Self-diffusion In Silicon Research Articles

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.

Atomic Diffusion Processes in Silicon

AbstractThe mechanisms of self-diffusion and dopant impurity diffusion in silicon have been the subject of intense debate since the 1960’s. Until the mid-1980’s, there was only limited experimental information and virtually no theory. In the last five years, however, first-principles calculations of many key quantities and new experimental data have led to significant progress. This paper traces the major theoretical advances and the key experimental data that have resolved many controversies and have provided a fairly comprehensive picture of diffusion processes. Theory has also recently provided detailed microscopic information about the diffusion of interstitial hydrogen.

Mechanism of self-diffusion in diamond.

It is shown via state-of-the-art theoretical calculations that self-diffusion in diamond is dominated by vacancies, independent of the position of the Fermi level. This is very different from self-diffusion in silicon and germanium, where vacancies, interstitials, and direct-exchange mechanisms all have comparable activation energies. The dominance of the vacancy mechanism is due to the stiffness of diamond bonds, which precludes bond twisting and large relaxations, and to the high electronic density and the large band gap in diamond, which result in a strongly repulsive potential-energy surface for self-interstitials.

Self-diffusion, deformation and melting in silicon—microscopic link

Abstract The possible role of Pandey's concerted exchange mechanism in silicon diffusion and deformation is discussed with reference to atomistic computer calculations using a form of interatomic total energy potential devised and modified by Tersoff. Our conclusion is that, if concerted exchange is viable for self-diffusion, then a similar mechanism should exist for the creation of edge dipoles in high-temperature-deformed silicon and in silicon near its melting point. We show that a metastable state created during concerted exchange is in fact the smallest conceivable faulted edge dipole.

Effect of Pressure on Self Diffusion in Crystalline Silicon

ABSTRACTThe effect of pressure on self diffusion in crystalline silicon is being studied using 30Si as a tracer. Diffusion experiments have been carried out in the pressure range of 1 to 35000 atmospheres at 1000°C. The 30Si is observed to diffuse faster at high pressures, indicating a negative activation volume.

On self-diffusion in silicon and germanium

Abstract The experimental results concerning self-diffusion in Si and Ge are discussed. We note, using recent direct experimental data, that there is no temperature variation of the activation energy for self-diffusion, as it was postulated by Seeger and coworkers. We calculate the sum of the formation and migration vibrational entropies for a vacancy, versus the lattice distortion which occurs around this vacancy. We obtain, using a Morse potential to obtain force constants, a lower limit for the value of this entropy at high temperature which is in correct agreement with the large (10–15 k) experimental value. We conclude that the model, proposed by Seeger and coworkers. that self-diffusion occurs through extended defects (vacancies or interstitials), can be definitively ruled out.

Oxygen, Oxidation Stacking Faults, and Related Phenomena in Silicon

ABSTRACTSome salient features of the phenomena of oxidation stacking faults (OSF) and oxidation enhanced diffusion(OED) are summarized, and some theories of OSF growth are critiqued. Then a new theory is developed which shows the growth to be reaction controlled, and the retrogrowth to be naturally a regime in the entire OSF growth process. The theory has provided an estimated bound on the activation energy of self-diffusion in silicon. It is shown that the observed power law growth kinetics can be explained quite naturally by a bimolecular annihilation process of the excess self-interstitials. A possible physical model of such an annihilation process is discussed. A number of phenomena related to the nucleation of oxygen precipitates in silicon are reported. Then a model of nucleation is presented which is shown to be consistent with all observed phenomena.In this model, the homogeneous nucleation proceeds not merely via the agglomeration of oxygen atoms, but in combination with small vacancy clusters. Evidence from the OSF and OED phenomena, and the nucleation of oxygen precipitates thus necessitates the dualism of vacancies and interstitials as thermal defects in silicon at high temperatures.

On the self diffusion entropy in silicon

It is shown that the high values observed for the entropy of self diffusion in Silicon can be explained by a local change in force constants due to the relaxation around the vacancy.

Self-diffusion in silicon as probed by the ( p,γ) resonance broadening method

The self-diffusion preexponential factor D0=8.0 cm2/s and activation energy Q=4.1 eV for intrinsic silicon have been determined with the ( p,γ) resonance broadening method in the temperature region 900–1100 °C, in a first application of this method to self-diffusion measurements. Its suitability was tested by extending the self-diffusion measurements to lower temperatures than those performed with other methods.

Self-diffusion in intrinsic silicon

The silicon self-diffusion in intrinsic silicon was investigated by a new method using stable isotope 30Si and the ion-analyzer technique. The temperature dependence of the diffusion coefficient was obtained in the range from 885 to 1175 °C from which an activation energy 110.6 kcal/mole was obtained.

Self-diffusion and dynamical recovery in silicon at high temperatures

Self-diffusion and dynamical recovery in silicon at high temperatures

Dynamical recovery and self-diffusion in silicon

Abstract The stress at the beginning of stage III of the strain-hardening curve has been measured as a function of temperature and strain rate in silicon single crystals. It is shown that the results can be successfully described by two current theories for steady-state creep, which were modified for the purpose of the dynamical test: the expression developed by Barrett and Nix (1965) on the basis of the diffusion-controlled motion of jogged screw dislocations and that of Mohamed and Langdon (1974) which is based on the diffusion-controlled climb of edge dislocations. For high temperatures the experimental results are fitted equally well by both theories while for low temperatures the agreement is better using the expression for the creep rate given by Barrett and Nix (1965). From this the activation energy of self-diffusion has been evaluated to be 3·6 eV; it may be ascribed to a mono-vacancy mechanism.

Role of point defects in the growth of the oxidation-induced stacking faults in silicon

A new mechanism, describing the growth of the oxidation-induced stacking faults (OISF) in silicon has been formulated. This mechanism predicts the temperature, time, and oxygen-pressure dependences of the length of the faults in agreement with experimental measurements. The formulation of the mechanism and the derivation of an equation for the length is based on the following assumptions. (a) The growth of the stacking faults at the heterogeneous nucleation sites is analogous to the crystalline growth at the surface kinks. (b) There is an excess of silicon atoms at the Si${\mathrm{O}}_{2}$-Si interface. The concentration of the excess silicon atoms depends on the partial pressure of oxygen during oxidation and on the concentration of the charged vacancies in the adjacent bulk of the silicon. (c) The self-diffusion in silicon occurs by the formation and migration of the charged vacancies. The resultant derivation and comparison with experiment strongly support the new mechanism. (i) The equation describing the length of OISF has been derived to be $L={K}^{\ensuremath{'}}{P}_{{\mathrm{O}}_{2}}^{m}{t}^{n}\mathrm{exp}(\ensuremath{-}\frac{Q}{\mathrm{kT}})$, which is exactly the same as borne out of experimental findings reported earlier. (ii) Values of $m$ and $n$ have been derived and were found to be in good agreement with previously measured values. (iii) Expressions for ${K}^{\ensuremath{'}}$ and $Q$ have been obtained. Using these expressions and available data from literature, ${K}^{\ensuremath{'}}$ and $Q$ were calculated and were found to be in excellent agreement with experiment. (iv) Two different sets of values of $m$, ${K}^{\ensuremath{'}}$ and $Q$ for lower and higher temperature ranges have been obtained. This is in agreement with experimental observation which clearly indicated existence of two temperature ranges (one \ensuremath{\le} 1150\ifmmode^\circ\else\textdegree\fi{}C and the other \ensuremath{\ge} 1200\ifmmode^\circ\else\textdegree\fi{}C).

The application of the loop annealing technique to self diffusion studies in silicon

The loop annealing technique has been applied to the study of self diffusion in silicon over a wide range of doping concentrations. The results show that the diffusion coefficient decreases as the concentration of n-type dopant decreases and the concentration of p-type dopant increases. At a fixed temperature, the diffusion coefficient is linearly dependent on the electron concentration and this behaviour is in accord with the point defects responsible for self diffusion behaving as acceptors. The values obtained for the self diffusion coefficient in intrinsic material are in good agreement with those obtained by other workers at higher temperatures using profiling techniques and indicate a slight curvature in the Arrhenius plot.