Showing papers on "Mean free path published in 1998"
TL;DR: In this paper, a model of the thermal conductivity and phonon transport in the direction perpendicular to the film plane of superlattices is established based on solving the phonon Boltzmann transport equation (BTE).
Abstract: Significant reductions in both the in-plane and cross-plane thermal conductivities of superlattices, in comparison to the values calculated from the Fourier heat conduction theory using bulk material properties, have been observed experimentally in recent years. Understanding the mechanisms controlling the thermal conductivities of superlattice structures is of considerable current interest for microelectronic and thermoelectric applications. In this work, models of the thermal conductivity and phonon transport in the direction perpendicular to the film plane of superlattices are established based on solving the phonon Boltzmann transport equation (BTE). Different phonon interface scattering mechanisms are considered, including elastic vs inelastic, and diffuse vs specular scattering of phonons. Numerical solution of the BTE yields the effective temperature distribution, thermal conductivity, and thermal boundary resistance (TBR) of the superlattices. The modeling results show that the effective thermal conductivity of superlattices in the perpendicular direction is generally controlled by phonon transport within each layer and the TBR between different layers. The TBR is no longer an intrinsic property of the interface, but depends on the layer thickness as well as the phonon mean free path. In the thin layer limit, phonon transport within each layer is ballistic, and the TBR dominates the effective thermal conductivity of superlattices. Approximate analytical solutions of the BTE are obtained for this thin-film limit. The modeling results based on partially specular and partially diffuse interface scattering processes are in reasonable agreement with recent experimental data on GaAs/AlAs and Si/Ge superlattices. From the modeling, it is concluded that the cross-plane thermal conductivity of these superlattices is controlled by diffuse and inelastic scattering processes at interfaces. Results of this work suggest that it is possible to make superlattice structures with thermal conductivity totally different from those of their constituting materials.
1,032 citations
TL;DR: In this paper, the optical properties of nanosized silver particles self-assembled in a 2D or 3D network were investigated. But the optical property of the self-assembly was not investigated.
Abstract: In this paper we compare the optical properties of nanosized silver particles dispersed in hexane solution and self-assembled in a 2D or 3D network. When the particles form monolayers organized in a hexagonal network, the plasmon peak of silver nanosized particles is shifted toward lower energy, with an increase in bandwidth compared to that observed with free coated particles dispersed in hexane solution. Such a shift is attributed to an increase in the dielectric constant of the matrix environment of the nanoparticles. When the particles form a 3D superlattice with a face-centered cubic (fcc) structure, the optical properties could be interpreted as an increase in the mean free path of the conduction electrons, which could indicate the presence of tunneling electrons across the double layers due to the coating of the particles.
373 citations
Abstract: The diffusive shock acceleration process can accelerate particles to a maximum energy depending on the shock speed and age and on any competing loss processes on the particles The shock waves of young supernova remnants can easily accelerate electrons to energies in excess of 1 TeV, where they can produce X-rays by the synchrotron process I describe a detailed calculation of the morphology and spectrum of synchrotron X-rays from supernova remnants Remnants are assumed to be spherical and in the Sedov evolutionary phase, though the results are insensitive to the detailed dynamics The upstream magnetic field is assumed uniform; downstream it is assumed to be compressed but not additionally turbulently amplified In all cases, spectra begin to depart from power laws somewhere in the optical to UV range and roll off smoothly through the X-ray band I show that simple approximations for the electron emissivity are not adequate; a full convolution of the individual electron synchrotron emissivity with a calculated electron distribution at each point in the remnant is required Models limited by the finite shock age, by synchrotron or inverse Compton losses on electrons, or by escape of electrons above some energy have characteristically different spectral shapes, but within each class, models resemble one another strongly and can be related by simple scalings The images and spectra depend primarily on the remnant age, the upstream magnetic field strength, and the level of magnetic turbulence near the shock in which the electrons scatter In addition, images depend on the viewing or aspect angle between the upstream magnetic field and the line of sight The diffusion coefficient is assumed to be proportional to particle energy (or mean free path proportional to gyroradius), but I investigate the possibility that the proportionality constant becomes much larger above some energy, corresponding to an absence of long-wavelength MHD waves Models producing similar spectra may differ significantly in morphology, which allows for possible discriminations I parameterize the model spectra in terms of a slope at 4 keV and a factor by which the X-ray flux density at that energy falls below the extrapolated radio spectrum Synchrotron radiation may contribute significantly to the X-ray emission of remnants up to several thousand years old
291 citations
TL;DR: In this article, a transport-backtransport (TBT) algorithm is proposed to reconstruct and distinguish between scattering and absorbing objects in the case of large mean free path (which corresponds to x-ray tomography with scattering).
Abstract: Optical tomography is modelled by the inverse problem of the time-dependent linear transport equation in n spatial dimensions (n = 2,3). Based on the measurements which consist of some functionals of the outgoing density at the boundary for different sources , , two coefficients of the equation, the absorption coefficient and the scattering coefficient b(x), are reconstructed simultaneously inside . Starting out from some initial guess for these coefficients, the transport-backtransport (TBT) algorithm calculates the difference between the computed and the physically given measurements for a fixed source by solving a `direct' transport problem, and then transports these residuals back into the medium by solving a corresponding adjoint transport problem. The correction to the guess is calculated from the densities of the direct and the adjoint problem inside the medium. Doing this for all source positions , , one after the other yields one sweep of the algorithm. Numerical experiments are presented for the case when n = 2. They show that the TBT-method is able to reconstruct and to distinguish between scattering and absorbing objects in the case of large mean free path (which corresponds to x-ray tomography with scattering). In the case of very small mean free path (which corresponds to optical tomography), scattering and absorbing objects are located during the early sweeps, but phantoms are built up in the reconstructed scattering coefficient at positions where an absorber is situated and vice versa.
197 citations
TL;DR: In this article, the suppression of thermal conduction by a static stochastic magnetic field is calculated for different ratios of the field scale length to the collisional mean free path, and the effects of magnetic trapping are determined through a two-scale analysis and Monte Carlo particle simulations.
Abstract: The suppression of thermal conduction by a static stochastic magnetic field is calculated for different ratios of the field scale length to the collisional mean free path. The effects of magnetic trapping are determined through a two-scale analysis and Monte Carlo particle simulations. In galaxy-cluster cooling flows, thermal conductivity is reduced from the Spitzer value by a factor of order ${10}^{2}$ to ${10}^{3}$.
184 citations
TL;DR: In this paper, a quasi-linear transport and acceleration model for cosmic ray particles interacting resonantly with undamped fast-mode waves propagating in a low-β plasma is presented.
Abstract: We calculate quasi-linear transport and acceleration parameters for cosmic ray particles interacting resonantly with undamped fast-mode waves propagating in a low-β plasma. For super-Alfvenic particles and a vanishing cross-helicity state of the fast-mode waves, we demonstrate that the rate of adiabatic deceleration vanishes, and that the momentum and spatial diffusion coefficients can be calculated from the Fokker-Planck coefficient Dμμ. Adopting isotropic fast-mode turbulence with a Kolmogorov-like turbulence spectrum, we demonstrate that Dμμ is the sum of contributions from transit-time damping and gyroresonant interactions. Gyroresonance refers to | n | ≠ 0 resonant particle-wave interactions. Transit-time damping refers to the n = 0 interaction of particles with the compressive magnetic field component of the fast-mode waves. We show that transit-time damping provides the dominant contribution to pitch-angle scattering in the interval ≤ | μ | ≤ 1, where is the ratio of Alfven to particle speed. In the interval | μ | < , transit-time damping does not occur, and gyroresonance provides a small but finite contribution to particle scattering. As a consequence, the momentum diffusion coefficient is mainly determined by the transit-time damping contribution. On the other hand, since the spatial diffusion coefficient and the related mean free path are given by the average over μ of the inverse of Dμμ, these spatial transport parameters are determined by the contribution from the interval | μ | < . We also calculate the cosmic ray transport parameters for plasma turbulence consisting of a mixture of isotropic fast-mode waves and slab Alfven waves. Here, the momentum diffusion coefficient is determined by the transit-time damping of the fast-mode waves, and is a factor ln -1 larger than in the case of pure slab Alfven wave turbulence. The mean free path and the spatial diffusion coefficient are modified significantly from the pure fast-mode case, since the crucial scattering at | μ | < is now provided by gyroresonances with slab Alfven waves. The mean free path is a constant at nonrelativistic energies, and may account for the legendary λfit-λQLT discrepancy of solar energetic particles.
162 citations
TL;DR: In this article, the mean free path parallel to the background magnetic field is calculated from quasi-linear theory for a composite slab/two-dimensional geometry model of turbulence, where diffusion perpendicular to the field is assumed to be anisotropic and proportional to parallel diffusion.
Abstract: We present analytical expressions for the mean free path parallel to the background magnetic field, calculated from quasi-linear theory for a composite slab/two-dimensional geometry model of turbulence. Diffusion perpendicular to the field is assumed to be anisotropic and proportional to parallel diffusion. For the variation in the magnetic field and the correlation length throughout the heliosphere, recent results of Zank et al. are used. We emphasize the role of the power spectrum of magnetic field fluctuations in determining the rigidity dependence of the parallel diffusion coefficient, and show that this rigidity dependence is unlikely to remain constant throughout the heliosphere. While we concentrate on Galactic protons at medium to high rigidities, we briefly discuss electron parallel mean free paths at low rigidities. Drifts are also included in the numerical modulation model, the results of which are compared with Ulysses, IMP 8, and Pioneer 10 measurements. Good agreement is found for energy spectra and latitudinal gradients in the inner heliosphere, but not for radial gradients farther away from the Sun in the ecliptic plane. We suggest that the combination of a turbulence, a scattering, and a modulation model presents a formalism that should prove useful for further studies.
72 citations
TL;DR: In this article, a model that describes grain-boundary-limited conduction in polycrystalline semiconductors, for thermally assisted ballistic as well as diffusive transport, both for degenerate and nondegenerate doping, is presented.
Abstract: We present a model that describes grain-boundary-limited conduction in polycrystalline semiconductors, for thermally assisted ballistic as well as diffusive transport, both for degenerate and nondegenerate doping. In addition to bulk parameters (the carrier effective mass and mean free path) the model contains grain boundary parameters (barrier height and width) and a coefficient of current nonuniformity. Temperature-dependent conductivity and Hall measurements on polycrystalline SnO2 thin films with different Sb concentrations are consistently interpreted.
71 citations
TL;DR: In this article, the authors investigated the pressure dependence of the deposition rate for magnetron sputter deposition of various elemental semiconductors and metals and found that the dependence of rate Φ on pressure-distance (pd) is well described by Φ = Φ 0(1−e−cpd)/cpd.
Abstract: The pressure dependence of the deposition rate for magnetron sputter deposition of various elemental semiconductors and metals was investigated by x-ray measurements on sputtered films and quartz monitor measurements. It was found that for all elements investigated the dependence of the rate Φ on pressure-distance (pd) is well described by Φ=Φ0(1−e−cpd)/cpd. The value of c equals the inverse characteristic pressure-distance product (pd)0, which is the characteristics of the exponential decay of rate with pressure for low pressures. The experimental data of (pd)0 vary from 4.6 Pa cm for aluminum to 120 Pa cm for tungsten. It is shown that (pd)0 depend on both material specific properties and process parameters. The material specific properties are mainly the atomic mass and diameter, and the surface binding energy. The process parameters target voltage and power density act via the increase of the mean free path and the reduction of gas density, respectively, on (pd)0. As a first approximation, the characteristic pressure-distance product for argon as sputtering gas is proportional to the product of target atomic mass, average atomic energy and thermal mean free path.
53 citations
TL;DR: In this paper, a model of the ionization layer which separates a thermal plasma close to full ionization from the space-charge sheath adjacent to the surface of an electrode or of an insulating wall is developed.
Abstract: A model is developed of the ionization layer which separates a thermal plasma close to full ionization from the space-charge sheath adjacent to the surface of an electrode or of an insulating wall. The multifluid description of the plasma is used. Asymptotic solutions are obtained for the cases in which the thickness of the ionization layer is much larger or much smaller than the mean free path for ion-atom collisions. The solution obtained for the latter case describes an interesting new regime which is in some aspects similar to the conventional diffusion regime, though essentially different from the diffusion regime in other aspects. Formulas are derived for the ion flux coming from the ionization layer to the edge of the space-charge sheath. Application of results to atmospheric-pressure argon and mercury plasmas is considered. @S1063-651X~98!08702-9#
51 citations
TL;DR: In this paper, the role of experimental geometry is systematically checked for elements with a wide range of atomic numbers: Si, Cu, Ag, and Au, and the observed effects are discussed in terms of the validity of the theoretical model and possible instrumental problems.
TL;DR: Among other things, use of added filtration reduces the intensity of the x-ray beam, increases the HVL, decreases patient exposure, and improves image quality for a given radiation dose.
Abstract: Attenuation is the reduction of the intensity of an x-ray beam as it traverses matter. The reduction may be caused by absorption or by deflection (scatter) of photons from the beam and can be affected by different factors such as beam energy and atomic number of the absorber. An attenuation coefficient is a measure of the quantity of radiation attenuation by a given thickness of absorber. Linear and mass attenuation coefficients are the coefficients used most often. The equation I = Ioe-mu x expresses the exponential relationship between incident primary photons and transmitted photons for a monoenergetic beam with respect to the thickness of the absorber and thus may be used to calculate the attenuation by any thickness of material. The quality or penetrating ability of an x-ray beam is usually described by stating its half-value layer (HVL). Another parameter used to describe the penetrating ability of a beam is the homogeneity coefficient. Among other things, use of added filtration reduces the intensi...
TL;DR: In this paper, shot-noise suppression in non-degenerate diffusive conductors is investigated by means of an ensemble Monte Carlo simulator. And the universal 1/3 suppression value is obtained when transport occurs under elastic collision regime provided the following conditions are satisfied: (i) the applied voltage is much larger than the thermal value; (ii) the length of the device is much greater than both the elastic mean free path and the Debye length.
Abstract: Shot-noise suppression is investigated in nondegenerate diffusive conductors by means of an ensemble Monte Carlo simulator. The universal 1/3 suppression value is obtained when transport occurs under elastic collision regime provided the following conditions are satisfied: (i) The applied voltage is much larger than the thermal value; (ii) the length of the device is much greater than both the elastic mean free path and the Debye length. By fully suppressing carrier-number fluctuations, long-range Coulomb interaction is essential to obtain the 1/3 value in the low-frequency limit.
TL;DR: In this paper, a linear chain of point masses coupled by harmonic springs is used to illustrate the mechanism of heat propagation in insulating crystals, where ballistic propagation is replaced by diffusive propagation on length scales larger than the mean free path for ballistic motion.
Abstract: A linear chain of point masses coupled by harmonic springs is a standard model used to introduce concepts of solid state physics. The well-ordered chain has sinusoidal standing wave normal modes (if the ends are fixed) or traveling wave normal modes (if the ends are connected in a ring). Ballistically propagating wave packets can be built from these normal modes, and illustrate the mechanism of heat propagation in insulating crystals. When the chain is disordered, new effects arise. Ballistic propagation is replaced by diffusive propagation on length scales larger than the mean free path for ballistic motion. However, a new length scale, the localization length, also enters. On length scales longer than the localization length, neither ballistic nor diffusive propagation occurs, and energy is trapped unless there are anharmonic forces. These ideas are illustrated by a computer experiment.
TL;DR: In this paper, the corrections to the conductivity and compressibility of disordered metal when the mean free path is smaller than the screening length were calculated for low densities and large disorder.
Abstract: We calculate the corrections to the conductivity and compressibility of a disordered metal when the mean free path is smaller than the screening length. Such a condition is shown to be realized for low densities and large disorder. Analysis of the stability of the metallic state reveals a transition to the insulating state in two dimensions.
TL;DR: In this article, the authors define a new parameter to describe the effects of elastic electron scattering in XPS and AES, which is the ratio of emitted intensity from a layer of atoms located at a given depth in a solid calculated from theories that take into account and neglect elastic electron scatterings.
Abstract: We define a new parameter to describe the effects of elastic electron scattering in XPS and AES. The parameter is the ratio of emitted intensity from a layer of atoms located at a given depth in a solid calculated from theories that take into account and neglect elastic electron scattering. We have found that the correction parameter can be expressed by a simple formula. This formula is of general validity for typical experimental geometries applied in practical XPS and AES. The formula was determined by fitting an analytical expression to the results of extensive Monte Carlo calculations made under variation in the full relevant range of electron energy, matrix atomic number, depth of origin of emitted electrons and angular emission anisotropy. The formula depends on the inelastic (λi) and the transport (λtr) mean free path for electron scattering. Three assumptions were made in the calculations, namely that the geometry is close to normal emission, that the angle between x-ray source and analyser axis is close to the magic angle (54°) and that the ratio λtr/λi is approximately constant over the analysed depth. However, the result is expected to vary only slightly when these assumptions are not strictly fulfilled. © 1998 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors have grown thin stable films of a good metal, Ag, that have characteristics of bad metals: high resistivity, strong temperature dependence of resistivity and lack of resistive saturation.
Abstract: We have grown thin stable films of a good metal, Ag, that have characteristics of bad metals: high resistivity, strong temperature dependence of resistivity, and lack of resistive saturation. For films of different thickness, the temperature-dependent resistance and the Hall effect resistance provide evidence that the apparent bad metallicity is a consequence of the microstructure of the film rather than the result of new physics. This microstructure, which we characterize with scanning probe techniques, occurs on length scales comparable to the mean free path, thereby changing the sign of the classical magnetoresistance from positive to negative.
TL;DR: In this paper, a hard sphere Percus-Yevick static structure factor was incorporated into the prediction of transport mean free path in highly concentrated (up to volume fraction ϕ∼0.55) dispersions measured by 100-fs laser pulses.
Abstract: The intensity temporal profiles of diffusive light propagation in highly concentrated (up to volume fraction ϕ∼0.55) dispersions measured by 100-fs laser pulses showed an increase in transport scattering mean free path above a critical concentration. This observation confirms the previous theoretical predictions of enhanced transmission at high particle concentrations due to correlated scattering. The correlation effects are accounted for by incorporating a hard sphere Percus–Yevick static structure factor into the prediction of transport mean free path.
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27 Apr 1998
TL;DR: The mean free path of a particle before undergoing a non-elastic interaction in a given medium is defined in this article, where the relevant cross-section is σ tot − σel- → also Collision Length.
Abstract: The mean free path (→) of a particle before undergoing a non-elastic interaction in a given medium. The relevant cross-section is σ tot — σel- → also Collision Length.
TL;DR: The Ioffe-Regel criterion predicts the existence of a metal-insulator transition in a film series when the parameter satisfies the criterion as mentioned in this paper ; here is the Fermi wavenumber and is the elastic mean free path of the carriers
Abstract: The Ioffe-Regel criterion predicts the existence of a metal-insulator transition in a film series when the parameter satisfies the criterion ; here is the Fermi wavenumber and is the elastic mean free path of the carriers According to this criterion, films having are metallic, while films having are insulating We experimentally observe the metal-insulator transition in amorphous indium oxide films at The values of were calculated from room temperature resistivity and Hall voltage measurements, while the metal-insulator transition was determined from low-temperature resistivity data using the `w'-criterion of Mobius and of Zabrodskii and Zinov'eva
TL;DR: In this article, a complex study of the electron-phonon interaction in thin NbC films with electron mean free path $l=2-13\mathrm{nm} gives strong evidence that electron scattering is significantly modified due to the interference between electronphonons and elastic electron scattering from impurities.
Abstract: A complex study of the electron-phonon interaction in thin NbC films with electron mean free path $l=2--13\mathrm{nm}$ gives strong evidence that electron scattering is significantly modified due to the interference between electron-phonon and elastic electron scattering from impurities. The interference ${T}^{2}$ term, which is proportional to the residual resistivity, dominates over the Bloch-Gr\"uneisen contribution to resistivity at low temperatures up to 60 K. The electron energy relaxation rate is directly measured via the relaxation of hot electrons heated by modulated electromagnetic radiation. In the temperature range 1.5--10 K the relaxation rate shows a weak dependence on the electron mean free path and strong temperature dependence $\ensuremath{\sim}{T}^{n},$ with the exponent $n=2.5--3.$ This behavior is explained well by the theory of the electron-phonon-impurity interference taking into account the electron coupling with transverse phonons determined from the resistivity data.
TL;DR: In this article, the electrical resistivity of the α 2 and γ phases has been modeled by fitting the data using the Bloch-Gruneisen formulation with certain simplifying assumptions.
TL;DR: In this paper, the size dependence of the band structure and the resulting effects on the optical constants are discussed for the model system of sputtered small gold particles embedded in an amorphous carbon matrix produced simultaneously by hydrogenated, plasma activated, chemical vapour deposition.
TL;DR: In this article, the authors presented an ab initio calculation of the fluence rate that is due to an isotropic point source in an infinite, anisotropic scattering medium.
Abstract: Starting from light transport theory, we present an ab initio calculation of the fluence rate that is due to an isotropic point source in an infinite, anisotropically scattering medium. To verify the results experimentally, a latex suspension with uniform particle size, corresponding to g=0.734, was prepared. In the suspension an isotropic light source and an isotropic light detector were placed, and the fluence rate as a function of distance was measured. We observed good agreement in absolute values between the calculated and the observed fluence rate over distances ranging from 1/4 to ∼8× the total mean free path, which corresponds to a fluence rate varying over some five orders of magnitude. Furthermore, the calculated fluence was obtained from measured values of μs and μa and a calculated phase function without any kind of fitting, and thus the calculation was completely independent from the measurement. This is the first time that the fluence was measured quantitatively with an isotropic probe and found to agree within experimental error with transport theory. The experimental results indicate that, far from the source, the behavior is diffusionlike, even for low albedos, albeit with a corrected effective extinction coefficient.
TL;DR: In this article, the results on (Bi 0.25 Sb 0.75 ) 2 Te 3 alloy films agree with the prediction of size effect theories, and the effective mean free path model with perfect diffuse scattering is used for the analysis of the data.
TL;DR: In this paper, measurements of the dc conductivity of epitaxial Ag films on a clean Si(111) $7\ifmmode\times\else\texttimes\fi{}7$ substrate at about 100 K reveal that the conductance for a thickness down to nearly a monolayer is well described by a simple Drude model with a mean free path given by the film thickness.
Abstract: Epitaxial metallic monolayers are models for two-dimensional conduction. They provide well-ordered monatomic films with an atom distance as in the bulk. Measurements of the dc conductivity of epitaxial Ag films on a clean Si(111) $7\ifmmode\times\else\texttimes\fi{}7$ substrate at about 100 K reveal that the conductance for a thickness down to nearly a monolayer is well described by a simple Drude model with a mean free path given by the film thickness. For lower temperatures (down to nearly 4 K) the conductance of very thin films is reversibly decreased by orders of magnitude. Whereas annealing increases the mean free path for thick films up to twice the thickness, the films with a thickness of less than 2 monolayers show no annealing effect. The results may be discussed with models of amorphous or granular films. The lack of agreement with theoretically predicted temperature dependences may be due to the special structure of epitaxial films.
TL;DR: In this article, the electron transport in semiconductors when electron-phonon interaction is considered is considered and the corresponding limits in the transport problem are carried out and shown not to commute.
Abstract: This paper deals with electron transport in semiconductors when electron–phonon interaction is considered. Smallness of the mean free path compared to a characteristic length scale and of the phonon energy compared to the thermal energy of the crystal are assumed. The corresponding limits in the transport problem are carried out and shown not to commute. An intermediate limit leads to a new macroscopic model.
TL;DR: In this paper, the magnetic response of normal-metal superconductor proximity systems for arbitrary concentrations of impurities and at arbitrary temperatures is investigated using the quasiclassical theory of superconductivity.
Abstract: We investigate the magnetic response of normal-metal‐superconductor proximity systems for arbitrary concentrations of impurities and at arbitrary temperatures. Using the quasiclassical theory of superconductivity a general linear-response formula is derived which yields a nonlocal current-field relation in terms of the zero-field Green’s functions. Various regimes between clean-limit and dirty-limit response are investigated by analytical methods and by solving the general formula numerically. In the ballistic regime, a finite mean free path reduces the nonlocality and leads to a stronger screening than in the clean limit even for a mean free path much larger than the system size. Additionally, the range of the kernel describing the nonlocality is strongly temperature dependent in this case. In the diffusive limit we find a crossover from local to nonlocal screening, which restricts the applicability of the dirty-limit theory. @S0163-1829~98!00445-7#
TL;DR: In this paper, the anomalous proximity effect between a d-wave superconductor and a surface layer with small electronic mean free path is studied theoretically in the framework of the Eilenberger equations.
Abstract: The anomalous proximity effect between a d-wave superconductor and a surface layer with small electronic mean free path is studied theoretically in the framework of the Eilenberger equations. The angular and spatial structure of the pair potential and the quasiclassical propagators in the interface region is calculated selfconsistently. The variation of the spatially-resolved quasiparticle density of states from the bulk to the surface is studied. It is shown that the isotropic gapless superconducting state is induced in the disordered layer.