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We propose that the transient vacuum fluctuations of quantum fields can be represented by transient vacuum quanta where both the lifetime and spatial extent are given by the Heisenberg Uncertainty Principle, HUP. Accordingly, a quantum field fluctuation at any spatial site results in the creation of a transient HUP-limited vacuum pair, corresponding to the particle and the antiparticle associated with that quantum field. All HUP-limited vacuum pairs, both massive and massless, are found to be on-shell particles, and are indistinguishable from each other except for differences related to their exchange symmetry. We find that the net vacuum energy density of all HUP-limited vacuum pairs is identically zero at any energy where both bosonic and fermionic transient vacuum pairs are present. The net vacuum energy density, from zero energy to the Planck limit, is found to be proportional to that of the rest mass of the lightest fermion, the lowest mass neutrino eigenstate. This net energy density is equal to the observed dark energy density if the mass of the lightest neutrino eigenstate is 3.2[Formula: see text]meV. The model predicts the absolute values of the masses of the three neutrino mass eigenstates and of the three neutrino flavor eigenstates for both normal and inverted ordering. The sum of the neutrino masses is found to be below the Planck satellite upper limit of 120[Formula: see text]meV, and the neutrino mass sum for normal ordering is below the most stringent upper bound of 78[Formula: see text]meV, indicating a preference for normal ordering.

A quantitative analysis based on a new three-dimensional nonlinear theoretical model of the experimental fundamental nonlinear photothermal response from multilayer structures containing a tungsten layer is presented. Two sets of wafers, one with a very rough tungsten overlayer surface and another with a smooth polished tungsten surface have been studied. It is shown that the rough tungsten surface gives rise to a very strong nonlinear behavior of the thermal-wave field.

A general three-dimensional theoretical model for fundamental and harmonic response generation as a result of periodic heating of a system consisting of a nonlinear layer with temperature-dependent thermal conductivity and specific heat and a linear substrate is developed. Analysis of the fundamental component of the surface temperature shows that the nonlinear thermal conductivity alone does not affect the phase of the thermal-wave field. The efficiency of the thin nonlinear layer as an energy conversion filter that drives the harmonic response of the substrate is shown by the analysis of the limiting cases of the theoretical model.

Beam‐profile reflectometry is a new technique for measuring the thickness and optical constants of dielectric, semiconducting, and thin metal films. The technique consists of measuring the intensity profile of a highly focused beam reflected from the sample. By using a linearly polarized light source and a tightly focussed beam, the S‐ and P‐polarization reflectivities of the film are simultaneously obtained over a wide range of angles. The focusing also provides a submicrometer spot, thus allowing these measurements to be performed in very small geometries. How the information present in the reflectivity profiles can reveal information about as many as three unknown film parameters simultaneously is described, and results from film samples for which the multiparameter fitting capability was essential to the success of the measurement are also presented.

Small repetitively pulsed lasers can be used with a photoacoustic detection method to obtain linear absorption measurements on optical thin films with a 5 x 10(-5) sensitivity using an acoustic-coupling procedure and with a 1 x 10(-5) sensitivity using a liquid-transducer procedure.

A method for automatic real-time damage monitoring on optical components with dielectric coatings, using piezoelectric photoacoustic detection, is developed.(AIP)

Low-intensity laser illumination has been found to induce recrystallization of amorphous layers in ion-implanted silicon wafers. With the conditions used here, the temperature rise is much lower than that usually required for annealing of amorphous silicon. Therefore, this is an observation of recombination-induced nonthermal recrystallization of amorphous silicon layers.

We describe a new technique for measuring the thickness and optical constants of dielectric, semiconducting, and thin metal films. Beam profile reflectometry provides excellent precision for films as thin as 30 A and as thick as 20 000 A. The technique is also capable of simultaneous 2 and 3 parameter measurements and it performs all measurements with a submicron spot size.

A general three-dimensional theoretical model is developed for the fundamental and harmonic photothermal response generation as a result of periodic heating of a system consisting of a nonlinear layer with temperature-dependent thermal conductivity and specific heat and a linear substrate. The efficiency of the thin nonlinear layer as an energy conversion filter that drives the harmonic response of the substrate is shown by the analysis of the limiting cases of the theoretical model.

A quantitative analysis of the experimental fundamental nonlinear photothermal responses from multilayer structures containing a tungsten layer is presented. Two sets of wafers, one with a very rough tungsten overlayer surface and another with a smooth polished tungsten surface have been studied. It is shown that the rough tungsten surface causes a very strong nonlinear behavior of the thermal-wave field. The effective nonlinear thermal conductivity k(T) dependence for the rough tungsten films has been found to decrease with increasing thickness of the layer.

We have developed a novel technique for performing simple phase-sensitive optical measurements in a sub-micrometer area. We presently use this technique to measure film stacks commonly found in the semiconductor industry. This article explains the theory behind this technique and presents several examples demonstrating the capabilities of the system.

Measurements of ultra-thin films (

Using a thermal wave imaging system we have been able to detect and identify a variety of microscopic defects commonly found in fine metal Al connector lines used in the IC industry. The defects of interest are hillocks, surface and subsurface Si and Cu precipitates and subsurface voids and notches. Defects as small as 0.1 μm have been detected. This thermal wave imaging system has also been used to detect subsurface defects in Al and W metal contact plugs.

In today’s semiconductor market, manufacturers face a daunting challenge. Product concepts evolve rapidly in response to rapidly changing markets while design rules, i.e., device geometries, become increasingly smaller and wafers become larger. Devices must run faster, reliability must improve and the resultant increasing complexity in IC design and fabrication technology intensifies the need for tighter controls of process variables. To compete effectively in this market, manufacturers must improve both product development and product manufacturing processes.

The IC industry has improved process yield and device reliability considerably over the last few years. Much of the improvement is the result of continuing reduction in the defect density on IC wafers, a result made possible in part through the use of suitable defect detection and wafer inspection systems. These systems, however, are useful only for surface or visible defects.

Thermal features on and beneath the surface of a sample can be detected and imaged with a thermal-wave microscope. Various methodologies for the excitation and detection of thermal waves are discussed, and several applications, primarily in microelectronics, are presented.

The exact form of the Rosencwaig‐Gersho theory for the photoacoustic effect in solids is used to depict how the magnitude and phase of the photoacoustic signal vary with chopping frequency and normalized length. Applications of the theory to studies of film‐substrate systems are discussed.

There are a great many substances, both organic and inorganic, that, because of their physical state, cannot be readily studied by conventional absorption or reflection techniques. In photoacoustic spectroscopy, light absorbed by the sample is converted into a measurable acoustic signal, and spectra closely corresponding to optical absorption spectra, can be obtained on any type of solid or semisolid material, whether it be crystalline, powder, smear, gel, etc. The physical processes underlying the photoacoustic effect in solids, and a mathematical analysis of the production of the photoacoustic signal will be presented. The methodology of photoacoustic spectroscopy will also be described. Various applications of this technique in the fields of physics, chemistry, biology, and medicine will be discussed. These applications will be treated under three main headings: bulk studies, surface studies, and de‐excitation studies.

Thermal wave physics is playing an ever increasing role in the on-line characterization of semiconductor materials and devices. This is especially true for thermal wave methods that employ laser beams for both the generation and detection of thermal waves. For the modulated reflectance method discussed here, the pump and probe beams are focused on the same spot. They therefore achieve the noncontact advantage of optical methods in addition to the optimum condition for high spatial resolution, a necessary condition for thermal wave measurements on product wafers.When a material is excited with an intensity-modulated laser beam or pump, a thermal wave is generated in the material and in the air above the sample. The material within this heated region will undergo a thermal expansion which can be detected with a probe beam interferometer or by deflecting the probe beam from the thermoelastic deformation of the surface. Since the complex refractive index of most materials depends on temperature, a modulated temperature will also induce a corresponding modulation in the refractive index and consequently a modulation on a probe beam passing anywhere near the thermal wave. A probe beam directed along the heated surface of the sample, for example, will be deflected as it passes through the heated region above the surface. This mirage effect can also be observed within the sample by directing a transmitting probe through the heated region beneath the surface. Likewise, using a probe beam directed onto the sample surface one can observe a modulation in reflection, transmission, or scattering. A related noncontact method is the photothermal measurement of infrared radiation emitted from the material's heated region. Note that with all these detection methods, thermal wave measurements can be, and most often are, done in air and at room temperature.

We report on the results of a study of the temporal behavior of the laser‐induced modulated optical reflectance from the surfaces of crystalline silicon wafers, epitaxial silicon films, and ion implanted but unannealed silicon wafers. The observed temporal behavior of this signal appears to be associated with the presence and temporal evolution of electronic surface states.

We have developed a one‐dimensional model for thermal‐wave depth profiling that provides expressions for the temperature at the surface of the sample and for the thermoelastic response beneath the surface. The model shows that elastic wave interference effects produce significant differences between samples with mechanically free and constrained surfaces, and that thermal‐ wave images of thermal conductivity variations are obtainable from the thermoelastic signal only if the front surface is mechanically free. We have also considered the case of subsurface heating and found that for heating occurring at depths of more than a few thermal diffusion lengths, the thermoelastic signal becomes independent of thermal conductivity variations. This has important implications for thermal‐wave image range and resolution.

We have investigated the use of photoacoustic techniques for obtaining absolute values of fluorescence quantum efficiencies in lightly doped Nd/sup 3 +/ laser materials. We have found that surface absorptions play an important role in gas-microphone measurements, and that thermal profiles are important in piezoelectric measurements. We have obtained fluorescence quantum efficiencies for Nd/sup 3 +/ in yttrium aluminum garnet, and in silicate and borate glasses that are in good agreement with lifetime measurements and Judd-Ofelt calculations.

We have developed two photoacoustic methods to perform low absorption measurements on optical components. One method can make measurements in the 10−4–10−5 absorption range, while the other can be used down to the 10−6 range.

Thermal wave technology has led to a new means of monitoring the dose and dose uniformity of ions implanted into wafers of silicon and gallium arsenide. New monitoring characteristics made available with this technique include nondestructive real-time dose measurements on product wafers as well as test wafers without annealing or other processing, dose measurements down to the 1E10 ions/cm 2 decade and up to 1E16 ions/cm 2 , dose measurements down to 5 keV ion energy and measurement through oxide or nitride overlayers. Furthermore, postanneal measurements of dose are also available in the high-dose range of 5E14-1E16 ions/cm 2 . In this paper we present examples to illustrate these capabilities.

Technique nouvelle de deflexion d'un faisceau laser induite par une onde thermique permettant de mesurer des epaisseurs de couches opaques ou transparentes de 500 a 25000 A. Application a la mesure des epaisseurs de couches minces de Al ou SiO 2 deposes sur du silicium

Thermal-wave microscopy (TWM), which employs heat flow to probe variations in the thermal properties of solid materials, can provide micron-level resolutions of subsurface features of opaque samples, this paper describes the principle of TWM, reviews its applications in material science, and presents the results of studies using this technique to imaging the microstructure and corrosion of cold-rolled steels. Preliminary results indicate that TWM can image the microstructure of cold-rolled steel with or without a corrosion layer. The results obtained also suggest that the technique can monitor and assess corrosion in its early stage of formation.

The 500–800 nm spectra of replicata phytoplankton cultures freeze-dried upon glass fiber filters were determined both by photoacoustic spectroscopy (PAS) and by photoelectric absorption spectrophotometry. A number of the features of biological interest are better resolved in the PAS spectra. Further, PAS is sufficiently sensitive that it could be applied in the analysis of readily obtainable field samples.

The scanning photoacoustic microscope (SPAM) is used in both the conventional and phase‐contrast modes to detect a well‐characterized subsurface flaw in Al. The physical mechanism is that of thermal diffusion, with a subsurface probe depth and flaw resolution length of approximately one thermal‐diffusion length. Comparison of the dependences of the photoacoustic signal upon chopping frequency from the different regions of the sample confirm that the differential signal from the flaw corresponds to a transition from thermally thick to thermally thin boundary conditions. Experimental results are in good agreement with calculations based upon a three‐dimensional thermal‐diffusion model.

A new method, based on thermal wave technology, is used to monitor the ion implantation process in silicon. It is a noncontact, nondestructive technique that requires no special sample preparation or processing, has high sensitivity even at low dose, and provides a one‐micron spatial resolution capability. This method allows, for the first time, the ability to monitor the critical ion implantation process directly on the patterned product integrated circuit wafers as well as on the usual test wafers.

A method and apparatus for thin film thickness measurements with thermal waves in which heating and detection laser beams are focused onto the film, normal to the surface of the film, with the two beams parallel and non-coaxial.

We have developed a photoacoustic method that is capable of detecting the occurrence of laser damage in optical thin films and of providing new data about energy transfer processes in the presence of damage.

Experiments on photoacoustic thermal‐wave microscopy are presented, for the first time, at high resolution. Using piezoelectric detection and a modulation frequency of 185 kHz, we obtain a thermal‐wave resolution of ∼7 μm. We show that the photoacoustic phase signal provides true thermal‐wave imaging even in the presence of surface features with strong optical contrast.

We describe a depth‐profiling concept using the critically damped plasma wave corresponding to the propagation of the free‐carrier plasma density generated by a modulated laser in a semiconductor.

Thermal‐wave electron microscopy has been used at 640‐kHz modulation frequency to detect and image P‐doped Si regions in a bare Si wafer.

We show that variations in local optical constants induced by the presence of thermal waves can be used for thermal wave detection and analysis through measurements of thermal wave‐induced modulated transmittance and scattering.

We have performed high‐resolution thermal‐wave microscopy of surface and subsurface features of an opaque solid using, for the first time, electron beams to generate the signal.

We show that thermal wave detection and analysis can be performed, in a noncontact and highly sensitive manner, through the dependence of sample optical reflectance on temperature. Applications to the study of microelectronic materials are illustrated by an example of measuring the thickness of thin metal films.

We describe a highly sensitive, noncontact method for inspecting important, but previously difficult to monitor, processes used in the manufacture of integrated circuits. This technique, based on the detection of thermal waves through laser-induced modulation of the sample's optical reflectance, has proven to be an excellent means for detecting and quantifying the extent of lattice damage or disorder in silicon and gallium arsenide wafers that results from chemopolishing, ion implantation and etching processes. This technique thus provides a powerful and cost effective method for monitoring the quality of incoming wafers, the dose and uniformity of ion implantations and the efficiency and uniformity of dry etch processes. Furthermore this method may be used on actual product wafers as well as test wafers since the measurements are performed in a completely nondamaging fashion and with micronscale resolution.

Thermal wave technology has proved a very effective means for investigating the near surface region of many different materials. We have performed thermal wave imaging experiments at room temperture on sintered, thin-film, and singlecrystal samples of high-T c superconductor materials. These images often exhibit features not visible in an optical image. In addition, we have used the thermal wave technique to measure the local anisotropy in the room-temperature thermal conductivity of single crystals of YBa2Cu3O7− x . Our results indicate that the anisotropy for the thermal conductivity is very similar to that reported for the electrical conductivity.

Conventional spectroscopic studies on opaque membranes are difficult to pursue because of excessive light scattering and complications arising from the specimen's surface. Recently, a new spectroscopic technique, photoacoustic spectroscopy, unlike conventional optical spectroscopy, has been demonstrated to be an informative technique amenable to spectroscopic studies of solids and membrane-like samples. We have applied photoacoustic spectroscopy to the study of hydration and maturation of newborn rat stratum corneum, and have obtained clean spectra in the 220 to 450 nm region indicative of a change in thermal diffusivity with increased hydration, and biochemical changes associated with the initial maturation period.

The measurement of low-level optical absorptions of highly transparent and highly reflective solids is of considerable importance in several fields. In addition, the ability to measure very low-level linear absorptions also permits the study of several weak nonlinear optical phenomena, such as two-photon absorption.

Thermal wave modulated optical reflectance is now the basis for a number of industrial optical inspection functions (1). We recently demonstrated that this method is capable of imaging crystallographic defects, such as dislocations and stacking faults, beneath the polished surface of silicon wafers (2). In this technique two lasers are employed in a pump-probe configuration. The pump beam, from an Ar+ laser, is acousto-optically modulated and focused to a 1-micron spot on the surface of the Si wafer. Absorption of these 2.5 eV photons perturbs the local electron-hole (or plasma) concentration and the temperature, both of which alter the optical reflectance (R) of the Si surface. A second, HeNe laser is employed to phase-synchronously probe the magnitude of the change in reflectance (ΔR), thus yielding the modulated optical reflectance (ΔR/R). Since subsurface damage or defects alter the plasma diffusion through recombination effects, the defects or damage can be detected with modulated optical reflectance measurements. We shall briefly review the metrology accomplishments of this new field of semiconductor optical inspection. We then describe modulated reflectance imaging of Si samples to illustrate detection of subsurface (a) stacking faults, (b) dislocations, (c) stress-induced slip, and (d) post-anneal implant damage.

Conventional optical spectroscopy of solids, semisolids, smears, and gels generally suffers from excessive light-scattering and opacity effects. Recently a new spectroscopic technique, called photoacoustic spectroscopy has been developed which overcomes both of the above problems. This new technique and some of its current applications are briefly described in this paper.