**Thermal and Energy Systems Research**

**PI: P.-f. Hsu**

**Capabilities:**

Numerical modeling of multi-dimensional
transient and steady state heat transfer processes: radiation heat transfer in
flames and thermal systems, remote sensing and optical diagnostics using
ultra-short pulsed laser, transient radiative transport in bio- and microscale
systems, radiative properties of thin films with surface roughness, combined
mode heat transfer, premixed combustion with detail multi-step chemistry
kinetics, and electromagnetic wave scattering of small particles and random
roughness surfaces.

Experimental study of
premixed combustion within porous ceramic burner, thermophysical
properties of porous ceramics, and emissions of porous ceramic burner. Radiation heat flux and surface property measurement. Industrial air-conditioning systems and heat
exchangers designs with computational fluid dynamics and heat transfer software
tools.

**AWARDS**

NASA/ASEE Faculty Fellowship (declined
due to schedule conflict), 2003.

The Boeing Company Welliver
Faculty Fellowship, 2002.

**On-going projects:**

The research will develop a fundamental
and quantitative understanding of the surface roughness effects on the
radiative properties of silicon-based thin film materials. The thin films usually have a randomly rough
back surface and a smooth or periodically patterned front surface. Thin film materials have many diverse
scientific and engineering applications, e.g., semiconductor chips, solar
cells, and electro-optical components.
During the manufacturing of these materials, the heating and cooling
rates as well as the associated radiation pyrometry for temperature monitoring
are critical steps that are needed to ensure the product quality and
reliability. The surface roughness on
the die areas and wafer backsides has the first order effects on the radiative
properties and the temperature control.
However, these effects can only be described qualitatively at the
present time. Two different models will
be developed and compared their relative effectiveness in predicting the
radiative properties. The research will
improve the advanced rapid thermal processes (RTP) in the semiconductor
industry. The research is supported by
NSF and in collaboration with semiconductor manufacturing companies.

(Left) wafer top side with devices - patterned
roughness. The reflection in a diagonal strip shows different reflectivity at
different wavelength. (Right) wafer back
side with random roughness.

Short pulse radiation is rapidly being
deployed in many new applications such as bio-medical optical tomography,
in-situ property evaluation, evaluation of particle size distribution, remote
sensing of oceans and atmosphere, and others, where it is becoming imperative
that accurate radiative models be developed to analyze, design, and optimize
these applications. Short pulse
radiation offers many unique features that have not been previously exploited
in the study of radiative transport and which present opportunities to obtain
accurate high-precision data and has the great potential for non-invasive,
non-destructive diagnostics and imaging applications. In this research we have developed several
numerical models that are computationally efficient, accurate, and scalable to
large computer system to handle the most challenging problems. The fundamental study will have a direct
impact on many new applications, as shown in some of our journal publications,
and has led to a patent application. The
research has been supported by Sandia National Lab and NSF.

The current
capabilities for simulating participating-media radiative heat transfer are too
limiting. Many of the practical
engineering applications of radiative heat transfer have to be greatly
simplified to be treated. There is a
consensus in the heat transfer community that better modeling and solution
techniques are very critical and in urgent need to study the radiative
transport processes. These processes are
relevant to applications such as combustion, advanced manufacturing techniques,
laser surgery, medical imaging, atmospheric radiation budget, global warming
effects, etc. I have developed a number
of efficient and scalable numerical methods, which include

This is a clean combustion technique
using the porous ceramics for burner construction. The combustion of the gaseous fuel and air
mixture occurs inside the solid matrix.
Such combustion processes have received much attention in recent years
from industry and academia in several nations.
The porous ceramic burner can extend the flammability limits, has high
turn-down ratio and favorable flame stability characteristics, and most
importantly, generates very low NOx and CO emissions, which are subjected to
various federal and state laws and regulations.
The power generation and boiler operators are especially interested in
the new burner designs and operations that have the potential to replace the
existing burners. Our research in this
area is currently funded by California Energy Commission. Partial support is also provided by a porous
ceramics manufacturer.

Burner Table for Cylindrical, Dual-Layer Porous
Ceramic Burner

Premixed Flame inside Porous Ceramic Disk

(In the initial warm-up stage)

Premixed Flame inside Porous Ceramic Disk

(Stable combustion is established)

Cylindrical Porous YZA
burner: (from left to right) full flame, 1/3 flame, and irregular flame.

Since the operation of Florida Tech's parallel
processing system – the Bluemarlin – was in
production run in 2001, we have gained tremendous amount of experience in using
the cluster to solve research problems.
The system was funded by NSF to a multi-disciplinary team. The parallel system has become a critical
asset of the university for research and students'
learning and training. Our group has
developed and tested various numerical methods with the system, incl. Monte
Carlo method, reverse Monte Carlo method, quasi-Monte Carlo method, integral
equation solvers, and several others. It
has also become a valuable, high performance computing tool for many faculty within the university to develop their own research work.

The 48-node Beowulf Cluster

(upgradeable to 96
processors), 32 GB system memory, and Myrinet
low-latency network.

**JOURNAL
AND ARCHIVAL PUBLICATIONS**

1) P.-f.
Hsu (1982), "The Front Wheels Alignment in Military Vehicles," *Ordnance Science J. *(in Chinese), 14:
pp.66-71.

2) J.
D. Felske, P.-f. Hsu, and J. C. Ku
(1986),"The Effect of Soot Particle Optical Inhomogeneity and
Agglomeration on the Analysis of Light Scattering Measurement in Flames," *J. Quant. Spect.** & Rad.
Transfer.* 35(6): pp.447-465.

3) P.-f.
Hsu, and J. R. Howell (1992), "Measurements of Thermal Conductivity and
Optical Properties of Porous Partially Stabilized Zirconia," *Exp. Heat Transfer* 5: pp.293-313.

4) P.-f.
Hsu, J. R. Howell, and R. D. Matthews (1993), "A Numerical Investigation
of Premixed Combustion within Porous Inert Media," ASME *J. Heat Transfer* 115(3): pp.744-750.

5) P.-f.
Hsu, W. D. Evans, and J. R. Howell (1993), "Experimental and Numerical
Study of Premixed Combustion within Nonhomogeneous Porous Ceramics," *Comb. Sci. &
Tech.* 90: pp.149-172.

6) P.-f.
Hsu, and R. D. Matthews (1993), "The Necessity of Using Detailed Kinetics
in Models for Premixed Combustion within Porous Media," *Comb. and Flame*
93: pp.457-466.

7) P.-f. Hsu, Z. Tan and J. R. Howell (1992), "A Correction of the YIX
method for the Solution of Radiative Heat Transfer," to be submitted to
AIAA *J. Thermophysics and Heat Transfer*.

8) P.-f.
Hsu, Z. Tan and J. R. Howell (1993), "Radiative Transfer by the YIX Method
in Nonhomogeneous, Scattering and Non-Gray Medium," AIAA *J. Thermophysics & Heat Transfer*
7(3): pp.487-495.

9) P.-f.
Hsu and J. C. Ku (1994), "Radiative Heat Transfer in Finite Cylindrical
Enclosures with Nonhomogeneous Participating Media," AIAA *J. Thermophysics & Heat Transfer*
8(3): pp.434-440.

10) P.-f. Hsu and J. C. Ku (1995),
"Detailed Spectral Radiation Calculations for Nonhomogeneous Soot/Gas
Mixtures Based on a Simulated Ethylene Jet Diffusion Flame," Proceedings
of the Int. Symp. on Radiative Heat Transfer,
pp.372-386, ed. by M.P. Menguc, Kusadasi,
Turkey, August 1995, Begell House, Inc. NY.

11) P.-f. Hsu and Z. Tan (1995), "Recent Benchmarkings of Radiative Heat Transfer within
Nonhomogeneous Participating Media and the Improved YIX Method," __invited
key-note lecture__ - Proceedings of the Int. Symp.
on Radiation Transfer, pp.107-126, ed. by M.P. Menguc,
Kusadasi, Turkey, August 1995, Begell
House, Inc. NY.

12) P.-f. Hsu and J. T. Farmer (1997),
"Benchmark Solutions of Radiative Heat Transfer within Nonhomogeneous
Participating Media Using the Monte Carlo and YIX Methods," ASME *J. Heat Transfer* 119(1): pp.185-188.

13) P.-f. Hsu and Z. Tan (1997), "The
Radiative and Combined Mode Heat Transfer within the L-shaped Nonhomogeneous
and Nongray Participating Media," *Numerical
Heat Transfer, Part A: Applications *31(8): pp.819-836.

14) P.-f. Hsu, Z.-M. Tan, S.-H. Wu, and C.-Y. Wu (1999),
"Radiative Transfer in Finite Cylindrical Homogeneous and Nonhomogeneous
Scattering Media Exposed to Collimated Radiation," *Numerical Heat Transfer Part A: Applications *35(6): pp. 655-679.

15) Z.-M. Tan, P.-f. Hsu, S.-H. Wu, and C.-Y. Wu,
(2000), "Modified YIX Method and Pseudoadaptive
Angular Quadrature for Ray Effects Mitigation," AIAA *J. Thermophysics & Heat Transfer*, 14(3): pp. 289-296.

16) Z.-M. Tan, and P.-f. Hsu (2001),
"An Integral Formulation of Transient Radiative Transfer," ASME *J. Heat Trans**fer*, 123(3): pp.466-475.

17)
P.-f. Hsu (2001), "Effects of Multiple Scattering and Reflective Boundary
on the Transient Radiative Transfer Process," *Int. J. Thermal Sciences*, 40(6), pp. 539-549, June 2001.

18) Z.-M. Tan, and P.-f. Hsu (2002),
"Transient Radiative Transfer in Three-Dimensional Homogeneous and
Nonhomogeneous Participating Media," *J. Quant. Spect. & Rad. Transfer*,
73(2-5), pp. 181-194.

19) M. Sakami, K. Mitra,
and P.-f.
Hsu (2002), "Analysis of Light-Pulse Transport through Two-Dimensional
Scattering and Absorbing Media," *J.
Quant. Spect. & Rad.
Transfer*, 73(2-5), pp. 169-179.

20) Book chapter: Radiative Transfer Modeling
and Experiments Using Short Pulse Lasers, S. Kumar, P.-f. Hsu, K. Mitra, B. Garetz, Z. Guo, and J. Aber, *Modeling and
Simulation Based Life Cycle Engineering*, ed. by
Ken P. Chong, Sunil Saigal,
Stefan Thynell, Harold S. Morgan, ISBN:* *0415266440
by Taylor & Francis, 2002.

21) X. Lu and P.-f. Hsu (2003),
"Parallel Computing of an Integral Formulation of Transient Radiation
Transport," AIAA *J. Thermophysics &
Heat Transfer* 17(4): pp.425-433.

22) J. C. Chai,
P.-f.
Hsu and Y. C. Lam (2004) "Three-Dimensional Transient
Radiative Transfer Modeling Using the Finite-Volume Method" *J. Quant. Spect.** & Rad.
Transfer*. Vol. 86, Iss. 3, pp. 299-313,
July 1, 2004.

23) X. Lu and P.-f. Hsu (2004),
"Reverse *J. Heat Transfer*,
Vol. 126(4): pp. 621-627, Aug. 2004.

24) X. Lu and P.-f. Hsu (2005),
"Reverse *J. Quant. Spect. & Rad.
Transfer*, Vol. 93(1-3), pp. 349-367.

25) X. Lu and P.-f. Hsu (2005),
"Reverse *J. Thermophysics &
Heat Transfer*, Vol. 19(3), pp.
353-359.

26) P.-f. Hsu (2005), *A
Low-NOx Porous Ceramics Burner Performance Study*, EISG Report 02-14, California Energy
Commission, peer-reviewed, institutional archive available online at www.energy.ca.gov/research/innovations.

27) K. Fu,
P.-f.
Hsu, and Z. M. Zhang (2006), "Unified Analytical Formulations of Thin-Film
Radiative Properties Including Partial Coherence," *Appl**.* *Opt*., Vol. 45(4), pp.
653-661, Feb. 2006.

28) P.-f. Hsu and T. Lai (2006),
"Experimental Study of the Premixed Combustion within the Nonhomogeneous
Porous Ceramic Media," under revision, to be submitted to *Exp. Heat Transfer*.

29) P.-f. Hsu (2006),
"Optical Diagnostics Using Temporal Reflectance from a Pulsed Laser
Irradiated Nonhomogeneous Medium," under revision, to be submitted to *Appl**. Optics*.

32) P.-f. Hsu and X. Lu (2007),
"Temporal Reflectance from a Light Pulse Irradiated Medium Embedded with
Highly Scattering Cores," accepted by *J.
Quant. Spect. & Rad.
Transfer*.

33) K. Fu and P.-f. Hsu (2007), "Radiative Property of Gold Surfaces with
One-Dimensional Microscale Gaussian Random Roughness," under review by *Int.** J. Thermophysics.*

34) L. H. Liu and P.-f. Hsu (2007),
"Analysis of Transient Radiative Transfer in Semitransparent Graded Index
Medium," accepted by *J. Quant. Spect. & Rad. Transfer*.

35) K. Fu and P.-f. Hsu (2007),
"Modeling the Radiative Properties of Microscale Randomly Roughness
Surfaces," *ASME J. Heat Transfer*
- special issue on micro- and nano-scale radiation heat transfer, Vol. 129(1);
pp. 71-78.

36) L. H. Liu and P.-f. Hsu (2007), "Superposition Principle for Solving Transient
Radiative Transfer Equation," under review by *ASME J. Heat Transfer*.

37) R. Buchanon
and P.-f.
Hsu (2007), "Bi-Directional Reflectivity of Surfaces
with Two-Dimensional Microscale Anisotropic Roughness," to be submitted to
*Optics Engr*.

38) K. Fu, Y.-B. Chen, P.-f. Hsu, Z. M. Zhang, and P. Timans (2007),
"Device Scaling Effect on
the Spectral Absorptance of Wafer Front Side," to be submitted to *Int. J. Heat Mass Transfer*.

Results in journal articles # 11
and 12 and conference paper #11 have been incorporated in a widely used
graduate level radiation heat transfer text by Siegel and Howell (2002).

1) Y.-K. Chen, P.-f. Hsu, I.-G. Lim, Z.-H. Lu, R. D. Matthews, J. R. Howell, and S. P.
Nichols (1988), "Experimental and Theoretical Investigation of Combustion
within porous inert media," Poster Paper P22-207, presented at the 22nd
Symposium (Int'l) on Combustion,

2) P.-f.
Hsu, J. R. Howell, and R. D. Matthews (1991), "A Numerical Investigation
of Premixed Combustion within Porous Inert Media," presented at the 3rd
ASME/JSME Joint Thermal Engineering Conference,

3) P.-f.
Hsu, Z. Tan, and J. R. Howell (1992), "Application of the YIX Method to
Radiative Heat Transfer within a Mixture of Highly Anisotropic Scattering
Particles and Non-Gray Gas," presented at the 28th National Heat Transfer
Conf.,

4) P.-f.
Hsu (1995), "Radiative Heat Transfer within Nonhomogeneous Participating
Media by the YIX Method" presented at the 6th CASAF Conf.,

5) P.-f.
Hsu (1995), "Preliminary Study of a Gas Burner-Driven and Ground-Coupled
Heat Pump System" presented at the 30th Intersociety Energy Conversion
Engineering Conf.,

6) S.
P. Burns, P.-f. Hsu, and J. T. Farmer (1995), "Optical Distance
Calculation within Materials with Spatially Varying Radiative Properties,"
presented at the 30th National Heat Transfer Conference - Open Forum for
Radiative Heat Transfer in Participating Media,

7) Z. Tan
and P.-f. Hsu (1995), "High Order Interpolation in the YIX Method,"
presented at the 30th National Heat Transfer Conference - Open Forum for
Radiative Heat Transfer in Participating Media,

8) P.-f.
Hsu and J. T. Farmer (1995), "Benchmark Solutions of Radiative Heat
Transfer within Nonhomogeneous Participating Media Using the

9) P.-f.
Hsu and Z. Tan (1996), "The Radiative and Combined Mode Heat Transfer
within the L-shaped Nonhomogeneous and Nongray Participating Media,"
presented at the 31st National Heat Transfer Conference, Houston, TX, August
1996, ASME HTD-vol.325: pp.13-24.

10) P.-f. Hsu (1996), "Experimental Study
of the Premixed Combustion within the Nonhomogeneous Porous Ceramic
Media," presented at the 31st National Heat Transfer Conference,

11) S.-H. Wu, C.-Y. Wu, and P.-f. Hsu (1996), "Solutions of Radiative
Transfer in Inhomogeneous Participating Media Using the Quadrature
Method," presented at the ASME 1996 Int. Mechanical Engineering Congress
& Exposition,

12) P.-f. Hsu, Z.-M. Tan, S.-H. Wu, and C.-Y. Wu (1998),
"Radiative Transfer in a Finite Cylindrical Enclosure with Homogeneous and
Nonhomogeneous Scattering Media Exposed to Collimated Radiation,"
presented at the Open Forum of Radiative Heat Transfer Solution Methods at the
1998 ASME/AIAA Joint Thermophysics and Heat Transfer Conference,

13) Z.-M. Tan, P.-f. Hsu, S.-H. Wu, and C.-Y. Wu,
(1999), "The QM-YIX Method and Adaptive Angular Quadrature for Ray Effects
Mitigation," presented at the 1999 National Heat Transfer Conference,

14)
Z.-M. Tan and P.-f. Hsu (1999), "Numerical
Results of an Integral Formulation of Transient Radiative Transfer,"
presented at the ASME 1999 Int. Mechanical Engineering Congress &
Exposition,

15) P.-f. Hsu (2000), "Effects
of Multiple Scattering and Reflective Boundary on the Transient Radiative
Transfer Process," the 2000 National Heat Transfer Conf.
Proceedings paper NHTC2000-12078, Pittsburgh, PA, August 2000.

16) Z.-M. Tan, and P.-f. Hsu (2000),
"An Integral Formulation of Transient Radiative
Transfer:— Theoretical Investigation," the 2000 National Heat Transfer
Conf. Proceedings paper NHTC2000-12077, Pittsburgh, PA, August 2000.

17) A. Sawetprawichkul,
P.-f. Hsu, and K. Mitra
(2000), "A Monte Carlo Study of the Transient Radiative Transfer within
the One-Dimensional Layered Slab," ASME 2000 Int. Mechanical Engineering
Congress & Exposition, ASME HTD-Vol. 366-1, pp.
145-153, Orlando, FL, November 2000.

18) M. Sakami, K. Mitra, and P.-f. Hsu (2000), "Transient Radiative Transfer in Anisotropically
Scattering Media using Monotonicity-Preserving
Schemes," ASME 2000 Int. Mechanical Engineering Congress & Exposition,
ASME HTD-Vol. 366-1, pp. 135-143, Orlando, FL,
November 2000.

19) Z.-M. Tan, and
P.-f. Hsu (2001), "Transient Radiative Transfer in a
Three-Dimensional Participating Medium," Proceedings of the 2001 Int. Symp. Radiative Transfer,

20) M. Sakami, K. Mitra,
and P.-f.
Hsu (2001), "Analysis of Light-Pulse Transport through Two-Dimensional
Scattering and Absorbing Media," Proceedings of the 2001 Int. Symp. Radiative Transfer,

21) P.-f. Hsu (2002), "Optical Diagnostics
Using Temporal Reflectance from a Ultra-Short Pulsed Laser," AIAA paper No. 2002-3106, Proceedings of the 8th
AIAA/ASME Joint Thermophysics & Heat Transfer Conf., St Louis, Missouri,
June 2002.

22) A. Sawetprawichkul,
P.-f.
Hsu, and K. Mitra (2002), "Parallel Computing of
Three-Dimensional Monte Carlo Simulation of Transient Radiative Transfer in
Participating Media," AIAA paper No. 2002-2901, Proceedings
of the 8th AIAA/ASME Joint Thermophysics & Heat Transfer Conf., St Louis,
Missouri, June 2002.

24) X. Lu and P.-f. Hsu (2003),
"Parallel Computing Performance of Two Numerical Quadratures for an
Integral Formulation of Transient Radiative Transfer Process," ASME Paper
No. HT2003-47235, Proceedings of the ASME Summer Heat Transfer Conf., Las
Vegas, NV, July 2003.

25) X. Lu, P.-f. Hsu, and J. C. Chai (2003),
"Transient Radiative Transfer of Light Pulse Propagation in
Three-Dimensional Scattering Media with Finite Volume Method and Integral
Equation Model," ASME Paper No. HT2003-47455, Proceedings of the
ASME Summer Heat Transfer Conf., Las Vegas, NV, July 2003.

26) X. Lu and P.-f. Hsu (2003),
"Reverse

27) N. Torlak and
P.-f.
Hsu (2004) "Feasibility of a Fiber-Optic Sensor for
High-Speed High-Pressure Cryogenic Flow Rate Measurement," AIAA Paper
No.2004-0824, Proceedings of the AIAA 42nd Aerospace Sciences Meeting and
Exhibit,

28) X. Lu and P.-f. Hsu (2004),
"Reverse

29) X. Lu and P.-f. Hsu (2004),
"Reverse

30) X. Lu and P.-f. Hsu (2004),
"Reverse Monte Carlo Simulations of Ultra-Short Pulse Propagation within
Three-Dimensional Nonhomogeneous Media," AIAA Paper No.2004-2680,
Proceedings of Thermophysics Conf.,

31) K. Fu, P.-f. Hsu and Z. M.
Zhang (2004), "Radiative Properties of Silicon-Based Thin Films for
Partially Coherent Radiation", Proceedings of the 12th IEEE Int. Conf. on
Advanced Thermal Processing of Semiconductors- RTP 2004, pp. 185-193, Portland,
OR, September 2004.

32)
C. Li and P.-f. Hsu (2005), "Emissions and Radiation Efficiency for
Methane Combustion within a Porous Medium Burner," AIAA paper No. 2005-5639, The Third Int. Energy Conversion Engr. Conf., San Francisco, August 2005.

33)
P.-f. Hsu and X. Lu (2005), "Temporal Reflectance from a Light Pulse
Irradiated Medium Embedded with Highly Scattering Cores," __invited
presentation__ at EUROTHERM Seminar
82 - Numerical Heat Transfer 2005, Gliwice-Cracow, Poland, September 13-16,
2005.

35) A. Asano, P.-f. Hsu, and B. Lojek (2005), "Temperature Non-Uniformity from
Combined Conduction and Radiation Heat Transfer within a Doped Wafer,"
Proceedings of the 13th IEEE Int. Conf. on Advanced Thermal Processing of
Semiconductors- RTP 2005, Santa Barbara, October 2005.

36) K. Fu and P.-f. Hsu (2005),
"The FDTD Computation of Electromagnetic Wave Scattering from Wafer
Surfaces," Proceedings of the 13th IEEE Int. Conf. on Advanced Thermal
Processing of Semiconductors- RTP 2005, Santa Barbara, October 2005.

37) K. Fu and P.-f. Hsu (2005),
"Modeling the Radiative Properties of Microscale Random Roughness
Surfaces," ASME Paper No. IMECE2005-81292, ASME Int. Mechanical
Engineering Congress & Exposition,

38) K. Fu and P.-f. Hsu (2006),
"Radiative Properties of Two-Dimensional Rough Surfaces based on an
Electromagnetic Wave Scattering Model," Proceedings of the AIAA/ASME Joint
Thermophysics and Heat Transfer Conf.,

39) K. Fu and P.-f. Hsu (2006),
"Radiative Property of Gold Surfaces with One-Dimensional Microscale
Gaussian Random Roughness," Proceedings of the 16the Symposium on Thermophysical
Properties, Colorado Springs, CO, July, 2006.

40) K. Fu, Y.-B. Chen, P.-f. Hsu, and Z. M. Zhang (2006), "Device Scaling Effect on the Spectral
Absorptance of Wafer Front Side," Proceedings of the 14th IEEE Int. Conf.
on Advanced Thermal Processing of Semiconductors- RTP 2006,

41) K. Fu and P.-f. Hsu (2006),
"Revisit the Regime Map of the Geometric Optics Approximation for
Scattering from Random Rough Surfaces," ASME Int. Mechanical Engineering
Congress & Exposition,

42)
Z. F. Huang, H. C. Zhou, P. F. Hsu, and Q. Cheng (2007), "The Existence of
Pulsewidth Scaling Relation for Optical Imaging Using Ultrafast Lasers," to be presented at the Fifth Int. Symp. of Radiation

43)
K.
Fu and P.-f. Hsu (2007), "New Regime
Maps of the Geometric Optics Approximation for Scattering from Random Rough
Surfaces," to be presented at the Fifth Int. Symp. of Radiation

44) R. Zhou, P.-f. Hsu, and B. Vu
(2007), "Plume Cratering Simulation and Comparison with Experimental
Data," abstract submitted to AIAA Applied Fluid Dynamics Conf., June 2006.

45) R. Buchanon and
P.-f.
Hsu (2007), "Bi-Directional Reflectivity of Wafer Backside with
Two-Dimensional Microscale Anisotropic Roughness," to appear in the
Proceedings of the 14th IEEE Int. Conf. on Advanced Thermal Processing of
Semiconductors- RTP 2007, Sicily, Italy, October 2007.