There has recently been an increased interest in being able to model optical systems that include sub-wavelength structures at one or more points in the system model. Software using the finite-difference, time-domain (FDTD) method can accurately model the interaction with the sub-wavelength structures, but cannot practically model the entire optical system. Therefore, in order to model the entire optical system including the sub-wavelength structures it is necessary to couple the FDTD software to optical system software. This type of coupling between macro and micro optical software codes has applications in a wide variety of fields including semiconductor lithography, optical data storage, telecom, biophotonics, metrology systems, and more. Conceptually all that is necessary to couple system software to a FDTD software is for each of the two optical software codes to be able to read in field files from the other and write out field files to the other. In practice several issues must be dealt with in order to ensure that this handing back and forth of fields is done correctly. This field handoff involves two major issues: (1) transferring an accurate and complete description of the field and (2) changing the sampling density of the field to be appropriate for further propagation inside of the other code. A brief explanation of the FDTD method is presented. This is followed by a listing of where the assumptions of scalar diffraction theory breakdown, requiring techniques such as FDTD. Lastly the steps involved in performing successful field transfers are presented.
Most telecom components use lenses to collimate the beam emerging from a single-mode fiber and again, after some manipulation of the beam, to focus the beam back into an output fiber. In response to the drive for smaller components, collimator lenses have shrunk and a number of new microcollimator types been introduced. Several of the newer collimator types involve lenses that are fused to the fiber. Optical software was used to model six different types of microcollimators divided into three different size categories. Because not all of the six types were applicable in all three of the size categories, a total of eleven different collimator systems were modeled. A collimator system consists of an input collimator and an identical output collimator. Each collimator includes a single-mode fiber and a collimating lens. In order to achieve equivalence, all of the collimators in the same size category produce an intermediate waist with the same mode field diameter and distance from the lens surface to the intermediate waist. An algorithm is presented to determine the necessary physical parameters (lengths and radii) for a collimator to produce the appropriate beam criteria for a given size category. Once the physical parameters for the collimator systems were determined, all of the collimator systems were examined for insertion loss in their ideal configuration as well as in the presence of fabrication and alignment errors. All of the insertion loss analyses were performed using coherent field propagation starting from the fundamental fiber mode of the input fiber, through the collimating lenses, and finishing with the calculation of the overlap integral of the field inside the output fiber with the fundamental fiber mode. No thin lens or paraxial propagation assumptions are made...The results indicate that the collimator types involving lenses that are fused to the fiber are less sensitive to longitudinal fiber and collimator shifts than the components with the fiber and lens not in direct contact.
There has recently been an increased interest in software that can propagate complex fields through optical systems. This type of optical software gives the user the ability to analyze and tolerance two main categories of coherent optical systems: (1) metrology systems and (2) systems used to propagate coherent optical signals. In order to demonstrate the methodology of modeling and analyzing coherent systems, a software model of a Fizeau interferometer was constructed. The model extended from the laser source through a 256 x 256 pixel detector with 8-bit gray level resolution. The reference mirror in the model is moved to create four, 90-degree phase shifted interferograms in the form of ASCII files. These four ASCII files are then input into another software code that calculates and unwraps the phase to determine the surface error. The peak-to-valley and RMS surface errors are calculated and the surface is fit to Zernike polynomials. This Fizeau model was and used to study the effects on surface measurement accuracy of the first surface of a test lens due to unwanted reflections from the second surface of the lens. This is the type of study for which non-sequential, coherent field propagation software has some advantage relative to geometrical ray trace codes.
There is a long tradition of analyzing lens designs and establishing their manufacturing tolerances in software. The lens-design codes used for this process are based on sequential, geometric ray tracing techniques and the tolerances are based on geometric image quality as determined by system aberration content. More recently, largely due to the rapid expansion of optical telecom applications, there has been increased interest in the non-sequential propagation of complex optical fields, rather than geometric rays, through optical systems. Starting with sources of varying degrees of coherence or from the output from fibers or waveguides, fields can be non-sequentially propagated through optical systems, and the amplitude and phase of these fields can be examined at any position in space. This has enabled an enormous increase in the ability to analyze and tolerance coherent optical systems used in two main categories of optical systems: (1) measurement systems and (2) systems used to propagate coherent optical signals. This paper addresses the methodology involved in modeling, analyzing, and tolerancing coherent systems and highlights the main differences between the methods used with coherent systems and traditional lens designs. Coherent systems models include components that require modeling diffraction and interference effects. They typically extend the path length of the model, beginning at the source and continuing through to a detailed description of the detector or a coupling into an output waveguide. They may even include a measurement algorithm within the system model. Additionally, unlike the traditional lens-design models, the performance parameters used in establishing the manufacturing tolerances of these coherent systems, are not necessarily based on the image quality of the system. Instead, tolerancing of coherent systems is usually more directly related to the functionality of that system. To further demonstrate the methodology of modeling, analyzing, and tolerancing coherent systems in software, two examples of coherent system models, an interferometer and a telecom component, are presented. Some of the tolerancing results from these systems are presented.
A new version of the Stepper Image Monitor (SIM) has been designed to evaluate best focus on Ultratech steppers.
The SIM is a portable unit which will support a number of steppers in a fab. Each stepper has a permanently mounted
detector assembly which uses a mirror to pick off the dark field image (except for a small portion required for Ultratech
alignment) above the fold mirror.
To run SIM, a chrome on glass amplitude diffraction grating with many 1 - 1.Sum wide by 1mm long windows on a Sum
pitch is placed in the reticle position on the stepper. A SIM wafer with a similar number of 03 - 1.Oum wide by 1mm
long bars on a Sum pitch is placed on the stage. The wafer is instructed to move by an external Run Mode 8 Ultratech
stepper program, first in X and then in Y, across the Sum pitch in a number of discrete steps (typically 20). The intensity
values measured by the SIM detector at each step are used to construct a discrete intensity profile that represents the
aerial image of the grating. This procedure is repeated at several Z positions (typically 5). Each intensity profile is
correlated to the appropriate diffraction limited intensity profile for the system being used. A parabolic fit is made from
the correlation values at the various Z positions. The Z value for the maximum of the parabola is considered to be best
focus.
This method has several advantages over other methods currently in use for checking Ukratech focus: (1) More precise
measurement; (2) Operator independent; (3) Faster; (4) No effects due to the resist or to processing; (5)SIM is a
permanent artifact (i.e. no variation due to wafer differences).
Results from beta site testing show that the method is very repeatable, with sigma =0.lSum being typical. SIM results
also correlate very well to results obtained by conventional methods. It also tracks well to changes in Z offset dialed into
the stepper. SIM has been shown to be an effective tool for quantifying the relationship between lens heating and focus
shift on the Ultratech stepper.
These improvements in speed and precision of focus measurements on the Ultratech stepper will lead to more usable
stepper time and better stepper performance, which in turn translates directly into more throughput and higher yields.
OAI would like to acknowledge the help of Suzanne Scullen and Synergy Semiconductor Corporation for their help and
the use of their Ultratech stepper.
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