The Ti/c-Si solid state reaction : III. The low-temperature reaction kinetics

Thin Ti layers (≈10nm) are grown on top of a clean Si(111) substrate. Heating these layers initiates a solid state reaction, yielding a monosilicide phase at ≈350°C and a C49 disilicide at ≈450°C. The present study concerns the growth kinetics of both phases by means of ellipsometry. A diffusion-limited growth kinetics is found for the monosilicide formation. However, two growth rates are observed, a fast initial one and a slow terminal growth rate. An enhanced Si diffusion in atomically disordered regions as compared to well ordered regions (grains or clusters) could be an explanation. From the measurements we have found a value of 2×10-15 cm2/s for the diffusion coefficient at ≈370°C and an activation energy of 0.62 ± 0.1 eV. Both values correspond to the fast process. Subsequently increasing the temperature to ≈450°C permits the growth of the homogeneous C49 TiSi2 phase. For this process, both planar layer growth and intermixing are observed, however, quantitative results could not be derived from the present study

A novel derivative ellipsometric method for the study of the growth of thin films: Titanium

The growth of a titanium film at room temperature from an evaporation source on a silicon substrate covered by its native oxide layer is continuously monitored with an ellipsometer at three wavelengths. The momentary positions and the derivatives of the trajectories thus obtained in the (Δ, Ψ) plane can be used for uniquely determining the momentary thickness and the momentary dielectric constants of the layer at each of the wavelengths. The optical properties of the titanium, which reflect the film structure and defect rate, strongly depend upon the growth conditions; the top region of a film approximately 40 nm thick appears to contain more voids and lattice defects than the region near the substrate

Systematic and random errors in rotating-analyzer, ellipsometry

Errors and error sources occurring in rotating-analyzer ellipsometry are discussed. From general considerations it is shown that a rotating-analyzer ellipsometer is inaccurate if applied at P = 0° and in cases when π = 0° or where Δ is near 0° or 180°. Window errors, component imperfections, azimuth errors and all other errors may, to first order, be treated independently and can subsequently be added. Explicit first-order expressions for the errors δΔ and δπ caused by windows, component imperfections, and azimuth errors are derived, showing that all of them, except the window errors, are eliminated in a two-zone measurement. Higher-order errors that are due to azimuth errors are studied numerically, revealing that they are in general less than 0.1°. Statistical errors are also discussed. Errors caused by noise and by correlated perturbations, i.e., periodic fluctuations of the light source, are also considered. Such periodic perturbations do cause random errors, especially when they have frequencies near 2ωA and 4ωA

The Ti/c-Si solid state reaction : I. An ellipsometrical study

This paper is the first of a series of three articles in which we present the results and analyses of an extended study of the c-Si/Ti solid state reaction. In this paper we will discuss the spectroscopic ellipsometric investigation. Thin (≈10nm) Ti films are grown on clean Si(111) surfaces and are subsequently heated. The Si indiffusion and the Si-Ti intermixing are continuously registered by three-wavelengths ellipsometry. Two metastable intermediate phases are observed to form before the final state is obtained Spectroscopic ellipsometry (E = 2−4.5 eV) is used to characterize the as-deposited layer, the metastable intermediate phase and the final state. Analysis of these spectra shows that: (1) Si and Ti intermix during the initial Ti deposition, (2) a fast reordering of the Ti atoms occurs when the system is slightly heated (≈175°C), (3) a metastable, probably monosilicide phase with a large Si concentration gradient is obtained at ≈350°C, (4) a homogeneous metastable TiSi2 forms at ≈450°C, at ≈700°C a roughened TiSi2 layer with a surplus of c-Si is formed

Strategic loyalty reward in dynamic price Discrimination

This paper proposes a dynamic model of duopolistic competition under behaviorbased price discrimination with the following property: in equilibrium, a firm may reward its previous customers although long term contracts are not enforceable. A firm can offer a lower price to its previous customers than to its new customers as a strategic means to hamper its rival to gather precise information on the young generation of customers for subsequent profitable behavior-based pricing. The result holds both with myopic and forward-looking, impatient enough consumers.Price discrimination ; Dynamic pricing ; Loyalty reward

The kinetics of titanium monosilicide growth studied by three-wavelength ellipsometry

Thin titanium layers (approximately 10 nm) have been grown on top of a clean Si(111) substrate. Heating these layers initiates a solid state reaction, yielding an amorphous monosilicide phase at about 350 °C. The kinetics of the solid state reaction has been followed using three-wavelength ellipsometry (340, 450 and 550 nm). A very coarse two-layer model has been applied in the analyses of the measured data: a top layer of pure titanium is consumed by a second layer of TiSi. The dielectric constants of titanium and TiSi are known and the layer thicknesses d1 and d2 have been fitted to the six ellipsometrical angles measured. These analyses reveal a diffusion-limited growth mechanism exhibiting two growth rates: a rapid initial rate followed by a slower final rate. The diffusion coefficient D of the rapid process and its activation energy Ea could be obtained: D = 2 × 10−15cm2s−1atT 370 °CandEa = 0.62 eV The two growth rates have been attributed to silicon diffusion along the grains and diffusion into the grains.\ud \u

On deflection fields, weak-focusing and strong-focusing storage rings for polar molecules

In this paper, we analyze electric deflection fields for polar molecules in terms of a multipole expansion and derive a simple but rather insightful expression for the force on the molecules. Ideally, a deflection field exerts a strong, constant force in one direction, while the force in the other directions is zero. We show how, by a proper choice of the expansion coefficients, this ideal can be best approximated. We present a design for a practical electrode geometry based on this analysis. By bending such a deflection field into a circle, a simple storage ring can be created; the direct analog of a weak-focusing cyclotron for charged particles. We show that for realistic parameters a weak-focusing ring is only stable for molecules with a very low velocity. A strong-focusing (alternating-gradient) storage ring can be created by arranging many straight deflection fields in a circle and by alternating the sign of the hexapole term between adjacent deflection fields. The acceptance of this ring is numerically calculated for realistic parameters. Such a storage might prove useful in experiments looking for an EDM of elementary particles.Comment: 8 pages, 5 figure

Taxonomy of Disruptive Behavior in Children and Adolescents

Taxonomic systems try to describe physical as well as behavioral and social phenomena in a meaningful way. Taxonomy can be defi ned as the grouping of cases, e.g. individuals, according to their distinguishing features. This grouping can be done on different, hierarchical levels of defi ning characteristics, such as, in medicine: individual problems or symptoms; symptom aggregates or syndromes; functional disorders; or etiological factors (Verhulst & Koot, 1992). Taxonomy is the process of the identifi cation of groups of individuals according to their properties, hence according to intrinsic criteria. Classifi cation is related to taxonomy, but is somewhat broader and includes the grouping of cases according to extrinsic criteria (e.g., source of referral) as well as intrinsic criteria, which are based on the features of the cases themselves. Diagnosis can be defi ned as the medical term for classifi cation (Achenbach, 1991c; Verhulst & Koot, 1992). Taxonomy should also be distinguished from assessment, although they are closely related. Assessment identifi es the distinguishing features of each individual case, which, in child and adolescent psychiatry e.g., can be expressed in behavioral, emotional, or physical measures (Achenbach, 1991c; Verhulst & Koot, 1992). While in taxonomy the central goal is identifying groups of individuals with similar intrinsic features, assessment aims to identify characteristics that distinguish one individual from others. Assessment can be used to classify an individual in the proper taxonomic category. Examples of assessment procedures are questionnaires, e.g. the Child Behavior Checklist (CBCL) and the Teacher’s Report Form (TRF) (Achenbach and Rescorla, 2001), as well as interviews, e.g. the Diagnostic Interview Schedule for Children – Parent Version (DISC-IV-P; Shaffer et al., 1998)