**Study of the radiative properties of rough surfaces for temperature measurements in rapid thermal processing**

The motivation of this research is to accurately measure the temperature of silicon wafers using radiation thermometers during rapid thermal processing (RTP), see Fig. 1. RTP is a key technique for the advance of integrated circuits to meet requirements towards the shrinkage of devices size and increasing packing density. With advantages in temperature control, short cycle, and process flexibility, RTP has expanded its application areas such as annealing for surface damage removal, the growth of thin oxides or nitrides, chemical vapor deposition, and so on. A challenging problem in the RTP technique is to accurately measure the temperature of silicon wafers (refer to Fig. 1). Due to fast response and non-intrusiveness, light-pipe radiation thermometers (LPRTs) are frequently chosen to monitor the temperature of the wafer during processing. However, in radiation thermometry, the variation in wafer emissivity and the stray radiation from the background significantly affect the measurement uncertainty [1]. The monitored surface of silicon wafers generally possesses roughness created by mechanical cutting and chemical etching. Surface roughness alters not only the emissivity of silicon wafers but also the effect of the background radiation by scattering the incident radiation. In fact, the effective emissivity considering the effect of background radiation is used in temperature reading with an LPRT instead of the intrinsic emissivity. Therefore, understanding the directional dependence of scattering from rough silicon surfaces is essential for radiometric temperature measurement of silicon wafers during RTP.

**Figure 1. A rapid thermal processing furnace and the temperature measurement of a silicon wafer using the radiation thermometer.**

The bidirectional reflectance and transmittance distribution functions (BRDF and BTDF) are fundamental radiative properties that describe the re-distributions of radiative energy after scattering from rough surfaces. Once the bidirectional properties are known, the emissivity can be obtained from the integration of them. However, the true importance of the bidirectional properties lies in considering the effect of background radiation. Because the background radiation originates from multiple reflections between a silicon wafer and an RTP chamber, knowledge of the bidirectional properties enables the modeling of effective emissivity [2].

We started this research by modeling the effective emissivity in an RTP furnace with the net-radiation method [3] and the Monte Carlo method [4], based on specular/diffuse reflection assumptions. At the same time, we made an effort to find appropriate analytical models for the BRDF of silicon wafers using the reference optical scatterometer at the National Institute of Standards and Technology (NIST) [5]. Subsequently, we developed a custom-designed optical reflectometer, namely, a three-axis automated scatterometer (TAAS), as shown in Fig. 2 [6].

**Figure 2. Picture and schematic representation of TAAS.**

The goniometric table composed of three rotary stages offers high angular resolution and repeatability to determine the incidence and reflection directions and allows us to measure both the BRDF and the BTDF in and out of the plane of incidence with high accuracy. A compact diode laser system provides high wavelength and power stabilization, and the fiber-coupled laser is easily interchangeable for a different wavelength. A lock-in amplifier modulates the power of the laser directly to avoid noises from the background radiation. Highly linear diode detectors with trans-impedance amplifiers provide a large dynamic range. A reference detector eliminates the unnecessary sample moving and enables fast sampling. The sample holder allows a large sample up to 8” diameter to be measured. Heated sample compartment and additional translation and rotation stages can be included in the system for the emissivity measurement and surface scan, respectively. Good agreement was obtained between the measured results from TAAS and the reference instrument in NIST, as shown in Figure 3 for two different silicon surfaces. The all-around capability of TAAS allowed extensive studies of the bidirectional radiative properties.

**Figure 3. Comparisons of measurement results from TAAS (solid line) and the reference instrument in NIST (mark) for two different silicon wafers.**

Because the statistics of surface roughness are essential for modeling approaches, we measured the surface topography of a number of silicon wafers with an atomic force microscope (AFM). While the height distribution function of a silicon wafer is close to a Gaussian functional form, the slope distribution function is anisotropic [7]. Consequently, a one-dimensional modeling approach with the assumption of isotropic surfaces is not applicable to the BRDF of silicon wafers. Figure 4 shows the slope distribution functions of two silicon wafers. Note that Si-1 is slightly anisotropy whereas Si-2 is highly anisotropy with side peaks. Further study demonstrated that the anisotropic orientation of silicon surface roughness is caused by the chemical etching process. Using the geometric optics-based model, the BRDF can be correlated with the crystalline structure of silicon at the microscale [8].

**Figure 4. Anisotropic slope distribution of two silicon wafers obtained from the measured surface topography using an atomic force microscope.**

Meantime, we have developed a Monte Carlo method to predict the BRDF and BTDF simultaneously and studied the variation of hemispherical properties under various conditions [9]. This Monte Carlo method furthermore has the potential to model the effective emissivity by employing the statistics of surface roughness such as the root-mean-square (RMS) roughness and autocorrelation length, without relying on the analytical BRDF model. We continued to improve and extend the Monte Carlo method for the radiative properties of rough surfaces with thin-film coatings [10] and evaluated the applicability of the geometric optics approximation with the Monte Carlo method [11]. Recently, the Monte Carlo method is further developed to directly incorporate the two-dimensional surface topography obtained from the AFM measurement. The predicted BRDFs of the anisotropic silicon wafers, based on the measured surface topography, are presented in Fig. 5, at a 30º incidence angle and a wavelength of 635nm. The BRDFs reveal the same anisotropic features as the slope distribution function shown in Fig. 4b, implying that the effect of microroughness is significant to the bidirectional radiative properties.

**Figure 5. The BRDF of the very anisotropic surface at predicted with the Monte Carlo method using the measured surface topography at 635 nm wavelength.**

In future research, we will study thin-film coatings on bidirectional properties by coating the silicon surfaces with metallic and dielectric coatings. The hemispherical radiative properties will be studied with an integrating sphere, and a monochromatic light source will be used to expand the spectral range. In the long run, this research will not only gain a better understanding of radiation heat transfer at the microscale but also benefit the semiconductor industry.

This work has been supported by the National Science Foundation (CTS-0236831) and the National Institute of Standards and Technology (Optical Technology Division).

**Selected Publications**

[1] Zhang, Z. M., “Surface Temperature Measurement Using Optical Techniques,” in Annual Review of Heat Transfer, vol. 11, C. L. Tien, Ed. New York: Begell House, 2000, pp. 351-411.

[2] Zhang, Z. M., Fu, C. J., and Zhu, Q. Z., “Optical and Thermal Radiative Properties of Semiconductors Related to Micro/Nanotechnology,” in Advances in Heat Transfer, vol. 37. New York: Academic Press, 2003, pp. 179-296.

[3] Zhang, Z. M., and Zhou, Y. H., 2001, “An Effective Emissivity Model for Rapid Thermal Processing Using the Net-Radiation Method,” International Journal of Thermophysics, 22, pp. 1563-1575.

[4] Zhou, Y. H., Shen, Y. J., Zhang, Z. M., Tsai, B. K., and DeWitt, D. P., 2002, “A Monte Carlo Model for Predicting the Effective Emissivity of the Silicon Wafer in Rapid Thermal Processing Furnaces,” International Journal of Heat and Mass Transfer, 45, pp. 1945-1949.

[5] Shen, Y. J., Zhang, Z. M., Tsai, B. K., and DeWitt, D. P., 2001, “Bidirectional Reflectance Distribution Function of Rough Silicon Wafers,” International Journal of Thermophysics, 22, pp. 1311-1326.

[6] Shen, Y. J., Zhu, Q. Z., and Zhang, Z. M., 2003, “A Scatterometer for Measuring the Bidirectional Reflectance and Transmittance of Semiconductor Wafers with Rough Surfaces,” Review of Scientific Instruments, 74, pp. 4885-4892.

[7] Zhu, Q. Z., and Zhang, Z. M., 2004, “Anisotropic Slope Distribution and Bidirectional Reflectance of a Rough Silicon Surface,” Journal of Heat Transfer, 126, pp. 985-993.

[8] Zhu, Q. Z., and Zhang, Z. M., 2005, “Correlation of Angle-Resolved Light Scattering with the Microfacet Orientation of Rough Silicon Surfaces,” Optical Engineering, 44, 073601.

[9] Zhou, Y. H., and Zhang, Z. M., 2003, “Radiative Properties of Semitransparent Silicon Wafers with Rough Surfaces,” Journal of Heat Transfer, 125, pp. 462-470.

[10] Lee, H. J., Lee, B. J., and Zhang, Z. M., 2005, “Modeling the Radiative Properties of Semitransparent Wafers with Rough Surfaces and Thin-Film Coatings,” Journal of Quantitative Spectroscopy and Radiative Transfer, 93, pp. 185-194.

[11] Zhu, Q. Z., Lee, H. J., and Zhang, Z. M., 2005, “The Validity of Using Thin-Film Optics in Modeling the Bidirectional Reflectance of Coated Rough Surfaces,” Journal of Thermophysics and Heat Transfer, 19, in press.