Wafer shape and thickness variation are important parameters in the IC manufacturing process. The thickness variation, also called flatness, enters the depth-of-focus budget of microlithography, and also affects film thickness uniformity in the CMP processing. The shape mainly affects wafer handling, and may also require some depth-of-focus if the wafer shape is not perfectly flattened by chucking. In the progression of technology nodes to smaller feature sizes, and hence smaller depth-of-focus of the lithography tool, the requirement for the PV-flatness over stepper exposure sites is becoming progressively tighter, and has reached 45nm for the next technology node of 45nm half pitch. Consequently, in order to be gauge-capable the flatness metrology tool needs to provide a measurement precision of the order of 1nm. Future technology nodes will require wafers with even better flatness and metrology tools with better measurement precision. For the last several years the common capacitive tools for wafer dimensional metrology have been replaced by interferometric tools with higher sensitivity and resolution. In the interferometric tools the front and back surface figure of the wafer is measured simultaneously while the wafer is held vertically in its intrinsic shape. The thickness variation and shape are then calculated from these single-sided maps. The wafer shape, and hence each wafer surface figure, can be tens of microns, necessitating a huge dynamic range of the interferometer when considering the 1nm measurement precision. Furthermore, wafers are very flexible, and hence very prone to vibrations as well as bending. This presentation addresses these special requirements of interferometric wafer measurements, and discusses the system configuration and measurement performance of WaferSight^TM, KLA-Tencor's interferometric dimensional metrology tool for 300mm wafers for current and future technology nodes.

To cope with advances in the electronic packaging industry, thinner wafers are being widely employed to produce thinner packages. However, this has lead to an increase in random cracks during the wafer singulation process, thus reducing the yield of the overall production. Large stresses are induced particularly during backside metal deposition. The wafers bend due to these stresses. This residual stress due to warpage lead to cracks which will severely re-orient the residual stress distributions, thus, weakening the mechanical and electrical properties of the singulated die. In this study, Computer aided reflection moiré technique is adapted to further investigates the warpage induced on wafers with different backside metallization (bare silicon, AuY, AuX). The backside metal on the wafer is then etched to remove the residual stress. Residual stress due to the effect of warpage caused by different backside metallization has been experimentally investigated and compared. Applicability of this technique to correlate with the random crack in the die is further validated.

This study proposes the auto-focusing procedure and the scan-range determining algorithm for white-light scanning interferometry. During white-light scanning interferometry, the interference fringe must be located and to the best-focus interferogram identified. The vertical-scan range must also be determined prior to the scanning procedure. A series of images, either in-focus or out-of-focus, are collected in a proposed interference-fringe searching step. The contrast and the sharpness indices of each image are calculated and applied in the auto-focusing scheme, and the vertical-scan range is determined accordingly. Some preliminary experiments are performed to demonstrate that the best-focus interferogram can be located precisely and the vertical-scan range can be determined.

We present a systematic investigation of the use of LED as light sources for interference microscopy, in comparison with more standard halogen illumination. For translation height mode (also known as vertical scanning or low coherence microscopy), five white LED-based illuminations setup have been tested, including the use of filters to remove the shoulder in the blue region often encountered in such LED. For the six white light illuminations (five LED plus halogen), we have measured the irradiance spectra and calculated and measured the corresponding correlograms. The influence of the combined effect of the illumination spectra and a dispersive phase shift on the calculated height reconstruction is shown for a center-of-mass algorithm. In phase shift mode, both monochromatic LED and white LED with inteference filters have been used. Blue LED illumination improves the lateral resolution compared to red illumination, a task which can be done with halogen lamp only with very reflecting sample due to its low power in the blue wavelengths. All measurements have been performed with our home-made interference microscope, which is described in Proc. SPIE 6188,61880T (2006).

Current development of replication technologies in plastics offers a variety of low-cost diffraction structures. Diffraction grating functionality depends on the designed technical parameters and fabrication procedures. For these reasons a specific knowledge about modeling, fabrication and achieved technical parameters of diffraction gratings are important and need to be tested. In the paper we propose an optical system for determination of global (angles of diffraction, diffraction efficiency) and local (diffracted wavefront quality (PV, RMS)) parameters of linear diffraction gratings. The system combines the capabilities of precise determination of intensity distribution in all existing orders of transmission and reflection type diffraction gratings with full-field measurement (based on grating shearing interferometry) of waverfronts generated by linear gratings. The functionality of the proposed system architecture was proven through exemplary measurements of gratings replicated in PMMA by hot embossing technology.

A reversed-wavefront Young interferometer has recently been proposed and demonstrated for a direct measurement of optical coherence. It relies on the creation of a reversed-wavefront replica of an electromagnetic beam in such a way that the coherence function of the initial beam can be mapped out by simple translation of a pair of pinholes in a Young's interference experiment. The same interferometer can, in principle, be used for polarization-dependent coherence measurements, but presents significant challenges. In this paper, we will describe the calibration of the interferometer and show measurements of the polarization-dependent coherence function of two optical sources.

The precision metrology of patterned wafer is increasingly demanded by the semiconductor device manufacturers. The most common methods include scanning probe microscopy (SPM) techniques such as stylus profilometry and Atomic Force Microscopy (AFM). These methods acquire data by contacting the surface over a sequence of one-dimensional scans. While high lateral resolution can be achieved in this way, such processes are time-consuming and can have the potential to deform the surface under test. An alternative non-contact interferometric method is presented here. The method uses the white-light interferometry (WLI) to provide wafer topography quickly in a direct three-dimensional format. The improved measurement throughput suggests that it is feasible to use this method for production monitoring. Most commercial interferometers with WLI are capable of measuring opaque surfaces with sub-nanometer precision. The described method extends this capability to determine the top surface topography of structured surfaces in the presence of varying phase shifts on reflection. The phase shift on reflection may be due to the material properties of bulk surfaces, single or multi-layer film stacks on a substrate, or other micro-structures on the wafer. Furthermore, this method simultaneously or separately provides additional parameters of the test piece e.g. layer thickness and/or material refractive index for film stacks, or line width and structure depth of micro-structures. The measurement results on various types of the wafer surfaces will be presented in this paper.

As the semiconductor industry progresses down the roadmap to smaller device geometries, precise metrology of the wafer nanotopography is increasingly needed by the wafer manufacturers and the semiconductor device manufacturers. To meet the demands, we have built an instrument that integrates our patented and proprietary white light interferometer with a motorized x-y stage. It measures height variation over the entire 200mm or 300mm wafer front surface with high lateral resolution and sub-nanometer height precision. This is accomplished by stitching together multiple maps obtained from a white light interferometer. Each individual map represents height variation over a part of the wafer surface. These individual maps are properly positioned to cover the entire wafer surface with sufficient overlapping area. With such properly arranged maps, we are able to produce an entire wafer surface by stitching them together. The map stitching expands the field of view available to our patented low coherence interferometer. This approach makes it possible to reveal more detail nanotopographic information over the entire wafer surface. In this paper, we will present the map stitching approach for the measurements of 200mm and 300mm wafers, including the theoretical foundations of stitching technique and the arrangements of individual measurements. We will also demonstrate measurement results on various wafers.

Constant development of microelements' technology requires a creation of new instruments to determine their basic physical parameters in 3D. The most efficient non-destructive method providing 3D information is tomography. In this paper we present Digital Holographic Tomography (DHT), in which input data is provided by means of Di-git- al Holography (DH). The main advantage of DH is the capability to capture several projections with a single hologram [1]. However, these projections have uneven angular distribution and their number is significantly limited. Therefore - Algebraic Reconstruction Technique (ART), where a few phase projections may be sufficient for proper 3D phase reconstruction, is implemented. The error analysis of the method and its additional limitations due to shape and dimensions of investigated object are presented. Finally, the results of ART application to DHT method are also presented on data reconstructed from numerically generated hologram of a multimode fibre.

For over three decades the Rayleigh Rice Perturbation Theory has been the method of choice for relating the surface power spectral density function (PSD) of smooth, clean, front surface reflectors to corresponding scatter patterns. This paper explores limitations with this traditional approach. In particular the annoying (anomalous) "hooks" at the high frequency (near grazing) end of a calculated PSD are investigated. In addition the smooth surface requirement is also probed for its limit. Experimental data involving different materials and wavelengths as well as variations in source polarization and incident angle are presented. The same data set is also used in a follow-on paper suggesting theoretical variations that may solve some of these issues.

A new unified surface scatter model has been developed that produces accurate results for rougher surfaces than the classical Rayleigh-Rice vector perturbation theory and for larger incident and scattered angles than the classical Beckmann-Kirchhoff theory. It is a generalization of the linear systems formulation developed by Harvey and Shack in the mid 1970s. The scattered light behavior is characterized by a two-parameter family of surface transfer functions. The rather computationally intensive process of calculating the scattered intensity from rough surfaces at large incident angles is described and shown to agree well with experimental data. Furthermore, the smooth-surface approximation to this new generalized surface scatter theory yields an improved solution to the inverse scattering problem of characterizing optical surfaces from BRDF measurements. The new obliquity factor greatly reduces the ubiquitous and annoying "hook" at the high spatial frequency end of surface PSDs predicted by the Rayleigh-Rice theory. Comparisons of this new theory and the Rayleigh-Rice theory will be made with experimental BRDF measurements provided by John Stover, author of the companion paper entitled "Limitations of Rayleigh-Rice perturbation theory for describing surface scatter".

We have studied the inverse scattering problem as an optimization problem. Firstly, we deal with the direct scattering problem of a one-dimensional, perfectly conducting rough surface. We discuss the complexity of the relation between the surface profile, the incident field, and the far-field intensity. Then, we approach the inverse problem as an optimization problem of constraint. In general we adopt a mathematical representation of the surfaces based on B-spline curves, and describe the evolutionary strategies. Concerning the mutation operator in evolutionary algorithm, some effort to facilitate self-adaptation of the mutation has been presented. The typical results are presented with our main conclusions.

We have studied the bi-directional reflection (BRDF) and mono-static bi-directional reflection (MBR) for a retro-reflected tag at 1.55 μm. The tag is specially designed for strong reflection in the retro-reflection direction for optical communication in free space. Due to multiple scattering, the larger the incident angle, the stronger the MBR.

We present approaches to the design of a structure that produces an enhanced backscattering peak the ratio of whose height relative to the height of the background at its position can be as high as 40-50.

We have studied the inverse scattering problem as an optimization problem for a 1-D surface. As the input data for our self-adaptation genetic algorithm for surface inversion, the scattered intensity has been measured with the laser BRDF instruments. In addition, the transmission data are collected. The typical reconstruction of inverse scattering for a 1-D random surface is compared with the profile measured by an atomic force microscope (AFM).

We present approaches to the design of two-dimensional randomly rough surfaces that produce scattered fields with specified coherence properties, and transform an incident beam with a specified intensity profile into a scattered beam with a different specified intensity profile. We also show how illuminating a single realization of a randomly rough surface, drawn from an ensemble of such random surfaces, by a partially coherent polychromatic (broadband) beam can be used to replace the average over the ensemble of realizations of the surface used to suppress the speckle produced when the incident field is monochromatic. Finally, we describe an experimental setup for producing a partially coherent beam by an optical feedback technique, and present experimental results demonstrating the reduction of speckle by the use of this beam.

The polarization of diffraction by a sawtooth reflection grating has been previously measured with fixed in and out directions while the grating was turned. The measured polarization and depolarization can provide more information about grating diffraction. The efficiency and polarization of diffraction by the two sawtooth facets are simulated based on the vector formulation of the Kirchhoff diffraction theory. The simulated diffraction pattern for the two-facet model agrees well with the measured one especially near the two specular peaks. The simulated diffraction polarization agrees with the measured one for diffraction orders with efficiency greater than 1%. For diffraction orders with efficiency < 1%, other diffraction mechanisms also come into place.

For angular resolved scatterometrical applications - besides the mechanical goniometer solutions - a lot of purely optical approaches are known. The paper first gives an overview on about 15 years of research in the field of non-goniometrical scatterometry at the Chair for Measurement and Information Technology at the University of the Federal Armed Forces in Hamburg with focus set on industrially applicable fast and rugged devices, allowing angular resolved measurements. In the technical part some aspects on the feature extraction problem in relation to the scatter mechanism of rough surfaces will be discussed. Further on the imaging properties of catadioptrical systems with elliptical and spherical mirrors will be treated in an engineer friendly way, concluding in easy-to-handle design rules and concepts.

Non-imaging optical critical dimension (OCD) techniques have rapidly become a preferred method for measuring nanoscale features in semiconductors. OCD relies upon the measurement of an optical reflectance signature from a grating target as a function of angle, wavelength and/or polarization. By comparing the signature with theoretical simulations, parameters of the grating lines such as critical dimension (CD) linewidth, sidewall angle, and line height can be obtained. Although the method is sensitive and highly repeatable, there are many issues to be addressed before OCD can be considered a traceable metrology. We report on progress towards accurate, traceable measurement, modeling, and analysis of OCD signatures collected on the NIST goniometric optical scatter instrument (GOSI), focusing on recent results from grating targets fabricated using the single-crystal critical dimension reference materials (SCCDRM) process. While we demonstrate good correlation between linewidth extracted from OCD and that measured by scanning electron microscopy (SEM), we also find systematic deviations between the experimentally obtained optical signatures and best fit theoretical signatures that limit our ability to determine uncertainty in OCD linewidth. We then use the SCCDRM line profile model and a χ² goodness-of-fit analysis on simulated signatures to demonstrate the theoretical confidence limits for the grating line parameters in the case of normally distributed noise. This analysis shows that for the current SCCDRM implementation, line height and oxide layer undercut are highly correlated parameters, and that the 3-σ confidence limits in extracted linewidth depend on the target pitch. Prospects for traceable OCD metrology will be discussed.

Based on the cross-correlation function (CCF), a new parameter called profile difference, D_s (or topography difference for 3D), is developed for measurement and comparison of 2D profiles and 3D topographies. When D_s = 0, the two compared profiles or topographies must be exactly the same (point by point). A 2D and 3D topography measurement system was established at the National Institute of Standards and Technology (NIST), that includes data acquisition stations using stylus instruments and a confocal microscope, and a correlation program using the proposed parameter D_s and the cross-correlation function maximum CCF_max. This system has been used for 2D and 3D ballistics signature measurements of the NIST Standard Reference Material (SRM) 2461/2461 Standard Bullets and Casings, and received high measurement reproducibility. It is suggested that the proposed parameter and algorithm can be generally used for measurement and comparison of 2D and 3D surface topographies in surface metrology and other areas.

A total integrated scattering (TIS) system consisting of an integrating sphere has been developed in KRISS for the purpose of measuring the effective roughness amplitude of gauge blocks and platens, which are necessary for the correction of phase shift due to roughness difference between gauge block and platen, in the calibration of gauge blocks by optical interferometry. Details on the TIS system and its calibration by using two different methods are described. The uncertainty of the effective roughness amplitude measurement by using the TIS system is evaluated to be 2 nm (k=1).

Tighter specifications for the deposition of thin, highly uniform films with low stress require new stress measurement techniques to resolve smallest deformations on the Nanometer scale. Uniformity maps need to cover measurement areas from a few millimeters up to whole 300 mm semiconductor wafers, which include small dies as well as lithography areas. Metrology able to measure sample's flatness, nanotopography and film stress components on all the variety of the samples, is very urgent today. Its accuracy and reproducibility should be at nanometers. We discuss a combined solution using complementary measurements of nanotopography, substrate thickness and film thickness, for the stress analysis and stress uniformity measurement on samples with thin films and with very low stress causing shallow deformations having a curvature radius up to several kilometers.

Spectroscopic Ellipsometry is the technique of choice to characterize thickness and refractive indices of thin layers. Atmospheric Ellipsometry Porosimetry (EPA) measures the change of the optical properties and thickness of the materials during adsorption and desorption of wet air at atmospheric pressure. Concentration of humidity changes at each step of measurement from dry air to saturated air. This non contact and non destructive technique is an effective and unique method to characterize porosity, pore size distribution (PSD) and Young modulus of thin porous films. It does not require to scratch the film, does not need low temperature or low pressure.Detailed description of the technique will be exposed in the paper and several meso-porous films (with pore size larger than 1nm) using the Kelvin formalism will be presented. The porosity of the layer ranges from few percent up to 40%. As it is an optical method, it is non contact, non destructive, fast (down to 15 minutes) and room temperature method. It does require low pressure or any preparation of sample. Solid oxide fuel cell is an electrochemical device that converts the chemical energy in fuels into electrical energy by exploiting the natural tendency of oxygen and hydrogen to react. The cell is constructed with two porous electrodes, which sandwich an electrolyte. Selection of materials for the individual components presents the most significant challenges in this technology. Each material must possess the correct chemical, electrical and structural properties to perform its function in the cell. Yttria stabilized Zirconia, (YSZ) is a suitable material for two of the components in this system: the anode and the electrolyte, where its morphology is notably different for each component. Using EPA technique, it becomes possible to characterize in term of porosity and pore size distribution the morphology of both components made by YSZ. We will show the characterization of material in thin film with different porosity and pore size distribution. Graded porosity versus depth could be also demonstrated and will be shown for the first time on such material.

Phase unwrapping is a very important processing step in phase shift interferometry. In this work, we propose a new method which combines the branch-cut method with error correcting. The method can avoid the propagation of the phase errors and have higher reliability. The experiment proves the proposed method is feasible and effective.

This paper presents the design and fabrication of a precision dual level stage composing a dimensional metrological system for large range surface topography, such as mask patterns for lithography, fine artifacts on a semi-conductor wafer and micro roughness on a large specular surface. The stage was configured as dual level, a fine stage on a coarse stage, to obtain large moving range and high resolution simultaneously. In the design of the coarse stage, we focused on a simple structure with low profile to achieve insensitivity to vibration and high accuracy. Therefore, a high quality flat surface plate was used as the reference plane of the coarse stage's movement, instead of a conventional simple stacking of two long stroke one-axis stages. The surface plate also has a role of metrological frame for very low thermal expansion coefficient and its size is 800 mm × 800 mm. The coarse stage is guided horizontally by a cross structure with two precision straight bars perpendicularly linked and vertically by the surface plate. The sliding pads made of PTFE are used to guarantee the smooth motion of the coarse stage for both horizontal and vertical directions. The fine stage fixed on the coarse stage generates five-axis fine motion, such as two-axis in-plane translation, one-axis in-plane and two-axis out-of-plane rotation. The fine stage is composed of flexure guided structures and actuated by five PZTs. The developed dual level stage can achieve a large range of 200 mm × 200 mm and a nanometric resolution simultaneously. Its movement is monitored and controlled using a five-axis laser interferometer system to be applied to a dimensional metrology having direct meter-traceability.

We develop a novel holographic reconstruction method that requires only an off-axis Fresnel digital hologram without the need for additional phase-retrieval elements in the experimental setup. With this approach we can reconstruct numerical phase profiles without twin-image blurring, using only an off-axis digital hologram. Furthermore numerical reconstruction and twin-image suppression can be rapidly accomplished with a personal computer. Not only is twin- image suppression easier but the constraints characteristic of the conventional phase-shifting digital holographic-based scheme that employs multiple exposures can be overcome. The experimental results clearly show that complex spatial frequency information about the object to be measured is not lost during numerical reconstruction and that the profile of the phase object can be exactly measured and presented.

The paper presents the technique and instrumentation for fully automatic measurement of angular intensity distribution of a light emitting diode (LED). The analysis of important factors that influence to measurement accuracy is done and algorithms for their minimization are identified. As a result the technique makes possible intensity measurements with angular spatial error smaller than 1 angular degree in half sphere with relative error of intensity registration smaller than 1%. The presented measuring system performs all operations automatically under computer control, generates the protocol of measurements with 3D diagrams of intensity distribution and makes conclusion how LED corresponds to its technical specification.