Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

The phase-shifting mask consists of a normal transmission mask that has been coated with a transparent layer patterned to ensure that the optical phases of nearest apertures are opposite. Destructive interference between waves from adjacent apertures cancels some diffraction effects and increases the spatial resolution with which such patterns can be projected. A simple theory predicts a near doubling of resolution for illumination with partial incoherence σ < 0.3, and substantial improvements in resolution for σ < 0.7. Initial results obtained with a phase-shifting mask patterned with typical device structures by electron-beam lithography and exposed using a Mann 4800 10× tool reveals a 40-percent increase in usuable resolution with some structures printed at a resolution of 1000 lines/mm. Phase-shifting mask structures can be used to facilitate proximity printing with larger gaps between mask and wafer. Theory indicates that the increase in resolution is accompanied by a minimal decrease in depth of focus. Thus the phase-shifting mask may be the most desirable device for enhancing optical lithography resolution in the VLSI/VHSIC era.

Improving resolution in photolithography with a phase-shifting mask

Lithography is a field in which advances proceed at a swift pace. This book was written to address several needs, and the revisions for the second edition were made with those original objectives in mind. Many new topics have been included in this text commensurate with the progress that has taken place during the past few years, and several subjects are discussed in more detail. This book is intended to serve as an introduction to the science of microlithography for people who are unfamiliar with the subject. Topics directly related to the tools used to manufacture integrated circuits are addressed in depth, including such topics as overlay, the stages of exposure, tools, and light sources. This text also contains numerous references for students who want to investigate particular topics in more detail, and they provide the experienced lithographer with lists of references by topic as well. It is expected that the reader of this book will have a foundation in basic physics and chemistry. No topics will require knowledge of mathematics beyond elementary calculus.

Principles of Lithography

An apparatus and method to determine a property of a substrate by measuring, in the pupil plane of a high numerical aperture lens, an angle-resolved spectrum as a result of radiation being reflected off the substrate. The property may be angle and wavelength dependent and may include the intensity of TM- and TE-polarized radiation and their relative phase difference.

Method and apparatus for angular-resolved spectroscopic lithography characterization

We present a new image-based process for measuring the bidirectional reflectance of homogeneous surfaces rapidly, completely, and accurately. For simple sample shapes (spheres and cylinders) the method requires only a digital camera and a stable light source. Adding a 3D scanner allows a wide class of curved near-convex objects to be measured. With measurements for a variety of materials from paints to human skin, we demonstrate the new method's ability to achieve high resolution and accuracy over a large domain of illumination and reflection directions. We verify our measurements by tests of internal consistency and by comparison against measurements made using a gonioreflectometer.

/pdf/image-based-brdf-measurement-including-human-skin-3l5eittk5y.pdf

Image-based BRDF measurement including human skin

An optical scatterometer system enables analysis of a sample material at various wavelengths without rotating or otherwise moving the sample material.

Method for broad wavelength scatterometry

The widths and overall profiles of dielectric grating lines can be determined by measuring the intensity of diffracted laser light from the sample over a specified range of incident beam angles. This technique, known as 2‐Θ scatterometry, is able to accurately and precisely measure photoresist structures in the subhalf micron regime. Moreover, a 2‐Θ scatterometer is capable of making measurements in a rapid and nondestructive manner. To test this technique we measured five identically processed wafers with nominal 0.5 μm line/0.5 μm space grating patterns. Each wafer comprised gratings in a Shipley 89131 negative photoresist exposed in a matrix of incremental exposure doses and focus settings. The scatterometry results were consistent with cross‐sectional and top‐down scanning electron microscopy (SEM) measurements of the same structures. The average deviation of 11 scatterometer linewidth measurements from top‐down SEM measurements, over a broad exposure range, is 14.5 nm. In addition, the repeatability (1σ) of the 2‐Θ scatterometer is shown to be excellent: 0.5 nm for consecutive measurements and 0.8 nm for day‐to‐day measurements.

Metrology of subwavelength photoresist gratings using optical scatterometry

Scatterometry, the analysis of light diffraction from periodic structures, is shown to be a versatile metrology technique applicable to a number of processes involved in the production of microelectronic devices. We have demonstrated that the scatterometer measurement technique is robust to changes in the thickness of underlying films. Indeed, there is sufficient information in one signature to determine four process parameters at once, namely the linewidth and thickness of the photoresist grating, and the thicknesses of two underlying film layers. Results from determining these dimensions on a 25 wafer study show excellent agreement between the scatterometry measurements and measurements made with other metrology instruments [top-down and cross-section scanning electron microscopy (SEM) and ellipsometer]. In particular, measurements of nominal 0.35 μm lines agree well with cross-section SEM measurements; the average bias is −1.7 nm. Similarly, for nominal 0.25 μm lines, the average bias is −7.3 nm. In ad...

Multiparameter grating metrology using optical scatterometry

Oxygen ion-assisted deposition of SiO2 and TiO2 has been investigated as a function of ion energy (30–500 eV) and current density (0–300 μA/cm2) at the optic. It is shown that both low and high energy ion bombardment improve SiO2 film stoichiometry, although slightly greater improvement is realized for the low energy case. For TiO2 films, low energy bombardment improves stoichiometry, while high energy bombardment is clearly detrimental. A reduction in H content by a factor of 10 is observed in SiO2 films deposited with high energy ion bombardment. Durable films are produced at low substrate temperatures (50–100°C). Film stress characteristics are discussed.

Ion-assisted deposition of optical thin films: low energy vs high energy bombardment

An optical scatterometer system enables illumination of a sample material at various angles of incidence without rotating or otherwise moving the sample material.

John R. McNeil

Papers

Method for broad wavelength scatterometry

Metrology of subwavelength photoresist gratings using optical scatterometry

Multiparameter grating metrology using optical scatterometry

Ion-assisted deposition of optical thin films: low energy vs high energy bombardment

Lens scatterometer system employing source light beam scanning means