Accurate measurements of the intrinsic diffusivities of boron and phosphorus in silicon

Abstract

All activity in modeling transient diffusion behavior relies on knowledge of the inert intrinsic diffusivities of dopants in Si. The measurements upon which these values are based were conducted over 15 years ago. Since then, the quality of wafers used in industrial applications has significantly changed. This will affect the effective diffusivity through changes in trap concentrations. The reliability of measurement techniques has also changed dramatically from tracer and staining methods to secondary ion mass spectrometry ͑SIMS͒ measurements that are dominant today. Finally, our understanding of diffusion behavior has changed significantly. For example, we now understand that the extraction of diffusivities from implanted samples with no pre-anneal includes a significant transient effect. We have measured the inert intrinsic diffusivities of As, B, P, and Sb in different substrates in defect-free Czochralski and float zone wafers and epitaxially grown layers. All samples underwent a 30 min anneal at 1000°C in dry oxygen in order to grow a cap oxide and eliminate transient enhanced diffusion. We performed SIMS analysis on an initial batch of samples to evaluate the different factors that may affect the diffusivity in a nonideal manner and concluded that there are no transient effects but that surface effects are important. Hence, for the fast moving dopants ͑B, P͒ we restrict our data extraction to the deep implants. Our data show that B and P diffusivities are different than the values commonly assumed in the literature at low temperatures. We compare our results to previously published data in light of the factors mentioned here.

Multiscale modeling of stress-mediated diffusion in silicon: Ab initio to continuum

“…18 We calculate v B ϩ at ϭϪ7.14 eV and s BI ϭϪ3.39 eV, which results in a net activation energy of E a ϭϪ( v B ϩ at ) ϩ s BI ϭ3.75 eV in good agreement with the experimental value of Ref. 22. Furthermore, we find (⍀ s BI ) ␣␤ ϭ␦ ␣␤ ͓9.5␦ ␣x Ϫ3.8(␦ ␣y ϩ␦ ␣z )͔ Å 3 in a principal-axis system with the x axis parallel to the ͑111͒ direction and ⍀ v B ϩ⍀ at ϭ2.4 Id Å 3 , respectively, with scalar values for the hydrostatic case of Tr(⍀ s BI )ϭ1.9 Å 3 and Tr(⍀ v B ϩ⍀ at )ϭ7.2 Å 3 .…”

Boron activation and diffusion in silicon and strained silicon-on-insulator by rapid thermal and flash lamp annealings

“…Close to the surface, which represents a sink, a source for self-interstitial atoms ͑SIAs͒, and a source for vacancies, a state close to global thermal equilibrium reached after long annealing may be assumed to become established in a limited but extending region in which the majority of boron atoms are on substitutional sites. Using for this region the values of 7.87 exp͑3.75 eV/ k B T͒cm 2 / s reported for the preexponential factor and the activation energy of B diffusion in Si, 15 we estimate about 5 nm profile broadening during 10 s RTA at 1000°C, which is reached by 3 ms FLA only close to the melting temperature of silicon. Thus, in both types of annealing, the boron profiles would broaden by less than 50%, which contrasts drastically with the wide spreading of the profile tails, as shown in Fig.…”

Diffusion in silicon and the predictive power of ab‐initio calculations

“…[3] by density-functional theory (DFT) within the localdensity approximation (LDA) [4] and generalized-gradient approximation (GGA) [5] predicts an overall activation energy of 3.5−3.8 eV around mid-gap, in excellent agreement with the experimental range of 3.25−3.87 eV. [1,6] Also, the predicted migration barrier for the mobile BI entity of 0.4 −0.7 eV and the migration-length exponent of −0.6 to −0.2 eV are in excellent agreement with experimental values of 0.6 eV [7] and -0.4 ± 0.2 eV [8], respectively. Therefore, in this case, ab-initio calculations seem to be a valuable and quantitative tool to provide input parameters for diffusion simulations.…”