Heat balance evaluation linked with a direct approach model using ray trace simulation ͑DARTS͒ was able to provide quantitative heat information which was applicable to the reflector design for a rapid thermal processing system. The absorbed ray intensity obtained by the DARTS model showed that the array of very small half-cylindrical hills built on the reflector surface had the function of flattening the sharp heat peaks formed beneath the infrared lamps. The temperature profile, obtained by the entire heat balance calculation using mainly the thermal conduction and the radiation heat to and from the susceptor, quantitatively agreed with the measurements. The power value for one ray defined in the DARTS model was consistent with that estimated from the division of power loaded into the lamp by the emitted ray number.Semiconductor device manufacturing processes widely use a rapid thermal processing ͑RTP͒ system 1-13 for obtaining both a great throughput and high-quality film formation. For the analysis and optimization of the entire radiation heat transport from the infrared lamps to the substrate in the RTP system, many researchers have developed theoretical calculation models. In these models, the ray tracing method is expected to evaluate the three-dimensional radiation heat transport in the RTP system having complicated reflectors, because the method uses only very simple principles and assumptions, that is, the angle of reflection and the conditions to terminate the ray trace. Therefore, in our previous studies, 23-27 we have developed the direct approach model using ray trace simulation ͑DARTS͒ and showed that theoretical calculation could provide nonempirical and a low-cost way to design an RTP system, particularly for the design of the major reflector geometry. However, these previous studies have unfortunately been limited to a qualitative evaluation of the temperature trend formed by the large and major parts of the reflector. Thus, for further improvement of the RTP system design method which can adjust the entire and local temperature profiles, the DARTS model should take into account the effects of various small and fine parts added and the effect of the reflector surface geometry modification.In addition to this, the DARTS model has the following subjects to be studied for further advance of the reflector design method: ͑i͒ The power for one ray ͑power loaded into the lamp/emitted ray number͒ should be consistent with that determined by the entire heat balance calculations, because this indicates the capability of the DARTS model to nonempirically predict the achievable temperature for any reflector geometry. ͑ii͒ The influence of the absorbed ray intensity fluctuation obtained by the DARTS model on the temperature profile should be evaluated. ͑iii͒ The effect of radiation from the heated objects, such as a wafer and a susceptor, being returned to them should be studied. These should be studied based on an entire heat evaluation of the radiation and the heat conduction, accounting for the measured ...

SummaryIt is important to optimize imaging parameters in 3D-double inversion recovery (DIR) magnetic resonance imaging (MRI) for detecting cortical micro lesions. However, inadequate parameters markedly raise blurring in 3D-DIR MRI. The purpose of this study was to evaluate the relationship between the blurring and refocus flip angle (RFA) in 3D-DIR MRI. White matter attenuated inversion recovery (WAIR) images as a test sample were obtained by 1.5T MRI with various RFA settings (30°, 40°, 60°, 100°, 140°, 180°, and variable refocus flip angle (VRFA)). Optimal RFA was evaluated using Schefféʼs method (Nakaya changing method) by five observers. The results of average preferences indicated that RFA settings of under the 60°of RFA or VRFA suppressed the blurring in 3D-DIR MRI. The yard sticks of RFAs of 30°and 40°were significantly higher than the yard sticks of other RFAs (p< 0.01). For detecting cortical microlesions, it is very important to obtain WAIR images with no blurring. Using low RFA or VRFA didnʼt cause significant differences of signal intensity between high-frequency region and lowfrequency region in k-space of 3D-DIR MRI. Therefore, it is recommended to set lower RFA (under 60°or VRFA) for suppressing blur in 3D-DIR MRI.

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