Silicon Diffusion Research Articles

Self-diffusion in crystalline silicon: A single diffusion activation enthalpy down to755∘C

Self-diffusion in silicon and the contribution of vacancies and self-interstitials have been controversially discussed for 50 yr. Most recent results show that the intrinsic silicon self-diffusion coefficient deviates from an Arrhenius-type, single exponential function for temperatures below $950{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ [Y. Shimizu, M. Uematsu, and K. M. Itoh, Phys. Rev. Lett. 98, 095901 (2007); R. Kube, H. Bracht, E. H\uger, H. Schmidt, J. L. Hansen, A. N. Larsen, J. W. Ager, E. E. Haller, T. Geue, and J. Stahn, Phys. Rev. B 88, 085206 (2013)]. This led us to propose temperature-dependent thermodynamic properties of vacancies in order to achieve full consistency to vacancy-mediated dopant diffusion in silicon. Concepts of temperature-dependent properties of native defects or distinct forms of defects with different formation entropies suggested by Cowern et al. [N. E. B. Cowern, S. Simdyankin, C. Ahn, N. S. Bennett, J. P. Goss, J.-M. Hartmann, A. Pakfar, S. Hamm, J. Valentin, E. Napolitani, D. De Salvador, E. Bruno, and S. Mirabella, Phys. Rev. Lett. 110, 155501 (2013)] question the present understanding on atomic transport in semiconductors. To verify these concepts, additional self-diffusion experiments under particular gettering conditions were performed. As a result, silicon self-diffusion was found to be accurately described by one single diffusion activation enthalpy of $(4.73\ifmmode\pm\else\textpm\fi{}0.02)$ eV down to $755{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. This provides full consistency to dopant diffusion without claiming native-defect concepts that were originally proposed by Seeger and Chik in 1968 [A. Seeger and K. P. Chik, Phys. Stat. Sol. 29, 455 (1968)] and confirms most recent density functional theory calculations on the activation energy of self-diffusion via vacancies and self-interstitials. Overall, this unravels the old debate of self-diffusion in silicon with the supposed intrinsic temperature dependence.

Implications of near-rim compositional zoning in rutile for geothermometry, geospeedometry, and trace element equilibration

In principle, compositional profiling of the near-rim region of minerals can provide insight into cooling rates, but presumes that loss or gain of material from the crystal rim is not kinetically restricted. Trace element depth profiles collected for Zr, Hf, Ta, Nb, and U in amphibolite-facies rutile grains of the Catalina Schist, southern California, show significant variability within a single rock: Profiles of the same element among different grains can have significantly different slopes, grains with indistinguishable Zr profiles show vastly different Nb profiles, and grains with indistinguishable Nb profiles show different Zr profiles. Textural and kinetic idiosyncrasies within the matrix apparently affect the ability of specific crystals to accept or release trace elements, and impugn the common assumption that mineral surfaces maintain equilibrium at amphibolite-facies conditions. A new model that limits the flux of Zr from rutile grains helps explain commonly observed compositional profiles, and implies that inversion of compositional profiles assuming equilibrium among grain surfaces will invariably overestimate cooling rates. Few grains may record the low closure temperatures that experimentally determined diffusivities imply. Rather, higher temperatures will be retained, depending on the proximity of reactants and products in the matrix. Silicon diffusion does not control Zr reequilibration in rutile, and relative diffusion coefficients (D’s) of trace elements in rutile are D Zr ~ D Hf ~ 10D Nb ~ 20D Ta ~ 40D U.

(Invited) Silicon Emission Mechanism for Oxidation Process of Non-Planar Silicon

Recent aggressive progress of the device technology demands development of three-dimensional non-planar channel MOSFETs. The oxidation process of non-planar silicon is one of the most important keys. Silicon oxidation is the fundamental but very important process for fabricating the gate dielectrics/silicon interface, which governs the performance of MOSFETs. Historically it had been believed that this process consists of only two elementary processes, the oxygen diffusion through the oxide and the oxygen reaction at the interface between the oxide and the silicon as explained by Deal and Grove in 1965. Afterwards, it has been revealed that this process also consists of the additional process of silicon emission from the interface into the oxide. Our theoretical studies combining the first-principles calculation approach with the rate-diffusion equation approach clearly showed that the inclusion of the silicon emission process can consistently explain the unaccounted initial enhanced oxidation. The theory can also naturally explain the oxidant pressure dependence and the substrate orientation dependence of the oxide growth kinetics. In addition, the experimental study with HRBS clearly detected silicon atoms diffused from the interface through the oxide after the thermal oxidation. Therefore, the silicon emission mechanism is inevitable for the atomic-level control of the gate-dielectrics-fabrication process. Even if the surface is covered with high-k dielectric films, thermal treatments promote silicon diffusion through the films towards the surface because the oxygen atoms in the films naturally react with the silicon at the interface. The silicon emission also causes interfacial defects, which become the charge traps. The emission further causes density fluctuation of the grown oxide, which leads to the leakage current paths for the stress-induced dielectric break down. The emission thus plays important roles for the performance of gate dielectrics. The situation could not be changed even when the channels of MOSFETs becomes non-planar from planar. For the typical non-planar MOSFET such as the vertical BC-MOSFET, the channel has the shape of a pillar. The experiment on the oxidation of the silicon pillar reported unaccounted missing silicon. 50% in maximum of silicon atoms in the initial pillar disappear after the thermal oxidation. This phenomenon can also be explained by the silicon emission mechanism if almost all of the silicon atoms diffused through the oxide evaporate from the oxide surface as SiO gas. Because the area of the interface is smaller than that of the oxide surface, the interface density of the emitted silicon is geometrically larger than the surface density. Therefore, the silicon diffusion through the oxide is enhanced more than that in the planar case. This means that the missing silicon is inevitable for the oxidation process of non-planar channels. Careful fabrication approaches are necessary to achieve high-performance non-planar MOSFETs. This work has been supported by a grant from "Three-Dimensional Integrated Circuits Technology Based on Vertical BC-MOSFET and Its Advanced Application Exploration" of ACCEL under JST.

Incubation behavior of silicon nanowire growth investigated by laser-assisted rapid heating

We investigate the early stage of silicon nanowire growth by the vapor-liquid-solid mechanism using laser-localized heating combined with ex-situ chemical mapping analysis by energy-filtered transmission electron microscopy. By achieving fast heating and cooling times, we can precisely determine the nucleation times for nanowire growth. We find that the silicon nanowire nucleation process occurs on a time scale of ∼10 ms, i.e., orders of magnitude faster than the times reported in investigations using furnace processes. The rate-limiting step for silicon nanowire growth at temperatures in the vicinity of the eutectic temperature is found to be the gas reaction and/or the silicon crystal growth process, whereas at higher temperatures it is the rate of silicon diffusion through the molten catalyst that dictates the nucleation kinetics.

Estimating Arrhenius parameters using temperature programmed molecular dynamics

Kinetic rates at different temperatures and the associated Arrhenius parameters, whenever Arrhenius law is obeyed, are efficiently estimated by applying maximum likelihood analysis to waiting times collected using the temperature programmed molecular dynamics method. When transitions involving many activated pathways are available in the dataset, their rates may be calculated using the same collection of waiting times. Arrhenius behaviour is ascertained by comparing rates at the sampled temperatures with ones from the Arrhenius expression. Three prototype systems with corrugated energy landscapes, namely, solvated alanine dipeptide, diffusion at the metal-solvent interphase, and lithium diffusion in silicon, are studied to highlight various aspects of the method. The method becomes particularly appealing when the Arrhenius parameters can be used to find rates at low temperatures where transitions are rare. Systematic coarse-graining of states can further extend the time scales accessible to the method. Good estimates for the rate parameters are obtained with 500-1000 waiting times.

Effect of Temperature and Sheet Temper on Isothermal Solidification Kinetics in Clad Aluminum Brazing Sheet

Isothermal solidification (IS) is a phenomenon observed in clad aluminum brazing sheets, wherein the amount of liquid clad metal is reduced by penetration of the liquid clad into the core. The objective of the current investigation is to quantify the rate of IS through the use of a previously derived parameter, the Interface Rate Constant (IRC). The effect of peak temperature and initial sheet temper on IS kinetics were investigated. The results demonstrated that IS is due to the diffusion of silicon (Si) from the liquid clad layer into the solid core. Reduced amounts of liquid clad at long liquid duration times, a roughened sheet surface, and differences in resolidified clad layer morphology between sheet tempers were observed. Increased IS kinetics were predicted at higher temperatures by an IRC model as well as by experimentally determined IRC values; however, the magnitudes of these values are not in good agreement due to deficiencies in the model when applied to alloys. IS kinetics were found to be higher for sheets in the fully annealed condition when compared with work-hardened sheets, due to the influence of core grain boundaries providing high diffusivity pathways for Si diffusion, resulting in more rapid liquid clad penetration.

Implantation and Diffusion of Silicon Marker Layers in In0.53Ga0.47As

Continued effort has been placed on maximizing activation while controlling the diffusion of silicon doping in InGaAs for present and future complementary metal-oxide semiconductor devices. In order to explore the diffusion and activation behavior, Si marker layers were grown in InGaAs on InP by molecular beam epitaxy. The nature of Si diffusion was explored using a series of isoelectronic implants to introduce excess point defects near the layer. It was observed that excess interstitials reduce the Si diffusion consistent with a vacancy-driven diffusion mechanism. A diffusion and activation model implemented in the Florida object oriented process simulator has been developed to predict silicon diffusion behavior over a variety of temperatures and times. Using current and previous experimental data and complimentary density functional theory results, the diffusion model employs the SiIII–VIII pair as the primary mechanism for silicon diffusion in InGaAs.

Impact ionization in nonuniformly heated silicon p +–n–n + and n +–p–p + structures

Experimental results on the effects of changes in the impact-ionization current in silicon diffusion p+–n–n+ and n+–p–p+ structures upon nonuniform heating are presented. It is shown that the revealed effects are associated with the transformation of band energy levels caused by thermoelastic stresses of the structures.

Diffusion of silicon in titanium dioxide thin films with different degree of crystallinity: Efficiency of TiO2 and TiN barrier layers

Two kinds of reactively sputtered titanium dioxide films with columnar and fine-grained structures were investigated as diffusion barriers, preventing the silicon diffusion. The only differences in the deposition conditions were the oxygen percentage concentration (OC) in the discharge, kept for 10% and 30% of the total working pressure. The resulting films were found to have different thicknesses being 800 and 240 nm for 10% and 30% OC, respectively. The films were studied by X-Ray diffraction spectrometry (XRD) and their composition by Rutherford Backscattering Spectrometry (RBS). In order to describe the diffusion processes, the two batches were annealed up to temperature of 800 °C. The diffusivity from 300° to 800 °C is D(m2/s)=2.43.10−18exp[−(15kJ/mol)/(RT)] andD(m2/s)=2.36.10−18exp[−(18.4kJ/mol)/(RT)] for (10% OC) and TiO2 (30% OC), respectively. The physical meaning of the derived diffusion parameters are discussed in view of the crystalline peculiarities of the obtained films. Arrhenius plots show clearly that higher activation energy is characteristics for films with better-packed crystallites. These results are compared with known diffusion barrier layer such as TiN.

On concentration dependence of arsenic diffusivity in silicon

An analysis of the equations used for modeling thermal arsenic diffusion in silicon has been carried out. It was shown that for arsenic diffusion governed by the vacancy-impurity pairs and the pairs formed due to interaction of impurity atoms with silicon self-interstitials in a neutral charge state, the doping process can be described by the Fick’s second law equation with a single effective diffusion coefficient which takes into account two impurity flows arising due to interaction of arsenic atoms with vacancies and silicon self-interstitials, respectively. Arsenic concentration profiles calculated with the use of the effective diffusivity agree well with experimental data if the maximal impurity concentration is near the intrinsic carrier concentration. On the other hand, for higher impurity concentrations a certain deviation in the local regions of arsenic distribution is observed. The difference from the experiment can occur due to the incorrect use of effective diffusivity for the description of two different impurity flows or due to the formation of nonuniform distributions of neutral vacancies and neutral self-interstitials in heavily doped silicon layers. We also suppose that the migration of nonequilibrium arsenic interstitial atoms makes a significant contribution to the formation of a low concentration region on thermal arsenic diffusion.

Investigation on Structures of Aluminum Melts Containing Small Amount of Silicon Element

Aluminum melt structures play significant roles in process of impurity element eliminations. In order to investigate the aluminum melt structures containing small amount of silicon element, several compositions of aluminum melts were simulated. Molecular dynamics simulation method was employed to investigate the melt structures, concentration profiles and diffusion properties. For purpose of studying structure stability, related calculations were performed by first principles molecular dynamics method. The calculated results suggest that silicon concentration has obvious influence on silicon-silicon radial distribution function; silicon element segregates in local zone in each concentration of aluminum; there is no obvious relationship between silicon concentration and silicon diffusion coefficient; the stable Al-Si phase is formed by substitution lattice point or interstitial space; and position of Fermi energy of the stable structure corresponds to the valley of density of states.

Oxygen and erbium distribution in diffusion doped silicon

Silicon doped with rare-earth metal erbium is a promising material for the fabrication of highly efficient light emitting structures that can be easily integrated into silicon electronics. The fabrication technology of these structures includes little if any diffusion processes because the efficiency of erbium luminescence in diffusion structures is low. It is still unclear what causes this low erbium luminescence efficiency: low impurity concentration, low optical activity of the luminescence centers or luminescence extinction by the defects. The composition of diffusion silicon layers doped by rare earth erbium has been investigated. The diffusion source was an erbium oxide layer on the surface of the test silicon wafer. The erbium and oxygen distribution profiles in silicon have been measured by SIMS. The concentration of electrically active erbium impurity in the diffusion layers on silicon has been determined by measuring the surface resistance and carrier mobility during consecutive etching of layers. The erbium diffusion coefficient at 1240°C has been estimated to be 4.8·10–13cm2·s−1. The concentrations of electrically active (8·1016cm−3) and total (3·1018cm−3) erbium in the surface silicon diffusion layers prove to differ noticeably in the presence of high oxygen concentration (>1019cm−3). A model of erbium and oxygen simultaneous diffusion has been suggested. The model takes into account the association of erbium and oxygen into complexes. The results of numerical simulation and experimental data are in a good agreement for the near-surface region of the diffusion layer.

First-principles study of hydrogen-enhanced phosphorus diffusion in silicon

We present a first-principles study on the interstitial-mediated diffusion process of neutral phosphorus (P) atoms in a silicon crystal with the presence of mono-atomic hydrogen (H). By relaxing initial Si structures containing a P atom and an H atom, we derived four low-energy P-H-Si defect complexes whose formation energies are significantly lower than those of P-Si defect complexes. These four defect complexes are classified into two groups. In group A, an H atom is located near a Si atom, whereas in group B, an H atom is close to a P atom. We found that the H atom pairs with P or Si atom and changes the nature bonding between P and Si atoms from out-of-phase conjugation to in-phase conjugation. This fact results in the lower formation energies compare to the cases without H atom. For the migration of defect complexes, we have found that P-H-Si defect complexes can migrate with low barrier energies if an H atom sticks to either P or Si atom. Group B complexes can migrate from one lattice site to another with an H atom staying close to a P atom. Group A complexes cannot migrate from one lattice site to another without a transfer of an H atom from one Si atom to another Si atom. A change in the structure of defect complexes between groups A and B during the migration results in a transfer of an H atom between P and Si atoms. The results for diffusion of group B complexes show that the presence of mono-atomic H significantly reduces the activation energy of P diffusion in a Si crystal, which is considered as a summation of formation energy and migration barrier energy, leading to the enhancement of diffusion of P atoms at low temperatures, which has been suggested by recent experimental studies.

Direct measurement of ambipolar diffusion in bulk silicon by ultrafast infrared imaging of laser-induced microplasmas

Carrier kinetics in the density range of N=1017−1020 cm−3 is investigated inside the bulk of crystalline silicon. Most conventional experimental techniques used to study carrier mobility are indirect and lack sensitivity because of charging effects and recombination on the surface. An all optical technique is used to overcome these obstacles. By focusing 1.3-μm femtosecond laser pulses in the volume, we inject an initial free-carrier population by two-photon absorption. Then, we use pump-and-probe infrared microscopy as a tool to obtain simultaneous measurements of the carrier diffusion and recombination dynamics in a microscale region deep inside the material. The rate equation model is used to simulate our experimental results. We report a constant ambipolar diffusion coefficient Da of 2.5 cm2 s−1 and an effective carrier lifetime τeff of 2.5 ns at room temperature. A discussion on our findings at these high-injection levels is presented.

Self-organized growth of graphene nanomesh with increased gas sensitivity.

A bottom-up chemical vapor deposition (CVD) process for the growth of graphene nanomesh films is demonstrated. The process relies on silicon nanospheres to block nucleation sites for graphene CVD on copper substrates. These spheres are formed in a self-organized way through silicon diffusion through a 5 μm copper layer on a silicon wafer coated with 400 nm of silicon nitride. The temperature during the growth process disintegrates the Si3N4 layer and silicon atoms diffuse to the copper surface, where they form the nanospheres. After graphene nanomesh growth, the Si nanospheres can be removed by a simple hydrofluoric acid etch, leaving holes in the graphene film. The nanomesh films have been successfully transferred to different substrates, including gas sensor test structures, and verified and characterized by Auger, TEM and SEM measurements. Electrical/gas-exposure measurements show a 2-fold increase in ammonia sensitivity compared to plain graphene sensors. This improvement can be explained by a higher adsorption site density (edge sites). This new method for nanopatterned graphene is scalable, inexpensive and can be carried out in standard semiconductor industry equipment. Furthermore, the substrates are reusable.

Influence of NH3 annealing on the chemical states of HfO2/Al2O3 stacks studied by X-ray photoelectron spectroscopy

The effect of NH3 annealing on the chemical properties and thermal stability of ultrathin HfO2/Al2O3 film grown on silicon substrate by atomic layer deposition are investigated as a function of post deposition annealing temperature. X-ray photoelectron spectroscopy shows that nitrogen incorporation can be approached by a NH3 annealing treatment and its composition evidently increases after annealing at 700 °C. Nitrogen atoms are found to bond to hafnium, aluminum and silicon atoms with annealing temperature above 800 °C, respectively. In addition, ultrathin Al2O3 layer is demonstrated as a robust barrier layer for preventing silicon diffusion.

New constraints on upper mantle creep mechanism inferred from silicon grain-boundary diffusion rates

The creep in the Earth's interior is dominated either by diffusion creep which causes Newtonian mantle flow, or by dislocation creep which results in non-Newtonian mantle flow. Although previous deformation studies on olivine claimed a transition from dislocation creep to diffusion creep with depth in the upper mantle, they might misunderstand the creep rates due to experimental difficulties. Since creep in olivine is controlled by silicon diffusion, we measured the silicon grain-boundary diffusion coefficient in well-sintered iron-free olivine aggregates as a function of temperature, pressure, and water content, showing activation energy, activation volume, and water content exponent of 220±30 kJ/mol, 4.0±0.7 cm3/mol, and 0.26±0.07, respectively. Our results based on Si diffusion in forsterite predict that diffusion creep dominates at low pressures and low temperatures, whereas dislocation creep dominates under high pressure and high temperature conditions. Water has negligible effects on both diffusion and dislocation creep. There is a transition from diffusion creep in the shallow upper mantle to dislocation creep in deeper regions. This explains the seismic anisotropy increases at the Gutenberg discontinuity beneath oceans and at the mid-lithosphere discontinuity beneath continents.

Transverse and longitudinal vibrations in amorphous silicon

We show that harmonic vibrations in amorphous silicon can be decomposed to transverse and longitudinal components in all frequency range even in the absence of the well defined wave vector q. For this purpose we define the transverse component of the eigenvector with given ω as a component, which does not change the volumes of Voronoi cells around atoms. The longitudinal component is the remaining orthogonal component. We have found the longitudinal and transverse components of the vibrational density of states for numerical model of amorphous silicon. The vibrations are mostly transverse below 7 THz and above 15 THz. In the frequency interval in between the vibrations have a longitudinal nature. Just this sudden transformation of vibrations at 7 THz from almost transverse to almost longitudinal ones explains the prominent peak in the diffusivity of the amorphous silicon just above 7 THz.

Si and O self-diffusion in hydrous forsterite and iron-bearing olivine from the perspective of defect chemistry

We discuss the experimental results of silicon and oxygen self-diffusion coefficients in forsterite and iron-bearing olivine from the perspective of defect chemistry. Silicon diffusion is dominated by VO ··-associated VSi″″, whereas oxygen diffusion is dominated by hopping of VO ·· under anhydrous conditions, and by (OH)O · under hydrous conditions. By considering the charge neutrality condition of [(OH)O ·] = 2[VMe″] in hydrous forsterite and iron-bearing olivine, we get D Si ∝ (\(C_{{{\text{H}}_{2} {\text{O}}}}\))1/3 and D O ∝ (\(C_{{{\text{H}}_{2} {\text{O}}}}\))0, which explains the experimental results of water effects on oxygen and silicon self-diffusion rates (Fei et al. in Nature 498:213–215, 2013; J Geophys Res 119:7598–7606, 2014). The \(C_{{{\text{H}}_{2} {\text{O}}}}\) dependence of creep rate in the Earth’s mantle should be close to that given by Si and O self-diffusion coefficients obtained under water unsaturated conditions.

Oxidation behavior of (Mo,W)Si2–Si3N4 composite coating on molybdenum substrate at 1600 °C

(Mo,W)Si2–Si3N4 composite coating on pure molybdenum (Mo) substrate was prepared by using in situ diffusion of tungsten (W), nitrogen (N) and silicon (Si) elements. The microstructures and phase compositions were investigated using scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS) and X-ray diffraction (XRD). A coarse columnar crystal structure was observed in the original dense (Mo,W)Si2–Si3N4 layer in the SEM micrographs. The transition layers of (Mo,W)5Si3 and (Mo,W)3Si were formed between the coating and Mo substrate during a oxidation process at 1600°C in air. The growth kinetics of (Mo,W)5Si3 transition layer in (Mo,W)Si2–Si3N4 coating obeyed a parabolic rate law and its growth rate constant was 7.22×10−10cm2/s. The strong hindering effect of W element in coating on the Si diffusion led to a longer antioxidation life of the (Mo,W)Si2–Si3N4 coating on Mo substrate at1600°C.