Self-interstitial Concentration Research Articles

Conversion of silicon wafer type from perfect-interstitial to perfect-vacancy by rapid thermal process

Vacancies, self-interstitials, and Frenkel pairs represent the basic point defects in silicon single-crystals and are unavoidably introduced in the ingots during the manufacturing process. In semiconductor technology, several problems are caused by points defects that are not at thermodynamic equilibrium. For this reason, virtually defect-free silicon wafers having a small residual concentration of vacancies in the bulk (“Perfect-vacancy”, or Pv silicon) are solely used for the fabrication of advanced microelectronic devices, whereas similar wafers containing a residual concentration of silicon self-interstitials (Pi silicon) are often regarded as unsuitable substrates for device fabrication. This paper describes the possibility of using Pi silicon wafers, after their conversion to Pv, for those applications requiring only vacancy-rich perfect silicon as the substrate. The conversion from Pi to Pv is achieved in these wafers by using rapid thermal annealing at high temperature to produce Frenkel pairs first and to re-install a specific vacancy concentration in the bulk of the wafer later, thus reassigning a new Pv character to the silicon substrate.

Uphill phosphorus diffusion in carbon co-implanted silicon

An intriguing uphill diffusion phenomenon related to phosphorus has been observed in carbon co-implanted silicon. This phenomenon has been investigated using Transmission Electron Microscopy, Secondary Ion Mass Spectroscopy, and Atom Probe Tomography. Our results indicate that uphill diffusion occurs in crystalline silicon, once the recrystallization of the amorphous layer induced by ion implantation has ended. This phenomenon results in the formation of a steep, highly concentrated, and electrically active dopant peak. A one-dimensional model has been used to understand the underlying mechanism of peak formation. The heterogeneous concentration of self-interstitials across the implanted region has been shown to be responsible for the uphill diffusion phenomenon.

Signatures of self-interstitials in laser-melted and regrown silicon

Photoluminescence spectroscopy investigates epitaxially regrown silicon single crystals after pulsed laser melting for atomic-level lattice defects. The measurements identify a transition from a regime free of defect-related spectral lines to a regime in which spectral lines appear originating from small self-interstitial clusters. This finding of self-interstitial clusters indicates supersaturated concentrations of self-interstitials within the regrown volume. Molecular dynamics simulations confirm that recrystallization velocities vre ≈ 1 m/s after laser melting lead to supersaturation of both self-interstitials and vacancies. Their concentrations ci and cv in the regrown volumes are ci ≈ cv ≈ 1017 cm−3. An analytical model based on time-dependent nucleation theory shows a very strong dependence of self-interstitial aggregation to clusters on the cooling rate after solidification. This model explains the transition identified by photoluminescence spectroscopy.

Diffusion and Point Defects in Elemental Semiconductors

Elemental semiconductors play an important role in high-technology equipment used in industry and everyday life. The first transistors were made in the 1950ies of germanium. Later silicon took over because its electronic band-gap is larger. Nowadays, germanium is the base material mainly for γ-radiation detectors. Silicon is the most important semiconductor for the fabrication of solid-state electronic devices (memory chips, processors chips, ...) in computers, cellphones, smartphones. Silicon is also important for photovoltaic devices of energy production.Diffusion is a key process in the fabrication of semiconductor devices. This chapter deals with diffusion and point defects in silicon and germanium. It aims at making the reader familiar with the present understanding rather than painstakingly presenting all diffusion data available a good deal of which may be found in a data collection by Stolwijk and Bracht [1], in the author’s textbook [2], and in recent review papers by Bracht [3, 4]. We mainly review self-diffusion, diffusion of doping elements, oxygen diffusion, and diffusion modes of hybrid foreign elements in elemental semiconductors.Self-diffusion in elemental semiconductors is a very slow process compared to metals. One of the reasons is that the equilibrium concentrations of vacancies and self-interstitials are low. In contrast to metals, point defects in semiconductors exist in neutral and in charged states. The concentrations of charged point defects are therefore affected by doping [2 - 4].

Precipitation of Cu and Ni in n- and p-type Czochralski-grown silicon characterized by photoluminescence imaging

Photoluminescence (PL) images and micro-PL maps were taken on Cu- or Ni-doped monocrystalline silicon wafers, to investigate the distribution of the metal precipitates. Several n-type and p-type wafers were used in which Cu or Ni were introduced in the starting melt of the ingots and precipitated during the ingot cooling (as opposed to surface contamination). The micro-PL mapping allowed investigation of the metal precipitates with a higher spatial resolution. Markedly different precipitation patterns were observed in n- and p-type samples: in both Cu- and Ni-doped n-type samples, circular central regions and edge regions were observed. In these regions, particles were distributed randomly and homogeneously. In the p-type Cu-doped and Ni-doped samples, by contrast, the precipitates occurred in lines along <110> orientations. The difference in the precipitation behaviour in n- and p-type samples is conjectured to be caused by different concentrations of self-interstitials and vacancies remaining in the crystal during the ingot cooling: there are more vacancies in the n-type ingots but more interstitials in the p-type ingots. The dopant effects on the intrinsic point defect concentrations in silicon crystals and possible precipitation mechanisms are discussed based on the findings in this work and the literature.

Molecular dynamics simulation of the early stages of self-interstitial clustering in silicon

We have studied the early stages of self-interstitial clustering in silicon using molecular dynamics simulation techniques. We have generated silicon samples of over 200,000 atoms where we introduced a 0.5% extra concentration of self-interstitials. Then samples were annealed at several temperatures. During the simulations we observed the formation of interstitial clusters with different atomic structures, ranging from spherical and amorphous-like clusters, to highly ordered extended configurations such as (110) chains, {111} rod-like defects and dislocation loops, and {100} planar defects. This last type of defects, while common in germanium, have not been observed in silicon until very recently, in ultra-fast laser annealing experiments. The particular morphology of formed interstitial clusters is found to be related to the annealing temperature, as it is observed in the experiments. From the molecular dynamics simulations we have analyzed the atomic mechanisms leading to the formation and growth of interstitial clusters, with special attention to the newly found {100} planar defects.

A study of as-grown, poled and reduced Rh-doped KNbO3 single crystals by high-resolution X-ray diffraction, Raman scattering, photoluminescence and dielectric measurements

As-grown and chemically reduced Rh-doped (1500 p.p.m.) KnbO3 single crystals grown by the Czochralski method have been characterized. Reduction of the grown crystals at different levels was carried out under a mixture of CO and CO2 gases as the crystals were grown with excess oxygen. The effect of reduction and poling on crystalline perfection was studied by high-resolution X-ray diffraction (HRXRD) using a multi-crystal X-ray diffractometer developed in-house. The diffraction curves of the as-grown, electrically poled, moderately reduced and heavily reduced single-crystal specimens show remarkable differences. The studies by HRXRD reveal that poling has some influence on the improvement of crystalline perfection, while chemical reduction has a great influence on crystalline perfection; at moderate reduction the crystal becomes nearly perfect, but when the reduction is very heavy the crystal quality decreases slightly, although it is still better than for unreduced samples. Asymmetry of the diffraction curves with respect to the peak position reveals that the as-grown specimens contain a high concentration of both vacancies and self-interstitials. After poling, the concentration of self-interstitial defects is lowered to some extent. When the specimen is moderately chemically reduced, the scattered intensity on both sides of the peak is greatly reduced, showing that the concentrations of both vacancies and interstitials are reduced to a great extent owing to chemical reduction. This clearly indicates that, as a result of the chemical reduction of oxygen in the crystal, crystalline perfection is enhanced significantly. However, under heavy chemical reduction, the number of vacancy defects is increased to a significant extent. Raman scattering, dielectric and photoluminescence studies also show interesting features, with excellent correlation with the degree of crystalline perfection influenced by the processes of reduction and poling.

(Invited) Si Crystal Growth from a Melt: The Secrets Behind the v/G Criterion

The so called v/G criterion defines a critical value of the ratio of the pulling rate v over the thermal gradient G at the melt solid interface. For a ratio larger than this critical value, the crystal is vacancy-rich while for values below the critical value, the crystal is interstitial-rich. When the ratio is equal to the critical value, the crystal would be defect free or made of "perfect silicon". The expression for the critical ratio is analyzed and it is shown that thermal stress at the melt/solid interface and doping have an important effect. Furthermore, DFT calculations suggest that near the melt/solid interface the formation energy of the intrinsic point defects is lower than in the bulk. This would lead to thermal equilibrium concentrations of vacancies and self-interstitials that are considerably higher than in the bulk of the crystal.

Formation Energy of Intrinsic Point Defects in Si and Ge and Implications for Ge Crystal Growth

The formation energies of intrinsic point defects in Si and Ge were calculated by means of Density Functional Theory applying thin film models. The obtained formation energy for a Ge vacancy is close to the value calculated by means of a hybrid exchange correlation potential (HSE06). Well accepted experimental data exist for the sum of the formation and migration energies of vacancies and self-interstitials in Si. Taking into account recent values for the migration energies of point defects, the results of the present study are in excellent agreement with the experimental data. Applying the thin film model for both Si and Ge, one can compare formation energies of intrinsic point defects for both semiconductors. The thermal equilibrium concentration of Ge self-interstitials is more than one order of magnitude lower than that of Si interstitials while the vacancy concentrations are of similar magnitude. Contrary to Si, the diffusivity of Ge self-interstitials cannot recover the unbalance of the thermal equilibrium concentrations even if the growth rate is reduced to very low values. Therefore, Ge crystals grown from a melt are always vacancy-rich which results in void formation independent of the growth condition.

Silicon Single Crystal Growth from a Melt: On the Impact of Dopants on the v/G Criterion

The so called v/G criterion defines a critical value Γ0crit of the ratio Γ of the pulling rate v over the thermal gradient G at the melt-solid/interface. For a ratio larger than this critical value, the crystal is vacancy-rich while for values below the critical value, the crystal is self-interstitial-rich. When the ratio is equal to the critical value, the crystal would be defect free or made of so called “perfect silicon”. The basic analytical expression for the critical ratio is analyzed and it is shown that thermal stress at the melt-solid interface and doping have an important effect on the Γ0crit value. Furthermore, DFT calculations suggest that near the melt-solid interface the formation energy of the intrinsic point defects is lower than in the bulk of the crystal. This would lead to thermal equilibrium concentrations of vacancies and self-interstitials at the free surface and most probably also at the melt-solid interface that are considerably different from those in the bulk. It is illustrated how the v/G criterion can be further refined by taking into account these effects.

Theoretical study of the impact of stress on the behavior of intrinsic point defects in large-diameter defect-free Si crystals

For the development of the crystal pulling process for 450mm-diameter defect-free Si crystals, it is important to evaluate the impact of thermal stress on intrinsic point defect behavior during crystal growth. In this study, we evaluated the impact of thermal stress between −30MPa (tensile) and 30MPa (compressive), which covers the complete range of stress levels that can be expected in mass production for 450mm-diameter crystals, on the so-called Voronkov criterion. This criterion predicts the dominant point defect based on a critical pulling speed over axial temperature gradient ratio. The internal pressure dependencies of both the formation and the migration enthalpies of intrinsic point defects were obtained with a density functional theory study, and it was found that assuming internal stress only, the thermal stress shifts the growing Si crystal towards more vacancy-rich under compressive and towards more self-interstitial-rich under tensile stresses. Also Si crystals containing interstitial clusters and heavily doped crystals were studied to evaluate the effect of thermal and dopant-related stresses on the intrinsic point defect formation and diffusivity. It was concluded that the experimentally observed increase in the number of interstitial clusters and the increase in the concentration of self-interstitials in heavily doped Si cannot be explained by the thermal and/or dopant-related stresses.

On the role of thermal gradient related stress in intrinsic defect formation during single crystal silicon growth from the melt

The incorporation of intrinsic point defects during silicon crystal growth from the melt is discussed using recent data for intrinsic point defect thermal equilibrium and diffusivity. It is shown that the impact of compressive stress on the thermal equilibrium concentration and diffusivity of vacancies and self-interstitials should be taken into account. An analytical expression is derived to quantify the relation between crystal diameter and the critical pull rate window to grow defect free crystals. The results are compared with published experimental data on grown-in defect formation for crystal diameters ranging from 1 to 40cm. It is shown that both the thermal stress due to the axial thermal gradient at the melt/solid interface and the silicon yield stress at high temperature play a crucial role. An empirical expression is proposed to describe the dependence of the thermal gradient on pulling rate.

On the impact of stress on intrinsic defect formation during single crystal silicon growth

The incorporation of intrinsic point defects during silicon crystal growth from the melt is discussed using most recent data for intrinsic point defect thermal equilibrium concentration and diffusivity. It is shown that by taking into account the impact of stress on the thermal equilibrium concentration of vacancies and self-interstitials, the intrinsic point defect properties derived from self- and metal-diffusion experiments can be used to model point defect incorporation and clustering during silicon crystal growth from the melt. The solution is however not unique and a large uncertainty still remains on the real thermodynamic parameters of both intrinsic point defects. Only comparison with a wide range of experimental data from crystal pulling experiments—taking into account also the stress effects—will allow to further narrow down the uncertainty ranges on the intrinsic point defect properties in silicon.

IR Studies on VO&lt;sub&gt;N&lt;/sub&gt;, C&lt;sub&gt;I&lt;/sub&gt;O&lt;sub&gt;I&lt;/sub&gt; and C&lt;sub&gt;I&lt;/sub&gt;C&lt;sub&gt;S&lt;/sub&gt; Defects in Ge-Doped Cz-Si

This paper reports experimental results on the production and annealing of oxygen-vacancy related (VOn, 1&lt;n&lt;5) and carbon-related (CiOi, CiOiI, and CiCs) defects in Ge-doped Czochralski-grown silicon (Cz-Si) materials containing carbon. The samples were irradiated by 2 MeV fast electrons and the behavior of radiation-produced defects is studied by means of infrared (IR) spectroscopy, monitoring the relevant bands in spectra. Regarding the VOnfamily, it was found that the presence of Ge affects the annealing temperature of VO defects as well as their fraction that is converted to VO2defects. Both effects are discussed in relation with an impact of Ge on the concentration of self-interstitials that take part in the annealing of VO defects via two reaction paths VO + I → Oiand VO + Oi→ VO2. Furthermore, two bands at 1037 and 1051 cm-1are attributed to the VO5defect, although three other bands at 762, 967 and 1005 cm-1are believed to be associated with VnOmclusters containing carbon, most likely having a VOnCsstructure. Regarding carbon-related complexes, it has been established that the annealing of the 862 cm-1band belonging to the CiOidefect is accompanied by the emergence of the 1048 cm-1band previously assigned to the CsO2icenter. The evolution of the CiCsand the CiOiI bands is monitored and the identification of bands at 947, 967 and 1020 cm-1making their appearance in IR spectra over the temperature range where CiCsand CiOiI defects are annealed out is discussed.

Phase-field simulation of irradiated metals: Part I: Void kinetics

We present a phase-field model of void formation and evolution in irradiated metals by spatially and temporally evolving vacancy and self-interstitial concentration fields. By incorporating a coupled set of Cahn–Hilliard and Allen–Cahn equations, the model captures the processes of point defect generation and recombination, annihilation of defects at sinks, as well as void nucleation and growth in the presence of grain boundaries. Illustrative results are presented that characterize the rate of void growth or shrinkage due to supersaturated vacancy or interstitial concentrations, void nucleation and growth kinetics due to cascade-induced defect production, as well as void denuded and peak zones adjacent to grain boundaries.

Probing the Behaviors of Point Defects in Silicon and Germanium Using Isotope Superlattices

In order to probe the fundamental behaviors of point defects in silicon and germanium, we studied the self-diffusion using isotope superlattices. In ion-implanted germanium, vacancies are in thermal equilibrium and transient enhanced diffusion is not present under the experimental conditions employed in this study. In contrast, silicon self-interstitials are supersaturated in ion-implanted silicon and the self-interstitial concentration is going down to the thermal equilibrium value toward the surface.

The influence of structural defects on phosphorus diffusion in multicrystalline silicon

We have investigated the diffusion of phosphorous (P) in multicrystalline Silicon (Si) during solar cell emitter formation by secondary ion mass spectrometry (SIMS). From the experimental results, we observe significantly increased in-grain diffusion depths in areas of structural disorder that are not readily observed by the naked eye. We believe that this effect is due to increased concentrations of Si self-interstitials in the areas surrounding the defects, causing an enhanced transient response of elemental P diffusion. In areas adjacent to a grain boundary a slight, but notably smaller, enhancement of the P diffusion depth is observed.

Determination of Silicon self-interstitial diffusivity using isotopically pure 30Silicon multi-layer

Si self-diffusion under oxygen ambient has been studied using multi-layer structures consisting of alternative layers with isotopically enriched 30Si and natural Si in order to determine the diffusivities of Si self-interstitials. Spreading of 30Si spikes of each layer due to the diffusion of Si self-interstitials generated at the surface was measured with SIMS analysis. The diffusivity of Si self-interstitials, DI, is obtained from the fitting with experimental results. In the temperature range between 820 and 920 °C, DI and thermal equilibrium concentration of Si self-interstitials, CIi, are described by the Arrhenius equations, D I = 3.48 × 10 4 exp ( − 3.82 eV / K T ) (cm 2/s) and C Ii = 9.62 × 10 18 exp ( − 0.475 eV / K T ) (cm −3), respectively.

Carbon-mediated aggregation of self-interstitials in silicon: A large-scale molecular dynamics study

The carbon-mediated aggregation of silicon self-interstitials is investigated with large-scale parallel molecular dynamics. The presence of carbon in the silicon matrix is shown to lead to concentration-dependent self-interstitial cluster pinning, dramatically reducing cluster coalescence and thereby inhibiting the nucleation process. The extent of cluster pinning increases with cluster size for the range of cluster sizes observed in the simulation. The direct effect of carbon on single self-interstitials is shown to be of secondary importance, and the concentration of single self-interstitials as a function of time is essentially unchanged in the presence of carbon. A quasi-single-component mean-field interpretation of the atomistic simulation results is proposed and further confirms these conclusions. Based on these results, it is suggested that the experimentally observed effect of carbon on transient-enhanced diffusion of boron could be due to the direct interaction between carbon atoms and self-interstitial clusters.

Simulation of boron effects on OISF-ring dynamics for Czochralski silicon growth: a comparative study

The simulation of boron effects on oxidation-induced stacking fault (OISF) ring is carried out for the Czochralski silicon growth. The simulation is based on either the reaction/diffusion model [Sinno et al., App. Phys. Lett. 75 (1999) 1544] or the electronic-shift model [Voronkov and Falster, J. Appl. Phys. 87 (2000) 4126], while the global heat transfer is simulated by using STHAMAS. The calculated critical V/ G values with and without boron doping are in good agreement with the reported values for both models; V is the pulling rate and G the thermal gradient on the ring position at the interface. Nevertheless, for a reasonable prediction by the reaction/diffusion model, the equilibrium concentrations of boron/point-defect pairs need to be several orders larger than the predictions by molecular dynamic simulation. A simplified model without considering the boron dimmers (B 2) and their associated pairs gives a good prediction as well. On the other hand, the electronic-shift model requires only a single parameter to fit the experimental results. For the electronic-shift model, the ratio of the equilibrium vacancy and self-interstitial concentrations is crucial, while the ratio of their formation energies is found insignificant, but this is not true for the reaction/diffusion model.