds and interface bonds defining zinc-blende nanocrystals as function of size, shape and surface orientation: Analytic tools to interpret solid state spectroscopy data
Abstract:Semiconductor nanocrystals (NCs) experience stress and charge transfer by embedding materials or ligands and impurity atoms. In return, the environment of NCs experiences a NC stress response which may lead to matrix deformation and propagated strain. Up to now, there is no universal gauge to evaluate the stress impact on NCs and their response as a function of NC size dNC. I deduce geometrical number series as analytical tools to obtain the number of NC atoms NNC(dNC[i]), bonds between NC atoms N bnd (dNC[i])… Show more
“…Accordingly, only a small percentage of all incorporated P-atoms resides on Si lattice sites where they can become donors by field emission, leaving the vast majority of P-atoms on interstitial sites. As discussed before, the trend of decreasing E
form for samples P5 to P3 might originate from the insufficient number of NC-internal bonds per Si-atom 42 that exert counter-stress against a substitutional P-incorporation. Indications of an increased doping probability of ultra-small NCs exist 4, 45 though characterization or computational treatment of this phenomenon is currently beyond state-of-the-art technical capabilities.Figure 6Formation energies of substitutional P-atoms in Si NCs.…”
Section: Discussionmentioning
confidence: 79%
“…Larger free carrier densities and doping efficiencies for smaller NCs appear counterintuitive. However, a glance at the ratio of NC-internal bonds per Si-atom for such small Si NCs reveals values significantly below the bulk limit of 2 bonds/atom 42 . Thus, a possible cause for the increasing η
D could be the inability of small NCs to provide enough counter-stress for preventing P to be incorporated substitutionally on a lattice site.…”
Phosphorus doping of silicon nanostructures is a non-trivial task due to problems with confinement, self-purification and statistics of small numbers. Although P-atoms incorporated in Si nanostructures influence their optical and electrical properties, the existence of free majority carriers, as required to control electronic properties, is controversial. Here, we correlate structural, optical and electrical results of size-controlled, P-incorporating Si nanocrystals with simulation data to address the role of interstitial and substitutional P-atoms. Whereas atom probe tomography proves that P-incorporation scales with nanocrystal size, luminescence spectra indicate that even nanocrystals with several P-atoms still emit light. Current-voltage measurements demonstrate that majority carriers must be generated by field emission to overcome the P-ionization energies of 110-260 meV. In absence of electrical fields at room temperature, no significant free carrier densities are present, which disproves the concept of luminescence quenching via Auger recombination. Instead, we propose non-radiative recombination via interstitial-P induced states as quenching mechanism. Since only substitutional-P provides occupied states near the Si conduction band, we use the electrically measured carrier density to derive formation energies of ~400 meV for P-atoms on Si nanocrystal lattice sites. Based on these results we conclude that ultrasmall Si nanovolumes cannot be efficiently P-doped.Since the first reports about (heavy) P-doping of silicon nanocrystals (Si NCs), luminescence quenching was often attributed to non-radiative exciton recombination with P-induced free carriers (Auger recombination) 1 . Only few works addressed alternative quenching mechanisms like defects 2-4 . We note that a direct proof of successful P-doping is nontrivial since a true free carrier is not generated due to its confinement in the quantum dot (QD). One important parameter in the investigation of P-doped, oxide-embedded Si NCs is the excess Si concentration that determines the size and separation of NCs as well as the degree of agglomeration. While isolated and mainly spherical NCs are formed at low Si concentrations, excess Si contents above the percolation threshold form highly irregular agglomerated Si NC networks. The threshold that separates these regimes is SiO x≈0.6 for very thin films in a superlattice (SL) and SiO x≲1 for thick bulk films [5][6][7] . While the investigation of P-doping of small and well-separated Si NCs remains a challenging task, it does not come as a surprise that extended Si NC networks can be doped successfully 8,9 . Another important parameter is the dopant concentration and the term doping itself. The latter requires a disambiguation for crystallites at the bottom end of the nanoscale where it is often used deceptively for: (i) the bare incorporation of P-atoms into nanocrystals, (ii) the observation of optical or electrical effects caused by P-incorporation, and (iii) the actual generation of free majority charge carr...
“…Accordingly, only a small percentage of all incorporated P-atoms resides on Si lattice sites where they can become donors by field emission, leaving the vast majority of P-atoms on interstitial sites. As discussed before, the trend of decreasing E
form for samples P5 to P3 might originate from the insufficient number of NC-internal bonds per Si-atom 42 that exert counter-stress against a substitutional P-incorporation. Indications of an increased doping probability of ultra-small NCs exist 4, 45 though characterization or computational treatment of this phenomenon is currently beyond state-of-the-art technical capabilities.Figure 6Formation energies of substitutional P-atoms in Si NCs.…”
Section: Discussionmentioning
confidence: 79%
“…Larger free carrier densities and doping efficiencies for smaller NCs appear counterintuitive. However, a glance at the ratio of NC-internal bonds per Si-atom for such small Si NCs reveals values significantly below the bulk limit of 2 bonds/atom 42 . Thus, a possible cause for the increasing η
D could be the inability of small NCs to provide enough counter-stress for preventing P to be incorporated substitutionally on a lattice site.…”
Phosphorus doping of silicon nanostructures is a non-trivial task due to problems with confinement, self-purification and statistics of small numbers. Although P-atoms incorporated in Si nanostructures influence their optical and electrical properties, the existence of free majority carriers, as required to control electronic properties, is controversial. Here, we correlate structural, optical and electrical results of size-controlled, P-incorporating Si nanocrystals with simulation data to address the role of interstitial and substitutional P-atoms. Whereas atom probe tomography proves that P-incorporation scales with nanocrystal size, luminescence spectra indicate that even nanocrystals with several P-atoms still emit light. Current-voltage measurements demonstrate that majority carriers must be generated by field emission to overcome the P-ionization energies of 110-260 meV. In absence of electrical fields at room temperature, no significant free carrier densities are present, which disproves the concept of luminescence quenching via Auger recombination. Instead, we propose non-radiative recombination via interstitial-P induced states as quenching mechanism. Since only substitutional-P provides occupied states near the Si conduction band, we use the electrically measured carrier density to derive formation energies of ~400 meV for P-atoms on Si nanocrystal lattice sites. Based on these results we conclude that ultrasmall Si nanovolumes cannot be efficiently P-doped.Since the first reports about (heavy) P-doping of silicon nanocrystals (Si NCs), luminescence quenching was often attributed to non-radiative exciton recombination with P-induced free carriers (Auger recombination) 1 . Only few works addressed alternative quenching mechanisms like defects 2-4 . We note that a direct proof of successful P-doping is nontrivial since a true free carrier is not generated due to its confinement in the quantum dot (QD). One important parameter in the investigation of P-doped, oxide-embedded Si NCs is the excess Si concentration that determines the size and separation of NCs as well as the degree of agglomeration. While isolated and mainly spherical NCs are formed at low Si concentrations, excess Si contents above the percolation threshold form highly irregular agglomerated Si NC networks. The threshold that separates these regimes is SiO x≈0.6 for very thin films in a superlattice (SL) and SiO x≲1 for thick bulk films [5][6][7] . While the investigation of P-doping of small and well-separated Si NCs remains a challenging task, it does not come as a surprise that extended Si NC networks can be doped successfully 8,9 . Another important parameter is the dopant concentration and the term doping itself. The latter requires a disambiguation for crystallites at the bottom end of the nanoscale where it is often used deceptively for: (i) the bare incorporation of P-atoms into nanocrystals, (ii) the observation of optical or electrical effects caused by P-incorporation, and (iii) the actual generation of free majority charge carr...
“…For the ICT, and thus the intensity of p- or n-type behaviour, the ratio of interface bonds to atoms forming the Si-NWell, -NWire or -NC is an important parameter [31]. It describes the amount of entities (Si atoms) to be ionized over a certain amount of transfer paths (interface bonds) and depends on the interface facet orientation of the usn-Si volume as well as on its surface-to-volume ratio.…”
Impurity doping of ultrasmall nanoscale (usn) silicon (Si) currently used in ultralarge scale integration (ULSI) faces serious miniaturization challenges below the 14 nm technology node such as dopant out-diffusion and inactivation by clustering in Si-based field-effect transistors (FETs). Moreover, self-purification and massively increased ionization energy cause doping to fail for Si nano-crystals (NCs) showing quantum confinement. To introduce electron- (n-) or hole- (p-) type conductivity, usn-Si may not require doping, but an energy shift of electronic states with respect to the vacuum energy between different regions of usn-Si. We show in theory and experiment that usn-Si can experience a considerable energy offset of electronic states by embedding it in silicon dioxide (SiO2) or silicon nitride (Si3N4), whereby a few monolayers (MLs) of SiO2 or Si3N4 are enough to achieve these offsets. Our findings present an alternative to conventional impurity doping for ULSI, provide new opportunities for ultralow power electronics and open a whole new vista on the introduction of p- and n-type conductivity into usn-Si.
“…To get a quantitative grip on the distribution of DBs on the corners, edges, and facets of the Si‐NCs as a function of , we resort to the analytic crystallographic description of zinc‐blende (zb) and diamond‐lattice NCs. [ 39 ] This reference relates the NC size to the product of the number of Si atoms forming the NC and the atomic volume of Si, , assuming a spherical NC shape:where by the integer variable presents the run index of the respective number series. The analytic expression for of an octahedral Si‐NC is given by [ 39 ] …”
Absorption and photoluminescence (PL) properties of silicon (Si) nanocrystals (NCs) covered with silicon dioxide (
SiO
2
) are fairly well unraveled; corresponding information for silicon nitride (
Si
3
normalN
4
) coverage is scarce. We elucidate important optical and electronic features depending on the embedding dielectric and interface defect (dangling bond, DB) properties. Using density functional theory (DFT) and time‐dependent (TD‐) DFT for ground state (GS) and excited state (ES) properties, respectively, we compute fully
NH
2
‐ and OH‐covered NCs of 11–26 Å size, enabling comparisons with experimental data. Our non‐radiative Shockley‐Read‐Hall (SRH) recombination model of DBs at NC/dielectric interfaces demonstrates that SRH recombination is substantially higher for
Si
3
normalN
4
‐covered NCs. An ensemble TD‐DFT calculation of the eight lowest fundamental transitions accurately describes the absorption edge. Exciton binding energies are significantly smaller in
SiO
2
‐ versus
Si
3
normalN
4
‐covered NCs due to the delocalizing versus self‐localizing impact of the dielectric onto the exciton. We find higher optical absorption rates for
Si
3
normalN
4
‐embedded NCs versus
SiO
2
‐embedded NCs. However, SRH interface recombination renders the PL of
Si
3
normalN
4
‐embedded NCs inferior to their
SiO
2
‐embedded counterparts. Finally, we explain a discrepancy in PL gaps of free‐standing oxidized versus
SiO
2
‐embedded NCs by considering adequate phononic boundary conditions.
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