Si Self-diffusion Research Articles

Self-Diffusion in Intrinsic and Extrinsic Silicon Using Isotopically Pure 30Silicon Layer

ABSTRACTSilicon self–diffusion coefficients were measured in intrinsic and extrinsic silicon from870 to 1070°C using isotopically pure 30Si layer. 30Si diffusion profiles are determined by secondary ion mass spectrometry. The temperature dependence of intrinsic diffusion coefficient in bulk Si isobtained. Comparing it in heavily As-doped or B-doped Si, it is found that Si self-diffusion is entirely mediated by interstitialcy mechanism at lower temperatures below 870°C.

Diffusion of 71Ge in the amorphous ceramic Si 28C 36N 36

The objective of this research was the determination of the Si self-diffusivity in the polymer-derived amorphous ceramic Si 28C 36N 36, which consists of two amorphous phases, a-Si 3N 4 and a-C. This diffusivity is of technological importance, since it contributes to the ceramic’s transition from its intermediate amorphous to its final crystalline state. The Si self-diffusion was simulated by the diffusion of 71Ge. This was done by a radiotracer technique, in which radioactive 71Ge atoms were implanted. After diffusion annealing, the specimens were serially sectioned by Ar +-beam sputtering. The 71Ge diffusion coefficients obey Arrhenius laws in the temperature regime investigated (850–1300°C) with a pre-exponential factor of 0.2 m 2 s −1 and a diffusion enthalpy that increases from 4.6 eV in as-produced to 5.5 eV in 1350°C-pre-annealed specimens. These data are interpreted in terms of 71Ge diffusion in the a-Si 3N 4 phase which is mediated by smeared-out thermal vacancies.

Application of one-bond-type migration to interstitialcy-type self-interstitial and phosphorus in silicon

(1) From the standpoint of the potential energy, the one-bond-type migration is divided into the BC (bond-centered type) and SP (split 〈1 0 0〉 type) migrations. In the BC migration, there are two kinds of atom migrations. One is that in which a BC atom pushes its neighboring atom to a BC site. This is the typical migration by the interstitialcy mechanism. The other is that in which a BC atom rotates about its neighboring atom and becomes the BC atom again. This is a feature of the BC migration. (2) The BC and SP migrations are applied to P diffusion in Si. Assuming there is no interaction between P and Si, the distance and probability for each step of the migration are obtained and applied to Si self-diffusion. Because they are not constant, the definition of the correlation factor for the self-diffusion is different from the usual one.

Nonequilibrium experiments on self-diffusion in silicon at low temperatures using isotopically enriched structures

Self-diffusion in silicon has been studied using epitaxially grown isotopically enriched structures under nonequilibrium concentrations of native point defects created by thermal oxidation and nitridation. Comparing identical anneals for phosphorus, antimony, and self-diffusion in Si, we obtain experimental evidence for a dual vacancy–interstitial mechanism of self-diffusion with the possibility of a small substitutional exchange component. We determine that in the temperature range 800–1100°C, the interstitial-mediated fraction of self-diffusion is confined between 0.50 and 0.62. The corresponding activation enthalpies are 4.68 and 4.86eV for the interstitial and vacancy mechanisms, respectively. Furthermore, both mechanisms exhibit large activation entropies. This constitutes direct experimental evidence of the remarkable similarity between the energetics of these native point defects in silicon.

Diffusion in isotopically controlled semiconductor systems

Isotopically controlled heterostructures of 28Si/natSi and Al71GaAs/Al69GaAs/71GaAs have been used to study the self-diffusion process in this elemental and compound semiconductor material. The directly measured Si self-diffusion coefficient is compared with the self-interstitial and vacancy contribution to self-diffusion which were deduced from metal diffusion experiments. The remarkable agreement between the Si self-diffusion coefficients and the individual contributions to self-diffusion shows that both self-interstitials and vacancies mediate Si self-diffusion. The Ga self-diffusion in undoped AlGaAs was found to decrease with increasing Al concentration. The activation enthalpy of Ga and Al diffusion in GaAs and of Ga diffusion in AlGaAs all lie in the range of (3.6±0.1)eV, but with different pre-exponential factors. The doping dependence of Ga self-diffusion reveals a retardation (enhancement) of Ga diffusion under p-type (n-type) doping compared to intrinsic conditions. All experimental results on the group-III atom diffusion are accurately described if vacancies on the group-III sublattice are assumed to mediate the Ga self- and Al–Ga interdiffusion in undoped AlGaAs and the Ga self-diffusion in Be- and Si-doped GaAs with an active dopant concentration of 3×1018cm−3. The doping dependence of Ga self-diffusion in GaAs provides strong evidence that neutral, singly and doubly charged Ga vacancies govern the self-diffusion process.

Enhanced and retarded Ga self-diffusion in Si and Be doped GaAs isotope heterostructures

Ga self-diffusion in undoped, Si- and Be-doped 71GaAs/ n at GaAs isotope heterostructures has been investigated at temperatures between 736°C and 1050°C. Concentration profiles of the Ga isotopes measured separately by secondary ion mass spectrometry reveal retarded (enhanced) self-diffusion when doped p-type (n-type), compared to intrinsic conditions. Electrochemical C–V profiling was performed to determine the free carrier concentrations before and after annealing. Detailed analysis of the doping dependence of Ga self-diffusion includes a compensation of Si donors by negatively charged vacancies and shows that one native defect, presumably the vacancy on the Ga sublattice, in the neutral, singly and doubly negatively charged states governs the self-diffusion process. The energy levels E V − − E v =0.42 eV and E V 2− − E v =0.60 eV of the singly and doubly negatively charged gallium vacancy have been deduced from the doping dependence of Ga self-diffusion. No significant contribution from the triply negatively charged Ga vacancy has been found. Our evaluation of the doping dependence of Ga self-diffusion is compared with literature data for the group-III atom diffusion in the AlGaAs material system. Seemingly inconsistent literature data can now be described consistently on the basis of our results. Finally, thermal equilibrium concentrations and transport coefficients of Ga vacancies in GaAs in their various charge states are calculated for different doping conditions taking into account the vacancy related energy levels and the thermal equilibrium concentration of neutral vacancies which were deduced from our self-diffusion data.

Diffusion in the B20-type phase FeSi

Abstract Self-diffusion of Fe and impurity diffusion of Ge in the B20 phase FeSi have been studied as a function of temperature using the radiotracer method with isotopes 59Fe and 71Ge. 71Ge has been used to simulate Si self-diffusion. Both diffusivities are very small, and their values for Fe are about one to two orders of magnitude smaller than for Ge. This uncoupled diffusion may be explained by vacancy-based diffusion on the Fe and Si sublattice. Both diffusivities reach a value of about D(T M) ≈ 10−14m2s−1 at T M = 1683 K. which is more typical for semiconductors than for metals. Results are discussed in comparison with other diffusion data on phases of the Fe-Si system and on other transition metal silicides.

Fractional contributions of microscopic diffusion mechanisms for common dopants and self-diffusion in silicon

An identical set of thermal oxidation and nitridation experiments has been performed for four common dopants and self-diffusion in Si. Selectively perturbing the equilibrium point-defect concentrations by these surface reactions is a powerful tool for identifying the relative importance of the various atomic-scale diffusion mechanisms. We obtain bounds on the fractional contributions of the self-interstitial, vacancy, and concerted exchange mechanisms for arsenic, boron, phosphorus, antimony, and self-diffusion in Si at temperatures of 1100 and 1000 °C. These bounds are found by simultaneously solving a system of equations making only very conservative assumptions. The validity of common approximations found in previous work and their effects on the results are also analyzed in detail. We find that B and P diffuse by a self-interstitial mechanism, whereas Sb diffusion is almost exclusively vacancy mediated. As and self-diffusion, on the other hand, exhibit evidence for a dual vacancy-interstitial mechanism with the possibility of some concerted exchange component.

Experimental Study of Self-Diffusion in Silicon Using Isotopically Enriched Structures

ABSTRACTSelf-diffusion in silicon has been studied using epitaxially grown isotopically enriched structures under nonequilibrium concentrations of intrinsic point defects created by thermal oxidation and nitridation. Comparison of identical anneals for self, antimony, and phosphorus diffusion in silicon enables us to determine bounds on the fractional contributions of microscopic mechanisms for Si self-diffusion in the temperature range 800–1100°C. We obtain direct experimental evidence for a dual vacancy-interstitial mechanism of self-diffusion in silicon and show that the fractional contribution of each mechanism has a weak dependence on temperature.

Experimental evidence for a dual vacancy–interstitial mechanism of self-diffusion in silicon

Epitaxially grown isotopically enriched Si layers have been used to study self-diffusion in Si directly at the temperatures of 1000 and 1100 °C. We obtain equilibrium diffusion coefficients in accordance with previous experiments and theoretical calculations. Comparison of diffusion data of self-, antimony, and phosphorus diffusion in Si under identical conditions of perturbed self-interstitial and vacancy concentrations created by surface reactions enables us to determine the microscopic mechanisms of Si self-diffusion. We find that, in this temperature range, self-interstitials contribute roughly 2/3 to Si self-diffusion, and vacancies 1/3, with the concerted exchange component being less than 14%. This constitutes direct experimental evidence that, on the atomic scale, self-diffusion in Si is mediated both by self-interstitials and vacancies.

Ostwald ripening of end-of-range defects in silicon

End-of-range (EOR) defects are interstitial type dislocation loops which nucleate just beneath the crystalline/amorphous (c/a) interface formed by ion implantation in Si, after the preamorphization of the substrate, and during the ramping-up of the anneal. They originate from the presence of a high supersaturation of “excess” Si self-interstitial atoms located just beneath the c/a interface. Upon annealing, the mean radius of the defects increases while their density decreases through the exchange of Si self-interstitial atoms between the loops. The number of interstitials stored in the loops stays constant. For sufficiently high thermal budgets, when the nucleation is finished, and when the local equilibrium between extended and point defects is established, the coarsening of the EOR defects can be modeled through the Ostwald ripening theory applied to the dislocation loops geometry. Indeed, and as expected from the theory, the square of the mean radius of the loop population increases with time while the loop density decreases proportional to 1/t. Furthermore, the theoretical function describing the size distributions perfectly matches the time evolution of the experimental stack histograms, for different annealing temperatures. During the asymptotic steady-state coarsening regime, the activation energy for the loop coarsening is 4.4 eV, which is in the range of values given in the literature for self-diffusion in Si. Nevertheless, an activation energy of about 1–2 eV is found during the transient period preceding the local equilibrium, i.e., in the range of the migration energy of self-interstitials. The limiting phenomenon for the loop growth appears to be diffusion, since it is the hypothesis that leads to the best fit between theory and experiment. An estimate of DiCi* has been derived from the growth laws of the EOR defects. A value of about 1.8×107 cm−1 s−1 at 1000 °C is obtained and compares well with the values given in the literature.

Self-Diffusion in Isotopically Controlled Heterostructures of Elemental and Compound Semiconductors

ABSTRACTWe report self-diffusion studies of silicon between 855 and 1388°C in highly enriched epitaxial 28Si layers. Diffusion profiles of 30Si and 29Si are determined with high resolution secondary ion mass spectrometry (SIMS). The temperature dependence of the Si self-diffusion coefficients is accurately described with an activation enthalpy of 4.76 eV and a pre-exponential factor of 560 cm2s-1. The single activation enthalpy indicates that Si self-interstitials dominate self-diffusion over the whole temperature range investigated. Self- and interdiffusion in buried Al71GaAs/Al69GaAs/71GaAs isotope heterostructures with different Al composition is measured between 800 and 1160°C. Ga self-diffusion in AlGaAs and interdiffusion of Al and Ga at the AlGaAs/GaAs interface show that Ga diffusion decreases with increasing Al composition and that the interdiffusion coefficient depends linearly on Al concentration. Furthermore Al is found to diffuse more rapidly into GaAs than Ga diffuses in GaAs. The temperature dependence of Ga and Al diffusion in GaAs and of Ga diffusion in AlGaAs is described by a single activation enthalpy in the range of 3.6±0.1 eV, but by different pre-exponential factors. Differences found for Ga and Al diffusion in GaAs and for Ga diffusion in AlGaAs with different Al concentrations are discussed.

Gold Diffusion in Silicon During Gettering by an Aluminum Layer

ABSTRACTPrevious modeling of Al gettering of Au in Si indicated that, for an Al gettering layer placed on one surface of a Si wafer, Au will be gettered from both surface regions of the wafer to progressively greater depths with time. This is because, in Si, Au is a substitutional-interstitial (Aus-Aui) species with its diffusion governed by the kick-out mechanism which is mediated by Si self-inter-stitials (I). During gettering by the Al-Si liquid at one wafer surface, Aus atoms change over to Au atoms to rapidly migrate out of Si into the liquid. The changeover process consumes I. At the two wafer surface regions, the consumed I will be quickly replenished, while in the wafer interior an I undersaturation develops which hinders the Aus-Aui changeover and hence the gettering process. Experimental evidences which confirm the predictions have been obtained. Au was indiffused into a FZ Si wafer at 950°C for 16 hr. After removing the Au source and etching, samples from the in-diffused wafer were annealed at 1000°C without or with an Al layer on one surface. For samples without Al, there is no change in the net Au content, while the U-shaped indiffused profile becomes flatter. For samples with an Al layer, both wafer surface region Au concentrations were significantly decreased in 30 min while the wafer interior Au concentrations decreased only after annealing for longer times. The model predictions, the experimental results, and the implications on Si self-diffusion parameters will be discussed.

Fast metal diffusers in Si in the presence of Si self-interstitial traps

The diffusion of Au, Pt, and Zn in Si yield Si self-interstitial diffusivities, DI, that exceed those obtained from dopant marker experiments by 6 orders of magnitude at 800 °C. Both types of experiments can be reconciled by assuming the existence of a nonannihilating interstitial trap, related to carbon. In this context, selected metal diffusion data are reanalyzed. Nonannihilating immobile traps and a second-order reaction involving interstitial carbon and carbon–carbon pairs are considered. Quantitative point-defect parameters are extracted at 1115 °C for an assumed trap concentration of Ctt=5×1016 cm−3. In all cases and independent of the value of Ctt, excellent fits to concentration versus depth profiles of Zn are obtained; the extracted equilibrium concentration of Si self-interstitials, CI*, varies inversely with Ctt, while DICI* remains approximately constant. Hence agreement, or disagreement, of metal diffusion results with the Si self-diffusion coefficient cannot be used to exclude or prove trap-limited diffusion. Literature values of point-defect parameters obtained by neglecting traps represent lower bounds on DI and upper bounds on CI*. The time evolution of the Zn profile in the presence of traps is discussed. Proper inclusion of traps in the analysis of metal diffusion data leads to a decrease in the extracted activation energy of DI.

Contribution of concerted exchange to the entropy of self-diffusion in Si.

The concerted-exchange (CE) mechanism is at present the only viable candidate for atomic exchange that does not involve intrinsic lattice defects. In order to evaluate its contribution to self-diffusion in Si, we calculate the entropy associated with CE. We include full relaxation of the energy surface through an interatomic potential and take into account the dominant contributions of vibrational modes through the harmonic approximation. This gives an entropy of 6.3${\mathit{k}}_{\mathit{B}}$, which accounts for a large portion of the experimental result (7${\mathit{k}}_{\mathit{B}}$--9${\mathit{k}}_{\mathit{B}}$). We conclude that the CE mechanism is a significant contributor to self-diffusion in Si.

Diffusion and solubility of zinc in dislocation-free and plastically deformed silicon crystals

Floating-zone Si crystals enclosed in quartz ampoules were exposed to Zn vapour released by an elemental diffusion source. Penetration profiles of Zn in Si were recorded using the spreading-resistance technique or neutron activation analysis. Both the erfc-type distributions observed in plastically deformed specimens and the non-erfc profiles determined on dislocationfree wafers are consistently interpreted within the framework of the kick-out model. As an implication, Si self-interstitials generated in excess by interstitial-to-substitutional transitions of in-diffusing Zn atoms annihilate not only at the surface but also at dislocations. On the other hand, dislocation-induced segregation of Zn appears to be rather minor, as revealed by transition electron microscopy. Combining the Zn incorporation rate in dislocation-free Si with solubility data from saturated specimens yields the self-interstitial contribution to the Si self-diffusion coefficient.

Vacancy-vacancy interaction in silicon studied using atomic potentials.

Vacancy-vacancy (V-V) interaction in Si is studied using the modified Stillinger-Weber atomic potential, under both strained and unstrained conditions. The potential is chosen out of a total of four potential forms by considering Si self-diffusion via vacancies. Monte Carlo simulations are performed on a 12\ifmmode\times\else\texttimes\fi{}12\ifmmode\times\else\texttimes\fi{}12 lattice. Both simulated annealing and steepest descent are applied while relaxing the lattice. The results obtained do not agree well with experimental observations regarding V-V interaction energy, indicating that electronic relaxations are present that are not accounted for in the atomic-potential method. The dominant mode of coalescence with and without strain is compared by evaluating barriers for coalescence.

Entropy of migration for atomic hopping.

The entropy of migration of an atom undergoing an atomic hop into a nearest-neighbor vacancy is calculated under the assumption that the entropy is translational at the saddle-point configuration and vibrational at the initial, equilibrium state prior to the hop. These contributions to the entropy of migration are calculated using standard statistical thermodynamic expressions, assuming that the translational entropy is given by the particle-in-a-box approximation and the vibrational entropy is that of a simple harmonic oscillator vibrating at the Debye frequency. This formulation of the entropy of migration is then quantitatively applied to explain the abnormal prefactors experimentally deduced in InP drain-current--drift measurements, in deep-level-defect--transformation kinetic studies of the metastable M center in InP, and in Si and Ge self-diffusion experiments.

Experimental evidence of both interstitial- and vacancy-assisted diffusion of Ge in Si

We present the first experimental identification of the diffusion mechanisms of Ge in Si. Using thermal nitridation reactions to create either excess self-interstitials or vacancies, it is established that under equilibrium conditions at 1050 °C Ge diffusion takes place by both substitutional-interstitial interchange and vacancy mechanisms, with comparable contributions from each. If previous conjectures that Ge diffusion in Si is similar to Si self-diffusion are correct, our findings support the idea that Si self-diffusion takes place by both interstitial and vacancy mechanisms.

Pressure and Strain Effects on Diffusion

AbstractWe have investigated, via parameter-free calculations, the effects of hydrostatic and nonhydrostatic strains on the energetics of defect formation and self-diffusion in silicon. The three microscopic mechanisms, vacancy, interstitial, and concerted exchange, have very similar activation enthalpies at zero pressure but exhibit different behavior with hydrostatic pressure. Our results suggest that experiments performed at different pressures can determine the relative contributions of each of these mechanisms. The calculations also show that the neutral Si vacancy has a negative relaxation volume, with the nearest neighbors of the vacancy relaxing inwards, in contrast to the Si (111) surface. Large nonhydrostatic strains, which are present in e.g. Si/GexSi1-x pseudomorphic heterostractures, substantially reduce the formation energy of the tetrahedral interstitial, but do not affect the formation energy of the vacancy. These findings suggest that, aside from being another useful tool for the investigation of self-diffusion in Si, nonhydrostatic strain may significantly affect annealing and impurity diffusion in strained heterostructures. In particular, the interstitial-assisted impurity diffusion may proceed more rapidly in Si lattice-matched to GexSi1-x, but be slowed down in GexSi1-x lattice-matched to Si. The compressed GexSi1-x layers may thus act as diffusion barriers for impurities diffusing with help of native interstitials, such as B or P.