Thermal uniformity and stress minimization during rapid thermal processes

Light-pipe radiation thermometers (LPRTs) are widely used to monitor temperature during thermal processing of materials, particularly semiconductor wafer rapid thermal processing. According to the International Technology Roadmap for Semiconductors 2004, temperatures for semiconductor wafer processing should be measurable to within an uncertainty of 1.5 C at 1000 C with temperature calibration traceable to International Temperature Standard-90. To achieve this accuracy level, the radiation signal transport process inside the light-pipe probe has to be fully understood. Few studies have been conducted to model the radiation transfer of LPRTs. In this paper, a Monte Carlo model has been created to simulate the signal transport from the measurement surface through the light-pipe probe. The model predicts the acceptance angle or aperture of the light-pipe. We also investigated the effect of nonspecular reflections caused by the sidewall surface roughness of the light-pipe probe using this model.Index Terms-Light-pipe, Monte Carlo modeling, radiative thermometer, rapid thermal processing.

“…4. Equation (4) (4) shows the relationship between the acceptance angle and incident plane distance and refraction index ratio . Based on this equation, Fig.…”

Section: Acceptance Angle and Aperturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monte Carlo Modeling of a Light-Pipe Radiation Thermometer

Howell

Ezekoye³

2007

“…Bentini et al [6] found the strip heater induces much lower thermal stresses than the irradiation of a free wafer. Furthermore, Perkins et al [7] used a nodal analysis to discuss the thermal uniformity and stress minimization during the steady state and transient phase of RTP. Jan and Lin [8] studied lamp configuration design for RTP systems to achieve the necessary temperature uniformity.…”

Section: Introductionmentioning

confidence: 99%

Thermal stress analysis for rapid thermal processor

Chao

Hung

2003

Within the framework of linearized thermoelasticity theory, the temperature and thermal stresses on the wafer for the rapid thermal processor are solved by using the finite-difference approach and a trapezoidal integration technique, respectively. Although the equations governing the present thermoelastic system are coupled in nature, the temperature can still be obtained independently due to the fact that the coupling term is negligible as a result of the strain rate being extremely small as compared with unity. Based on the maximum shear stress failure criterion, the calculated results show that material failure always occurs at the edge of the wafer at the beginning of cooling processes. Furthermore, the maximum stress control scheme is proved to be more efficient that it can significantly reduce the required cooling time and thermal budgets. Thus, the conventional constant cooling-rate control scheme or linear temperature ramp-down scheme is not appropriate for the rapid thermal processor.

“…Single-wafer rapid thermal processing (RTP) has become an alternative to the conventional furnace-based batch processing in many processes [1], [2]. To obtain uniform processing across the wafer and to prevent the creation of slip defects due to thermal stresses, the temperature must be nearly uniform on the wafer throughout the process cycle [3].…”

Section: Introductionmentioning

confidence: 99%

“…Cho et al [10] optimized the incident heat flux profile over a wafer by determining the heat loss profiles using Lord's thermal model [3], which simulates radial temperature gradients by assuming uniform temperature through the wafer thickness. Following the work of Riley and Gyurcsik [9], Perkins et al [2] used their special wafer-edge node analysis to show that idealized intensity profiles can maintain thermal uniformity at steady-state temperatures, and that dynamic continuously changing profiles are required to maintain temperature uniformity during thermal transients. The works mentioned above describe quantifying incident heat flux over a wafer to achieve the necessary thermal uniformity requirement during RTP.…”

Section: Introductionmentioning

confidence: 99%

Thermal uniformity of 12-in silicon wafer during rapid thermal processing by inverse heat transfer method

Lin

Chu

2000

Through an inverse heat transfer method, this paper presents a finite difference formulation for determination of incident heat fluxes to achieve thermal uniformity in a 12-in silicon wafer during rapid thermal processing. A one-dimensional thermal model and temperature-dependent thermal properties of a silicon wafer are adopted in this study. Our results show that the thermal nonuniformity can be reduced considerably if the incident heat fluxes on the wafer are dynamically controlled according to the inverse-method results. An effect of successive temperature measurement errors on thermal uniformity is discussed. The resulting maximum temperature differences are only 0.618, 0.776, 0.981, and 0.326 C for 4-, 6-, 8-and 12-in wafers, respectively. The required edge heating compensation ratio for thermal uniformity in 4-, 6-, 8-and 12-in silicon wafers is also evaluated.Index Terms-12-in silicon wafer, inverse heat-transfer method, rapid thermal processing, thermal uniformity.