Efficient Signal Transport Model for Remote Thermometry in Full-Scale Thermal Processing Systems

Light-pipe radiation thermometers are predominantly used to monitor wafer temperature during rapid thermal processing (RTP) of semiconductors. The processes used in fabrication of semiconductor devices during rapid thermal processing are extremely temperature sensitive and the errors associated with light-pipe measurements are great concerns across the industry. Modeling of the light-pipes has helped in understanding the signal transport process and errors associated with the light pipe measurements. However, due to the smaller size of the light-pipe sensor area with respect to the total system area, full scale modeling of such a system including the light pipe thermometer has not been possible due to the computational demand. In this paper, the reverse Monte Carlo method is used to model the signal transport through a light-pipe thermometer used in a RTP system. The Monte Carlo model considers the spectral and angular dependent optical properties of the chamber and quartz materials. The reverse Monte Carlo model is applied to the full scale instrumented system with characteristics of a RTP system with a quartz light pipe probe and the results are compared against previously published measurements from the same system.

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Use of the attainable region method to simulate a full-scale ball mill with a realistic transport model

Minerals Engineering ◽

10.1016/j.mineng.2014.06.012 ◽

2015 ◽

Vol 73 ◽

pp. 116-123 ◽

Cited By ~ 6

Author(s):

Ngonidzashe Chimwani ◽

François K. Mulenga ◽

Diane Hildebrandt ◽

David Glasser ◽

Murray M. Bwalya

Keyword(s):

Ball Mill ◽

Transport Model ◽

Full Scale ◽

Region Method ◽

Attainable Region

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The Potential Effect of Multilayer Patterns on Temperature Uniformity During Rapid Thermal Processing

MRS Proceedings ◽

10.1557/proc-387-21 ◽

1995 ◽

Vol 387 ◽

Cited By ~ 9

Author(s):

Jeffrey P. Hebb ◽

Klavs F. Jensen ◽

Erik W. Egan

Keyword(s):

Thermal Processing ◽

Transport Model ◽

Rapid Thermal Processing ◽

Potential Effect ◽

Electromagnetic Theory ◽

Radiative Properties ◽

Temperature Uniformity ◽

Wafer Temperature ◽

Single Side ◽

Side Illumination

AbstractThis work aims to systematically gain an understanding of the effects of multilayer patterns on wafer temperature uniformity during rapid thermal processing, and explore possible solutions to the problem. Steady state and transient wafer temperature distributions are simulated by combining a detailed reactor transport model with multilayer electromagnetic theory to predict wafer radiative properties. A generic axisymmetric RTP system with single-side illumination is used as a testbed to explore pattern effects for a simulated source/drain implant anneal.

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The Potential Effect of Multilayer Patterns on Temperature Uniformity During Rapid Thermal Processing

MRS Proceedings ◽

10.1557/proc-389-293 ◽

1995 ◽

Vol 389 ◽

Author(s):

Jeffrey P. Hebb ◽

Klavs F. Jensen ◽

Erik W. Egan

Keyword(s):

Thermal Processing ◽

Transport Model ◽

Rapid Thermal Processing ◽

Potential Effect ◽

Electromagnetic Theory ◽

Radiative Properties ◽

Temperature Uniformity ◽

Wafer Temperature ◽

Single Side ◽

Side Illumination

ABSTRACTThis work aims to systematically gain an understanding of the effects of multilayer patterns on wafer temperature uniformity during rapid thermal processing, and explore possible solutions to the problem. Steady state and transient wafer temperature distributions are simulated by combining a detailed reactor transport model with multilayer electromagnetic theory to predict wafer radiative properties. A generic axisymmetric RTP system with single-side illumination is used as a testbed to explore pattern effects for a simulated source/drain implant anneal.

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Relation of Statistically Significant, Abnormal, and Typical WAIS-R VIQ-PIQ Discrepancies to Full Scale IQs

European Journal of Psychological Assessment ◽

10.1027//1015-5759.16.2.107 ◽

2000 ◽

Vol 16 (2) ◽

pp. 107-114 ◽

Cited By ~ 3

Author(s):

Louis M. Hsu ◽

Judy Hayman ◽

Judith Koch ◽

Debbie Mandell

Keyword(s):

Graphical Method ◽

The United States ◽

Full Scale ◽

True Score ◽

Absolute Value ◽

Normative Population ◽

The Us ◽

The Mean ◽

And Performance ◽

Quadratic Models

Summary: In the United States' normative population for the WAIS-R, differences (Ds) between persons' verbal and performance IQs (VIQs and PIQs) tend to increase with an increase in full scale IQs (FSIQs). This suggests that norm-referenced interpretations of Ds should take FSIQs into account. Two new graphs are presented to facilitate this type of interpretation. One of these graphs estimates the mean of absolute values of D (called typical D) at each FSIQ level of the US normative population. The other graph estimates the absolute value of D that is exceeded only 5% of the time (called abnormal D) at each FSIQ level of this population. A graph for the identification of conventional “statistically significant Ds” (also called “reliable Ds”) is also presented. A reliable D is defined in the context of classical true score theory as an absolute D that is unlikely (p < .05) to be exceeded by a person whose true VIQ and PIQ are equal. As conventionally defined reliable Ds do not depend on the FSIQ. The graphs of typical and abnormal Ds are based on quadratic models of the relation of sizes of Ds to FSIQs. These models are generalizations of models described in Hsu (1996) . The new graphical method of identifying Abnormal Ds is compared to the conventional Payne-Jones method of identifying these Ds. Implications of the three juxtaposed graphs for the interpretation of VIQ-PIQ differences are discussed.

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A Modification of the Payne-Jones Method of Identifying Abnormal Differences in WISC-R Performance and Verbal IQ's

European Journal of Psychological Assessment ◽

10.1027/1015-5759.12.1.27 ◽

1996 ◽

Vol 12 (1) ◽

pp. 27-32 ◽

Cited By ~ 1

Author(s):

Louis M. Hsu

Keyword(s):

Full Scale ◽

True Score ◽

Verbal Iq ◽

Score Difference ◽

The Difference ◽

And Performance

The difference (D) between a person's Verbal IQ (VIQ) and Performance IQ (PIQ) has for some time been considered clinically meaningful ( Kaufman, 1976 , 1979 ; Matarazzo, 1990 , 1991 ; Matarazzo & Herman, 1985 ; Sattler, 1982 ; Wechsler, 1984 ). Particularly useful is information about the degree to which a difference (D) between scores is “abnormal” (i.e., deviant in a standardization group) as opposed to simply “reliable” (i.e., indicative of a true score difference) ( Mittenberg, Thompson, & Schwartz, 1991 ; Silverstein, 1981 ; Payne & Jones, 1957 ). Payne and Jones (1957) proposed a formula to identify “abnormal” differences, which has been used extensively in the literature, and which has generally yielded good approximations to empirically determined “abnormal” differences ( Silverstein, 1985 ; Matarazzo & Herman, 1985 ). However applications of this formula have not taken into account the dependence (demonstrated by Kaufman, 1976 , 1979 , and Matarazzo & Herman, 1985 ) of Ds on Full Scale IQs (FSIQs). This has led to overestimation of “abnormality” of Ds of high FSIQ children, and underestimation of “abnormality” of Ds of low FSIQ children. This article presents a formula for identification of abnormal WISC-R Ds, which overcomes these problems, by explicitly taking into account the dependence of Ds on FSIQs.

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