In situ fast ellipsometric analysis of repetitive surface phenomena

We present an ellipsometric technique and ellipsometric analysis of repetitive phenomena, based on the experimental arrangement of conventional phase modulated ellipsometers (PME) c onceived to study fast surface phenomena in repetitive processes such as periodic and triggered experiments. Phase modulated ellipsometry is a highly sensitive surface characterization technique that is widely used in the real-time study of several processes such as thin film deposition and etching. However, fast transient phenomena cannot be analyzed with this technique because precision requirements limit the data acquisition rate to about 25 Hz. The presented new ellipsometric method allows the study of fast transient phenomena in repetitive processes with a time resolution that is mainly limited by the data acquisition system. As an example, we apply this new method to the study of surface changes during plasma enhanced chemical vapor deposition of amorphous silicon in a modulated radio frequency discharge of SiH4. This study has revealed the evolution of the optical parameters of the film on the millisecond scale during the plasma on and off periods. The presented ellipsometric method extends the capabilities of PME arrangements and permits the analysis of fast surface phenomena that conventional PME cannot achieve.

Plasma-enhanced chemical vapor deposition of boron nitride thin films from B2H6-H2-NH3 and B2H6-N2 gas mixtures

Highly transparent and stoichiometric boron nitride (BN) films were deposited on both electrodes (anode and cathode) of a radio-frequency parallel-plate plasma reactor by the glow discharge decomposition of two gas mixtures: B2H6-H2-NH3 and B2H6-N2. The chemical, optical, and structural properties of the films, as well as their stability under long exposition to humid atmosphere, were analyzed by x-ray photoelectron, infrared, and Raman spectroscopies; scanning and transmission electron microscopies; and optical transmittance spectrophotometry. It was found that the BN films grown on the anode using the B2H6-H2-NH3 mixture were smooth, dense, adhered well to substrates, and had a textured hexagonal structure with the basal planes perpendicular to the film surface. These films were chemically stable to moisture, even after an exposition period of two years. In contrast, the films grown on the anode from the B2H6-N2 mixture showed tensile stress failure and were very unstable in the presence of moisture. However, the films grown on the cathode from B2H6-H2-NH3 gases suffered from compressive stress failure on exposure to air; whereas with B2H6-N2 gases, adherent and stable cathodic BN films were obtained with the same crystallographic texture as anodic films prepared from the B2H6-H2-NH3 mixture. These results are discussed in terms of the origin of film stress, the effects of ion bombardment on the growing films, and the surface chemical effects of hydrogen atoms present in the gas discharge.

Rheotaxial growth of CuInSe2 thin films

CuInSe2 thin films were deposited onto glass and liquid¿indium¿coated glass substrates by coevaporation of copper, indium, and selenium. The morphology, composition, and crystalline properties have been studied in relation to the deposition process parameters. The deposition rate and the grain size are higher in films grown on liquid indium than on glass and depend on the indium film thickness. Films grown on indium do not show the same crystalline phases of films grown on glass, and in order to obtain films free of spurious phases the Cu fluxes must be increased.

Influence of pressure and radio frequency power on deposition rate and structural properties of hydrogenated amorphous silicon thin films prepared by plasma deposition

The influence of radio frequency (rf) power and pressure on deposition rate and structural properties of hydrogenated amorphous silicon (a-Si:H) thin films, prepared by rf glow discharge decomposition of silane, have been studied by phase modulated ellipsometry and Fourier transform infrared spectroscopy. It has been found two pressure regions separated by a threshold value around 20 Pa where the deposition rate increases suddenly. This behavior is more marked as rf power rises and reflects the transition between two rf discharges regimes. The best quality films have been obtained at low pressure and at low rf power but with deposition rates below 0.2 nm/s. In the high pressure region, the enhancement of deposition rate as rf power increases first gives rise to a reduction of film density and an increase of content of hydrogen bonded in polyhydride form because of plasma polymerization reactions. Further rise of rf power leads to a decrease of polyhydride bonding and the material density remains unchanged, thus allowing the growth of a-Si:H films at deposition rates above 1 nm/s without any important detriment of material quality. This overcoming of deposition rate limitation has been ascribed to the beneficial effects of ion bombardment on the a-Si:H growing surface by enhancing the surface mobility of adsorbed reactive species and by eliminating hydrogen bonded in polyhydride configurations.

Nucleation of diamond on silicon, SiAlON, and graphite substrates coated with an a-C:H layer

We investigated the influence of a hydrogenated disordered carbon (a-C:H) layer on the nucleation of diamond. Substrates c-Si<100>, SiAlON, and highly oriented pyrolytic graphite {0001} were used in this study. The substrate surfaces were characterized with Auger electron spectroscopy (AES) while diamond growth was followed with Raman spectroscopy and scanning electron microscopy (SEM). It was found that on silicon and SiAlON substrates the presence of the a-C:H layer enabled diamond to grow readily without any polishing treatment. Moreover, more continuous diamond films could be grown when the substrate was polished with diamond powder prior to the deposition of the a-C:H layer. This important result suggests that the nucleation of diamond occurs readily on disordered carbon surfaces, and that the formation of this type of layer is indeed one step in the diamond nucleation mechanism. Altogether, the data refute the argument that silicon defects play a direct role in the nucleation process. Auger spectra revealed that for short deposition times and untreated silicon surfaces, the deposited layer corresponds to an amorphous carbon layer. In these cases, the subsequent diamond nucleation was found to be limited. However, when the diamond nucleation density was found to be high; i.e., after lengthy deposits of a¿C:H or after diamond polishing, the Auger spectra suggested diamondlike carbon layers.

Gravitational wave pulse and soliton wave collision

We study the collision of a gravitational wave pulse and a soliton wave on a spatially homogeneous background. This collision is described by an exact solution of Einsteins equations in a vacuum which is generated from a nondiagonal seed by means of a soliton transformation. The effect produced by the soliton on the amplitude and polarization of the wave is considered.

Semiclassical back reaction in the formation of a straight cosmic string

We derive the back reaction on the gravitational field of a straight cosmic string during its formation due to the gravitational coupling of the string to quantum matter fields. A very simple model of string formation is considered. The gravitational field of the string is computed in the linear approximation. The vacuum expectation value of the stress tensor of a massless scalar quantum field coupled to the string gravitational field is computed to one loop order. Finally, the back-reaction effect is obtained by solving perturbatively the semiclassical Einsteins equations.

Stochastic semiclassical equations for weakly inhomogeneous cosmologies

Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.

Stochastic semiclassical cosmological models

We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless nonconformal matter fields in the early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so-called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological model introduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.

Noise induced transitions in semiclassical cosmology

A semiclassical cosmological model is considered which consists of a closed Friedmann-Robertson-Walker spacetime in the presence of a cosmological constant, which mimics the effect of an inflaton field, and a massless, non-conformally coupled quantum scalar field. We show that the back-reaction of the quantum field, which consists basically of a nonlocal term due to gravitational particle creation and a noise term induced by the quantum fluctuations of the field, are able to drive the cosmological scale factor over the barrier of the classical potential so that if the universe starts near a zero scale factor (initial singularity), it can make the transition to an exponentially expanding de Sitter phase. We compute the probability of this transition and it turns out to be comparable with the probability that the universe tunnels from ``nothing'' into an inflationary stage in quantum cosmology. This suggests that in the presence of matter fields the back-reaction on the spacetime should not be neglected in quantum cosmology.

Stochastic semiclassical gravity

In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.

Mode decomposition and renormalization in semiclassical gravity

We compute the influence action for a system perturbatively coupled to a linear scalar field acting as the environment. Subtleties related to divergences that appear when summing over all the modes are made explicit and clarified. Being closely connected with models used in the literature, we show how to completely reconcile the results obtained in the context of stochastic semiclassical gravity when using mode decomposition with those obtained by other standard functional techniques.

Stochastic semiclassical fluctuations in Minkowski spacetime

The semiclassical Einstein-Langevin equations which describe the dynamics of stochastic perturbations of the metric induced by quantum stress-energy fluctuations of matter fields in a given state are considered on the background of the ground state of semiclassical gravity, namely, Minkowski spacetime and a scalar field in its vacuum state. The relevant equations are explicitly derived for massless and massive fields arbitrarily coupled to the curvature. In doing so, some semiclassical results, such as the expectation value of the stress-energy tensor to linear order in the metric perturbations and particle creation effects, are obtained. We then solve the equations and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. In the conformal field case, explicit results are obtained. These results hint that gravitational fluctuations in stochastic semiclassical gravity have a non-perturbative behavior in some characteristic correlation lengths.

Vacuum decay in quantum field theory

We study the contribution to vacuum decay in field theory due to the interaction between the long- and short-wavelength modes of the field. The field model considered consists of a scalar field of mass M with a cubic term in the potential. The dynamics of the long-wavelength modes becomes diffusive in this interaction. The diffusive behavior is described by the reduced Wigner function that characterizes the state of the long-wavelength modes. This function is obtained from the whole Wigner function by integration of the degrees of freedom of the short-wavelength modes. The dynamical equation for the reduced Wigner function becomes a kind of Fokker-Planck equation which is solved with suitable boundary conditions enforcing an initial metastable vacuum state trapped in the potential well. As a result a finite activation rate is found, even at zero temperature, for the formation of true vacuum bubbles of size M-1. This effect makes a substantial contribution to the total decay rate.

Induced quantum metric fluctuations and the validity of semiclassical gravity

We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.