• Korean Journal of Optics and Photonics
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• v.14 no.5
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• pp.504-508
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• 2003

We present a new point-diffraction interferometer, which has been devised for the three-dimensional profile measurement of light scattering rough surfaces. The interferometer system has multiple sources of two-point-diffraction and a CCD camera composed of an array of two-dimensional photodetectors. Each diffraction source is an independent two-point-diffraction interferometer made of a pair of single-mode optical fibers, which are housed in a ceramic ferrule to emit two spherical wave fronts by means of diffraction at their free ends. The two spherical wave fronts then interfere with each other and subsequently generate a unique fringe pattern on the test surface. A He-Ne source provides coherent light to the two fibers through a 2${\times}$l optical coupler, and one of the fibers is elongated by use of a piezoelectric tube to produce phase shifting. The xyz coordinates of the target surface are determined by fitting the measured phase data into a global model of multilateration. Measurement has been performed for the warpage inspection of chip scale packages (CSPs) that are tape-mounted on ball grid arrays (BGAs) and backside profile of a silicon wafer in the middle of integrated-circuit fabrication process. When a diagonal profile is measured across the wafer, the maximum discrepancy turns out to be 5.6 ${\mu}{\textrm}{m}$ with a standard deviation of 1.5 ${\mu}{\textrm}{m}$.

• Korean Chemical Engineering Research
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• v.46 no.3
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• pp.486-491
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• 2008

This paper describes a model identification method that has been applied to a commercial 12-inch RTP (rapid thermal processing) equipment with an ultimate aim to develop a high-performance advanced controller. Seven thermocouples are attached on the wafer surface and twelve tungsten-halogen lamp groups are used to heat up the wafer. To obtain a MIMO balanced state space model, multiple SIMO (single-input multiple-output) identification with highorder ARX models have been conducted and the resulting models have been combined, transformed and reduced to a MIMO balanced state space model through a balanced truncation technique. The identification experiments were designed to minimize the wafer warpage and an output linearization block has been proposed for compensation of the nonlinearity from the radiation-dominant heat transfer. As a result from the identification at around 600, 700, and $800^{\circ}C$, respectively, it was found that $y=T(K)^2$ and the state dimension of 80-100 are most desirable. With this choice the root-mean-square value of the one-step-ahead temperature prediction error was found to be in the range of 0.125-0.135 K.