Diffusion in silicon of elements from columns III and V of the Periodic Table is reviewed in theory and experiment. The emphasis is on the interactions of these substitutional dopants with point defects (vacancies and interstitials) as part of their diffusion mechanisms. The goal of this paper is to unify available experimental observations within the framework of a set of physical models that can be utilized in computer simulations to predict diffusion processes in silicon. The authors assess the present state of experimental data for basic parameters such as point-defect diffusivities and equilibrium concentrations and address a number of questions regarding the mechanisms of dopant diffusion. They offer illustrative examples of ways that diffusion may be modeled in one and two dimensions by solving continuity equations for point defects and dopants. Outstanding questions and inadequacies in existing formulations are identified by comparing computer simulations with experimental results. A summary of the progress made in this field in recent years and of directions future research may take is presented.

Point defects and dopant diffusion in silicon

In this thesis, the existence and uniqueness of gradient trajectories near an A2singularity are analysed. The A2-singularity is called a birth-death critical point in the real case. The birth-death critical point appears in a one-parameter family of functions. Such a family of functions has precisely two Morse critical points of index difference one, on the birth side. The result of the real case states that these two critical points are joined by a unique gradient trajectory up to time-shift. Here the gradient flow is defined with respect to any family of Riemannian metrics. This can be viewed as a converse to Smale’s cancellation theorem. We also look at the complex analogue of the result in Picard–Lefschetz theory. This analogue considers a holomorphic one-parameter family with an A2-singularity. Such a family has two critical Morse critical points near the singularity for every small non-zero parameter. We prove that the two Lagrangian vanishing cycles associated to these critical points intersect transversally in exactly one point in all regular fibres along a straight line. The result is obtained by analysing the gradient trajectories of the real part of these functions. Both proofs start with a normal form in local coordinates for such families of functions. The gradient equations in these coordinates can be rescaled into a fast-slow system of non-linear differential equation. Existence will rely on an adiabatic limit analysis whereas uniqueness follows from a Conley index pair construction. The latter construction will also show that connecting gradient trajectories cannot leave the local charts. Even though the proof of these two results follow from similar lines of argument, the real case cannot be reduced to the complex case and vice versa.

Doctoral Thesis by

New carrier mobility data for both arsenic- and boron-doped silicon are presented in the high doping range. The data definitely show that the electron mobility in As-doped silicon is significantly lower than in P-doped silicon for carrier concentrations higher than 1019cm-3. By integrating these data with those previously published, empirical relationships able to model the carrier mobility against carrier concentration in the whole experimental range examined to date (about eight decades in concentration) for As-, P-, and B-doped silicon are derived. Different parameters in the expression for the n-type dopants provide differentiation between the electron mobility in As-and in P-doped silicon. Finally, it is shown that these new expressions, once implemented in the SUPREM II process simulator, lead to reduced errors in the simulation of the sheet resistance values.

Modeling of carrier mobility against carrier concentration in arsenic-, phosphorus-, and boron-doped silicon

The outstanding properties of SiO2, which include high resistivity, excellent dielectric strength, a large band gap, a high melting point, and a native, low defect density interface with Si, are in large part responsible for enabling the microelectronics revolution. The Si/SiO2 interface, which forms the heart of the modern metal–oxide–semiconductor field effect transistor, the building block of the integrated circuit, is arguably the worlds most economically and technologically important materials interface. This article summarizes recent progress and current scientific understanding of ultrathin (<4 nm) SiO2 and Si–O–N (silicon oxynitride) gate dielectrics on Si based devices. We will emphasize an understanding of the limits of these gate dielectrics, i.e., how their continuously shrinking thickness, dictated by integrated circuit device scaling, results in physical and electrical property changes that impose limits on their usefulness. We observe, in conclusion, that although Si microelectronic devices...

Ultrathin (<4 nm) SiO2 and Si-O-N gate dielectric layers for silicon microelectronics: Understanding the processing, structure, and physical and electrical limits

A review is presented of the recent advances in the study of oxygen precipitation and of the main properties of oxide precipitates in silicon. After a general overview of the system ‘‘oxygen in silicon,’’ the thermodynamics and the kinetics of the precipitate formation are treated in detail, with major emphasis on the phenomenology; subsequently, the most important techniques for the characterization of the precipitates are illustrated together with the most interesting and recent results. Finally, the possible influence of oxygen precipitation on technological applications is stressed, with particular attention to recent results regarding device yield. Actually, the essential novelty of this review rests on the attempt to give an extended picture of what has been recently clarified by means of highly sophisticated diagnostic methods and of the influence of precipitation on the properties of semiconductor devices.

Oxygen precipitation in silicon

Diffusions of impurities in silicon under oxidizing ambient and under extrinsic conditions have been analyzed by developing the Hu’s model. The general expression of diffusion coefficient, which includes both the vacancy and interstitialcy mechanisms, is used. The temperature dependences of a fraction of interstitialcy mechanism for arsenic fAs, phosphorus fP, and boron fB are obtained from the data of oxidation enhanced diffusion (OED) and oxidation induced stacking faults.  fAs =42 exp(−0.542/kT), fP =156 exp(−0.666/kT), and fB =860 exp(−0.829/kT). Time dependence of OED and the concentration dependence of the diffusion coefficient of arsenic and boron under extrinsic conditions can be explained by this model.Diffusions of impurities in silicon under oxidizing ambient and under extrinsic conditions have been analyzed by developing the Hu’s model. The general expression of diffusion coefficient, which includes both the vacancy and interstitialcy mechanisms, is used. The temperature dependences of a fraction of interstitialcy mechanism for arsenic fAs, phosphorus fP, and boron fB are obtained from the data of oxidation enhanced diffusion (OED) and oxidation induced stacking faults.  fAs =42 exp(−0.542/kT), fP =156 exp(−0.666/kT), and fB =860 exp(−0.829/kT). Time dependence of OED and the concentration dependence of the diffusion coefficient of arsenic and boron under extrinsic conditions can be explained by this model.

Oxidation enhanced and concentration dependent diffusions of dopants in silicon

CuGaSe2 chalcopyrite compounds were grown heteroepitaxially on both GaAs and GaP substrates by means of the low‐pressure metalorganic chemical‐vapor deposition method. Optical and structural properties were characterized comprehensively by photoreflectance (PR), photoluminescence (PL), x‐ray diffraction, transmission electron microscopy, transmission electron diffraction, and electron‐probe microanalysis. The CuGaSe2 epilayers had c(001) surface on GaAs(001) substrates and a(100) surface on GaP(001) substrates, respectively, the results being similar to the case of CuAlSe2. Energies of A, B, and C excitons associated with uppermost valence bands were determined from analysis of PR spectra, and the energies of good‐quality epilayers are close to those of the bulk crystal. The slight increase of the crystal‐field splitting in the valence bands were discussed in terms of the lattice strain in the epilayer caused by the lattice mismatch. Low‐temperature PL spectra exhibited an intense peak at 1.71 eV, the ene...

Heteroepitaxy and characterization of CuGaSe2 layers grown by low‐pressure metalorganic chemical‐vapor deposition

It was investigated and found that the enhanced diffusion of arsenic and phosphorus in silicon by thermal oxidation is dependent on the crystal orientation of a substrate, diffusion temperature, and time. Impurities are prediffused into a silicon substrate from impurity‐silica film, and then subjected to a drive‐in diffusion in oxidizing (dry ) and inert (dry ) atmosphere. Diffusion coefficients are determined by adopting best fitted parameters in the numerical simulation of the experiments. The diffusion coefficients of arsenic and phosphorus are enhanced by thermal oxidation of silicon. This enhancement measured in (100) silicon is greater than that in (111) silicon. The diffusion coefficients obtained in oxidizing atmosphere can be expressed as a function of diffusion temperature and time. From the form of this equation, it is considered that arsenic and phosphorus diffuse by the dual mechanism (vacancy and interstitialcy mechanism). The enhancement increases in order of arsenic, phosphorus, and boron.

The Enhanced Diffusion of Arsenic and Phosphorus in Silicon by Thermal Oxidation

Variation of silicon melt viscosity with boron addition

Phosphorus diffusion into germanium is carried out at 600°–750°C by using red phosphorus powder as a diffusion source. Source temperatures are maintained at 240° and 430°C, corresponding to low and high surface concentrations, respectively. At low surface concentration, , concentration profiles agree well with the erfc curves, showing the behavior of Fick's law. While at high surface concentration, , profiles deviate from the erfc curves. Diffusion coefficients depend both on the local and surface concentrations, representing the same result as that of phosphorus diffusion into silicon.

Satoru Matsumoto

Papers

Oxidation enhanced and concentration dependent diffusions of dopants in silicon

Heteroepitaxy and characterization of CuGaSe2 layers grown by low‐pressure metalorganic chemical‐vapor deposition

The Enhanced Diffusion of Arsenic and Phosphorus in Silicon by Thermal Oxidation

Variation of silicon melt viscosity with boron addition

Concentration Dependence of a Diffusion Coefficient at Phosphorus Diffusion in Germanium