Diffusion of silicon in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained film structure (B ₊ films) have been examined as diffusion barriers, preventing the silicon diffusion in silicon devices. The silicon diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) after annealing at temperatures up to 900° C, in view of application of high-temperature processes. The diffusivity from 400 to 900° C: D (m² s^–1)=2.5×10^–18 exp[–31 kJ/mol/(RT)] in B ₀ layers and D (m² s^–1)=3×10^–19 exp[–26 kJ/mol/(RT) in B ₊ TiN layers. The diffusivities determined correspond to grain boundary diffusion, the difference being due to the different microstructure. The very low diffusivity of silicon in B ₊ TiN layer makes it an excellent high-temperature barrier preventing silicon diffusion.     

Volume and grain boundary diffusion of implanted 113Sn in aluminium

Volume and grain boundary diffusion of ¹¹³Sn in aluminium was investigated with the radiotracer method. The implantation technique was used for tracer deposition to avoid problems of tracer hold-up caused by the oxide layer always present on aluminium. The diffusion penetration was chosen large enough to permit serial sectioning of samples with the aid of a microtome.The temperature dependence of the volume diffusivity was determined as D(T)=4.54×10^–5×exp[–(114.5±1.2)kJmol^–1/RT] m ² s ^–1. This confirms previous measurements from our group which already showed that Sn is the fastest foreign metal diffusor so far investigated in aluminium.Grain boundary diffusion of ¹¹³Sn in Al polycrystals was measured in the type-B kinetic regime. The grain boundary diffusion product P=sD _gb (s=segregation factor, =grain boundary width, D _gb=grain boundary diffusivity) was found to be strongly affected by the impurity content of aluminium. For Al polycrystals of 99.9992% nominal purity we obtained P _5N(T)=1.08×10^–8exp [–(96.9±7.5) kJ mol^–1/RT] m³ s^–1 and for less pure Al polycrystals of 99.99% nominal purity P _4N(T)=3.0×10^–10 exp [–(90.1±4.2) kJ mol^–1/RT] m³ s^–1 was determined. The grain boundary diffusion product in the purer material is more than one order of magnitude higher than in the less pure material. Very likely this is an effect of co-segregation of non-diffusant impurities into the grain boundaries.     

Boron neutralization and hydrogen diffusion in silicon subjected to low-energy hydrogen implantation

Using the hydrogen neutralization of the boron acceptor, the diffusion of hydrogen is investigated in the temperature range 20 °–160 °C. The hydrogenation is performed by low-energy implantation. We observe a fast initial hydrogen migration, followed by a long-time diffusion phase that is described by an effective diffusion coefficientD _eff=D _{0 eff} exp(–E _a/kT) withD _{0 eff}–cm²s^–1 andE _a=(0.83±0.05) eV. No deeper hydrogen migration is detected for implantation times longer than – 30 min. Our data are explained by the build-up of a large amount of molecular hydrogen beneath the surface, which strongly hinders the transfer of the implanted hydrogen to the bulk. The thermal reactivation kinetics of the neutralized boron show a rapid initial step followed by a longtime thermally activated second order phase, which is limited by the recombination of hydrogen into molecules.     

Analysis of the <Emphasis Type="Italic">Y</Emphasis>(4140) and related molecular states with QCD sum rules

In this article, we assume that there exist scalar D^*[`(D)]<sup>*</sup>{D}^{\ast}{\bar {D}}^{\ast}, D<sub>s</sub><sup>*</sup>[`(D)]_s^*{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B^*[`(B)]<sup>*</sup>{B}^{\ast}{\bar {B}}^{\ast} and B<sub>s</sub><sup>*</sup>[`(B)]_s^*{B}_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states, and study their masses using the QCD sum rules. The numerical results indicate that the masses are about (250–500) MeV above the corresponding D ^*–[`(D)]<sup>*</sup>{\bar{D}}^{\ast}, D <sub>s</sub> <sup>*</sup>–[`(D)]_s^*{\bar {D}}_{s}^{\ast}, B ^*–[`(B)]<sup>*</sup>{\bar{B}}^{\ast} and B <sub>s</sub> <sup>*</sup>–[`(B)]_s^*{\bar {B}}_{s}^{\ast} thresholds, the Y(4140) is unlikely a scalar D_s^*[`(D)]<sub>s</sub><sup>*</sup>{D}_{s}^{\ast}{\bar{D}}_{s}^{\ast} molecular state. The scalar D<sup>*</sup>[`(D)]^*D^{\ast}{\bar{D}}^{\ast}, D_s^*[`(D)]<sub>s</sub><sup>*</sup>D_{s}^{\ast}{\bar{D}}_{s}^{\ast}, B<sup>*</sup>[`(B)]^*B^{\ast}{\bar{B}}^{\ast} and B_s^*[`(B)]<sub>s</sub><sup>*</sup>B_{s}^{\ast}{\bar{B}}_{s}^{\ast} molecular states maybe not exist, while the scalar D￠<sup>*</sup>[`(D)]^￠*{D'}^{\ast}{\bar{D}}^{\prime\ast}, D_s^￠*[`(D)]<sub>s</sub><sup>￠*</sup>{D}_{s}^{\prime\ast}{\bar{D}}_{s}^{\prime\ast}, B<sup>￠*</sup>[`(B)]^￠*{B}^{\prime\ast}{\bar{B}}^{\prime\ast} and B_s^￠*[`(B)]_s^￠*{B}_{s}^{\prime\ast}{\bar{B}}_{s}^{\prime\ast} molecular states maybe exist.     

Grain Boundary Diffusion and Segregation in Interstitial Solid Solutions Based on BCC Transition Metals: Carbon in Niobium

Bulk and grain boundary (GB) diffusion of ¹⁴C in Nb has been studied by the radiotracer serial sectioning technique. B and C kinetic regimes were realized for GB diffusion in the temperature range from 800 to 1173 K. The values of P = sD _gb, D _gb and s follow the Arrhenius dependencies: P = 5.15 × 10^–15 exp[–(83.1 kJ/mol)/RT] m³/s (973–1173 K), D _gb = 2.3 × 10^–6 exp[–(133.0 kJ/mol)/RT] m²/s (800–950 K), and s = 4.7 exp[(49.9 kJ/mol)/RT].The increase in the GB diffusion compared with self-diffusion is very large despite the probable retardation effect due to the strong segregation.The results for GB diffusion of C in Nb as well as for other interstitial solutes (P, S) in bcc transition metals (- Fe, Mo) are discussed in the framework of the transition state theory. It is assumed that GB segregation decreases the energy of the ground state whereas the change in the diffusion mechanism (e.g. from vacancy to interstitial) leads to a strong decrease of the transition state energy. This change in the diffusion mechanism results in a fast GB diffusion of interstitial solutes in spite of their large tendency to segregate to GBs.     

Diffusion of chromium and manganese in γ-TiAl

The γ-TiAl intermetallic compound with suitable alloying additions has shown considerable promise as a material for high-temperature applications. Diffusion studies in this alloy system are useful in assessment of their creep behaviour and structural stability in service conditions. Tracer diffusion coefficients of ⁵¹Cr and ⁵⁴Mn in a γ-TiAl intermetallic compound containing 54.1 at. % aluminium were determined in the temperature range from 1095 to 1470?K. The temperature dependence of both the diffusing species follows a linear Arrhenius behaviour and can be expressed as D _Cr?=?4.4?×?10^?3exp(?350?kJ?mol^?1/RT)?m^2?s^?1 and D _Mn?=?1.2?×?10^?3?×exp(?326?kJ?mol^?1/RT)?m^2?s^?1. The data are analysed on the basis of empirical correlations between the diffusion and melting parameters applicable for conventional mono-vacancy diffusion mechanism in metals. It is concluded that impurity diffusion in γ-TiAl occurs through the migration of thermal vacancies via nearest-neighbour or next-nearest neighbour jumps.     

Diffusion of nitrogen in ion-implanted chromium and tungsten

The diffusion of N in the group VI B metals Cr and W has been studied in the previously uninvestigated temperature ranges 300°–550 °C (Cr) and 600°–800 °C (W) using ion-beam techniques. Diffusion couples were created by ion-implantation. The timedependent diffusion profiles were monitored by the use of the Nuclear Resonance Broadening (NRB) technique. The linear Arrhenius plots extracted from the measured diffusivities indicate that the diffusivity of implanted N in Cr and W can be described by the activation energyQ=1.39±0.06 eV and 2.32±0.16 eV and the pre-exponential factorD ₀=(7.0±7.2)×10^–4cm^2/s and 4.3±8.3cm^2/s, respectively. The solubilities of N in Cr and W from the implanted distributions were found to deviate from those obtained using conventional metallographical methods.     

Possible molecular states of D*s[`(D)]*sD^{*}_{s}\bar{D}^{*}_{s} system and Y(4140)

The interpretation of Y(4140) as a D^*_s[`(D)]<sup>*</sup><sub>s</sub>D^{*}_{s}\bar{D}^{*}_{s} molecule is studied dynamically in the one boson exchange approach, where σ, η and φ exchange are included. Ten allowed D<sup>*</sup><sub>s</sub>[`(D)]^*_sD^{*}_{s}\bar{D}^{*}_{s} states with low spin parity are considered, and we find that the J ^PC =0⁺⁺, 1⁺⁻, 0⁻⁺, 2⁺⁺ and 1⁻⁻ D^*_s[`(D)]<sup>*</sup><sub>s</sub>D^{*}_{s}\bar{D}^{*}_{s} configurations are most tightly bound. We suggest that the most favorable quantum numbers are J <sup>PC</sup> =0<sup>++</sup> for Y(4140) as a D<sup>*</sup><sub>s</sub>[`(D)]^*_sD^{*}_{s}\bar{D}^{*}_{s} molecule; however, J ^PC =0⁻⁺ and 2⁺⁺ cannot be excluded. We propose to search for the 1⁺⁻ and 1⁻⁻ partners in the J/ψ η and J/ψ η′ final states, which is an important test of the molecular hypothesis of Y(4140) and the reasonability of our model. The 0⁺⁺ B^*_s[`(B)]^*_sB^{*}_{s}\bar{B}^{*}_{s} molecule should be deeply bound; experimental search in the ϒ(1S)φ channel at Tevatron and LHC is suggested.     

Model and theory for the determination of diffusion coefficients by Auger electron spectroscopy measurements and an application to oxygen diffusion along the [0001] and [101¯0] axes in single crystal zirconium

A simple hopping model of the diffusion of adsorbed species from a surface into the bulk of a material has been formulated and solved mathematically. The difference in the energy barriers for an atom moving between the atomic layers at the surface and in the bulk are explicitly considered. This model is also capable of describing the initial stages of diffusion, something that conventional solutions of the continuum diffusion equation cannot handle. Auger electron spectroscopy has been used to measure the dissolution rate of oxygen from Zr(0001) and Zr(101¯0) surface into the bulk. Satisfactory results were obtained by applying our model to the diffusion data for these two zirconium surfaces for two different heating schedules: (i) rapid temperature ramp-and-hold and (ii) continuous linear heating with respect to time. The resulting Arrhenius expressions for diffusion are: D = (0.115 ± 0.031)exp[(−44.45 ± 4.82)kcal/RT]cm²/s along Zr[0001] and D = (1.07 ± 0.26)exp[(−46.18 ± 4.22)kcal/RT]cm²/s along Zr[101¯0].     

Diffusion of Al in ion-implanted Pd and Pt

The diffusion coefficients of aluminium have been measured in polycrystalline fcc Pd and Pt. The Al-implanted palladium and platinum samples were annealed at 400°–800 °C and 450°–900 °C, respectively. The aluminium profiles were probed using the nuclear resonance broadening (NRB) technique. Values of (1.41±0.09) and (1.38±0.09) eV for the activation energy and (1.5 _–1.0 ⁺⁵ )×10^–6 and (4 _–3 ⁺¹⁰ )×10^–7cm²/s for the frequency factor were obtained for Al in Pd and Pt, respectively. These anomalous results, compared to the normal impurity diffusion, were checked using also Al-evaporated samples.     

Diffusion of gold in dislocation-free or highly dislocated silicon measured by the spreading-resistance technique

The diffusion of Au in dislocation-free or plastically deformed Si (10¹¹ to 10¹³ dislocations/m²) was measured with the aid of the spreading-resistance technique. The Au profiles produced indislocation-free Si slices by in-diffusion from both surfaces possess nonerfc-type U shapes as predicted by the so-called kick-out diffusion model. This model is used to calculate the contribution of self-interstitials to the (uncorrelated) Si self-diffusion coefficient,D _I ^SD =0.064×exp(–4.80 eV/kT)m² s^–1, from the present and previous data on the diffusivity and solubility of Au in Si in the temperature range 1073–1473 K. Inhighly dislocated Si the diffusion of Au is considerably faster than in dislocation-free Si. From the erfc-type penetration profiles found in this case, effective Au diffusion coefficients were deduced and combined with data on the solubility of Au in Si. ThusC _i ^eq D _i=0.0064 ×exp(–3.93 eV/kT)m² s^–1 was obtained in the temperature range 1180–1427 K, whereC _i ^eq andD _i are the solubility and diffusivity of interstitial Au in Si.     

Diffusion coefficient of selenium in indium antimonide

The diffusion of selenium in indium antimonide has been studied in the temperature range 400–490°C, by the method of removing layers. Two regions have been distinguished in the donor distribution profiles. The first has a low diffusion coefficient and a high surface concentration, near to the limit of solubility of selenium (8·10¹⁸ cm^–3). In the second region, a much larger diffusion coefficient and a surface concentration lower by two orders of magnitude (8·10¹⁶ cm^–3) with weak temperature dependence are found. The temperature dependences of the diffusion coefficients of the first and second regions can be described by the expressions: D=4.8·10¹³ exp(–4.1 eV/kT) cm²/sec, D₂=1.9·10¹³ exp(–3.9 eV/kT) cm²/sec.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 40–43, November, 1991.     

Conservation laws for classical and relativistic collisions. II

On the basis of elementary symmetry arguments it is shown that (1) if in classical mechanics there exists a quantity λ+Σ_iμ_iυ_i+1/2νυ ² that is conserved, where λ,μ _i, andν are particle parameters, then theμ _i andν are all proportional to a single parameterμ and the quantityAμ+Σ_iB_iμυ_i+C(λ+ 1/2Dμυ ²), whereD ≡ν/μ, is conserved for all values ofA, B _i, andC; (2) if in relativistic mechanics there exists a quantity λ+Σ_iμ_iυ_i[1−(υ ²/c ²)]^−1/2+νc[1−(υ ²/c ²)]^−1/2 that is conserved, then theμ _i andν are all proportional to a single parameterμ and the quantityAλ+Σ_iB_iμν_i[1−(υ ²/c ²)]^−1/2+Cμc [1−(υ ²/c ²)]^−1/2 is conserved for all values ofA, B _i, andC.     

Measurement of Vcb from the decay process

A new precise measurement of |V_cb| and of the branching ratio BR ) has been performed using a sample of about 5000 semileptonic decays , selected by the DELPHI detector at LEP I by tagging the soft pion from D^*+→D⁰π⁺. The results are: V_cb=(39.0±1.5 (stat.)^+2.5_−2.6 (syst. exp.)±1.3 (syst. th.))×10⁻³,

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. The analytic dependencies of the differential cross-section and of the Isgur–Wise form factor as functions of the variable w=v_B⁰·v_D^* have also been obtained by unfolding the experimental resolution.     

Influence of the noise driving force on the diffusion of copper in aluminium thin films

The diffusion of copper in thin polycrystalline aluminium films subjected to current stressing at 140 C was studied. Experimental aluminium stripes were doped with copper in a limited (source) region and the movement of copper away from this region was investigated by electron probe microanalyser. Samples were stressed both by dc and by superimposed dc and noise current. The dc density (5×10⁵ A/cm²) was equal to that of the effective (r.m.s.) value of superimposed current. The frequency range of the noise signal with the Gaussian distribution of amplitudes was 5 Hz to 20 kHz. Under the described conditions copper diffused due to the concentration gradient as well as the electromigration driving force. The diffusion coefficients of copper at both current stressings were obtained by fitting the measured concentration profiles to those calculated theoretically. The results yield that the diffusion becomes enhanced when the noise is applied. The values of thermal grain boundary-assisted diffusion coefficient obtained in six independent measurements with dc loading vary betweenD _Tb=8×10^–13 cm²/s and 25×10^–13 cm²/s. The corresponding values of total diffusion coefficient (i.e. the sum of the thermal and noise induced component) areD _b=(20÷83)×10^–13 cm²/s. The noise-induced enhancement of the diffusion was predicted theoretically. Thus, the present results confirm the previous theoretical calculations.The authors wish to thank Dr. V. Bezák for stimulating discussions.     

Ion–ion interactions of LiPF6 and LiBF4 in propylene carbonate solutions

Self-diffusion coefficients of Li⁺ D_Li⁺, PF₆⁻ D_PF6⁻ and solvent propylene carbonate (PC) D_PC in LiPF₆−PC solutions were determined at 298 K by the pulse gradient spin echo (PGSE) NMR technique over the salt concentration range of 0.1–3.0 M (M = mol dm^– 3). The order of the diffusion coefficients was found to be D_Li⁺ < D_PF6⁻ < D_PC over the concentration range examined, and they were monotonically decreased with increasing the salt concentration. Haven ratio Λ/Λ_NMR, where Λ and Λ_NMR represent the ionic conductivity measured electrochemically and that estimated via the Nernst-Einstein equation using the diffusion coefficient, respectively, was evaluated as the measure of the ion–ion interaction in the LiPF₆–PC solutions. Though Λ/Λ_NMR values for LiPF₆-solutions decrease with increasing the salt concentration, they were greater than those for LiBF₄–PC solutions over the whole concentration range examined, which indicates that the ion pair formation ability of PF₆^– ion is weaker than that of the BF₄^– ion. The smaller value of the ionic conductivity for the highly concentrated LiPF₆–PC solution (above 2.0 M) than that of the LiBF₄-solutions can be attributed to the more rapidly increased viscosity relative to the LiBF₄-solution. Classic molecular dynamics (MD) simulations for the respective LiPF₆ and LiBF₄-solution of 0.5 and 1.0 M were also carried out based on the effective pair potentials. Diffusion coefficients, ionic conductivity and Haven ratio for these solutions were calculated from MD trajectories, and they qualitatively agree with those evaluated by experiments. Pair correlation functions g_LiO(r) (for Li⁺–O (PC) pair) and g_LiPF6(r) (for Li⁺–PF₆^– pair) or g_LiBF4(r) (for Li⁺–BF₄^– pair) revealed that the lithium ion weakly forms the contact ion pairs with PF₆^–, whilst strongly with BF₄^–, which supports the present experimental results. Moreover, the simulation results show that both anions in the contact ion pairs predominantly take the monodentate form, which is in contrast to the multidentate coordination predicted by ab initio calculation in gas phase.     

Tantalum and cobalt suicides: Temperature sensor applications

Ion bombardment induced mixing of Ta-Si films has been studied using 400 keV argon ions. Doses varied from 7×10¹⁴ to 1×10¹⁷ Ar⁺ cm^–2 with post-bombardment anneals of 180–900 s at temperatures in the range 600–860 °C using radiant heating. Silicide uniformity and stoichiometry were determined using alpha backscattering spectrometry. Optimum fabrication parameters were determined with regard to subsequent material sheet resistivity, temperature coefficient of resistance and application as a temperature sensing material. Similar measurements were made on CoSi₂ layers prepared by annealing ion bombarded samples and comparison with silicide films arising from purely thermal annealing was made.CoSi₂ was found to be the more suitable material for temperature-sensor applications, showing a positive linear variation in sheet resistivity in the range 0–400 °C for samples which could be prepared simply and reproducibly.     

Dynamic recrystallization of austenite during hot plastic deformation

The kinetics of dynamic recrystallization is dependent on the thermomechanical conditions in which plastic deformation is taking place. To determine the timet _p needed for the onset of dynamic recrystallization, experimental work was performed on low-carbon austenite to check the validity of the equationW= 2·1 × 10^–1 Z ^–0.94, whereW= t_pexp(–Q/RT),Z represents the Zener-Hollomon parameter, and Q=276 kJ mol^–1.     

Diffusion of titanium atoms in Ni-Si-B metallic glass

The diffusion ot Ti atoms in the Ni₇₇Si₃B₂₀ metallic glass was studied by the Auger electron spectroscopy. The temperature dependence of the diffusion coefficient obeys the Arrhenius relation with the activation energyE=1·7 eV and the pre-exponential factorD ₀=0·86 × ×10^–4 m² s^–1. Possible mechanisms of the atomic transport in metallic glasses are discussedThe authors wish to thank Dr. P. Duhaj for providing the metallic glass samples.     

Diffusion of Al in ion-implanted α-Zr and α-Hf

The diffusion of Al in the group IVa metals Zr and Hf has been studied for the first time in the temperature ranges 600°–800°C (Zr) and 750°–900°C (Hf) using ion-beam techniques. Diffusion couples were created by ion-implantation. The time-dependent diffusion profiles were monitored by the use of the Nuclear Resonance Broadening (NRB) technique. The linear Arrhenius plots extracted from the measured diffusivities indicate that the diffusivity of implanted Al in Zr and Hf can be described by the activation energyQ=2.9±0.2eV and 3.7±0.3eV and the pre-exponential factorD ₀=17±42cm²/s and 170±600cm²/s, respectively.